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This is to certify that the
dissertation entitled

Thermal and Chemical Modification
of Collagenous Tissues

presented by
Alptekin Aksan

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Engineering

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THERMAL AND CHEMICAL MODIFICATION OF COLLAGENOUS TISSUES
By

Alptekin Aksan

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Mechanical Engineering

2002

ABSTRACT
THERMAL AND CHEMICAL MODIFICATION OF COLLAGENOUS TISSUES
By

Alptekin Aksan

Over the last decade, Sub-Ablative Thermotherapy has found ever-increasing
application in orthopaedic (in the treatment of the instabilities of the knee, ankle, hip and
shoulder joints and in the elimination of the discogenic pain in spine) and Ophthalmologic
surgery (for the correction Of near/farsightedness). Utilizing sub-ablative levels of heating,
the therapy aims at altering the configuration of the strain-damaged, pathological or
congenitally anomalous collagenous tissue (such as tendon, ligament, skin, joint capsule,

cornea, etc.) in order to re-establish stability and function.

This thesis describes research directed towards understanding, modeling and
controlling the heat-induced responses of collagenous tissues. The main aim of the

research was to establish the scientific basis and develop the tools to increase the safety

and eflicacy of Sub-Ablative Thermotherapy procedures.

In-vitro therrnomechanical experimentation with a model collagenous tissue (New
Zealand white rabbit patellar tendon) is performed in order to determine the constitutive
relationships between the accumulated thermal damage and the resultant mechanical
response and the stress-state of the collagenous tissues. Finite Element Analysis-based
simulation tools are also developed in order to quantify the differences among clinically

applied heating modalities such as, monopolar/bipolar radiofrequency and Ho:YAG laser.

It is shown that there is a trade-off between the kinematical stability established by
altering the configuration of the collagenous tissue and the mechanical stability
compromised by the heat-induced degradation of its mechanical properties. For a
homogeneously heated tendon tissue, existence of different shrinkage regimes and a
mechanical optimum state in the heat-induced response is shown. Through Finite Element
Analysis, thermal damage fields created by clinically applied heating modalities are
established and the effects of clinically important parameters such as probe sweep speed,
radiofi'equency power and saline circulation are examined. A computer-based simulation
tool is also developed in order to simulate the heat-induced mechanical behavior of the

collagenous tissues.

To accurately simulate the heat-induced mechanical response of a collagenous
tissue, future studies should extend the analyses established here to multi-dimensions and
should take into consideration the non-homogeneous nature of the tissues. After these
studies are completed, the next challenge would be to apply the technology developed to

the clinical setting.

ACKNOWLEDGMENTS

I do not think I can find the words to describe how thankful I am to my mentor Dr.
John J. McGrath for not only helping me be a better researcher but also a better person. He
made my research experience an exceptional one and I consider myself very lucky to be in
a position to say that I tremendously enjoyed every single second working for/with him.
He did not only want me to get a Ph.D. degree but also helped me in every way to be ready
for the academic career I wanted to pursue. He supervised, encouraged and supported,
always with a kind smile. He taught me how to think rationally and how to strongly
express what I think. I do not think I could every find a better mentor, and a friend no

matter how hard I searched. Thank you for everything you have done for me Dr. McGrath!

I had great discussions with Dr. Roger Haut, he opened his laboratory to me, and
treated me like one of his own students. His kindness and advices were invaluable. He was
always available and extremely helpful. I would like to thank Dr. Steven Amoczky for
suggesting the research area and helping me establish the research guidelines. He always
helped, supported and made all his resources available to me; his laboratory, the help of
his staff. His guidance was peerless. His ability to criticize constructively at critical times,
always friendly and supportive attitude made this research possible and help me bridge
over the border separating academic disciplines. I had great discussions with Dr. Andre

Benard and he always believed in my abilities and trusted me, always supportive.

I would also like to extend my thanks to Dr. Hungyu Tsai for his invaluable

contributions to this research at very critical times, understanding and suggesting brilliant

iv

ideas, directions. I always felt that he knew exactly what I would say even before I said it

and he already had the answer. It was a great pleasure knowing him.

Through four and a half years of hard work, good and bad days, I enjoyed the help
and support I received from my coworkers. Late nights washed with excessive amounts of
coffee and enlightening discussions with Dr. Scott Morris enabled me to understand the
meaning of “Quality” and the value of feeling passion for whatever one is doing. I
consider myself to be very luck to be doing what I enjoy the most, and I believe I know at

least one other person who feels the same way. It was great knowing you Scott!

I would also like to thank my dear fiiends Dr. Paul Hoke and Damien Fron for their
endless support, help and friendship at all times. I also would like to thank Dave
Nielobowich, Scott Dixon, Jessica Paskiewich and Rachel Tuttle for their hard work and

the fim they brought into the lab.

I would like to thank my mom, dad and brother for being so understanding,
supportive and loving, so much that they could even accept to be far away from me; so
that I could pursue my dream. I can never be thankful enough for what these selfless,
brave, wonderful people have done for me. My thanks are extended to my very good
friends Can Murat Alpaslan and Dr. Selcuk Avci who always supported me and made me
feel at home away fiom home and to my precious Istar, for eleven years of love, support

and understanding me so well and helping me break down the walls I surrounded myself.

Last, but not least, I thank my second family, for never leaving me alone and

always saving a place in their hearts and home for me: Thank you all so much McGraths.

TABLE OF CONTENTS

LISt 0f TableSOOOOOOO0.0....0.0......OCOO...O0.00.0...0.0.0....O0.0......OOOOOOOOOOOOOOOOOOOOOO .......... OOOOOOOOix

LISt 0‘ Fig“ MOOOOOOOOOOOOOOOOOOOOOOO..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO..OOOOOOOIOOOOOOO0.0.0.0.....OOOOOOOOOOOOOX

Key to symbOIs and AbbreViationSOOOOOOOOOOOOOOOOOOOO..OOOOOOOOOOOOOOOOOO...OOOOOOOOOOOOOOO..OOOOOOOXV

Chapter 1: Introduction 1

1.1
1.2
1.3

1.4

 

 

Collagenous Tissue Structure: From Microscale to Macroscale ........... 2
Shoulder Instability - 4
Treatment options for Shoulder Instability - -- -6
13 1 Conventional Methods ..................................................................... 7
1.3 2 Thermotherapy ................................................................................. 8
1.3 3 Mechanism of Thermotherapy (Heat-Assisted Capsular Shift) ....... 9
Research Objectives -- -- - - - --12

 

Chapter 2:Heat-Induced Mechanical Response Analysis 14

2.1
2.2

2.3

2.4

2.5
2.6

 

 

 

 

Overview of Literature —- - .......... 14
Thermal Analysis (Collagen Denaturation Kinetics) - u 17
2. 2.1 Isothermal Heating Experiments ................................................... 18
2. 2. 2 Differential Scanning Calorimetry Experiments ........................... 23
Arrhenius Damage IntegraL- - 33
Mechanical Analysis (Heat-Induced Mechanical Response) ............... 35
2.4.1 Specimen Preparation .................................................................... 35
2.4.2 Experimental Setup ........................................................................ 37
2.4.3 Experimental Protocol ................................................................... 41
2.4.4 Analysis Parameters ....................................................................... 44
Mechanical Response to Accumulating Thermal Damage .................. 47
Empirical Correlations....... ............ -- - 51
2.6.1 Equilibrium Shrinkage (eat) and Thermal Damage (0) ................. 51

2.6.2 Normalized Tensile Modulus (E/Eo) and Thermal Damage (0) ...55

Chapter 3:Thermal Exposure Simulations for Thermotherapy.............59

3.1

Modeling the Temperature Distributions Created by Thermotherapy ..
- -- -------------- - 60

 

vi

3.2

3.3

3.4

3.1.1 Overview of Clinically Applied Heating Modalities ..................... 62

 

 

3.1.1.1 Ho:YAG Laser Heating ...................................................... 62

3.1.1.2 Bipolar Radiofrequency Heating ....................................... 63

3.1.1.3 Monopolar Radiofrequency Heating ................................. 65
3.1.2 Hydrothermy .................................................................................. 66
3.1.3 Finite Element Analysis ................................................................. 66
Temperature Distribution Results-- ------- - - 68
3.2.1 Temperature Field on the Surface Of the Control Volume ............. 68
3.2.2 Temperature Field within the Control Volume .............................. 71
3.2.3 Model Verification ......................................................................... 74
Modeling the Thermal Damage Accumulated During Thermotherapy .
....... - -- 75
Temperature COntrOIIed Monopolar Heating Probe Experiments &
Simulations 87

 

Chapter 4:Collagenous Tissue Thermomechanics................................... 92

 

 

 

 

 

 

 

 

4.1 Characteristics of Thermal Stresses- - - - 94
4.2 Thermomechanical Modeling Primer-- 95
4.3 Thermomechanical Response Simulation Algorithm 97
4.4 Two-Dimensional Simulations - 102
Chapter 5:Chemical Enhancement Methods (Cross-Linking) ....... 106
5.1 Materials and Methods 109
5.2 Results- - - - -- - - - - - - -- 112
5.2.1 Equilibrium Shrinkage, e2 ----- 112

5.2.2 Recovery Ratio, R ........................................................................ 114

5.2.3 Tensile Modulus, E ...................................................................... 115

5.3 Cytotoxicity ...... - -- - - ------ 116
5.4 Other Studies“ - - - ....... - 118

 

Chapter 6:Conclusions ...1.....20

Chapter 7 :Directions for Future Research 131

Appendix A: Eshelby’s Method” ...... .....133

vii

Appendix B: User Subroutines ............................................................... 136

 

 

 

 

B.1 Subroutine Plotv: -- - - - 136
B.2 Subroutine Flux: . - - -- 138
Appendix C: Determination of Glutaraldehyde Penetration ................ 142
C.1 :Experimental Protocol - - - - 142
C.2 : Sample Merged Images - - -- - ------ 143
Bibliography ............................................................................................... 144

viii

LIST OF TABLES

CHAPTER 1:

Table 2.1: RPT Collagen Denaturation Endotherm Characteristics .............................. 28

Table 2.2: Enthalpy of RPT Collagen Denaturation ...................................................... 30

CHAPTER 3:

Table 3.1: Values Used in Simulations ............................................................................... 68

CHAPTER 4:

Table 4.1: Mechanical Response Simulations Performed ................................................. 103

CHAPTER 5:

Table 5.1: Experimental Groups ...................................................................................... 112

LIST OF FIGURES

CHAPTER 1:

Figure 1.1 : Collagenous Tissue Hierarchy [Hayashi, et al., 1996]. (From Triple-Helical
Collagen Molecule to F ibril Level) ................................................................. . 3

Figure 1.2 : (A) Anatomy of the Glenohumeral (Shoulder) Joint, (B, C) Anatomy of the
Glenohumeral (Shoulder) Capsule and Rotator-Cuff Muscle Group. (httpzl/
scortho-docs.org/shoulder.html) ..................................................................... . 5

Figure 1.3 : Shoulder Dislocation Causing Traumatic Shoulder Instability. (1) Stable
Shoulder Joint, (2) Dislocated and Locked Joint, (3) Reduced, Unstable Joint 6

Figure 1.4 : Arthroscopic Thermotherapy of the Shoulder (A) Schematic of HACS
Procedure [Wolf, 1998], (B) Photograph Taken During HACS by an

Arthroscopic Camera (http://www.communityorthopedics.com/pages/
thermal.htm) .................................................................................................... . 9

Figure 1.5 : Heat-induced Collagen Denaturation [Amoczky & Aksan, 2001] .............. 10

Figure 1.6 : Loss of Fibrillar Structure with Heating. (Inserts A Through E Show the Effect
of Accumulating Thermal Damage on F ibrillar Structure) [Wall, et al., 1999]11

CHAPTER 2:

Figure 2.1 : Isothermal Shrinkage of Bovine Chordae Tendineae [Chen, et al., 1998b].. 15

Figure 2.2 : Isothermal Heating Experiments with Rabbit Patellar Tendon ................... 21
Figure 2.3 : QIOO DSC Machine Response at 200°C/min. Heating (Scanning) Rate ..... 22

Figure 2.4 : Characteristic DSC Experimental Data Collected from one RPT Sample. ..26

Figure 2.5 : Transition Peak Temperature, Tmax, as a Function of Heating (Scanning) Rate,
r. (Data for Rat Tail Tendon (RTT) is fiom Miles, et a1. [Miles, et al., 1995])29

Figure 2.6 : Peak Width at Half Height, AT, as a Function of Heating (Scanning) Rate, r.
(Data for Rat Tail Tendon (RTI) is from Miles, et al. [Miles, et al., 1995], data

for Porcine Lens Capsule (PLC) is from Miles [Miles, 1993].) .................... 31
Figure 2.7 : Variation of Rabbit Patellar Tendon Collagen Apparent Specific Heat with

Accumulating Thermal Damage .................................................................... 34
Figure 2.8 : Laser Shadowgraph System for Dimension Measurements ........................ 36
Figure 2.9 : Patellar Tendon Specimen ........................................................................... 38
Figure 2.10 : Schematic of the Experimental Setup ....................................................... 38
Figure 2.11 : Photograph of Experimental System ......................................................... 40

Figure 2.12 : Zoom View of the Hydrothermy Bath and the Patellar Tendon Sample Fixed
to the Grips of the Materials Testing Machine .............................................. 41

Figure 2.13 : Patellar Tendon Load History in One Heating Cycle Comprised of Three
Testing Phases (Mechanical Preconditioning, Mechanical Testing and Thermal
Testing). (Data is taken from Cycle #1 in Figure 2.15) ................................. 42

Figure 2.14 : Patellar Tendon Elongation/Shrinkage History in One Heating Cycle
Comprised of Three Testing Phases (Mechanical Preconditioning, Mechanical
Testing and Thermal Testing). (Data is taken fiom Cycle #1 in Figure 2.16) 43

Figure 2.15 : Load History of a Patellar Tendon Specimen Subjected to Successive Heating

Cycles ............................................................................................................. 44
Figure 2.16 : Shrinkage History of a Patellar Tendon Specimen Subjected to Successive
Heating Cycles. .............................................................................................. 45
Figure 2.17 : Heat-Induced Elongation and Shrinkage (Effect of Test Load on Heat-
Induced Response) ......................................................................................... 48
Figure 2.18 : Progression of Equilibrium Shrinkage (e2) with Accumulated Thermal
Damage (.0) at Different Test Loads (F). ....................................................... 49
Figure 2.19 : Variation of .0", as a Function of Test Stress, s, (s=F/A*). ....................... 52
Figure 2.20 : Variation of Maximum Equilibrium Shrinkage (32mm) as a Function of Test
Stress, 0', (o=F/Ao). ........................................................................................ 53
Figure 2.21 : Master Curve for Heat-Induced Shrinkage of Rabbit Patellar Tendon (for
2.5£F£10.0N) ................................................................................................. 54

Figure 2.22 : Effect of the Accumulating Thermal Damage, {2, on the Stretch-Load
Response of a Representative Tendon Specimen. (Test Load=5N, Bath
Temperature=75°C, Exposure Increment=303) ............................................. 55

Figure 2.23 : Master Curve for the Variation of Normalized Tensile Modulus (E/Eo) with
Equilibrium Shrinkage (e2). (Both E and E() are the Tangent Moduli Calculated

at lMPa) ......................................................................................................... 56
Figure 2.24 : Variation of Thermal Stress with Equilibrium Shrinkage ......................... 58
CHAPTER 3:
Figure 3.1 : The Control Volume for F EA ..................................................................... 61
Figure 3.2 : Probes used in HACS procedures ............................................................... 64
Figure 3.3 : The Temperature Distribution Created on the Surface of the CV by a Stationary
Heating Probe (V =0). (Convection Coefficient, h=50W/m2K). .................... 69

Figure 3.4 : The Temperature Distribution Created on the Surface of the CV by a Moving
Probe (V =0.002m/s). (Convection Coefficient, h=50W/m2K). (The probe was
located at x=8.0E-O3 m and moved to the right at a speed of 2mm/s) ............ 70

xi

Figure 3.5 : The Temperature Distribution Created on the Surface of the CV by a Moving
Probe (V =0.004m/s). (Convection Coefficient, h=50W/m2K). (The probe was

located at x=8.0E-03 m and moved to the right at a speed of 4mm/S) ............ 71
Figure 3.6 : Temperature Distributions at t=4$ ............................................................... 72
Figure 3.7 : The Temperature Distribution Created within the CV by a Stationary Heating
Probe (V =0). (Convection Coefficient, h=500W/m2K) ................................. 73

Figure 3.8 : The Temperature Distribution Created within the CV by a Moving Probe
(V =0.002m/ s). (Convection Coefficient, h=500W/m2K). (The probe was located
at x=8.0E-03 m and moved to the right at a speed of 2mm/s). ...................... 73

Figure 3.9 : The Temperature Distribution Created within the CV by a Moving Probe
(V =0.004m/s). (Convection Coefficient, h=5 OOW/mzK). (The probe is located at

x=8.0E-03 m and moving to the right at a speed of 2mm/s). ......................... 74
Figure 3.10 : Comparison of FEA Results with the Exact SolutiOn ............................... 75
Figure 3.11 : Thermal Damage Accumulation at t=48 .................................................... 76

Figure 3.12 : Thermal Damage Accumulation in the Tissue A) h=500W/m2K,
aFro=0.001m, V=0; B) h=500W/m2K, w=ro=0.001 m, V=0.002 m/s; C)
h=500W/m2K, a)=r0=0.001 m, V=0.004 mm/s. (E0: Laser (L) Surface Heat Flux
[W/mz], q": Bipolar (BP) Surface Heat Flux [W/mz], P: Monopolar (MP) Joule
Heating [W]). ................................................................................................. 78

Figure 3.13 : Thermal Damage Accumulation in the Tissue A) h=50W/m2K, aFro=0.001m,
v=o; B) h=50W/m2K, a)=r0=0.001m, V=0.002m/s; C) h=50W/m2K,
a)=r0=0.001m, V=0.004m/s. (E0: Laser (L) Surface Heat Flux [W/mz], q":
Bipolar (BP) Surface Heat Flux [W/mz], P: Monopolar (MP) Joule Heating

[W]). ............................................................................................................... 81

Figure 3.14 : Thermal Damage Accumulation on the Tissue Surface A) h=50W/m2K,
aFro=0.001m, V=0; B) h=50W/m2K, co=r0=0.001m, V=0.002m/s; C) h=50W/
mzK, aFro=0.001m, V=0.004m/S. (E0: Laser (L) Surface Heat Flux [W/mz], q":
Bipolar (BP) Surface Heat Flux [W/mz], P: Monopolar (MP) Joule Heating

[W]). ............................................................................................................... 84
Figure 3.15 : Photograph of the Motor Driven Carriage ................................................ 88
Figure 3.16 : Experimental Setup for the Verification of FEA Simulations .................. 89

Figure 3.17 : Temperature at the Origin During Stationary and Moving Heating
Simulations with a Temperature Controlled Monopolar Radiofrequency Probe
........................................................................................................................... 89

Figure 3.18 : Penetration of Thermal Damage, {2, Predicted at the Origin ...................... 91

Figure 3.19 : Temperature Distribution at t=8s Within the Tissue Subjected to a Moving,
Temperature Controlled Monopolar Radiofrequency Heating Probe ............. 91

xii

CHAPTER 4:

Figure 4.1 : Arthroscopic View Showing the Parallel Zones of Denaturation Created on the
Shoulder Capsule by Monopolar Radiofrequency Heating (http://

www.communityorthopedics.com/pages/thennal.htrn) ................................. 94
Figure 4.2 : Collagenous Tissue Thermomechanical Response Simulation Algorithm ..98
Figure 4.3 : REV Approach and Schema of Thermomechanical Coupling ................ . 101
Figure 4.4 : Results of the Heat-Induced Mechanical Response Simulations ............. . 104
Figure 4.5 : Variation of the Normal Stress in y-direction (oyy) (Range: White: 2.907 MPa

compressive, Black: -1.975 MPa tensile). (ds: Laser spot Size) ................. . 105
Figure 4.6 : Variation of the Normal Stress in x-direction (oxx) (Range: White: 0.2589 MPa

compressive, Black: -1 .142 MPa tensile). (d3: Laser spot Size) ................. . 105
CHAPTER 5:

Figure 5.1 : Normalized Fluorescence Intensity (I*=I/Imax) at 520nm as a Function of
Normalized Tendon Width (x*=x/xmax). ................................................... . 109

Figure 5.2 : Characteristic Heat-Induced Response of Rabbit Patellar Tendon Specimen
........................................................................................................................ l l 1

Figure 5.3 : Variation Of Equilibrium Shrinkage, e2 with Treatment Temperature and
Exposure Time ........................................................................................... . 113

Figure 5.4 : Variation of Recovery Ratio, R, with Treatment Temperature and Exposure
Time ........................................................................................................... . 1 14

Figure 5.5 : Variation of Modulus Ratio, E with Treatment Temperature and Exposure
Time ........................................................................................................... . 116

Figure 5.6 : Results of Cytotoxicity Tests with Rabbit Patellar Tendon Fibroblasts .. . 118
APPENDIX A:

Figure A.1 : Eshelby’s Method for Stress-free Transformation of an Ellipsoidal Region
[Clyne & Withers, 1993] ............................................................................ . 133

Figure A.2 : Transformation Stresses and Determination of the Final Configuration . 134

xiii

APPENDIX C:

Figure C.1 : Transmitted Light Microscopy Across the Width of the Tendon Specimen

........................................................................................................................ 143
Figure C.2 : Fluorescent Light Microscopy (520nm) Across the Width of the Same Tendon
Specimen .................................................................................................... . 143

(Images in this dissertation are presented in color)

xiv

KEY TO SYMBOLS AND ABBREVIATIONS

Molecular collision frequency, [1 /S]

Cross-sectional area [m2]

specific heat [kJ/kg-K]

Coefficient in Equation 2.11
Coefl'icient in Equation 2.11
Coefficient in Equation 2.11
Instantaneous shrinkage, [mm]
Equilibrium shrinkage, [mm]

Laser spot diameter [mm]
Instantaneous strain

Equilibrium strain

Tensile Modulus [MPa]

Denaturation activation energy, [J/mol]
Peak surface irradiation for laser heating [W/mz]
Laser pulse frequency [Hz]

Test load, [N]

Heat Generation [W/m3]

Enthalpy of denaturation, [J /mol]
Convection Coefficient [W/mz-K]

Normalized fluorescence intensity
Fluorescence intensity
Centeroid x-coordinate of the REV
Centeroid y-coordinate of the REV
Thermal conductivity [W/m-K]
Temperature dependent reaction rate constant, [1/ S]
Number of collagen molecules at native state
Joule heat [W]

Surface heat flux [W/mz]

XV

.9? Universal gas constant, [8.314 J/mol-K]
R Recovery Ratio

r Scanning (heating) rate, [l/min]

r0 l/e radius of the Gaussian Profile [m]
t Time, [s]

T Temperature [K]

AT Endotherm width at half height, [K]
T m Temperature when denaturation endotherm reaches its peak, [K]
V

Probe sweep speed [m/s]
8* Subregion

Region
x x-coordinate [m]
x* Normalized tendon width

y y-coordinate [m]
Greek:

(It) Arrhenius damage integral
1 Time to denaturation, [S]

p density [kg/m3]

3 Strain

1. Stretch Ratio

fit) Window function in Equation 3.4

p, Absorption coefficient [1/m]

A Latent Heat of Phase Change [kJ/kg]
ac. Perturbation in heat capacity, [J/mol-K]
At Time increment [3]

Al Intemode distance [m]

1, Laser pulse width [s]

0),, Probe radius [m]

a Thermal diffusivity [mZ/S]

xvi

g. . Stress tensor for the REV

1,]

Subscripts:

gegsme

Apparent
Initial
Midline
Maximum
Native state
Set value

th Theoretical

x x-component

xx x-component

y y-component

yy y-component

00 Far field conditions

Abbreviations:

BP Bipolar

CV Control Volume

DPPA diphenylphosphorylazide

DSC Differential scanning calorimetry
EDC 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide
FE4 Finite Element Analysis

GTA Glutaraldehyde

HACS Heat assisted capsular shift
HMDC hexamethylene diisocyanate

IR Infi'ared

ADSC Modulated differential scanning calorimetry
MP Monopolar

MRI Magnetic resonance imaging
N20. Non cross-linked

OCT Optical coherence tomography

xvii

REV Representative elementary volume
RF Radiofrequency
UV Ultraviolet

xviii

Chapter 1: Introduction

This dissertation describes research directed towards understanding, modeling and
controlling the heat-induced responses of collagenous tissues. The main aim of the
research was to establish the scientific basis and develop the tools to increase the safety
and efficacy of Sub-Ablative Thermotherapy procedures applied to treat instabilities of

the knee, ankle and Shoulder joints and in the elimination of discogenic pain in the spine.

Arthroscopic thermotherapy in the form of Heat-Assisted Capsular Shift (HACS)
procedures for shoulder instability-related diseases served as a focal problem. To date,
over 70,000 patients have been treated with sub-ablative thermotherapy and this number is
growing rapidly. By some estimates, as much as 8% of the US population suffers from
shoulder joint instability. The number climbs to an estimated 35% of the population if
knee and shoulder connective tissue diseases and injuries are included [Praemer, et al.,

1999].

In the HACS procedure, mechanically deformed, lax collagenous tissues
surrounding the Shoulder joint (the shoulder capsule and the underlying ligaments
[O'Brien, et al., 1990]) are thermally shrunk by means of laser or radiofi'equency heating
[Amoczky & Aksan, 2001; Anderson, etal., 1999]. Even though the safety and long-term

efficacy of these procedures are still being questioned [Perry & Higgins, 2000], in the year

2000 alone approximately 20,000 patients in the US underwent arthroscopic

capsulorrhaphy operations [Praemer, et al., 1999].

1.1 Collagenous Tissue Structure: From Microscale to Macroscale

Dense, oriented collagenous tissue (such as tendon and ligament) structure follows
a strict hierarchy [Figure 1.1]. The main structural element of soft tissues like tendon, joint
capsule, ligament and skin is the Type I collagen molecule (approximate length is 300
nm). The collagen molecule is comprised of three polypeptide a-chains wound around
each other in a helical pattern. Each a-chain is made up of approximately 1500 amino acid
residues. Every third residue in this chain is glycine followed usually by proline or
hydroxyproline. The structural stability of the collagen molecule is established by the
inter-chain hydrogen bonds among the glycine residues of different (it-chains and the intra-
chain hydrogen-bonded water bridges between the proline and hydroxyproline residues
within each (II-chain. At a higher level of the hierarchy is the microfibril. The microfibril is
made up of a parallel arrangement of five collagen molecules in a cylinder-like formation.
Following similar assembly rules, moving further up in the hierarchical ladder the

microfibrils form the fibrils and the fibrils form the fibers.

F ibrils are the smallest structures seen with transmitted light microscopy. In a
dense, oriented soft tissue (tendon and ligament), the vast majority of the fibrils are
aligned in the same direction whereas in other kinds of soft tissues (such as skin and joint

capsule) there is a spatial variation in fibril orientation and density.

Hydrogen bonds are known to be responsible for the thermal and mechanical
stability of the collagen molecule. The higher the hydroxyproline content, the higher the
stability and the higher the denaturation temperature of the molecule [Nemethy, 1998].
This well-organized, hierarchical structure, which is enforced by the inter/intramolecular
and inter/intrafibrillar chemical bonds (cross-links), determines the response of the tissue
to various mechanical and thermal stimuli [Miles, et al., 1995; Olde Damink, et al., 1995;

Wren & Carter, 1998].

 

   
  

g...” w ..3...........

”IIDIIIDIDIDE)“

5m '91. sill-Innlrllnnmn

’ I ‘ Fibril
(I l " 67nm

  

 

 

 

 

 

 

 

I "s a
1 ‘~ 300nm Molecule

I, I“ ~
1...... IW a...

Figure 1.1: Collagenous Tissue Hierarchy [I-Iayashi, et al., 1996]. (From Triple-Helical
Collagen Molecule to F ibril Level)

1.2 Shoulder Instability

In order to allow a wide range of motion, the shoulder (glenohumeral) joint lacks
bony stability (Figure 1.2 A). The integrity of the joint is maintained mainly by the
surrounding capsuloligamentous tissues (the shoulder capsule and its regional thickenings
known as the glenohumeral ligaments [O'Brien, et al., 1990]) and the rotator cuff muscles
and tendons (Figure 1.2 B, C). Low resilience of these surrounding structures contributes

to the increased sensitivity to injury.

Kinematically, the shoulder instability may be defined as the inability to maintain
the humeral head (the ball) centered in the glenoid (the socket) caused by the pathological
redistribution of the forces that keep the joint in equilibrium. Redistribution Of the forces
is usually initiated by soft tissue problems. These can occur from a single acute event that
deforms the capsule and causes capsular and ligamentous laxity (traumatic injury),
recurrent micro-trauma that damages the biological microstructure of the joint capsule or

by congenital disorders such as Ehlers-Danlos and Marfan's Syndrome.

In the case of traumatic injury, the problem is often initiated by joint dislocation
(Figure 1.3). Subjected to lateral impact forces, the humeral head slips over the labrum
(the protrusions around the glenoid fossa) and locks. In this locked position, the excessive
tensile forces created may cause plastic deformation of the capsuloligamentous tissues.
Even if the dislocated joint is reduced immediately, some irreversible laxity of the
surrounding soft tissues remain. This is easily observed upon examination by the

increased distance of the humeral head fiom the glenoid fossa [Baeyens, et al., 2001].

In the case of recurrent micro-trauma initiated instability, the possible mechanism
of injury is the modification of the collagenous tissue structure due to microdamage
created by interfibrillar slippage. Similar to the traumatic case, when subjected to
repetitive high stresses, the tissue stretches beyond its anatomical length. This type of
injury is usually seen in professional athletes (such as baseball pitchers, golfers and tennis

players) performing overhead sports [Jobe, 1991].

     

Humoral Head

Figure 1.2: (A) Anatomy of the Glenohumeral (Shoulder) Joint, (B, C) Anatomy of the
Glenohumeral (Shoulder) Capsule and Rotator-Cuff Muscle Group. (ht_tp://scortho—
docs.o shoulder: him]

It is estimated that at least 200,000 people in the US suffer from Marfan’s
Syndrome. In Ehlers-Danlos and Marfan's Syndrome, the triple helical structure of the
collagen is altered causing hyperextensibility of the collagenous tissues. There has been
no basic research on the feasibility of applying sub-ablative thermotherapy in persons

suffering from such diseases resulting from a pathology of the collagen structure.

1.3 Treatment options for Shoulder Instability

Depending on the type (anterior, posterior or multidirectional) and severity of
instability and the existence of complementary injuries such as capsule or rotator cuff
muscle tears and fractures in the glenoid, different treatments are proposed. Currently

applied therapies for the treatment of glenohumeral instability problems include closed,

open and arthroscopic techniques.
Stable 0
S h o u Id er
plastically ‘ fds

  
   

deformed capsule

stretched capsule

9

._/du>>ds

Dislocated Reduced,
Shoulder Unstable
Shoulder Superior

(Top) View

Figure 1.3: Shoulder Dislocation Causing Traumatic Shoulder Instability. (1) Stable
Shoulder Joint, (2) Dislocated and Locked Joint, (3) Reduced, Unstable Joint

1.3.1 Conventional Methods

Closed Technique: This technique, based on exercise, depends on strengthening
the muscle groups that surround the shoulder joint. In addition to a requirement for a very
long treatment period (6-12 months), the high reoccurrence rate limits its application as a
stand-alone method [Hayashi, et al., 1997]. While some success is achieved in the
treatment of atraumatic subluxation cases (80-90%), only 16% success is obtained in the

treatment of the traumatic ones [Burkhead, et al., 1992].

Open Techniques: Depending on the type of instability (anterior, posterior or
multidirectional) approximately 300 different operative procedures have been applied for
the surgical management of instability [Zayne, et al., 1995]. These operations aim at re-
stretching the lax joint tissues, usually by folding the excess capsule beneath itself and
stitching it by sutures or by tightening the capsule using surgical anchors attached to the
glenoid. In addition to being technically difficult, these operations which are performed
for the capsule shift or repair, are generally known to result in pain and have the potential
to reduce range of motion and even cause loss of motion, nerve injury and osteoarthritis
[Banas, et al., 1993; Bigliani, 1989; Jobe, 1989; Neer, 1990]. Only 30% of patients

undergoing surgical operations appear to achieve their pre-injury function.

Arthroscopic Techniques: Although this technique has less risk of neuromuscular
injury and requires a Shorter rehabilitation period compared to open techniques, the
reoccurrence rates observed (between 0% to 50%) Show that this technique requires

extreme technical expertise and is very much dependent on the skill of the surgeon. Long-

term follow-up studies indicate that the failure rate climbs in the case of generalized

ligamentous laxity [Manta, et al., 1997].

1.3.2 Thermotherapy

Recently, arthroscopic thermotherapy (HAC S) has been applied for the treatment
of glenohumeral instability problems [Thabit, 1994]. This form of therapy aims to reduce
the excessive capsular volume and laxity by heating the glenohumeral capsule and the
surrounding ligaments (Figure 1.4 A). A Ho:YAG (HolmiumzYttrium-Almninum-Garnet)
laser or radio-frequency probe (Figure 1.4 B) is used by the surgeon to heat these soft
tissues to sub—ablative levels (65-85°C). Heating to this level causes collagen denaturation
resulting in overall tissue shrinkage. The amount of shrinkage Obtained is, to a large
extent, determined by the thermal protocol applied. Depending on the heating modality
used during heating, in the literature the acronyms LACS (Laser-Assisted Capsular _S_hift)
and ETAC (Electrolhermally-Assisted Capsulorrhaphy) are fiequently used. For brevity,
in this thesis the acronym HACS (Heat-Assisted Capsular Shift) will be used when

referring to any one of them.

Although results of Short-term follow-ups Show that the therapy is promising and
the side effects seem to be nearly nonexistent, questions about the long-term success
remain unanswered [Savoie III & Field, 2000; Tyler, et al., 2000]. Improved range of
motion of the repaired shoulder, accelerated patient healing as well as lower recurrence

rates are the major advantages of this therapy.

ArthroscoplyI Came
- . .‘H.

 

Figure 1.4: Arthroscopic Thermotherapy of the Shoulder (A) Schematic of HACS
Procedure [Wolf, 1998], (B) Photograph Taken During HACS by an Arthroscopic Camera
(hggflwww. communityorthogedics.com/gages/thermalhtm)

The disadvantages are the time-dependent decrease of tissue stifl‘hess and strength
and the trend for tissue recovery back to its untreated length. This kind of response is
observed in research done on animal models [Chen & Humphrey, 1998; Chen, et al., 1998;
Schaefer, et al., 1997], as well. Time-dependent changes in mechanical properties and
behavior are thought to be the major reason for recurrence and failure of the therapy in the

long mm.

1.3.3 Mechanism of Thermotherapy (Heat-Assisted Capsular Shift)

Increased temperatures (higher than 60°C) cause a reaction at the tropocollagen
level; the collagen molecules start to unwind due to breaking of the hydrogen bonds
(Figure 1.5). This reaction causes weakening and shortening of the tropocollagen

molecule. In a domino effect manner, these structural alterations in the microscale (as seen

in Figure 1.6) produce irreversible changes all the way up to the tissue level. At the fiber
level, it is seen that the fiber lengths decrease while their diameters increase. At the tissue
level, the observed response is Shrinkage in the major direction of fiber orientation

accompanied by a swelling in the other directions.

After heating, if the tissue is allowed to cool back to its initial, neutral state
temperature, it may expand slightly (recovery). This is attributed to the partial re-
naturation of the collagen structure. The magnitude of this recovery fi‘om shrinkage

depends on the reversibility of the thermal-mechanical modification achieved.

  

In
; Tropocollagen
, Molecule

  

Tropocollagen
Molecule

Collagen I

i "‘ "Molecule
Thermal Shrinkage

a: lntramolccular Cross-Links
b: Intermolecular Cross—Links

 

Figure 1.5: Heat-induced Collagen Denaturation [Amoczky & Aksan, 2001]

A very effective method for the determination of denaturation at the micro scale is

optical birefringence measurement [Pearce, et al., 1993]. The birefringence in collagenous
tissues is due to the differences between the refractive indices of the ordered fibril

structure and the surrounding ground substance [Sankaran, & Walsh, 1998]. Optical

10

measurement of the birefringence decay during the helix-tO-coil transition of
tropocollagen molecules (loss of ordered structure) has proved to be a very valuable
nondestructive method to model thermal denaturation of various tissues [Maitland &
Walsh, 1997]. This method is vital in understanding the relationships between the
denaturation phenomena at the micro-scale and the bulk tissue shrinkage observed at the

macro-scale.

 

Figure 1.6: Loss of Fibrillar Structure with Heating. (Inserts A Through E Show the Effect
of Accumulating Thermal Damage on F ibrillar Structure) [Wall, et al., 1999]

There are two important factors that accompany the denaturation-induced
shrinkage of collagenous tissues. These are: the mechanical property degradation and the
partial loss of shrinkage upon cooling back to lower temperatures (defined as recovery).
Recovery is thought to be the result of re-naturation i.e., refolding of the partially unfolded
tropocollagen molecules upon cessation of heat [Hormann & Schlebusch, 1971]. This is
the main cause of ambiguity in measuring the exact amount of shrinkage produced by

heating. This factor may be particularly important during HACS surgery where the

success of the operation is to a large extent dependent on the amount of shrinkage

achieved.

The reduction in the tensile modulus and strength (up to 70-90% of the untreated
tissue) of the collagenous tissue upon heating is reported in the literature [Vangness, et al.,
1997; Schaefer, et al., 1997; Berend, et al., 1996; Hecht, et al., 1999]. This fact, coupled
with the strain injury (microdamage yielding to plastic deformation) created in the
glenohumeral capsular and ligamentous structures during subluxation or dislocation,
indicates that immediately after the Operation the tissue is excessively weak and

vulnerable.

One possible candidate to solve these problems is to apply a chemical cross-
linking method in conjunction with heating as a means of reducing the recovery of the
tissue while enhancing the mechanical properties. Examination of the feasibility of this

idea was the motive for preliminary research conducted as a part of this thesis (Chapter 5).

1.4 Research Objectives

The main aim of the research was to establish the scientific basis and develop the
tools to increase the safety and efficacy of Sub-Ablative Thermotherapy procedures. To

achieve this goal, the following objectives are established:

a) Modeling the thermal damage accumulation in collagenous tissues when they
are subjected to clinically applied heating modalities. Research aimed at reaching this

Objective is presented in Chapter 3 of this thesis.

12

b) Determination of the constitutive relationships between the measured thermal
and mechanical parameters (temperature, time, load) and the final state of the tissue (state-
of-stress and mechanical properties). Chapter 2 of this thesis describes the experimental
analysis performed with a model collagenous tissue (rabbit patellar tendon) in order to

establish these relationships.

c) Modeling the thermomechanical responses of collagenous tissues in order to
develop a simulation tool to be used for optimizing currently applied sub-ablative
thermotherapy procedures (e.g. HACS, therrnokeratoplasty, etc.). Chapter 4 of this thesis

describes the thermomechanical response simulation algorithm developed for this

purpose.

Additionally, the feasibility of applying chemical enhancement methods as a
means of reducing the recovery of the tissue while enhancing the mechanical properties is
examined in Chapter 5. Chapter 6 summarizes the results, presents the conclusions drawn
from the research presented here and discusses important issues that are addressed by this

research. Chapter 7 discusses the directions for future work.

13

Chapter 2: Heat-Induced Mechanical Response Analysis

2.1 Overview of Literature

Collagenous tissue denaturation and shrinkage in response to heating by laser,
microwave, radio frequency devices and hydrothermy are extensively studied phenomena
[Naseef III, 1997; Hayashi, 1996; Allain, 1980]. The amount and the extent of the
irreversibility of tissue shrinkage (i.e., thermomechanical strain formation) depend on
many factors. These factors include the maximum temperature reached and the exposure
time [Miles, 1995; Cilesiz, 1997; Pearce, 1993; Le Lous, 1983] as well as the mechanical
stress applied on the tissue during heating [Kang, 1995]. Other factors include the
surrounding medium pH and electrolyte concentration [Privalov, 1982] as well as the type
of collagen Hang, 1997], its hydration level [Privalov, 1989], and the degree of the cross-
linking [Olde Damink, 1995; Ruijgrok, 1994]. In other words, the amount and rate of heat
deposition, coupled to the properties of the tissue and the surrounding medium govern the

response at both the microscopic and macroscopic scales [Le Carpentier,1993].

The heat-induced respOnseS of a collagenous tissue for isothermal, stress-flee and
isotonic shrinkage conditions have been quantified recently for a bovine model [Chen, et

a1, 1997, 1998a,b,c] under hydrothermal heating conditions. These studies have revealed

14

that heat-induced denaturation of collagenous tissues (expressed in terms of thermal-
mechanical strain formation) can be quantified by a single Arrhenius type of relationship.
This relationship depends on the temperature, exposure time and mechanical stress
applied to the tissue. This finding, together with the differentiation of various thermal-
mechanical response regimes, may be considered the first attempt to establish a unique
relationship which couples thermal and mechanical factors together in a model of the

tissue thermal response.

 

Shrinkage ,Kfiecovery 4

0‘- O 0-- O. O.

    

 

 

 

SHRINKAGE E, (°/.)

 

1:a 11 12 Tb

Figure 2.1: Isothermal Shrinkage of Bovine Chordae Tendineae [Chen, et al., 1998b]

Although the Observation of Shrinkage in response to various heating loads is well
documented in the literature, a consensus regarding the magnitude and irreversibility of
thermal-mechanical strain formation is far fi'om being reached. Examination of the

following examples chosen from the many in the literature, highlights this conclusion:

I. Hydrothermal heating (where the tissue is completely immersed in a saline bath

and the saline temperature is increased) of bovine calf knee capsule at 65°C

for 60 seconds causes 50% shrinkage [Naseef ID, 1997],

15

II. Hydrothermal heating of bovine chordae tendineae at 65°C for 100 seconds

results in 20% Shrinkage [Chen, et al., 1997],

III. Hydrothermal heating of cadaver glenohumeral capsule at 65°C for 600

seconds causes 11% shrinkage [Hayashi, et al., 1997],

IV. Ho:YAG laser ablation until tissue opacity changes at a dose of 300 J/cm2 for

rabbit patellar tendon results in 6.6% shrinkage [Schaefer, et al., 1997],

V. Ho:YAG laser ablation until tissue opacity changesat a dose of 300 J/cm2 for

canine patellar tendon results in 56% shrinkage [Berend, et al., 1996],

VI. Ho:YAG laser ablation until tissue opacity changes at a dose of 180 J/cm2 for
rabbit femoropatellar joint capsule causes 38% shrinkage [Hayashi, et al.,

1995].

The inconsistencies and the contradictions of trends among the shrinkage values
reported by different researchers are thought to result from the differences among the
heating modalities and protocols applied. The differences in tissue composition in addition
to the distribution of collagen types and variation of collagen fiber orientation inside the
tissue also contribute [Olde Damink, 1995; Chvapil and Jensovsky, 1963; Horgan, et al.,
1990]. The inconsistencies include the great difference in Shrinkage values between
examples IV and V for the same tendon tissue harvested from two different species but
exposed to the same heating load. The contradictions include the decrease in observed
shrinkage values with increase in exposure times in examples I, II, III, which is contrary
to current knowledge. The differences between species, the age of the tissue sample, as

well as the duration of heating and the maximum temperature reached are considered to be

16

major factors, which detemrine shrinkage [Olde Darrrink, 1995; Le Lous, et al., 1985;
Allain, et al., 1980]. Additionally, there are some other parameters that have not been
considered comprehensively in the literature. These are; a) the effects of the differences in
thermal histories created by different energy deposition modalities, b) the correlation
between the level of denaturation achieved at the micro scale and the thermomechanical
response at the macro scale and c) the effects of stress and the chemical state of the tissue
on thermal response characteristics. Examination Of these parameters will be performed as

part of this thesis.

2.2 Thermal Analysis (Collagen Denaturation Kinetics)

Traditionally, heat-induced denaturation of collagen has been modeled as a first-
order reaction between its native and denatured states [Miles, 1993] or a second-order
reaction (similarly between the native and denatured states) through an intermediary,
activated state [Lyubarev & Kurganov, 1998]. The activated state corresponds to the

partially unfolded configuration of the protein.

The first-order reaction theory [Miles, 1993] dictates that during denaturation
phase change of the collagenous tissue, the decline in the number of molecules in the

native state can be represented as a firnction of time, t, as follows:

dN
— = —k N. 201
dt (T)

17

In the equation above, N is the number of molecules in the native state and MI) is
the temperature dependent reaction rate constant. Isothermal heating experiments are
performed in order to determine how the reaction rate constant changes with temperature.
In these experiments, the collagenous tissue is kept at the isothermal test temperature, and

the time required for the completion of the chemical reaction (denaturation) is measured.

There are two major issues with the implementation of isothermal heating
experiments. Firstly, the tissue temperature Should instantly be increased to the isothermal
test temperature and be constant throughout the test. Due to the thermal response
characteristics of the experimental equipment used, this condition may be very hard to
achieve. Secondly, a very accurate method is required to determine the completion of the
chemical reaction. For heat-induced denaturation of collagenous tissues, the alternatives
are optical (measurement of the variation of structural birefringence with denaturation
[Pearce, et al., 1993]), chemical (determination of the number of hydrogen bonds broken
[Usha & Ramasami, 1999]), mechanical (measurement Of stress-relaxation during heating
[Le Lous, et al., 1983]) and thermal (calorimetric analysis [Burdzhanadze, et al., 1997])
methods. Since thermal denaturation of collagen is intrinsically a heat-induced
phenomenon, methods measuring the heat absorbed by the collagenous tissue during

denaturation (i.e., calorimetric analysis) appear to be the natural choice.

2.2.1 Isothermal Heating Experiments

In order to determine the denaturation kinetics of the rabbit patellar tendon tissue

(the tissue model used in the mechanical analysis), a model QIOO (TA Instruments, New

18

Castle, DE) Differential Scanning Calorimeter (DSC) was used. The cell temperature

reading of the calorimeter was calibrated using Indium (melting point 156.6°C) as the

standard.

A total of 18 isothermal heating experiments were performed with rabbit patellar

tendon tissue samples excised from three different tendons. The frozen (kept at
temperatures below -120°C), intact New Zealand White rabbit patellar tendon (RPT)

tissues were thawed ovenright at -5°C and kept in room temperature saline until testing.
Before the experiment, small tissue samples, weighing between 5 and 25 mg were excised,
weighed using a high precision scale (Sartorius 2842, Sartorius GMBH, Goettingen,
Germany) and placed in aluminium heating pans. IOul of saline was added to the sample
pan to ensure proper hydration of the sample during the course of the experiment. The
sample pan was then hermetically sealed and placed into the heating cell of the DSC

together with a reference pan. The reference pan also contained 10ul of saline and was
hermetically sealed. In the experiment, the sample was initially equilibrated at 25°C and
then the sample temperature was increased to the test temperature at a rate of 200°C/min.
(the maximum rate for the DSC used). The isothermal test temperature was set at half

degree increments between 54°C and 56°C and kept constant for the duration of the
experiment (maximum 3 hours). During the experiment, the heat flow to the sample pan,
normalized with respect to that to the reference pan, was measured and recorded at 10 Hz.
The onset of the denaturation phase change was marked by an increase in the rate of the

heat flow to the sample. When the sample was fully denatured, the heat flow rate returned

19

to its baseline (pm-denaturation) value. The time between the onset and completion of

denaturation was recorded for each experiment.

Nine out of the 18 experiments performed failed to produce dependable results due
to high noise or sample pan movement during denaturation. It was observed that if the
sample was small (less than 8 mg) the signal to noise ratio in the heat flow signal was very
low and if the sample was big (weighing more than 10 mg), denaturation induced shape
change of the sample caused sample pan movement. When the sample moved, the thermal
contact resistance between the tissue sample and the sample pan and/or between the
sample pan and the heating cell changed and very sharp, unnatural peaks were observed in

the heat flow signal.

The results obtained from the remaining 9 experiments are presented below in
Figure 2.2. Regression analysis performed on the data established an exponential
correlation between the absolute value of the isothermal test temperature and the time
required for full denaturation of the sample. The data showed that the reaction rate
constant, k(7), (which is equal to the mathematical inverse of the denaturation completion
time) is a function of temperature as given by the well-known Arrhenius equation [Miles,
1993]:

El

k(T)=A-e 9”, 2.2

 

where A is defined as the molecular collision frequency, E * is the denaturation activation

energy, 9? is the universal gas constant equal to 8.314 J/molXK, and T is the absolute

20

temperature. For the data presented below in Figure 2.2, the constants were calculated as
E“=4.045x105 J/mol and A=6.311x1061 1/s.
There were two major problems identified with the isothermal heating experiments

performed in this research. One apparent problem was the limitation imposed by the

temperature response of the DSC used. In Figure 2.3, the temperature response of the DSC

at a heating (scanning) rate of 200°C/min. is presented. As shown in this figure, it took

approximately 3 minutes (the region between t=13 and t=16 minutes in Figure 2.3) to heat

the sample to the set isothermal test temperature from the initial temperature (T;=25°C).

    
  

 

 

1.E+04 “;
Tendon # 1 Tendon # 2
g t = 1545269277" 0
g 1.5+03 «» R’ = 0.9948
E i o
l t = 4Ee1e“°3’"
~ R2 = 0.9576
!
{
‘1.sz L l I l l l I
3005-03 3015—03 3025-03 3035-03 3.04503 3.05503 3.06E-03
"Temperature [1IK]

Figure 2.2: Isothermal Heating Experiments with Rabbit Patellar Tendon

This was far from satisfactory for the “instant heating” condition imposed by the
experimental procedure. During this initial temperature transient, the heat flow signal for

the sample experienced a transition as well. If in an experiment, the isothermal test

21

temperature was set to a high value where the reaction rate was high (i.e., denaturation
reaction progressed fast), the denaturation phase change occured during this initial
transition and was completed even before the isothermal test temperature was reached. In

this thesis, this fact limited the higher end of the temperatures that could be experimented
with to 56°C.

The lower temperature limit for the experiments was determined by the very long
time required for the completion of the test. Since denaturation progressed very slowly,

the heat flow signal was very weak and the signal to noise ratio decreased, making it

impossible to deterrrrine the onset and completion of the phase change. Therefore,

experimentation with test temperatures below 54°C did not yield any results. These factors

limited the temperature range at which experiments could be performed to a very narrow

range of 54-56°C.

 

 

 

 
 
  

 

 

 

 

 

6° ] Isothermal Test Temperature\ 1 2
r
55 -l _ -2
8' 50 A “r -4 E
3' Temperature E
3 45 4 + -6 a;-
o
g. 40 1 Hut F'Ow A“ -8 E
E 5 I r sorter-200°ctmin. :
535i 2 +40:
3° r.-25°c J ‘J “ "2
25 l -._14
20 “i I I —m—*-— r——— --—r~— ————T— _-1.— .__7_ . _____T -16
10 11 12 13 14 15 16 17 18 19 20

Time [minutes]

Figure 2.3: QIOO DSC Machine Response at 200°C/min. Heating (Scanning) Rate

22

Due to the reasons presented above, the results of isothermal heating experiments
and the values for the coefficients of the Arrhenius rate equation (A, E *) calculated from
these experiments should be approached with extreme care. Validity of these constants at
high isothermal test temperatures or for non-isothermal heating conditions (which are
clinically relevant for the sub-ablative thermotherapy of collagenous tissues) could not be
determined with this method. One method to check the validity of these coefficients is by
examining the denaturation kinetics of the collagenous tissue by constant temperature
increase tests. For this purpose, a method proposed by Miles, et a1. [Miles, et al., 1995]

was implemented and the details are presented in the following section.

2.2.2 Differential Scanning Calorimetry Experiments

Differential Scanning Calorimetry (DSC) has extensively been used to
characterize the thermal behavior of acid soluble collagen [Tiktopulo and Kajava, 1998;
Burdzhanadze, et al., 1997] and collagenous tissues [Miles, 1993; Miles, et al., 1995;

Kampmeier, et al., 2000].

In the DSC method, the energy absorbed/released by the sample during ramp
temperature increase is measured. The characteristic behavior of collagenous tissue in a
DSC experiment is such that up to a certain temperature (denaturation temperature), the
specific heat (the incremental amount of heat absorbed by the specimen during unit
temperature rise) shows very little temperature dependence. As seen in Figure 2.4,

denaturation is characterized by a sudden increase in the energy absorption endotherm

(starting at approximately 55°C in Figure 2.4) in the neighborhood of the denaturation

23

temperature, Tm. With further heating, the endotherm reaches its maximum value (at

approximately 67°C in Figure 2.4) and then decreases and finally returns back to its

baseline value (at approximately 80°C in Figure 2.4). It is reported in the literature that the
denaturation endotherm characteristics are heating (scanning) rate dependent.
Burdzhanadze [Burdzhanadze, et al., 1997] reports that with dilute solutions of collagen,
an increase in denaturation enthalpy and denaturation temperature (endotherm maximum)
is seen with increasing scan rates while the half width of denaturation remains unaltered.
He explains that these “unexpected” results are due to the temperature dependent negative

enthalpy created by “disturbing hydrophobic interactions”.

Miles, et a1. [Miles, et al., 1995] show that the location and the shape of the
denaturation endotherm changes with scanning rate but the enthalpy of denaturation
remains constant. They also Show that the constants, (A, E *), calculated from isothermal
heating tests performed on rat tail tendon samples can be used to predict the characteristics
of the denaturation endotherm (such as its shape and position) at different heating

(scanning) rates during a DSC test.

If during the an experiment, the temperature is increased linearly (as would be the

case in a Differential Scanning Calorimetry (DSC) experiment) as a function of time as,

T = Ti+rt, 2.3

where 7} and r are the initial temperature and the heating (scanning) rate, respectively and

if the temperature dependence of the reaction rate constant, kn), is given by the Arrhenius

equation (Equation 2.2), the location (the temperature at which it reaches its maximum

24

(peak) value, T m") and the Shape of the denaturation endotherm can be predicted using

the following equations [Miles, 1993]:

 

 

 

rE* I:_R? ]
= e "m 2.4
ARTfim
RT2
AT = 2.446% 2.5
(5C0) - E‘ 26
AH Tm eRT2 °

where r, T m, A1; {I}, AH are the scanning rate, the temperature when the endotherm

reaches its denaturation peak (determines the endotherm location), the peak width at half
height, perturbation in heat capacity and the enthalpy of denaturation, respectively (see

Figure 2.4 for details).

Once the Arrhenius equation rate constants (A, E *) are calculated from isothermal

heating experiments, the location of the denaturation endotherm, Tm can be determined
as a function of the scanning rate, r (from Equation 2.4). When the value of T mu is
determined, it is possible to calculate AT from Equation 2.5, and fi/AH from Equation

2.6. These two variables determine the shape (the flatness or sharpness) of the

denaturation endotherm.

25

3.00 1

2.75 i

 

250 SC.”

 

2.25 —

C. [NIKON

 

 

 

 

 

 

35 45 55 85 75 85 95
Temperature [°C]

Figure 2.4: Characteristic DSC Experimental Data Collected from one RPT Sample

A series of conventional (DSC) and modulated differential scanning calorimetry
(MDSC) tests were performed using a calorimeter (Q100, TA Instruments, New Castle,
DE). Similar to the procedure followed in the isothermal heating tests (described in the
previous section), the cell temperature reading of the calorimeter was calibrated using
Indium and the absolute specific heat measurement was calibrated using Sapphire as the

standard.

A total of 43 rabbit patellar tendon specimens were subjected to ramp heating

experiments (at a rate of either 1, 5 or 10°C/min.) in the range of 25°C to 90°C and their
heat absorption were measured and recorded over the course of the experiments. Samples

were prepared in the same way as the samples used in the isothermal heating tests

26

described in the previous section. The differential scanning calorimetry test was

comprised of these following steps:

1. The temperature of the sample was increased to 25.00 °C.
2. Sample was equilibrated at 25.00 °C.
3. Sample was kept at 25.00 °C for 2 minutes.

4. Temperature was modulated by 1.00 °C every 60 seconds (this step was

included only in W8C experiments).
5. Sample was kept at 25.00 °C until it reached thermal equilibrium.

6. The temperature was increased to 90.00 °C at a predetermined scanning

(heating) rate (r = 1, 5 or 10°C/minute).
7. The sample was kept at 90°C for 2 minutes.

8. Sample was cooled back to 25.00 °C.

After the experiment was completed, the samples were weighed again and their
post-experimental weights were compared to their pre-experimental weights to ensure that
there was no change (i.e., saline has not leaked from the sealed pans). Measurements

showed that none of the samples tested has leaked during the experiments.

27

Table 2.1: RPT Collagen Denaturation Endotherm Characteristics

 

 

 

 

 

 

 

3311“ M... E"??? 3:122: . Matt“: ”3:: .
’, Temperature, Two-tailed Peak, Two-tailed
r [°C/mm.] T m [°C] P value AT [°C] P value
1 (n=4) DSC 61.477 5 0.581 0.0682 3.187 a 0.320 0.2182
5 (n=6) DSC 63.347 i 0.824 0.0433 6.485 1 0.361 0.0886
10 (n=6) DSC 67.427 :1: 0.442 0.3527 13.438 :1: 1.413 0.0002
1 (n=3) MDSC 60.397 :1: 0.397 - 2.458 :1: 0.656 -
5 (n=2) NIDSC 64.615 :1: 0.389 - 3.820 :1: 0.485 -
10 (n=4) MDSC 66.608 5 1.449 - 5.518 :5 1.498 -

 

 

 

 

 

 

The data collected during the experiment were analyzed using the Universal

Analysis software (Universal Analysis, V3.4C, TA Instruments, New Castle, DE). Out of

the 43 experiments, 18 failed due to pan movement during denaturation of the collagen

sample inside the pan. These data were discarded.

The parameters that were determined with data analysis were, the denaturation

peak width at half height, AT; the temperature when the endotherm reached its

denaturation peak (the denaturation temperature), T m the perturbation in heat capacity,

sea, and the enthalpy of denaturation, AH (see Figure 2.4 for details). Except for the case

of r = 5°C/min., the difference between the T mu values obtained from DSC and MDSC

experiments for the same heating rates were not statistically significant (see Table 2.1 on

page 28).

28

O)
a:

a
‘t
I

Peak Temperature, Tm [°C]
a: o:
O N

OI
Q

01
O)

The data showed that irrespective of the method used (DSC or MDSC) the

 

W .WMUTW (RPT) Tmn=0.698r+60.136
o Rat Tail Tendon (RTT) R2 = 0,9999

 

 

 

n=10

 
    
  

T... arm scanning rate = 60.14°C
(Isottrermd Heathgof RPT)

o
.-.—-
‘.—
.‘0
.-.—.
.—
_o
o.
'-
a‘
..n'

   

Equation 2.4 It! RPT:
E'=0.562 MJlmol. Ln(A)= 198.2 1/8

n-
_.—C—
'I ."
—.
"
"
—'
.a‘

Equation 2.4 for RPT:
980.405 MJIrnol. Ln(A)= 142.3 1/8

 

 

0 1 2 3 4 5 6 7 8 9 1 0
Heating (Scanning) Rate, 1' [°Clmln]

29

11

Figure 2.5: Transition Peak Temperature, T mu, as a Function of Heating (Scanning) Rate,
r. (Data for Rat Tail Tendon (RT!) is fi'om Mles, et al. [Miles, et al., 1995])

transition peak temperature, Tm“, increased linearly (R2=0.9999) with the scanning rate,
r (Figure 2.5; filled circles). Tm changed approximately 6°C over a change of an order
of magnitude in the scanning rate, r. A similar increasing trend in transition peak
temperature with scanning rate is also Observed by Miles, et al. [Miles, et al. 1995] in

experiments performed with rat tail tendon (RTT) specimens but the increase is

established as logarithmic rather than linear (Figure 2.5; solid line connecting the open

The difference between the RTT data and the RPT data (in the scanning rate range

examined) were within 2°C, therefore, it is believed that the exact form of the

mathematical relationships established were not of great significance when the

experimental error and the limitations of the calorimeters were considered.

Table 2.2: Enthalpy of” RPT Collagen Denaturation

 

Scanning Denaturation (x/AII) at
Rate, Enthalpy, Tm
r [°C/min.] AH [J/g] [l/K]

 

1 (n=7) 7.296 :h 1.469 0.139 d: 0.054
5 (n=8) 8.664 2h 3.931 0.218 :t 0.050
10 (n=10) 10.486 at 3.798 0.283 :1: 0.025

 

 

 

 

 

Transition half width, AT; values found with DSC and MDSC experiments

however, were significantly different for the same heating rate with the exception of the

values calculated at r=1°C/min. (Figure 2.6). The results from MDSC experiments
showed higher AT values. This may be explained by the variation (modulation) of the
temperature during MDSC experiments which slowed the denaturation behavior and that
the model proposed by Miles, et al., is based on DSC measurements with constant
temperature increase (given by Equation 2.5). In MDSC, even though the mean
temperature Of the sample increased linearly with time, there was a superimposed

sinusoidally varying component (modulation). Both DSC and MDSC data showed

exponential dependence of AT on the scanning rate (R2>0.98 for DSC and R2>0.99 for
MDSC) (see Figure 2.6). For rat tail tendon and porcine lens capsule the method proposed

by Miles et al. [Miles, et al., 1995; Miles, 1993] predicts a linear relationship (see the

30

curve for RTT in Figure 2.6) but nevertheless their measured values (see the RTT and PLC

data in Figure 2.6) are very close to the values measured with DSC for RPT.

Peek Wldth at Half Height. AT [°C]

 
  
   

     

 

 

 

16 1
14 AT = 2.789e°"°"
12 , AT at zero scanning rate at 285°C
(Isothermal Healing of RPT)
10 1 Equation 2.5forR‘I‘T: mm
520.521 MJ/mol, Ln(A)= 183.8 m AT = 2.9280 '

8 1 R2 = 0.9833

6 1 ,

4 4 “q,

4
2 i Equation 2.5 for RPT: Equation 2.5 for RPT:
0 E‘=0.405 MJlmol, Ln(A)= 142.3 1/8 E'=0.562 MJlmol, Ln(A)= 198.2 1/8
0 1 2 3 4 5 6 7 8 9 10 1 1

Heating (Scanning) Rate, r [°Clmln]

la DSC of Rabbit Patellar Tendon (RPT) e MDSC of Rabbit Patellar Tendon (RP?)
x Ratjail Tendon (RTT) _ _ o‘Pfiorcine Lens Capsule (PLC) J

L—

 

 

Figure 2.6: Peak Width at Half Height, A]; as a Function of Heating (Scanning) Rate, r.
(Data for Rat Tail Tendon (R77) is fiom Miles, et al. [Miles, et al., 1995], data for Porcine

Lens Capsule (PLC) is from Miles [Miles, 1993].)

The change in denaturation enthalpy, AH, with scanning rate, calculated by

integrating the area under the endotherm over time was found to be insignificant (P=O.41),

however the standard deviations of these measurements were extremely large (see

Table 2.2 on page 30).

When the Arrhenius equation coefficients calculated from isothermal heating

experiments (13"’ =4.O45x105 J/mol and A =6.311x1061 US) are used in Equations 2.4 and

2.5 to determine the variation of T m and AT with heating (scanning) rate, it was seen that

31

the predicted values were significantly lower than the measured values. This is
demonstrated in Figure 2.5 for T m by comparing the measured values of T m for RPT to
the predictions (lower dash-dot line in Figure 2.5 for 1?" =0.405 MJ/mol and Ln(A)
=142.3 Us) and in Figure 2.6 for AT by comparing the measured values of AT for RPT to
the predictions (higher dash-dot line in Figure 2.6 for E" =0.405 MJ/mol and Ln(A)
=142.3 Us). This difference was attributed to the problems inherent to isothermal heating

experiments (please see the previous section for a detailed discussion).

Through least-squares analysis of Equations 2.4 and 2.5, it was determined that in

the scanning rate range experimented, E *=5.623x105 J/mol and A=1 .136x1086 8'1 yielded

the best predictions when compared to the measured values. Additionally, the difference

between the predictions and measurements vanished in the neighborhood Of r =2°C/rnin.
(which also corresponded to the temperature change recorded in the hydrothermy bath
during mechanical testing; see Section 2.4 for details). These values were also well within

the range reported in literature for similar biological materials (for example,

A=6.6577x1079 s'1 and E *=5.21x105 J/mol for rat-tail tendon specimens [Miles, et al.,

1995]) [Pearce & Thomsen, 1995; Pearce, et al., 1993]. Therefore, these values
(E"“=5.623x105 J/mol and A=1.l36x1086 S'l) were used for the remainder of this thesis
instead of the values calculated by isothermal heating experiments (li"'=4.045x105 J/mol

and A=6.311x1061 Us).

32

2.3 Arrhenius Damage Integral

The Arrhenius damage integral is frequently used in order to characterize the
combined efl‘ects Of temperature and exposure time on protein denaturation [Kampmeier,
et al., 2000] and collagen birefringence loss [Pearce, et al., 1993]. The Arrhenius damage
integral is given as [Henriques & Moritz, 1947]:

t _ 5*
mt) = [ A-e 9”writ. 2.7
0

 

In this formulation, {2(7) is the thermal damage accumulated up to time, ‘t'. A is the
molecular collision frequency, E * is the denaturation activation energy, .9? is the universal
gas constant equal to 8.314 J/mOlXK, and T is the absolute temperature. The values for A
and E * are specific for each kind of tissue and phenomenon examined. These constants
govern the kinetics of thermal denaturation and establish the dependence Of the rate
constant of the reaction, k( 7) = dfldt, to the temperature, 7; at which the reaction takes

place.

In order to determine how the rate constant of the reaction changes with
temperature, (and therefore to calculate the corresponding activation energy, E *, and the
collision frequency, A, isothermal heating experiments were performed. However, it has
been shown in this research that due to the errors encountered in isothermal heating tests,
DSC experimentation was to be used to determine these constants. It was therefore
possible (through integration as seen in Equation 2.7) to determine the state of a chemical

reaction (here in this research, the heat induced denaturation of collagenous tissue) when it

33

experienced an arbitrary thermal history (not necessarily isothermal) through the use Of
the Arrhenius damage integral concept (Equation 2.7). As explained in the previous

sections, the constants for New Zealand white rabbit patellar tendon were chosen as

A=1.136x1086 s'1 and E*=5.623x105 J/mol in this research.

3.00 1
2.75 (“=1
2.50 -

2.25 ~
Q=10

c, [kJIkgK]

2.00 . /

1-75 " K n=o.1

 

 

 

1.50 1F‘ I .T_ ' 1

35 55 75 95
Temperature [°C]

Figure 2.7: Variation of Rabbit Patellar Tendon Collagen Apparent Specific Heat with
Accumulating Thermal Damage

When these constants were used in the calculation of the Arrhenius damage
integral during a constant heating rate test, for a stress-free patellar tendon tissue .0=1
corresponded to the peak of the apparent specific heat curve and 0=I0 corresponded to
the completion of denaturation transition where no further change in apparent specific

heat was recorded (Figure 2.7).

34

Utilization of the Simple Arrhenius thermal damage integral representation would
not be possible for a stressed tissue if the load applied on the tissue were to change the
denaturation enthalpy. Based upon the evidence presented above, it was reasonable to
assume that when normalized with respect to the effect of the stress-state (which changes
the phase transition entropy [Miles & Ghelashvili, 1999]), the thermal response of
collagenous tissues could be represented as a function of the Arrhenius damage integral

calculated at the stress-flee (reference) state.

2.4 Mechanical Analysis (Heat-Induced Mechanical Response)

In this chapter of the thesis, one-dimensional, heat-induced response of
collagenous tissues has been characterized experimentally using a New Zealand white
rabbit patellar tendon model. The tissue model chosen for this research is suitable to
quantify the one-dimensional behavior since the great majority of fibers in the patellar

tendon are oriented in one direction (along the axis connecting the patella and the tibia).

2.4.1 Specimen Preparation

Patellar tendon samples were harvested from the hind legs of the New Zealand
White rabbits supplied from other researchers at Michigan State University (Dr. Steven
Amoczky of the College of Veterinary Medicine and Dr. Hangboa Ma of the College of
Human Medicine). None of the animals had undergone experimentation that would affect

their musculoskeletal tissues. Patellar tendon complexes (patella-patellar tendon-tibia)

35

were harvested immediately after sacrifice and were stored in a cryogenic freezer at -

120°C until testing. Prior to testing, the samples were thawed overnight at -5°C followed

by 1-2 hour immersion in room temperature saline solution. It has been reported for

tendons and ligaments stored at -70°C that there is no significant variation in the
mechanical properties due to the freezing [Bechtold, et al., 1994; Woo, S.L.-Y., et al.,
1986]. Additionally, all of the specimens included in this study were exposed to the same
freezing and thawing protocol. It is therefore reasonable to assume that even if there may
have been some changes in the mechanical properties of the fi'ozen-stored specimens
(when compared to those of the fresh tissues), among the specimens tested, mechanical

property variation due to the specific fieeze/thaw protocol applied was not significant.

 

\CCD Camera
.1.
to Frame Grabber
Board
Cylindrical .\ 7
Laser Lens Sample \ l,
Source F \\\\\ I

I f/
<

Figure 2.8: Laser Shadowgraph System for Dimension Measurements

The cross-sectional dimensions and the length Of the patellar tendon were

measured optically by a custom-made, non-contact laser Shadowgraph system (Figure

36

2.8). In this method, a laser sheet was formed by passing a low intensity laser light through
a cylindrical lens. The laser light was then projected on the patellar tendon specimen and
the part of the light that was not blocked by the specimen was projected on a screen. With
a CCD camera (connected to a frame-grabber board in a PC) focused on the screen, the
image of the interrupted laser line (see insert in Figure 2.8) was captured and the length of
the laser light blocked by the specimen was compared to that from an image of a cylinder

of known diameter (placed at the same location as the sample).

By this non-nontact method, the width and thickness of the tendon specimen was
measured at multiple locations along its length. After these measurements were
completed, the tibia was potted in an aluminum tube by an inert glue and was then seemed
using two steel pins inserted in the holes drilled through the tubing and the bone (Figure

2.9).

2.4.2 Experimental Setup

The aluminum tube was then clamped to the base of a materials testing machine
(DDL Inc., Eden Prairie, MN) using a custom made, adjustable angle, horizontal offset
compensation grip (Figure 2.11). The upper grip of the materials testing machine
enclosing the patellar bone was connected to a 50—lb. load-cell (MFG Inc., Scottsdale,

AZ).
A hydrothermy cabin, which was connected to two circulation pumps (one for hot

(70-80°C) saline circulation and the other for room temperature (22-24°C) saline

circulation) enclosed the grips and the tendon sample (Figure 2.12).

37

 

Figure 2.9: Patellar Tendon Specimen

WIVERSAL TESTING MACHINE

 

 

 

 

 

 

 

 

  
    
 

 
 
 

 

 

 

Hot FLUID
RESERVOIR

 

 

 

 

COLD FLUID
RESERVOIR

Figure 2.10: Schematic of the Experimental Setup

38

The objective of this setup was to apply a tensile load on the patellar tendon
specimen along its anatomical axis when the tendon was immersed in saline solution. One
major advantage of using patellar tendon complexes in mechanical testing was that the
bones (patella and tibia) on both sides of the patellar tendon tissue facilitated gripping.
This eliminated any error resulting fi'om slippage in grips or damage created on the

tendon specimen due to the stress concentration created by the grips.

The sequencing and timing of the pumps were controlled with a D/A board
(DAS18OZST-DA, Keithley Instruments Inc., Cleveland, OH) connected to a PC. The
load and displacement data were also routed to the same board from the materials testing
machine, sampled and recorded at 8 Hz. The temperature Of the saline solution was
measured at 8 Hz using three T-type thermocouples connected to a thermocouple data
acquisition board (DAS/TC-B, Keithley Instruments Inc., Cleveland, OH). The
thermocouples were immersed into the saline circulating inside the hydrothermy cabin
and were placed very close (~O.5mm) to the surface of the tendon sample at various points
along the specimen's diaphysis. Finite element analysis [Aksan, et al., 2001] indicated that
the temperature difference between the center of the tendon and the circulating saline
solution did not exceed 4K any time during the experiments. It was therefore concluded
that the thermocouple readings represented the actual temperature of the tendon sample

quite well for the purpose of this research.

39

 
   

,4 ....

. . u .-
13 all“

("1.11421 ‘

  
  
     
 
    
 

  

1: Load Cell
2: Universal Joint

3: Upper Grip for Patella
4: Specimen

5: Hydrothermy Cabin
6: Lower Grip for Tibia

Figure 2.11: Photograph Of Experimental System

One shortcoming of the experimental setup being used was that the temperatures

during high temperature saline circulation increased slightly due to the non-optimum

response of the temperature controller. During the course of heated saline circulation (30-

50s), the temperature of the bath increased 2-2.5°C.

40

   

1: Upper Grip for
I Patella

2: Specimen

3: Hydrothermy Cabin

4: Lower Grip for Tibia

 

Figure 2.12: Zoom View of the Hydrothermy Bath and the Patellar Tendon Sample Fixed
to the Grips of the Materials Testing Machine

2.4.3 Experimental Protocol

The thermomechanical testing protocol applied was comprised of successive
repetition of three distinct test phases, which made up one test cycle. Each cycle contained
all of the three phases starting with mechanical preconditioning followed by mechanical
testing and ending with thermal testing. Mechanical preconditioning was applied to
minimize the viscoelastic response of the tissue [Fung, 1993; Humphrey, 2002]. Figure
2.13 shows the load history of the tendon specimen recorded during one cycle and Figure
2.14 shows the elongation/shrinkage response of the same sample during the same cycle.
Therefore, the mechanical test performed in any cycle reflected the effects of the thermal

and mechanical history that the specimen experienced in the previous cycles.

41

During the mechanical preconditioning phase, the tendon sample was subjected to
sinusoidal excitations (10 times) at a frequency of 0.1 Hz. The amplitude of the excitations
was 0.8 mm. After completion of Sinusoidal stretching, the tendon was kept at 1.5N for
208. Following this protocol, tensile testing at a rate of 0.05mm/s was applied until a load
of 20N was reached. Tensile testing in this low load range (1 .5-20N) was performed to
eliminate subfailure mechanical injury. This range was considered safe since three control
tendons undergoing 30 cycles of continuous experimentation did not exhibit signs of
subfailure injury. Additionally, there is evidence in literature that this range (the
corresponding stress and strain values) is safe for rabbit anterior cruciate ligaments, which

are of similar composition [Panjabi, et al., 1996].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mechanical Mechanlcd Thermal
Preconditioning Tooting Tooting
A __A__ A \
E. 15 ' f thTW RoomTenperature
'-' Salaam sun-elucidation
“g torso-soc romeo-130.
_| 10 " e e: c
5 J ‘ W
0 l .l l} J) in. 9
Thermal Damage (0)
Time (t)

 

.5-1

Figure 2.13: Patellar Tendon Load History in One Heating Cycle Comprised Of Three
Testing Phases (Mechanical Preconditioning, Mechanical Testing and Thermal Testing).
(Data is taken fiom Cycle #1 in Figure 2.15)

42

After tensile testing was completed, the tendon was kept at 20N for 108 and then
unloaded (at a rate of 0.05mm/s) to the predetermined test load (F = 2.5, 5.0, 7.5, 10.0 N).
These test loads were chosen to simulate physiological loading conditions. Once the test
load was reached, heated saline solution was circulated in the hydrothermy cabin for 30,

40 or 50s depending on the heating protocol applied.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o_4 Wed Wed
Preoonrltloning
A
0.2
l l {1 l l W
E 0.01
.5.
E -0.2-i
o
.5.
g -0.4- J
g I I I l
0 -0.6-
WWII:
-084 MMdr-drydr
' 1, ThermalDamagam)
1 0 Time (t)

 

Figure 2.14: Patellar Tendon Elongation/Shrinkage History in One Heating Cycle
Comprised of Three Testing Phases (Mechanical Preconditioning, Mechanical Testing and
Thermal Testing). (Data is taken fi'om Cycle #1 in Figure 2.16)

The total duration of the heating and cooling phases was set at 1805. During that

time, the materials testing machine kept the sample at a constant load (see the load data

43

during thermal testing phase in Figure 2.13), and recorded the length of the sample (see

the displacement data during thermal testing phase in Figure 2.14).

551

2““ Cycle: Reference Cycle

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Thermal Damage ((2)
Time (1)

Figure 2.15: Load History of a Patellar Tendon Specimen Subjected to Successive Heating
Cycles

2.4.4 Analysis Parameters

The maximum displacement recorded during the heating phase is called the

instantaneous shrinkage, d1 (Figure 2.14). After the completion of the heating phase, room

temperature saline solution (22-24°C) was circulated around the specimen for (150, 140 or
1308). It was observed that during cooling, the tendon recovered slightly from its shrunken

length. This is caused by re-naturation, which is due to re-winding of the partially un-

44

wound tropocollagen molecules [Horrnann & Schlebusc, 1971]. The plateau shrinkage
value reached at room temperature is called the equilibrium shrinkage, d2 (Figure 2.14).
Another important parameter defined here is the recovery ratio, R, defined as the
percentage of instantaneous shrinkage recovered upon cessation of thermal stimulus. Each
sample has been subjected to a number of cycles (between 20 and 30) until no change in
specimen length or material properties was observed. The total number of cycles required
to reach this point depended on the severity of the thermal protocol applied. The higher the
saline temperature and the longer the exposure time, the fewer the number of cycles
required. Finally, the test was stopped and the tendon sample was removed from the test

setup, its dimensions were measured and the specimen was discarded.

  

Thermal Damage (9)
Time (t)

L
fi

 

  
  

'g' -0.5 - 3
E 1. @ T1],
. a I
o
g '1-5 7 © I
\_Y_l l
“a '2'0 2"Cyclo: Reference Cycle ®
a
E -2.5 -
-3.0 -
'3-5 ' Enclrclednumbelslrdcate
thecycle count
-4.0 -

 

Figure 2.16: Shrinkage History of a Patellar Tendon Specimen Subjected to Successive
Heating Cycles.

45

The tendons in the control group experienced the same mechanical history as the
experimental groups but without any thermal loading. Therefore, for control experiments,

at each cycle the thermal testing phase was skipped.

During the mechanical preconditioning phase, in response to sinusoidal excitation,
all of the three tendons tested in the control group experienced stress relaxation. This
phenomenon is revealed by the progressive decrease in the peak load measured
(approximately 25% decrease between the first and the tenth peaks). This was attributed to
the viscoelastic nature of the tissue (possibly due to interfibrillar slippage and
displacement of unbound water within the fibers) [Woo, et al., 1981; Hubbard & Chun,
1988]. Additionally, with increasing number of cycles an increase in the average peak load
measured at each cycle was detected. The cycle-to-cycle increase was significant between

the first and the second cycles but then diminished.

For the experimental groups, in order to minimize viscoelastic contributions and to
isolate the heat-induced response of the specimen, the experimental protocol was designed
such that in the first cycle no thermal testing was applied. In Figure 2.15, the load history
recorded during the course of a representative experiment (only the first 10 cycles is
shown) is presented. The shrinkage/elongation response recorded during the same
experiment is also given in Figure 2.16. The values for tissue length and tensile modulus
obtained at the beginning of the second cycle were taken as the reference values (see

Figure 2.15 and Figure 2.16).

46

2.5 Mechanical Response to Accumulating Thermal Damage

For the experimental groups each cycle was made up of three phases; mechanical
preconditioning, tensile testing and thermal testing. It was imperative to distinguish
between the two viscoelastic phenomena observed: a) the successive decrease in the peak
load within each cycle and b) the cycle-to-cycle increase in the average peak loads in
consecutive cycles. Adaptation of the above-mentioned experimental protocol helped
minimize the effects of the latter (cycle-to-cycle variation) while the former (in-cycle
variation) was still observed in the experiment data. However, with increasing thermal
damage this response disappeared as well. This indicated that heat-induced denaturation
inhibited the viscoelastic character of the tissue and that for the resultant amorphous state
(gelatinous form), the tissue mechanical response was elastic (though still not linear). The
same behavior was Observed in thermomechanical analysis as well; with the accumulation
of thermal damage (with increasing number of cycles), the recovery ratio, R, converged

towards its plateau value of 100% (dlatO but d2=0). This Showed that for the resultant

amorphous state the tissue behavior was thermoelastic; thegtissue returned to its previous
mechanical state upon cessation of thermal stimulus without further permanent shrinkage

or Change in its mechanical properties.

For all of the samples tested, the resultant effect of the thermal damage
accumulation was shrinkage in the dominant direction of fiber orientation (along the
length of the tendon). However, each specimen went through distinct shrinkage

(accumulated d2) regimes before reaching its respective final state. The final state was

reached quickly if the thermal damage accumulation in each cycle was accelerated by

47

either increasing the temperature of the circulated saline solution or the exposure time. On
the contrary, if the thermal damage accumulation in each cycle was kept to a minimum by
decreasing the temperature of the saline solution or decreasing the exposure time, an

interesting regime in tendon response (one not easily observed in accelerated denaturation

experiments) became apparent (Figure 2.17).

F=1ON, TW=75°C

Datum for 1

—1

 

’ Elongation
..me /

 

 

 

 

 

 

 

 

 

Datum for 2 — 2..
Tendon . /r5hrinkage
Length i
:. F=2.5N, T,.,,,,,,=75°C
g 2
-* Coding
. . >
Thermal Damage (0)

Figure 2.17: Heat-Induced Elongation and Shrinkage (Eflect of Test Load on Heat-Induced
Response)

This regime corresponded to an initial elongation response just before the onset of
shrinkage and was characterized by a gradual increase in sample length corresponding to
approximately 0.5% strain (Tendon Sample 1 (Fr-ION) in Figure 2.17). This was
accompanied by a significant increase in tensile modulus (up to 125% that of the native

tendon). The tensile modulus was determined from the slope of the stress-strain curve at

48

o=lMPa (when the tensile moduli was determined at different stress values and
normalized with respect to the values at the native state, similar trends were observed).
The elongation response observed in this regime was purely heat-induced and irreversible.
Once a certain amount of energy was absorbed, the specimen would start to shrink with
firrther heating (Tendon Sample 2 (F=2.5N) in Figure 2.17). Even if the experiment was
paused after the elongation stopped and the tendon was returned back to rest in room
temperature saline solution (tests done for up to 1 hour), and then reheated, it continued to
shrink with firrther heating without elongating further. Note that the temperatures and the
exposure times (therefore the Arrhenius damage integral values) were identical for both of

the specimens even though the test load was different.

 

 

 

 

 

 

4o -
F. M
ES.
11,“ 30 -
3 0.5.2....
5'2
5
s 20 "
a, 7
E
3
t
g 10‘ on...
'5
5'
III
0 l
1 10 100 1000 10000

Thermal Damage (:2)

Figure 2.18: Progression of Equilibrium Shrinkage (e2) with Accumulated Thermal
Damage (.0 at Different Test Loads (F).

49

Once the initial elongation regime was completed, the overall instantaneous

shrinkage (calculated by summing the d, values measured at consecutive cycles) Of every

specimen increased exponentially with accumulated thermal damage. However, after a
rapid increase, the recovery ratio converged to its plateau value of 100%. Irrespective of
the test load applied, the overall equilibrium shrinkage varied in a sigrnoidal fashion with

increasing thermal damage (Figure 2.18).

The permanent (equilibrium) shrinkage of the tendon did not increase indefinitely
but was bounded. Briefly, the heat-induced thermomechanical response of the patellar
tendon composed of three distinct regimes determined by the changes in its length and

tensile modulus (examined in the next section). These regimes were:

I. Irreversible Elongation: Elongation up to 0.5% strain accompanied by an
increase in tensile modulus (E ~ 125% of the native tendon calculated at the reference

state).

2. Irreversible Shrinkage: Decrease in the overall length of the sample in the
dominant direction of fiber orientation accompanied by an exponential decrease in tensile

modulus (with respect to the native value) and disappearance of viscoelastic response.

3. Reversible Shrinkage: Defined by thermoelastic response where shrinkage was
completely reversible. Upon returning to room temperature, the tissue regained its pre-
heating length (which was the length at the beginning of the cycle, not the experiment) as
also shown by R, converging to 100% with increasing thermal damage, .(2 In this regime,

There was no decrease in tensile modulus with further heating.

50

2.6 Empirical Correlations

2.6.1 Equilibrium Shrinkage (e2) and Thermal Damage (Q

The mechanical load plays a very important role in determining the denaturation
kinetics and the final state of the tissue. Experimental results revealed that increased test
load delayed the shrinkage of the tendon sample, as indicated below in Figure 2.19. With
increasing load, the sigmoidal equilibrium shrinkage curve shifted towards higher thermal
damage. {2", is defined as the thermal damage accumulated in the tendon specimen where

50% equilibrium shrinkage is reached. When the variation of .0", with stress, a, is plotted

(for all of the samples tested, n=9) it was observed that there was a direct correlation

between the stress applied on the tissue and the denaturation midpoint (Figure 2.19). An

exponential curve fit (RZ=O.9593) gives this correlation as:

am = 5.7027e7'9899" 2.8

As discussed previously in the Introduction part of this thesis, for a stress-free
patellar tendon specimen the denaturation rate was maximum at {#1 and the tissue was
completely denatured at .0=10. The intercept of the function given in Equation 2.8 with
(F0, gives {21557027, which was well within the limits determined by the DSC studies
given above. The reason for transition retardation is a decrease in the activation entropy of

denaturation [Miles & Ghelashvili, 1999].

51

10000 «1

  

 

 

r
1000 -.
a... 100
10 -
f n... . 5.702761” °
R’ = 0.9593
1.1.1.... .mcriur ._,t . r-H
0 0.25 0.5 0.75 1
Stress (o)[MPa]

Figure 2.19: Variation of {2", as a Function of Test Stress, a; (FF/Alt).

Another question that needs to be answered is whether the applied stress has an
effect on the amount of final Shrinkage achieved. When the maximum Shrinkage each
specimen experienced when it was fully denaturated was plotted as a function of the test
stress applied on the tissue during denaturation (Figure 2.20), a significant reduction with
increasing test load was observed (n=9). The larger the stress on the tissue during heating,

the less the final shrinkage. This relationship was given as:

= —10.728 - lno + 15.752. 2.9

e2max

To explain this behavior, the following hypotheses are ofl‘ered: when tropocollagen

molecules unwind by heat-induced denaturation, they exert tensile forces on the

52

neighboring molecules through heat resistant intermolecular cross-links (this is the
mechanism of gross tissue shrinkage). Meanwhile, the strength of the molecules also
decreases (due to losing intramolecular heat-labile bonds). When the point is reached
where the local thermomechanical stress is greater than the yield stress (or tensile
strength) of the weakened molecule, the molecule plastically deforms (or ruptures). The
elastic energy of the molecule dissipates and the overall thermal stress decreases causing a
lower overall shrinkage. This hypothesis also explains the degradation of the mechanical

properties (decrease in the resistance to deformation).

 

 

50 T
92...... 1%] 25
e2..." = .1 012814118) + 15.752
R’ = 0.7973
0 . A. ~. _1_ ___.L_____;_L_L.__;_L___L_rl
0.1 1
Stress (0) [MPa]

Figure 2.20: Variation of Maximum Equilibrium Shrinkage (82m) as a Function Of Test
Stress, a, (o=F/Ao).

When the data presented in Figure 2.18 were modified by dividing the equilibrium

shrinkage by the shrinkage plateau value, (e2/e2m) and the accumulated thermal damage

53

was normalized (tr/{2,9, all of the heating protocols converge on the same master
shrinkage curve (Figure 2.21). The correlation between the damage parameter (0.0,) and

the resultant nondimensional Shrinkage may be represented by a dose response

 

 

(R2=O.9875) given by:
82 = —0.005 + 09965 '97 2.10
eZmax 1 + [Q/Qm]— '
2.24

As seen in Figure 2.21, irrespective of the stress-state of the tissue, once it starts,

shrinkage progresses rapidly and then converges to a final value.

1.00 7

0.75 -‘

 

Gzlezmax 0.50 ~ ‘ ‘

+ 2.5" A 2.5N_2
0.25 4 ' a 5 N o 5N_2

' o 7.581 x 7.5N_2
8 10H x 10N_2
0.00 ‘ h": "“h‘ __ T T l l

 

 

0 5 10 15 20 25

Figure 2.21: Master Curve for Heat-Induced Shrinkage of Rabbit Patellar Tendon (for
2.5£F£10.0N)

54

2.6.2 Normalized Tensile Modulus (E/Eo) and Thermal Damage (.0)

Irrespective of the thermal and mechanical history of the specimen, during tensile

testing (in the load range the test was performed: 1.5-20N) the mechanical stress, a; varied

exponentially (R2>0.999) with the applied strain, a:

C3/e

0' = CI+C2e 2.11

In the equation above, C1, C2 and C3 are functions of the thermal damage, a
accumulated before the onset of the particular tensile test. In Figure 2.22 the effect of
accumulating thermal damage on the tensile behavior of a representative tendon specimen
is given. As shown, the tendon became more compliant with accumulated thermal

damage.

' 7 77 ' ' I 7'" T 7 Y 77'? V T 7_7_77 V a; I —Y 7 7 I a— 7 I V
20 »— , D ’9. C? A #9 —<
147] 7 ’7‘ r“5 45‘
x ‘ I’ll ) a go
' ‘ .‘ . {J A u +
15 e " 9 ~, . A c 7‘
(V ,3} A +
l l 7 n6 4+
L.
z 1 +“
“J a ,4‘
[ ‘, n VAC’
10 re "~ .. 0' 0” 3’9 + ’7
_ . . +4‘

 

 

 

 

1.02 1.03 1.04

Stretch Bad“ I.)

Figure 2.22: Effect of the Accumulating Thermal Damage, {2 on the Stretch-Load
Response of a Representative Tendon Specimen. (Test Load=5N, Bath

Temperature = 75°C, Exposure Increment=3 Us)

55

The three distinct regimes observed in the shrinkage analysis reflected on the
mechanical properties as well. The irreversible elongation regime corresponded to an
increase in tangent modulus (up to 125% of the reference state). During the irreversible
shrinkage regime, with each additional heating cycle, a progressively lower stress value
corresponded to the imposed strain, indicating a decrease in tangent modulus. In the
reversible shrinkage regime, a plateau value for tangent modulus was reached. The one-to-
one correspondence between the shrinkage behavior and mechanical state indicated that
the mechanism responsible for shrinkage and mechanical property degradation was the

same.

125
. so_1 o . so_1o
. ao_7.5 . ao_7.5 g 100
- so_5 u 75_5 +: i
a 75_5 - 75_7.5 ' - :
. 75_10 + so_1o_2 . T 75
x so_7.5_2 x 75_5_2 + . q EIEo [%]
75_2.5 . 75_2.5_2 . 7 50

 

 

 

Equilibrium Shrinkage (92) [%]

Figure 2.23: Master Curve for the Variation of Normalized Tensile Modulus (E/Eo) with
Equilibrium Shrinkage (e2). (Both E and E, are the Tangent Moduli Calculated at lMPa)

56

The variation of tangent modulus, E, with thermal damage at different stress
values (a=0, 0.5, 1 MPa) was calculated and the same trend was observed. In Figure 2.23,
1
the tangent modulus calculated at lMPa is plotted as a function of equilibrium shrinkage

achieved.

One very important observation made here was that the mechanical properties of
the tissue degraded exponentially with shrinkage. Behavior similar to that for shrinkage
was observed if the decrease of the tensile modulus at any given stress was plotted for
each test load as a function of the thermal history of the specimen. Such a representation
revealed that the decrease in the tensile modulus at a higher test stress was more
prominent with each incremental heating. Once shrinkage started, the variation of

normalized tensile modulus as a function of equilibrium shrinkage could be represented as

(R2=0.975):

e2/ 1 1.893

= 100.01e 2.12

E
E0

Briefly, the equilibrium shrinkage increased with the accumulated thermal damage
while the tensile modulus decreased. As mentioned before, these observations pointed to
the existance of a mechanical optimum in terms of the thermal stress formed in the tissue.
It was reasonable to choose the thermal stress as the parameter to be maximized during
heating since it was the main driving force determining the final configuration and state of
the heat-treated tissue. As a first order approximation, the tissue response was assumed to

be governed by the Hooke’s Law, and that the thermal stress, 03],, formed in the uniformly

57

heated tissue, as a result of sub-ablative heating, was determined by the product of the

equilibrium shrinkage and the tensile modulus.

Below, the variation of the thermal stress with the achieved equilibrium shrinkage
is presented (Figure 2.24). From a purely mechanistic standpoint, there was an optimum
final state (corresponding to approximately 12% shrinkage where the thermal stress
formed in the tissue was maximum) that can be reached. Beyond this point, the thermal
stress started to decrease since the material became excessively compliant with additional
heating and therefore, the mechanical stability reduced. At the point where the thermal
stress reached its maximum, the uniformly heated tissue was at its optimum state; both

mechanically and kinematically stable.

  
  

     
   

 

Normalized Thermal _ 100
Stress (Gth/Gth,max) / E.
I X
\ 75 E
6
. so ‘5
Normalized Tensile ' . ' t3
Modulus (Elli-0‘)“‘." 25 2°
_________ ' I.l.|

{ 77777 i e o

 

-40 -30 -20 -10
Equilibrium Shrinkage (e2) [%]

O

Figure 2.24: Variation of Thermal Stress with Equilibrium Shrinkage

58

Chapter 3: Thermal Exposure Simulations for Thermotherapy

A sub-ablative level of thermal damage produced in collagenous tissues is known
to be the result of micro-scale structural changes driven by the helix-coil transition of the
collagen molecules. When heat is applied, this highly oriented parallel structure
transforms to an amorphous, randomly coiled state (denaturation) since the tropocollagen
molecules lose the harness of their heat-labile intramolecular bonds. The efi‘ect of

denaturation in the macro scale is tissue shrinkage. For tendon collagen, this phenomenon

is observed at temperatures in excess of 62°C. In the sub-ablative heating levels, the non-
thermal effects of the heating modalities are insignificant. It is hypothesized here that
different heating modalities (laser, monopolar and bipolar radiofrequency), owing to the
variations in their modes of action, create significantly different temperature distributions
and thermal histories within the tissue. It is felt that this fact alone contributes prominently
to the variations in the results reported in the literature related to the outcome of the
therapy. Therefore, an effort has been made here to simulate the various heating conditions
in a virtual environment to examine the effects of different clinical parameters of interest.
These parameters are: beating modality, heating probe power setting, probe sweep speed

and the influence of arthroscopic fluid circulation.

59

A finite element method-based simulation tool was therefore utilized to predict the

temperature distributions and thermal damage gradients for different heating conditions.
3.1 Modeling the Temperature Distributions Created by Thermotherapy

The conservation of energy equation in a two-dimensional, Cartesian coordinate

system (x, y) for a homogeneous, isotropic material is:
6 6 _ a

k—T(X, y, t) + k—T(X, y, t) + g(X, y, t) 77 pC—T(X, ya t) 3’1
6x fly at

T, t, k, g, p, c are the temperature, time, thermal conductivity, spatially varying volumetric
heat generation, mass density and specific heat, respectively. If the material is also
undergoing phase change, the thermal inertia term on the right hand side of Eqn. 3.1
should be modified to account for the latent heat effects. Introducing the definition of

apparent specific heat, ca,

c =c+a— 3.2

in terms of the latent heat of phase change, A, it can be shown that Equation 3.1 can be

written as,

kgm, y, t) + k§§T(x, y. t) + g(x, y, t) = pc.9"r(x. y, t) 3.3

60

where the effect of collagen denaturation, modeled as a solid-to-solid phase change (helix-

to—coil transition) is incorporated in the specific heat term.

The solution to the governing equations for each heating modality was obtained
using commercial finite element analysis (FEA) soflware (MSC.Marc Mentat®, MSC
Software Corporation, Los Angeles, CA) on a UNTX® platform using a Sun Enterprise
250 compute server with two 296 MHz UltraSPARC-II processors (Sun Microsystems,
Inc., Palo Alto, CA). Two user subroutines were incorporated into the main FEA code (see
Appendix C for details). One of the subroutines was used to impose spatially and
temporally varying heat flux and generation and the other one was used to calculate the

thermal damage accumulation.

The control volume (CV) used in these simulations was two-dimensional
Cartesian, homogeneous and isotropic (Figure 3.1). The dimensions were, 10 mm in the
horizontal direction, x, and 2 mm in the vertical direction, y. The CV was uniformly

divided into 50000 rectangular elements with an intemode distance of 20pm.

V
b
(0.0) saline

x tissue 2
/
I
5

a
Z Z
I
Z (10, 2) 5
’IIIII]III[IIIII/I/IIIIIIIIIIIIIII/IIIIIIIIIIIII/Illllll

[Illa—b Adiabatic

Figure 3.1: The Control Volume for FEA

61

3.1.1 Overview of Clinically Applied Heating Modalities

The heating modalities are discussed below.

3.1.1.1 Ho:YAG Laser Heating

In the simulations of laser heating, the photon energy deposition on the surface
was assumed to be a Gaussian pattern with an exponential decay into the tissue following
Beer’s absorption law [Welch, 1985]. “Cold-tip” lasers are used fi'equently to shrink
collagenous tissues without causing ablation [Schaefer et al., 1997] (Figure 3.2, Probe #3).
The term “cold-tip” refers to an application where the laser probe is kept 1-2 m away
from the surface of the target tissue. Owing to the short penetration depth of the Ho:YAG
laser (~300 um), and the practice of keeping the laser tip 1-2 m away from the surface, it
is reasonable to assume that in this application, the laser has no direct thermal effect on the

tissue other than heating the surrounding fluid.

Modeling the complex interactions among the laser probe, the surrounding fluid
and the tissue was far too complicated for the objectives of the research presented here.
For this reason, a different path was taken here, and a “hot-tip” laser with a slightly lower
power setting was used. In this application, the laser probe touched the tissue surface. The
thermal effect of laser light penetrating into the tissue causes volumetric heat generation
[Welch, 1985]. If the light is assumed to be absorbed by the tissue without scattering, then

the volumetric heat generation is expressed as:

62

2 2
go”) = ¢(t)- ”$0.9 (2x yr. ) . e< my) 3.4

where, ¢(l) is a window function used to represent the pulsating nature of the laser. This

function gives the value of one during a pulse and zero elsewhere. E0, y, and to are the

peak irradiance on the surface, absorption coefficient and (He) radius of the Gaussian
beam profile, respectively. The motion of the probe on the surface at constant velocity, V,
was established by replacing the variable x with the transformed variable (x- Vt). The

boundary condition at the free surface was expressed as:
a h _ h
‘a_y‘7r(x, y) t)|y=0+ I (X, ya t)|y=0 — TTOO 3'5

whereas all the other boundaries were assumed to be adiabatic. The validity of the

adiabatic boundary assumption was checked against the results later. Twis the surrounding

arthroscopic fluid temperature and is assumed to be constant at 37°C~3 10 K at all times. It
is also assumed that before heating starts, the tissue is also at the deep core body

temperature of 310K. Therefore the initial condition was established as:

T(x, y, t)|t=0 = Ti = 310K 3.6
3.1.1.2 Bipolar Radiofrequency Heating

The bipolar radiofrequency method uses a saline-based arthroscopic cooling
solution to establish electrical contact between the active and the passive electrodes placed

on the body of the heating probe [Nath et al., 1994] (Figure 3.2, Insert 2).

63

fl . +\J"I:8/Iflatlon + Insulation

LL «1

 

1 2

Arthrocare Arthrowand. 3mm CAPSure

2: Monopolar Radiofrequency Probe:
Oratec Vulwn TAC-S Electrotherrnal Probe

3: Ho:YAG Laser Probe:
Trimedyne OmniTlp Model 20474-HP

4: Ground Plate for Monopolar Radiofrequency
Probe: (sized for in-vitro experimentation)
Oratec

1 1: Bipolar Radiofrequency Probe:
3

Ali
Mr

Figure 3.2: Probes used in HACS procedures

The mode of action of this method is that of heating the arthroscopic liquid in the
immediate vicinity of the tissue instead of directly heating the tissue itself. Therefore, it
was hypothesized that tissue heating with a bipolar probe was mainly a surface heat

transfer phenomenon that could be modeled as a Gaussian surface flux on the upper

boundary ofthe CV as:

—a—-T(x y t)| = S-ue‘axz)”: where (le <r ) 3.7
By ’ ’ y =0 k 7 0

ET“ y t)| +}-‘T(x y t)| = 1-IT where (le >r ) 3.8
6y a , y=0 k a , y=0 k w 0

such that there was no volumetric heat generation within the tissue. The heat flux, q”, in

Equation 3.7 is defined as the magnitude of the surface heat flux and r0 is the (He) radius

of the Gaussian distribution. The other boundary conditions and the initial condition were

taken to be identical to those of the laser heating case.

3.1.1.3 Monopolar Radiofrequency Heating

For monopolar radiofrequency heating, frequencies between 300kHz and lMHz
are applied through an activeelectrode [Penascu et al., 1995] (Figure 3.2, Insert #2). The
passive, ground electrode is placed on the skin surface (Figure 3.2, Number 4). The tissue
in the vicinity of the active probe is heated volumetrically by the Joule effect [Shitzer,

1985]:

 

p.
g(x, y) = r0 2 for ,/(x2 + y2) 2 r0 3.9

41r(x2 + yz)
6 h = _h_
6—yT(x’ y, t)|y = 0 + ETOI, y, t)|y = 0 k Too 3.10

where P is the Joule heat produced by the electrical current passing through the tissue and

r0 is the probe diameter. In modeling this heating modality, the interactions between the

probe and the surrounding liquid were neglected. The other boundary conditions and the

initial condition were taken to be identical to those of the laser heating case.

65

3.1.2 Hydrothermy

During hydrothermal heating, the tissue was completely immersed in a saline bath
and the saline temperature was increased. Even though this method is not suitable for
clinical applications, it is the method of choice in most in-vitro experiments because of the
simplicity of its application. The surface heat transfer phenomena is governed by:

6 h = l_r
537T“, y, t)|y = 0 + l-(T(x, y, t)|y = 0 kT°° 3.11

where the circulating saline temperature, T“, took a constant value for each simulation in

the range fi'om 62 to 90°C.
3.1.3 Finite Element Analysis

The control volume (CV) used in these simulations is shown in Figure 3.1. For the
radiofi'equency heating cases, a constant time increment of 0.053 was used. For laser
heating cases an adaptive variable scheme utilizing a time increment of 0.00005s during
the pulses and 0.019958 between the pulses was employed. This was done to ensure that
the temperature change between consecutive time increments was not more than 0.25K.
The stability of the solutions was ensured by checking the time increment and mesh size
values used against the stability criteria established by the software publisher. The
singularity ratio of the mass matrix was recorded at each time increment and checked

against the dependability range given by the software manufacturer. The sensitivity of the

66

solution to mesh size was also analyzed and the same optimum mesh was used throughout

the simulations.

In this analysis, all of the material properties except the apparent specific heat were
assumed to be isotropic and temperature independent. The cases simulated included

stationary and moving probes as well as different energy deposition magnitudes.

The mesh for the rectangular control volume was created automatically using the
mesh generation interface of the FEA software utilized. For this geometry, rectangular
elements of equal size were generated. Control simulations utilizing triangular elements
were performed and compared to rectangular element simulations. No difference in the
results was observed. Due to the finite difference approximation used when calculating the
time increments, in the transient heat transfer analysis algorithm, stability and
convergence of the solution became issues. In order to ensure convergence of the solution,

the following condition should be satisfied:
pc 2

At 2 — Al 3.12
6k( )

where 2!, Al, p, c, k are the time increment, internode distance where the higest
temperature gradients are expected, mass density, specific heat and thermal conductivity,
respectively.

Depending on the heating modality simulated, the solutions for 2-D simulations
took approximately 2-8 hours (8 hours was for the laser heating case) on a Sun Enterprise
250 compute server with two 296 MHz UltraSPARC-II processors. For each one of the 3-

D sirnulations however, ther run time was approximately 10 days.

67

3.2 Temperature Distribution Results

3.2.1 Temperature Field on the Surface of the Control Volume

The temperature distributions predicted in each simulation were closely monitored

and attention was focused on choosing low enough values for the power settings such that

a temperature of 100°C was not exceeded either on the surface or inside the control
volume. This was done to ensure that latent heat effects fi'orn water evaporation or tissue

ablation were not significant when compared to the collagen phase change energy levels.

Table 3.1: Values Used in Simulations

 

 

 

 

 

 

 

 

 

 

Variable Explanation Value Range
15, [W/mz] Laser Peak Irradiance 0.75x10°-1.75x106
r0 [m] 1/e Radius of Gaussian Profile 0.5x10'3-2.Ox10’3
V[m/s] Probe Sweep Speed 0, 2x10'3, 4x10'3
q” [W/mz] Surface Heat Flux (Bipolar) 0.75x105-1.5x105
P [W] Joule Heat (Monopolar) 5.0-12.5
1' [Hz] Laser Pulse Frequency 5
Mr [l/m] Absorption Coefficient 1x104
h [W/mzK] Convection Coefficient 5x10], 5x102
1, [ms] Laser Pulse Width 200

 

 

 

Simulations for four different heating modalities namely, Ho:YAG laser, bipolar
and monopolar radiofrequency and hydrothermy were considered. Temperature and

thermal damage distributions created with each heating modality were determined for two

68

 

Vt

(161
Sig
by -

different convection coefficients, two different velocities and a stationary case. The values
used in the simulations were taken fiom the literature for the clinical application of
respective modalities (Table 3.1 on page 68). Depending on the modality 4-5 different

power settings were simulated.

 
  
  
 
 
 
 
 
 
 

11:50 W/mzK - q"max= 1.0E+05
- q"rnax= 7.5E+04
V=0 . q"max= 5.0E+04
- P= 7'.5E+00
. P= 5.0E+00
. P= 6.125E+00
+ Eomax= 5.0E+05
x Eomax= 2.5E+05
:- Eomax= 7.5E+05
- Eomax= 1.0E+06

r [K]

  

 

300 i

 

0.0E+00 5.0E LOB-03 1.5E-03 2.0E-03 2.5E-03 3.0E-03 3.55-03

x [m]

Figure 3.3: The Temperature Distribution Created on the Surface of the CV by a
Stationary Heating Probe (V =0). (Convection Coeflicient, h=50 W/mzK).

From the predictions obtained, it was observed that with increasing probe sweep
velocity, the temperature field tended to get narrower. Additionally, when the probe was
moved, for the same power settings, the maximum temperatures reached in the tissue
decreased significantly. Owing to the differences among their modes of action, there were
significant differences among the temperature profiles created at the surface of the tissue

by the difi‘erent heating modalities. This is demonstrated in Figure 3.3 for the case of

69

h=50W/m2K when the heating probes were kept stationary at the origin. In Figures 3.4
and 3.5, the surface temperature distributions created by moving probes (at V=2mm/s and
V=4mm/s, respectively) are shown for the three different modalities. In each case, the
probe was swept from left to right and the temperature distribution inside the CV at t=4

seconds were simulated. For both cases, the convection coefficient, Ir, was taken as SOW/

mzK.

  
  
  
 
 
 
  

 

370 a
360 i 2 - q"max= 1.00E+05
h=_5° W’” K . q"max= 7.sor~:+04
350 » V“°'°°2 "”3 - P= 7.51~:+oo
- P= 6.125E+00
340 . P= 5.or=.+oo

T [K]

i + Eomax= 1.0E+06
' x Eomax= 1.25E+06
I Eomax= 7.50E+05

330

320 ‘_

310

 

 

300 .L—L_L—+_4L_+. l ._+_ __L_L_ 4 % I L 1 r 1 L A J

0.E+00 2.13-03 4.5-03 6.E-03 8.E-03 1.5-02

x [m]

Figure 3.4: The Temperature Distribution Created on the Surface of the CV by a Moving

Probe (V =0.002m/s). (Convection Coefi‘icient, h=5 0W/m21(). (The probe was located at
x=8. 0E-03 m and moved to the right at a speed of 2mm/s).

70

360 1

i h=50 W/mzK

350 l v=o.oo4 m/s

 
 
   
 
 
 
 
    

- q”max= 1.25E+05
o q"max= 1.00E+05
‘ q"max= 7.50E+04

 

     

 

- P= 1.0E+01

34° . P= 7,513+oo
H - P= 5.0E+00
95 330 + Eomax=1.5E+06
[— ! Eomax= 1.25E+06

320

310

3ooefiw.

0.E+00 2.5-03 4.5m era-03 8.5.03 l.E-02
XIm]

Figure 3.5: The Temperature Distribution Created on the Surface of the CV by a Moving

Probe (V =0.004m/s). (Convection Coeflicient, h=50 W/mzK). (The probe was located at
x=8. 0E-03 m and moved to the right at a speed of 4mm/s).

3.2.2 Temperature Field within the Control Volume

In the simulations presented below (Figure 3.6), the temperature scales are taken to
be identical. It was observed that the temperature distributions created by bipolar and laser
heating were distinctly different from that of the monopolar heating. Upon inspection of
the temperature distributions near the surface, it was detected that the temperature
gradients produced by the laser heating were steeper than those of the bipolar heating
Also, because of the pulsating behavior of the laser, a series of hot spots were observed

near the surface.

71

3 to K (37°C) 360 x (87°C) Bipolar

l q”m= 1.25E+5 W/rn2
L.._____ its—i m = 1m

w

 

310 K (37°C) 360 K (87°C) Ho:YAG laser

‘ Em =1.25E+6W/m2
1 3A w=1mf=5HZ

3 lo K (37°C) 360 K (87°C) “WOW"!r

‘ P=10W/m3
l_ ;‘ 'o=1m

Figure 3.6: Temperature Distributions at t=4s

 

 

 

 

Among the three modalities examined, the monopolar radiofrequency heating
created the most uniform heating patterns. It is also important to note that the thermal
penetration of this modality is very high when compared to others (see Figures 3.7, 3.8
and 3.9). Since it is mainly a surface phenomenon, bipolar heating created a heated region
near the surface, similar to that of laser. On the other hand the temperatures decreased
gradually fiom the surface into the tissue. The gradients created were not as sharp as the
ones created by the laser. The temperature distributions predicted and the observations

made fi'om the simulations were in agreement with the published reports [Glen, et al.,

1996].

72

 

 

370 i o q”max= 1.0E+05
0"...- _ 2
360 '5. h75°31wm K o q"max= 7.5E+O4
If”. '0 - P= l.OE+01
350 1’ '3. ”°o., . P= 7.SE+OO
€32}. . P= 5.0E+00
E. 340 if“ -._ . Eomax= 7.5E+05
330 ‘ “:37 “ . ”-5.555. I Eomax= 1.0E+06
{tin “m... 7°”... 8 Eomax= 5.0E+05
$41., A.
320 .13.; M.
310 """"""""""""""
300 +—-——--— -- — — r . . .
0.0E+OO 5.05-04 LOB-03 1513-03 2.05-03
y [m]

Figure 3.7: The Temperature Distribution Created within the CV by a Stationary Heating
Probe (V=0). (Convection Coeflicient, h=500 W/mzK)

 
 
  
 
  
 
 
 
 
   

- q"max= 1.3E+05
h=50 W/mzK - q"max= 1.0E+05
V=0.002 m/s . qt'm: 7,513+04

- P= 1.0E+01

"._ - P= 7.5E+00
- P= 5.0E+00

I Eomax= 1.3E+06
x Eomax= 1.0E+06
+ Eomax= 7.50E+05

 

300 J,____ ___.__._____. _T __ _. ~__T. _._ .__ _._._ ,__ _ ___ _ ___,
0.0E+OO 5.08-04 LOB-03 1513-03 2.0E-03
y [m]

Figure 3.8: The Temperature Distribution Created within the CV by a Moving Probe

(V =0.002m/s). (Convection Coeflicient, h=500W/m2K). (The probe was located at
x=8.0E-03 m and moved to the right at a speed of 2mm/s).

73

a q"max= 1.00E+05
h=500 W/mzK ° q"max= L255+05
V=0.004 m/s ‘ P: 7-5E+00

- P= 1.3E+01

I Eomax= 1.5E+06

I Eomax= 1.3E+O6

 
 
 
 
 
 
   

 

 

 

".3"; + Eomax= 1.8E+06
700%
320 C no!"
3oo~L—--~--—--—— . . . .
0.OE+00 5.0304 1.0543 1513-03 2.01203

y [m]

Figure 3.9: The Temperature Distribution Created within the CV by a Moving Probe

(V =0.004m/s). (Convection Coeflicient, h=500W/m2K). (The probe is located at x=8. 0E-
03 m and moving to the right at a speed of 2mm/s).

3.2.3 Model Verification

For the case of a 2 mm wide probe with uniform heat flux moving on the surface of
the rectangular CV, the exact solution to the surface temperature given by Rosenthal
[Rosenthal, 1946] was compared to the FEA predictions (Figure 3.10). For both 2 mm/s
and 4 mm/s probe sweep speeds, the results showed very good agreement (within 1K).
Thus the numerical simulations were considered acceptably accurate to extend to other

cases of interest.

74

 

N
M
l

  
  
   

 

 

 

g + FEM Solution v=2 mm/s

20 -— Rosenthal's Exact Solution v=2 mm/s
g 0 FEM Solution v=4 mm/s
E: — Rosenthal's Exact Solution v=4 mm/s
3 l5 .
g.
g 10
g...
8 .
g 5
m

o — - ~ — ~- - — r
0 0.002 0.004 0.006 0.008 0.01
Distance from Origin [m]

Figure 3.10: Comparison of F EA Results with the Exact Solution

3.3 Modeling the Thermal Damage Accumulated During Thermotherapy

In order to quantify the accumulation of thermal damage by the three difl‘erent
heating modalities, an Arrhenius formulation of a damage integral was utilized. The

details are presented in Sections 2.2.1 and 2.2.2 of this thesis.

It has been shown by various researchers and by the results from our laboratory
[Aksan & McGrath, 2001] that collagenous tissue denaturation phenomena is not only a
flmction of the maximum temperature reached but also the exposure time, the mechanical

load applied and the chemical state of the tissue.

75

Using a user subroutine and the built-in functions of MARC, thermal damage
accumulation was also calculated for each simulation. In Figure 3.11 the results for
thermal damage accumulation are shown for the same cases presented in Figure 3.6. This
information was very important in determining the final mechanical and structural state of
the tissue and its corresponding shrinkage behavior. It was observed that even though the
maximum temperatures created by different heating modalities were similar, the thermal
damage accumulated within the tissue was drastically different (0:7, 240 and 6000).
Additionally, it is important to stress the fact that it is not the temperature distributions but

the accumulated thermal damage that governs the heat-induced response of the

collagenous tissues.
Q=O {F240 Bipolar
i ' q"m= 1.25E+5 wmn2
C:“T"_-___. mzlmrn
9‘0 0'77 Ho:YAG Laser

l | Em= l.ZSE+6 W/nn2
E::ipi :::‘;_ o = 1 mm. f = 5H2

(F6000 Monopolu

Q=0
J P = 10 W/m3
r—:::‘ If I m

Figure 3.11: Thermal Damage Accumulation at t=4s

In Figure 3.11, the thermal damage penetration into the tissue is given for the three
difi‘erent modalities. Examination of the laser heating simulations (Figures 3.11, 3.12 and
3.14) showed that for this modality, thermal damage was superficial and was composed of

small high damage spots surrounded by low damage regions. This was caused by the

76

pulsed application of the laser energy when it was swept on the tissue surface. The main
reason for utilizing pulses rather than a continuous exposure is to give tissue some time to

uniformly distribute the thermal energy and to reduce overheated regions within the tissue.

The damage profiles created by the bipolar radiofrequency probe were similar to
those created by laser in terms of the penetration depth but the magnitude of the damage
created was greater. The main difference was thaf these profiles were more uniform due to
the continuous application of energy as opposed to the pulsed application of laser. If, on
the other hand, a temperature-controlled bipolar probe were used (it automatically turns
off when a certain temperature at the probe tip is reached) damage profiles more similar to

those of laser would be observed.

The monopolar case depicted in Figure 3.11 shows a very interesting
characteristic. This picture shows an isolated high damage zone deep in the tissue with

surrounding regions of very low or no-damage. It should be noted that these simulations

were performed with a rather high convection coefficient (h=500W/m2K). The cooling
effect of the surrounding fluid was therefore very significant and the thermal damage was
confined to the regions deep within the tissue. This is a very important finding, especially
from the clinical point of view. In the operating room setting, the visual perception of the

surgeon is the only tool available to quantify the extent of the thermal damage established.

77

Accumulated Thermal Damage ( Q)

Accumulated Thermal Damage ( Q)

  

['11
5
w

 
  
  

h=500 W/m’K

  
 
 
 

 

 

  
  
   

 

 

    
   

v=o

“W T- “35°“ "=5“ W“ l _— q"m = 1.005+5 W/mz, BP
\ 2 —-q"m=0.75E+5 W/mz. BP

{6. “=11“ 3 — P =10.0 W/m3. M”

._ = 3

o co ou\ou ........ WA 4 P 7.5 WIm; W

’ 77777 "‘ 5 '— = 5.0 WIm : M)
0.0. .00 ooooooooooo eon 6 W = l'me WImz’ L

7 M em = 0.75B+6 W/mz, L
3 " °°°°°° 8 Em = o.505+o WIm’, L

.0
0. ......

 

 

1.0503 1.5503 205-03
y [m] A
=500 W/m’K l _- q”m = 1.255+5 WIm’, BP
3 V=0.002 m/s

  

2 _. q”m = 1.00E+5 “”1112. BP
=350 K. h-SOO W/nr’K 3 _ qflm = 0.75E-i-5 W/mz, BP
9:10 4 — P = 10.0 WIm’. m

_ = 3
...... 0:1 5 P 7.SWIm,MP

Hydrothermy. T.

163

 

* .. “w. . ., 6 — P = 5.0 W/ 3,1er
..,....-%\ \\ °°S‘o........9fQ-l m

 

... 7 .... em = 1.25E+6 “”1112, L
8 .... 5m= 1.00E+6 W/mz, L
9 -~ 5“ = 0.75E+6 WIm’, L

 

........

 

 

 

2.0E-03

B

l .0503
y [m]

l .5E-03

Figure 3.12: Thermal Damage Accumulation in the Tissue A) h=500W/m2K,
m=r0=0.001m, V=0; B) h=500W/m2K, ar=r0=0.001 m, V=0.002 m/s;

78

h=500 W/mzK

   
 
 
 
 
 
 
 
 
  

 

V=0.(X)4 Int/S $10
HT 1; -350 K. li-soo wm‘x 9:1

 

l —- q"m = 1.255+5 W/mz, BP
2 —- q"m = 1.005+5 W/mz, BP
3 — P = 12.5 WIm’, MP

4— P = 7.5 W/m3,1lfl’

5 ..... 5m = 1.7SE+6 W/mz, L
6 w 5.,.,,,.x = l.SOE+6 W/mz, L
7 .. em = 1,255+5 WIm’, L

Accumulated Thermal Damage ( Q)

 

 

l .OE-03 1 .5E-03 2.0E-03

y [m] C

Figure 3.12. (Continued): C) h=500W/m2K, ar=r0=0.001 m, V=0.004 mm/s. (Ea: Laser

(L) Surface Heat Flux [W/mz], q": Bipolar (BP) Surface Heat Flux [W/mz], P: Monopolar
(MP) Joule Heating [W]).

The undamaged, unheated zone on the surface of the tissue may easily act as a
visual barrier by hiding the damaged zone, which is deep inside the tissue. In response, the
surgeon thinking that he/she has not heated the tissue yet, more than likely would go over
the same region repeatedly, creating significant damage deep within the tissue. This may
also cause extreme necrosis of the untargeted surrounding tissues and weakening of the
targeted collagenous tissue. This fact becomes increasingly important and obvious by
close inspection of the damage penetration curves of the different cases as given in Figure

3.12 and Figure 3.13. In the close proximity of the surface, accumulated damage

79

decreased with increasing convection coefficient. When the arthroscopic fluid circulation
rate was increased, the convection coefficient also increased. While irrigation of the target
tissue surface is essential for decreasing the hot spots on the surface and cleaning the
debris, too much of it can result in underestimation of the thermal damage generated. The
horizontal black lines in Figures 3.12-3.14 are the threshold damage lines. These lines

indicate the progress of the phase change process.

When the damage penetration depths in Figures 3.11 and 3.12 are examined, it is
seen that the convection coefficient as well as the power output of the heating probe,
regardless of the heating modality, plays a very important role in determining the extent of
damage. In all the cases examined, the monopolar radiofrequency probe was found to
cause the highest damage penetration with lower surface temperatures. The negative
aspects of this modality may be the damage created in the underlying, untargeted tissues
and the fact that the maximum damage zone is deep inside the tissue where it is hidden

from the surgeon.

Another observation fi'om these figures is that for the same power setting, the
damage accumulated in the tissue decreases with increasing probe sweep velocity (Figures

3.12-3.14). The stagnant probe simulations (Figures 3.12A, 3.13A and 3.14A) indicate

severe damage even after very brief exposure.

Figure 3.14 shows the distribution of the accumulated thermal damage on the
surface of the tissue. One major observation is the undulations created by the laser probe.
These are the same hot spots seen in the 2-D pictures (Figure 3.11). After the probe starts
its motion at x=0, there is a transient region, followed by a steady damage region. The

length of the transient region is a function of the probe sweep velocity.

80

11:50 W/mzK

 

 

 

 

 

 

 

 

 

 

   
   

 

 

 

1.134073: V =0 2
“a. _. " = , +
A1505; .1 1 qm 1005 5W/m2,BP
c. 5 ~. 2 -- q”m = o.755+5 W/m , BP
3’ 1.5+03 i 3 - q”m = o.505+5 W/mz, BP
2° : 9:10 4—P = 7.500 wxm’, MD
9 1.5+01 5 9:1 5 —P=6.125 W/m3, MD
1 +.. ‘ __ = 3
E 1.501, . ;. ‘ 6 P 5.ooowm,MP2
is a 3'), x 4 7 M 5m =1.00E+6 W/m , L
,3; 1.503 3 " ' , 5 8 .... 13...... = 0.75E+6 W/mz, L
at : ‘ +,. I‘
'5 : 9 a, ~ 6 9 ~~~ 50m = 0.SOE+6 W/m’, L
5 1.505 a 3;, ~.
3 5 8 iii-‘K
1.507 i ‘3’
1.5—097 “‘i““i‘*“i“4‘i" ""rm'w"‘i
0.05+00 5.0504 1.0503 1.5503 2.0503 2.5503 3.0503 3.5503
x [m] A
2
1.5+03 , 11:50 W!“ K 1 —- q”m = 1,005+5 W/m2,BP
in, 3 V=°'°°2 "”3 2 —- on,“ = o.755+5 W/m’, BP
3 1.13.01 0=10 3 _- q"m = o.505+5 W/mz, BP
1'.“ 5 1 \ 0:1 4 — P = 7.500 WIm’, m
g 1501 ..K \ \ 0:01 5 --P=6.125 W/m3, MP
3 o — P = 5.000 W/m3, MP
E ”a; _ 7 ..... 5m = 1.00E+6 W/mz, L '
[5 ”3‘03 it, “a.“ + s .... 5,“, = 0.7SE+6 W/mz, L
13 ; "*. * \ 9 .... EN = 0.SOE+6 WIm’, L
g 1.505 3 “it ‘5:
g _1 . «1:, ‘ +
g 1.507
1.E_09 ..i—L. L_C_ 1_. l ___1_-.r__ _lm ..1_.___L 4T7 4 A _LQ + fl
0.05+oo 5.0504 1.0503 1.5503 2.0503
y [m] B

Figure 3.13: Thermal Damage Accumulation in the Tissue A) h=50W/m2K,
ar=r0=0.001m, V=0; B) h=50W/m2K, ar=r0=0.001m, V=0.002m/s; C) h=50W/m2K,

81

h=50 W/mzK 1 —- (1",... = 1.255+5 W/mz, BP

 

 

 

 

 

 

 

 

 

1.5+02 1
1 5 +01 : V=0-004 m/S 94L 2 —- q"um = 1.005+5 W/m2,BP
61‘ 15+00 4 3 —- q"m = o.755+5 W/mz, BP
5; ' 4—P=10.0 W/m3,MP
an 1.501 a, 5 — P = 7.5 WIm’, m
O 1.502 6— P = 5.0 W/m’, MD
c— E . . on» — 2
5 1.504 1" 8 50m =1.25E+6 W/m , L
3. 1.505 g
3 3 “ -+ +
g 1.5-06% ‘0. ‘\:.++
g 1.8.07 % ‘. ‘:::;::::‘. ‘ \
I.E-08 ; “9%. . .......................
3 53. .:::::szzsssW
1.E.09 .5 -_._L_1__ r 1 ___.f___L__,___.L 1__ _l..__+—L_1l_- 1 1 j; 1.. 1 1 1 1
0.05+00 5.0504 1.0503 1.5503 2.0503
y [m] C

Figure 3.13 (Continued): C) h=50W/m2K, w=r0=0.001 m, V=0.004 mm/s. (E0: Laser (L)

Surface Heat Flux [W/mz], q": Bipolar (BP) Surface Heat Flux [W/mz], P: Monopolar
(MP) Joule Heating [W]).

The changes in the temperature distributions and the thermal damage profiles after
multiple sweeps with a heating probe as well as the effects of the changes in the material
properties with denaturation, and the geometrical effects were not included in this

resrearch but deserve attention in future work.

The dependence of collagen shrinkage on various factors like temperature,
exposure time and mechanical load is well established. Mechanical property degradation
of the tissue is also documented as a function of the severeness of the thermal protocol

applied.

82

The main purpose of the research presented here was to quantify the differences
among clinically utilized heat deposition modalities namely, laser, bipolar and monopolar
radiofrequency. The initial results of the collagenous tissue heating simulations performed
using a commercial finite element analysis software (MARC.Mentat) were presented. It
was shown that there were significant differences in terms of the temperature distributions
and thermal damage produced within the virtual tissue. Specifically, it was concluded that
the thermal effects of the laser and the bipolar probe were very superficial when compared
to monopolar heating. This could be observed by comparing the penetration depths of
various modalities into the tissue, as shown by (Figures 3.12 and 3.13). On the other hand,
it was observed that the thermal damage accumulated by the pulsating Ho:YAG laser was
not spatially uniform, but rather created high damage "islands" surrounded by low damage

regions.

Temperature distribution simulations performed showed that the phase change
energy levels of collagen denaturation were significant and that if realistic models to
quantify the thermal-mechanical behavior of collagenous tissues are to be constructed, this
factor should be taken into consideration. Other clinically important parameters examined
here include the convection coeflicient and the probe sweep velocity. The convection
coefficient is a function of the flowrate of the irrigation solution circulated around the
target tissue during heating. It was concluded that the increased probe sweep velocity and
irrigation solution circulation tend to smooth the thermal gradients created, yielding a

more uniform thermal damage within the tissue.

83

h=50 W/mzK

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    
  
 

1.507% v=o 2
am.\ ..- N = . +
A1.5+05; ‘1 1 q m 1005 5W/m2,BP
c: a 2 -- (1",, = o.755+5 W/m , BP
3’ 1.5+03 i 3 _- q"m = 0.505+5 W/mz, BP
9 15+“ \ \ / 9:1 5 —P =6.125 W/m3, MP
v" \\ ._ = 3
E 1501! . 6 P 5.000W/m,111P2
:5 7w5m=1.005+6WIm,L
3 8 M 50“., = 0.75E+6 wnn’, L
d
"g 9 M 50m = O.50E+6 W/mz, L
8
<
1.509‘~+4141~1H~1l~~el
0.05+00 5.0504 1.0503 1.5503 2.0503 2.5503 3.0503 3.5503
X m
[ l A
2
j 3 V=0.002 m/s
A1.5+02-} -------- A-
g 1 l / k ‘ ‘ 42:10
0 * . 7 a.
g LEW a 'v """"""" . .
E 1.502 I 8
L I
r— 1.504 r
g 1 _- q"m = 1.005+5 W/mz, BP
"g 1.E-06 2 _- q"m = o.755+5 W/mz, BP
33 3 — P = 7.500 W/m’, MP 5 ..- Em = 1,255+6 W/mz, 5

1.508. 4—P=6.125W/m3,w 7wEm=],00E-I-6W/m2,L

_. 3
E 10 5 ”1,-5.000 W/m , W 8 ..m =7.50E+6 w/mz, L
]._,._..,...,.wg.+g..%,

O.E+OO 2.E—03 4.E—03 6.E-03 8.E-03 l.E-02

x [m] B

Figure 3.14: Thermal Damage Accumulation on the Tissue Surface A) h=50W/m2K,
ar=r0=0.001m, V=0; B) h=50W/m2K, aJ=r0=0.001m, V=0.002m/s;

84

1.5+02 3 h=50 WIm’K

 

 

 

 

 
 
    

 

1.5+01 j 2\ V=0-004 m/S (2:10
a 1.5+00 ; figngagggggggng§t 9:1
‘0’ 1.501; . 7¢‘_-_,__M_‘_-_‘_w_ '3' 0:01
5* 1,5,0, / v‘vzvnvnvnvgv‘ ..1 4

1.503 if 7 8 5 Eur—1
E l.E-04 3 fi/ 6 i 1
g 1.5-05 1 f 1
g ”3'06 51 --q".,.,=1.255+5 W/m2,BP '
'5 1-5‘07 2 —-q"m= 1.005+5 W/m2,BP
g ”3'03 ' 3--q"m=0.75E+5 W/m2,BP6—P= 5.0 W/m3,}lfl’

”"309 4 — P =10.0 W/m3, MP 7 “m Em =1-SOE+6 W’m,

 

 

 

”3'10 “ 5 — = 7.5 W/m3, MP 3 ..... 50m = 1.25E+6 W/mz, L
1.31] .1- ._._1__n_+_1___1.,,m_+ 1 1 1 i 1 1 1 f 1 ”1.. ..L_1
0.E+00 2.E-03 4.E-03 6.E-03 8.E-03 l .E-02
X [m]
C

Figure 3.14 (Continued): C) h=50W/m2K, w=r0=0.001 m, V=0.004 mm/s. (E0: Laser (L)

Surface Heat Flux [W/mz], q": Bipolar (BP) Surface Heat Flux [W/mz], P: Monopolar
(MP) Joule Heating [W]).

The heating pattern created by the laser heating may be preferred if one wishes to
boost the healing response of the tissue since the migration of the cells from the
surrounding regions would be facilitated. Additionally, this characteristic may be useful if
only superficial tissue damage is desired as in the case of skin resurfacing or as in cases
when underlying nerve damage is an issue. One other point that should be stressed here is
that the simulations presented are for the Ho:YAG laser (2.1mm) which has a very small
penetration distance (~300 mm). Light at this wavelength is mainly absorbed by the bound

water in the superficial layers of the tissue. In order to increase thermal penetration and

85

minimize hot spots, pulsating the laser light, increasing the arthroscopic fluid circulation
around the treated region and low power settings were used. If, for instance, an Nd:YAG
laser (1064 nm) with a penetration depth of approximately 1400 mm was used instead,
deeper and more uniform thermal damage might be expected. On the down side, the
undulations created on the surface by the laser may create a composite medium where the
high damage "islan " act as stress concentration zones that may have adverse effects,

especially on the tensile properties of the sofi tissue.

The advantage of having irrigation circulation, from a thermal point of view, is to
smooth the temperature gradients within the tissue. The disadvantage of having very high
circulation around the target tissue, especially when modalities with volumetric heat
generation effects (such as monopolar radiofrequency) are used is that the damage created
deep inside the tissue may be underestimated. This may result in repetitive heating of the
same region of the tissue causing overexposure and significant decrease in the mechanical
properties of the tissue. The effect of an increase in sweep velocity is similar to that of
increased irrigation circulation. The sweeping action tends to smooth the thermal
gradients within the tissue. Keeping the probe stagnant over the tissue for even a few

seconds was shown to cause extreme thermal damage.

The simulations presented in this thesis did not take into account the
nonhomogeneity and anisotropic character of the tissue. They did not consider the
interaction between the probe and the surrounding fluid, variations in probe geometry and
the probe design by different manufacturers. Therefore, these simulations should be taken

as first approximations until further detailed studies are performed.

86

The main objective of this research was to prove that the temperature profiles and
the accumulated thermal damage profiles created by the clinically applied heating
modalities are considerably different. Performing 2-D simulations served this purpose in a
very fast and efficient way. In a 3-D analysis, additional information would be available
concerning the accumulation of thermal damage in the third direction. This would help

examine other parameters such as the distance between consecutive probe sweep paths.

The next step in this research was to combine the thermal model with a mechanical
model. The mechanical model predicted the final mechanical state of the tissue subjected
to various thermal loads. The transition between these two models (thermal and
mechanical) was achieved through in-vitro experimentation, which determined the

variation of mechanical and thermal properties with damage accumulation.

3.4 Temperature Controlled Monopolar Heating Probe Experiments & Simulations

In order to verify the results of the FEA simulations, in-vitro experimental analysis

with rabbit patellar tendons was performed. A custom-made, computer controlled stepper-
motor driven carriage was immersed in 37°C saline solution.
A rabbit patellar tendon sample was placed on the carriage and secured using two

clamps on each end of the carriage (Figure 3.15). A temperature controlled monopolar

heating probe (Oratec, Vulcan TAC-S Electrothermal Probe, Oratec Interventions Inc.,

Menlo Park, CA) set to operate at a temperature of 75°C and a power setting of 30W was

used to heat the tendon specimen.

87

. ~.\/,,,,,,
r/ \.

 

Figure 3.15: Photograph of the Motor Driven Carriage

The return (ground) electrode was placed underneath the specimen (Figure 3.16).
During the experiment, initially, the heating probe was kept stationary for Is and then was
swept along the major axis of the tendon at a predetermined speed. The sample was then
from prior to Optical Coherence Tomography (OCT) and Magnetic Resonance Imaging
(MRI) experiments in order to determine the extent of thermal denaturation within the

tissue.

In order to simulate the temperature control of the monopolar radiofrequency
probe, the Fortran subroutine used in the simulations presented in the previous sections
was modified. In the modified version, the node temperature corresponding to the location
of the probe (stationary or moving) was checked against the set temperature value
(fif75°C) at each time increment. An hysterysis temperature was utilized in order to
eliminate excessive hunting of the on/off controller simulation. Through the use of the
hysterysis temperature, if the node temperature was within 2.5K of the set value, the heat

flux was turned off for the following time increment.

88

Monopolar Heating Probe
Probe Sweep Path

Stationary Heating Spot Return Electrode

- —‘ ' / Tendon Sample

Carriage

 

 

 

 

Figure 3.16: Experimental Setup for the Verification of F EA Simulations

Variation of Temperature at Node #4 (nod-0)

 

 

 

5 330 j, Stationary Moving I Wpflow; $4m4m”;
1. C: C5 +P=30w, V=2mmla

 

 

 

Figure 3.17: Temperature at the Origin During Stationary and Moving Heating
Simulations with a Temperature Controlled Monopolar Radiofrequency Probe

89

In two-dimensional heating simulations, the temperature history for node #4
located at the origin is presented below during stationary and moving heating (Figure
3.17). As long as the probe was stationary, the tip temperature of the probe and therefore
the corresponding tissue temperature where the tip was located could be controlled within
certain limits. The interesting finding here was the increase in the tissue temperature at the
origin afier the onset of probe motion. Since at any instant, the temperature of the tissue
where the probe tip was located was the main criterion for the control system and since
with the sweeping motion the probe moved to a new location which was considerably
cooler than the previous location, the heat was turned on. However, the heat flux
distribution was Gaussian in the x-direction, not only the tip of the probe, but also the
surrounding tissue (including the downstream location which is already at a high
temperature) was heated. This caused overheating of downstream locations (Figure 3.19).
This phenomenon may be characterized by the Peclet number, which is here of the order
of unity, meaning that the axial conduction in the tissue is as important as the heat
convected by the motion of the probe (not to be confused with the uniform convection
heat transfer on the surface of the tissue caused by the circulation of saline). In order to
solve this problem, one alternative would be to decrease the diameter of the probe or to
sweep the probe faster. However, faster probe speeds cause new problems, such as limited
thermal damage penetration. Below in Figure 3.18, the penetration of thermal damage into
the tissue, predicted by the FEA simulation is presented for different power settings
(P=30, 40W) and probe sweep speeds (V=2, 4 mm/s). As seen below, there is not a
significant difference between the simulations. The onset of denaturation is shown to be

located at approximately 900 um below the tissue surface. The same simulations predicted

9O

that in a band (Osys600um), the tissue was completely denatured.

‘lllfl

 

 

 

1.5+05 ,
1: g A + P=30W.V=4mmls
‘1 x o a A P=40W.V=4mmls
1.E+03 ‘ g - P=30W,V=2mmls
Q o P=40W,V=2mmls
" 2
5. 1.5+o1 1
a s
E B
3 1.501 .38
'5 ‘ 2 2
E 1 E-03 ’ 9 9
E . 0 . 2 g 2
a
9 1:
a 2
1.505 on ’22,...“
¢ . . . . .
A
1.507 1" ' 1 9% ‘

 

 

 

0.0E+OO 5.0E-04 1.0E-03 1.5E-03 2.0E—03 2.5E-03 3.0E-03

y [mm]

Figure 3.18: Penetration of Thermal Damage, {2 Predicted at the Origin

; .ssanoz

:56104-02 Origin (0,0)

I . 1192+O2
I . 101¢+02

 

2515.02 Current Position
= €333,183 of the Probe

at t=8s

: .413a+02 ,
: .395u02

: .377a+02 3mm

: .358u02

: .34o.+02

Figure 3.19: Temperature Distribution at t=8s Within the Tissue Subjected to a Moving,
Temperature Controlled Monopolar Radiofrequency Heating Probe

9|

Chapter 4: Collagenous Tissue Thermomechanics

As long as it is properly hydrated, the post-denaturation mechanical state of a
collagenous tissue is defined mainly by its thermal and mechanical histories [Chen, et al.,
1998, Aksan & McGrath, 2002]. These two parameters determine the heat-induced
deformation (as shown in Figure 2.20 by the decrease in the maximum equilibrium
shrinkage as a function of the load applied on the tissue during heating) and the
mechanical properties of the tissue (as seen in Figure 2.23 by the decreasing trend of the
normalized tensile modulus with increasing shrinkage and hence with accumulated

thermal damage).

It was shown in Chapter 2 of this thesis that, in a collagenous tissue, heat-induced
deformation and mechanical properties are inversely correlated. As seen in Figure 2.23,
heat-induced shrinkage causes an exponential decrease in tensile modulus. When this
observation is extended to the clinic (to the application of sub-ablative thermotherapy for
treatment of joint instability) it is transformed into the trade-off between the kinematic and
mechanical stabilities of the joint. Kinematic stability of the joint is achieved by the heat-
induced shrinkage of the lax tissue while the mechanical stability is compromised by the
heat-induced degradation of the mechanical properties of the tissue. Hence, there is a very

close relationship between the success of sub-ablative thermotherapy and the mechanical

92

state of the joint tissue. At this point, the usefulness of a thermomechanical model
representing the heat-induced behavior of collagenous tissues becomes obvious. This
model is crucial for analyzing the parameters mentioned above in terms of their individual
and synergistic contributions to the outcome of sub-ablative thermotherapy and for
establishing guidelines for optimum treatment protocols. Other important clinical
parameters that can be analyzed using this model are the effrcacies of different heating

modalities, techniques and patterns.

In clinical practice of sub-ablative thermotherapy, there is not yet a well-defmed
recipe to follow to achieve successful therapeutic outcome. Such a recipe could not yet be
established partly due to the different heating modalities (Ho:YAG laser, monopolar/
bipolar radiofrequency) utilized and partly due to the variety of heating techniques (e.g.
continuous or repetitive heating) and patterns applied. Some surgeons prefer paintbrush
patterns, unifome heating the overall capsule surface while others prefer creating grid

patterns or parallel lines of denatured regions (Figure 4.1).

Due to the variations in clinical application and the problems in defining optimum
treatment protocols, it is not surprising to see controversial reports on the outcome of the
HACS procedures. The patient-to-patient variations in the anatomy and histology of the
joint [Obrien, et al., 1990] and the pathology (variations in the tissue microstructure due to
repetitive microdarnage or congenital disorders such as Ehlers-Danlos and Marfan’s

Syndromes) of the targeted tissue introduce additional challenges.

93

Denatured Zones
(RF Heating)

 

Figure 4.1: Arthroscopic View Showing the Parallel Zones of Denaturation Created on the
Shoulder Capsule by Monopolar Radiofrequency Heating (http.'//

a 4' J'
I r

w pages/thermal.htm)

4.1 Characteristics of Thermal Stresses

Thermal stresses are created in the collagenous tissue due to the heat-induced
structural transition (denaturation) of the collagen network. Denaturation causes
considerable dimensional change mainly in the direction of the collagen fiber orientation.
Accompanying this response are the strains formed in the transverse directions. Tissue
volume may also increase due to water influx [Wiederhom & Reardon, 1952]. If an
isotropic and homogeneous tissue is uniformly heated, and it is at an otherwise uniform
(or zero) stress state, the thermal stresses formed cause it to deform uniformly. However, if
any of the following conditions apply then the thermal stresses formed will be nonuniform
resulting in a nonuniform and complex stress/strain field: a) the tissue is structurally
inhomogeneous, b) the tissue has an initial (prior to heating) nonuniform stress

distribution due to traction boundary conditions, c) its deformation is confined due to

94

displacement boundary conditions, & there are thermal gradients within the tissue (due to

localized heating).

4.2 Thermomechanical Modeling Primer

To model the thermomechanical response of collagenous tissues, the conventional
approach is either to perform an experimental analysis to establish empirical relationships
between the measured parameters (temperature, time, load, elongation, tissue hydration,
etc.) and the final state (defined by its state-of-stress (or deformation) and mechanical
properties) of the tissue or to solve the coupled thermoelasticity equations [Nowacki,

1986] that govern the thermomechanical phenomena in a continuum.

The former approach is species and tissue specific, requires tremendous effort and
a very large number of specimens. In the latter case, when solution of the thermoelasticity
equations are considered, two major problems arise: a) a solution to these equations can
only be obtained for very simple tissue geometries if very radical simplifying assumptions
are made, and b) these equations do not carry phase change or history information (these
models assume that upon cessation of heating, when the material is returned back to its
initial temperature, no permanent effect remains). In the case when denaturation causes a
phase change of the collagen however, the effect of heating is irreversible beyond a certain

temperature (for a stress-free tendon tissue the threshold temperature for irreversible

transition is approximately 60°C. Yet, there is evidence that even at 40°C there are certain

irreversible changes in the microstructure [Hormann & Schlebusch, 1971]). During

95

transition, in addition to formation of permanent thermal stresses (yielding to permanent

thermal deformations), the physical properties of the tissue change irreversibly as well.

Hypothetically, it is also possible to model the heat-induced gross tissue response
based on the configurational and structural transformations of the collagen molecule. If all
the mechanical interactions between the consecutive structural levels of the tissue
hierarchy could be established, it would be possible to extrapolate the microstructural
response to the macroscale tissue behavior. As a first step in understanding the microscale
mechanics of tissues, some studies focused on measuring the mechanical properties of a
single collagen fiber using conventional biomechanical experimentation techniques
[Svendsen & Thomson, 1984] and of a single tropocollagen molecule using laser tweezers
and optical strain measurement techniques [Luo, et al., 1997]. Due to inherent technical
challenges in establishing the complex interactions among the tissue structures at different
hierarchical levels, there are as yet no reported studies focusing on the thermomechanical

behavior of these microscopic structures.

In this research, in order to model and simulate the heat-induced collagenous tissue
response, a radically different approach is taken. It is proposed that the thermomechanical
response of a collagenous tissue to local heating (such as by laser or radiofrequency) can
be modeled based on the thermomechanical response of a dense, oriented tissue to a
uniform heating modality (such as by hydrothermy for very high Biot numbers) by a
combination of experimental and numerical analysis. Details of this new approach are

presented in the following section.

96

4.3 Thermomechanical Response Simulation Algorithm

In this part of the thesis the computer-based simulation tool that has been
developed in order to model the thermomechanical responses of collagenous tissues will
be described. As a first step in the development of the software, a two-dimensional
analysis in simple geometries has been performed. Later in the development stage, the

analyses have been extended to three dimensions.

The virtual tissue (the Control Volume (CV) used in the Finite Element Analysis
(F EA)) was hypothetically divided into small, representative elementary volumes (REVS)
at the same hierarchical level. It was assmned that each REV is large enough to be
considered a continuum. A REV was also considered to be structurally homogeneous,
thermally lumped and to be in mechanical interaction with the surrounding REVS. The
heat-induced thermomechanical behavior of each REV was assumed to be identical to that
of a dense, oriented collagenous tissue when it was subjected to uniform heating (i.e.,

when there were no thermal gradients in the tissue except at the boundaries).

The schematic representation of the algorithm used for collagenous tissue
thermomechanical response simulation is shown in Figure 4.2. Basically, there are three

main routes:

1) Heat Transfer Analysis by which the temperature distributions and thermal
damages created in a collagenous tissue by clinically used heating methods (Ho:YAG
laser, Monopolar or bipolar radiofrequency) can be modeled using finite element analysis

(see Chapter 2 of this thesis for details).

97

2) In-vitro Experimentation with a dense, oriented collagenous tissue model

(rabbit patellar tendon) in order to establish empirical correlations between the mechanical

and thermal histories and the final state of the tissue. Details of this research are presented

in Chapter 3 of this thesis.

3) Mechanical Analysis, which allows the prediction of the pre-heating mechanical

stress fields within the control volume and the mechanical history of the tissue.

   

Heat Transfer
Analysis

 
 

 

 

 
  
  
  

FEA Rout_e

  
 

Thermomechanical
Experimentation

 

 

 

Thermal History

Correlations

  
 
     
  

Empirical

 

  
  

 

Thermal
Stresses

 

 

 

 

 

 

Mechanical

 

 

 

Analysis

FEA Rout_e

     

Mechanical
History

I U FEA Route
7

 

 

 

Mechanical
Modeling

 

 

T

Figure 4.2: Collagenous Tissue Thermomechanical Response Simulation Algorithm

The information collected though these analysis routes was used to model the

thermal stresses formed in the virtual tissue (the CV) and the resultant state of the tissue.

Details of each step are presented below.

98

For a given problem the thermomechanical response simulation began with the
solution of the heat transfer problem through finite element analysis (F EA) following the
procedures established in Chapter 2 of this thesis. Through this analysis, the temperature
distributions created in the tissue by clinically applied heating modalities and the thermal
damage accumulation (calculated by the Arrhenius damage integral) were determined.
These values were calculated and recorded for each node in the finite element mesh
comprising the CV. For each REV (which is equivalent to an element in the FEA), a single
representative thermal damage value, {2 was calculated by averaging the thermal damage
accumulated at each node of the element. In Figure 4.3A, the thermal damage
accumulated inside a two-dimensional control volume is shown. In this figure, the blue
color indicates undamaged zones and the yellow color shows highly damaged regions.
The white squares in Figure 4.3A are the REVS covering the CV (some space is left
between REVS for visual clarity). Figure 4.3B shows the Arrhenius damage integral value
corresponding to each REV. It is shown that the REVS in columns 1 and 5 and in the third
row are not damaged and therefore not assigned any value. The black line in each REV

shows the primary direction of fiber orientation that can be assigned for each REV.

For the same geometry, a static mechanical analysis was performed in order to
determine the state of stress of each REV prior to heating. Consequently, through these
two analyses, for every REV (each element in the mesh) represented by its respective

center coordinates (ij), the corresponding representative thermal damage (a scalar

quantity), Q], and the state of stress (a tensor), 9 were determined.

ij 9
In collagenous tissues collagen fiber orientation may vary spatially (except in

dense, oriented soft tissues such as tendon). However, it was reasonable to assume that the

99

direction of collagen fiber orientation in a REV coincides with the axis of the maximum
principal stress. The rationale behind this assumption is that in collagenous tissues,
collagen fibers align themselves in the direction of the maximum load. Once the state of
stress is known, the maximum principal stress for any REV”, 03;], can be easily calculated

fiom azjas follows:

 

_ °x1'+° r" oxi'_6 i' 2 2
(Hi1. _ _2J_2__.XJJ+J[ 2 ] +(Txy,ij) 4.1

In Equation 4.1 Obi}, 03,,” and 1ny]- are the normal stress in the x-direction, the
normal stress in the y-direction and the shear stress in the x-y plane for REVy,
respectively. In order to account for the delay in transition (as seen in Figure 2.18, with
increasing load, equilibrium shrinkage curves shift towards higher thermal damage
values) with increased stress, the midpoint thermal damage, and], corresponding to the
maximum principal stress, a" ,1, for the same REV was determined using Equation 2.8
(also shown in Figure 2.19). Increase in stress also effects the maximum equilibrium
shrinkage (see Figure 2.20). Therefore, maximum equilibrium shrinkage, egmij,
corresponding to the maximum principal stress, at 1}, was calculated from Equation 2.9.

These values were inserted into Equation 2.10, which in turn was solved for the

equilibrium shrinkage, e2, REV” undergoes when it was subjected to a thermal damage,

a}, and when wat is at an initial state of stress represented by 9i}-

The calculated equilibrium shrinkage, e2, would be equal to the resultant shrinkage

if REV” was completely isolated from its surroundings (Figure 4.3C). In Figure 4.3C, the

100

deformation of each REV (REVs A through F) are shown as if they were completely
isolated from their surroundings (i.e., not in mechanical interaction with surrounding
REVS). However, this is not the case since the surrounding interacting REVS are also
undergoing denaturation at different levels and are exerting additional stress on their
surroundings (and on REV”, as well). In order to account for the interactions among all of
the REVS in the CV (including the native REVs as well as the thermally damaged ones) a

procedure utilizing transient mechanical analysis by means of FEA was developed.

DLJEHL]
ELM J1 l

flifl”m/13
U\:\ Vie/EU ,,
DEL L] ] ULJLTDL

Figure 4.3: REV Approach and Schema of Thermomechanical Coupling

 

 

 

 

 

 

 

 

 

 

 

 

Following the same rationale used to develop Eshelby's Method [Eshelby, 1957], it
is assmned that the global effects of the transformation stresses (such as the stresses due to
the denaturation of collagen) created in a sub-region, N", enclosed by a region N can be

calculated from the stress-free transformations of the sub-region 8* when it is completely

lOl

isolated (see Appendix A for details). Therefore, the stress-free transformation

(equilibrium) strain, e2, calculated for each REV was converted to a resultant potential
stress, 02, using Hooke’s Law. The material constants were taken at the transformed state

as a function of equilibrium shrinkage (see Figure 2.23). The stress calculated for each
REV was assumed to be acting at the boundary of the respective REV at its undeformed
(pre-heating) configuration. This was analogous to an initial value problem, where there is
an initial stress distribution (at t=0) over a volume and through transient analysis, the final
deformations of the system were calculated. Using this analogy the problem was
converted into an initial value problem and was solved using FEA (as seen in Figure
4.3D). The solid lines around the REVS Show the final deformed state of the CV and the
dashed lines show its shape at the initial (reference) configuration prior to heating. Note

the difference in the shape of the REVS between (Figure 4.3C and Figure 4.3D).

The applicability of the algorithm presented here is tested for a two-dimensional

geometry and the analysis is presented below.

4.4 TWO-Dimensional Simulations

A two dimensional control volume (2mm x 20mm) representing a rabbit patellar
tendon specimen was heated by a Ho:YAG laser on one face (Figure 4.4). The top surface
of the control volume was assumed to be immobile simulating a suspended specimen. In
the single spot heating simulations, the laser beam was focused on the center of the right
face of the CV. In the multiple spot beatings, heating was symmetric about the same

center point.

102

Thermal stresses were calculated for each REV (in this case a square element in
the mesh with the dimensions 20m x 20m) and assigned as initial stresses distributed
over the heated region. Following the methodology established below, mechanical
response to six different heating conditions with an Nd:YAG laser (1064nm) were

simulated. The following table (Table 1) lists those conditions:

 

 

 

 

 

 

 

 

Simulation Laser Spot Size Number of Spots Distance Between Spots
Number (lle Diameter) [mm]
[min]
1 0.25 1 N/A
2 0.50 1 N/A
3 0.75 1 N/A
4 0.50 3 0.5
5 0.50 5 0.5
6 0.50 3 1.0

 

 

 

 

 

Table 4.1: Mechanical Response Simulations Performed

The results of the heat-induced mechanical response simulations performed are
presented below in Figure 4.4. In this figure the white rectangle represents the outline of
the tissue at its native state (before heating). In all of the simulations performed, it is
observed that local heating by laser causes bending of the tissue. The bending angle is a
function of exposure time and spot size (which is the Gaussian beam diameter). A similar

response to laser heating was observed during experiments performed in our laboratory.

103

 

Figure 4.4: Results of the Heat-Induced Mechanical Response Simulations

As seen below in Figures 4.5 and 4.6, these simulations could be very useful tools
in determining the stresses formed in the tissue afier heating. In those figures a zoom view
of the center of the tendon is presented. In Figure 4.5, the variation of the y-component of
the normal stress (039,) is shown. As expected, the initial compressive thermal stresses
relax and cause the rest of the tissue to bend. The amount of bending is directly
proportional to the laser spot diameter. This simulation tool is able to accommodate
various heating modalities and effects like probe speed, the power deposited and other

factors like heat transfer boundary conditions and tissue Structure.

104

I W

11 llulnm \1 “511111111 ‘1 '1‘5111111

4 5 (\

1| H‘VIHIIII 11 It‘lllmll .1 11511111111

 

Figure 4.5: Variation of the Normal Stress in y-direction (0”,) (Range: White: 2.907 MPa
compressive, Black: -1.975 MPa tensile). (d3: Laser spot size)

 

 

Figure 4.6: Variation of the Normal Stress in x-direction (an) (Range: White: 0.2589
MPa compressive, Black: -1 .142 MPa tensile). (d5: Laser spot size)

105

Chapter 5: Chemical Enhancement Methods (Cross-Linking)

There are two important factors that accompany the denaturation-induced
shrinkage of collagenous tissues. These are: the mechanical property degradation and the
partial loss of shrinkage (tissue elongation) upon cooling back to lower temperatures
(defined here as recovery). Recovery is thought to be the result of re-naturation i.e.,
refolding of the partially unfolded tropocollagen molecules upon cessation of heating
[Hormann & Schlebusch 1971; Watanabe, et al., 1997]. This may be the main cause of
ambiguity in measuring the exact amount of shrinkage produced by heating. This factor
may be particularly important during HACS surgery where the success of the operation is

to a large extent dependent on the amount of shrinkage achieved.

The reduction in the tensile modulus and strength (up to 7 0-90% of the untreated
tissue) of the collagenous tissue upon heating is reported in the literature [Schaefer, et al.,
1997; Berend, et al., 1996; Vangness, et al., 1997; Hecht, et al., 1999]. This fact, coupled
with the strain injury created in the glenohumeral capsular and ligamentous structures
during subluxation or dislocation, indicates that immediately after the operation the tissue

is excessively weak and vulnerable.

One possible solution to these problems is to apply a chemical method in

conjunction with heating as a means of reducing the recovery of the tissue while

106

enhancing the mechanical properties. Examination of the feasibility of this idea was the

motive for the preliminary research described here.

The ongoing search for a method to minimize the drawbacks (degradation of
mechanical properties and recovery from the shrunken state) of the HACS procedures
suggested the possibility of utilizing chemical cross-linking agents. The chemical
modification of collagen films and collagenous tissues using cross-linking agents like
glutaraldehyde (GTA), 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide (EDC),
hexamethylene diisocyanate (HMDC) and diphenylphosphorylazide (DPPA) is a known
procedure which induces inter/intramolecular bonds. These agents are generally used for
fixation in histological examinations [Simionescu, et al., 1991], controlled drug release
[Gohel & Amin, 1998], delaying the in-vivo degradation of [Lynn, et al., 1990] and
suppressing the recipient immune response [Simionescu, et al., 1991; Gohel & Amin,
1998] to soft tissue xenografis like porcine heart valves and arteries. On the macro scale,
the effects of these modifications are known to be pronounced with respect to mechanical
properties like stiffness, strength and viscoelasticity [Finger, et al., 1987; Lee, et al., 1994;
Davidson, 1989; Naimark, et al., 1998] as well as with respect to the denaturation
temperature [Ruijgrok, et al., 1994; Horgan, et al., 1990; Moore, etal., 1996; Gavilanes, et
al., 1984]. The most effective of these cross-linking agents is reported to be
glutaraldehyde [Rault, et al., 1996; Jorge-Herrero, et al., 1999], which reacts with the e-
amine groups of lysine and hydroxylysine residues in the collagen. The chemical bonds
induced by glutaraldehyde enhance the strength and stiffness of the collagenous tissues
[Ruijgrok, et al., 1994; Rault, et al., 1996]. The penetration and reaction characteristics of

glutaraldehyde are very much dependent on concentration and temperature. It is also

107

known that at high concentrations glutaraldehyde polymerizes on the tissue surface,
forming a crust layer between the solution and the tissue [N irnni, et al., 1988]. This layer
reduces further diffusion of the cross-linking agent into the tissue. In the glutaraldehyde
penetration studies done in our laboratory, this fact has also been established as shown
below in Figure 5.1. In these experiments, a fluorescent probe is utilized
(Carboxyfluorescein Succinimidyl Ester, 5-FAM, SE: Molecular Probes, Eugene, OR),
which binds to the sites within the tendon collagen (between the Lysine and
Hydroxylysine residues) where glutaraldehyde molecules also attach. Therefore, the
absence of fluorescence (the probe, 5-FAM, SE, is excited at 495 nm and its emission at
520nm is measured) in the tissue after exposure to a glutaraldehyde solution reveals the
presence of glutaraldehyde bonding. The details of sample preparation, experimentation
and sample results can be found in Appendix C. In Figure 5.1 below, the penetration
characteristics of glutaraldehyde as a function of its concentration in saline and exposure
time is presented. As seen in the figure, after 24 hours of exposure, the tendon is uniformly
perfused with glutaraldehyde and all of the available Sites are cross-linked. Therefore,
there are no sites available for the fluorescent probe to attach and thus no fluorescence
emission at 520 nm. On the other hand, after 15 minute exposure to 0.1% glutaraldehyde
solution, there are very sharp intensity gradients at the boundaries of the tendon Specimen

indicating the cross-linking has not penetrated suffrciently into the tendon.

Glutaraldehyde was chosen as the strongest candidate for the preliminary studies
performed to test the feasibility of using an adj uvant chemical treatment to thermotherapy.
Considering the inherent cytotoxicity of this chemical at high concentrations (>5% w/v)

[Nimni, et al., 1988], experiments are performed using very low concentrations (0.1-0.5%

108

w/v). Also a blocking agent solution (0.025M Glycine, 0.05M Sodium Borate, pH8.0) was
applied after exposure to glutaraldehyde to neutralize the uncross-linked glutaraldehyde

molecules during the test protocol.

    

1.00] .
A" i . 'i ° ’
i "1
0.75« - ~

'11 .
!M a 13’: '°.
LO.501-%: 1": ’V~ . f

1.

   
      
 
 
  

0.25 i

 

3' .1
. ‘ iii

 

 

0.00 . . . .
0.00 0.25 0.50 0.75 1.00
x.
—0.5* GTA. 24 Hours 0 0.5% GTA, 15 mm 0 0.1% GTA. 15 Mnutea
‘0' 0.1%GTA.3OMMIO8 I 0.1*GTA.BOW

Figure 5.1: Normalized Fluorescence Intensity (I*=I/Im) at 520nm as a Function of
Normalized Tendon Width (x*=x/xm).

5.1 Materials and Methods

In this section, the preliminary results of the in-vitro experiments performed to

examine the feasibility of using a chemical cross-linking method in combination with

thermotherapy are presented.

109

The experiments performed were mainly directed at quantifying the mechanical
property enhancement achieved with the combined thermal-chemical treatment. After
preparation and mechanical preconditioning, the specimens were heated, either immersed

in a cross-linking solution or a saline solution and their responses were compared.

The specimens used were the patellar tendons of New Zealand white rabbits
obtained from other researchers at MSU. A total of 30 specimens were collected from the
hind legs of 30 animals. None of the animals had undergone experimentation that would
affect their musculoskeletal tissues. The experimental specimens were prepared following
the same protocol described in Section 2.4.1 of this thesis. The experimental setup was the

same as the one described in Section 2.4.2.

The experimental procedure consisted of mechanical preconditioning which was
aimed at minimizing the viscoelastic response of the tissue. The tissue was then loaded to
test stress (~0.5MPa) and the testing protocol was initiated. The test stress was chosen in
order to simulate physiological loading conditions and to limit the shrinkage of the
specimen.

Testing consisted of three main steps. The first step was hydrothermal heating
performed by circulating preheated cross-linking agent solution at a prescribed

temperature in the range (65-85°C) around the specimen. In the control group however,

heated phosphate buffered saline solution (PBS) instead of cross-linking agent solution

was circulated. The second step was the circulation of a room temperature (24°C) cross-
linking blocking agent. The cross-linking blocking agent was used to neutralize the

unreacted cross-linking agent molecules therefore stopping the reaction and reducing

110

cytotoxicity. Temperature was monitored by three T-type thermocouples and sampled at
5112 by a thermocouple board (DAS-TC/B, Keithey Instruments Inc., Cleveland, OH).
Stress and strain data were collected at 10 Hz by an MD board (DAS-1800-ST/DA,

Keithey Instruments Inc., Cleveland, OH).

A representative temperature history of the specimen and the shrinkage response
obtained is presented below in Figure 5.2. At the end of the testing protocol, a tensile test
was applied on the specimen until failure. The specimens were then flash frozen and saved

until fluorescence testing was performed to determine the extent of penetration of cross-

 

 

 

 

 

 

 

linking agent.
0.05 € Heating 8. Cross-Lmkmg AA Cooling & Blockrng _ 80
0.00 4 —Strain —Temperature 70
-0.05 -
— 60 8
-O.1O 1 °—-
o
.E 5
g -0.15 . Recovery - 50 ‘5
<0 e2: Equilibrium Shrinkage ,/ g
«0.20 - ”7"?- """"""""""""""""""" «E:
1 1 ' 40 l-
0.25 - 1 1
g '1 _ 30
1 e1: Initial Shrinkage
'0.35 I I I I I I I I I 20
0 100 200 300 400 500 600 700 800 900 1000

Time [s]

Figure 5.2: Characteristic Heat-Induced Response of Rabbit Patellar Tendon Specimen

111

—_..._

5.2 Results

For each specimen tested, the variation of strain with respect to temperature was
recorded and the initial, e], and equilibrium shrinkage values, e2, as well as the recovery
ratio, R, were calculated. The post-treatment tensile modulus, E, was calculated from the
slope of the stress-strain data obtained during the tensile tests. The experimental groups

and their respective controls completed are presented in Table 5.1 on page 112.

Table 5.1: Experimental Groups

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Group Exposure Time Treatment Tempearture Heating Blocking

[8] [°C] Solution Solution
T 1 (n=5) 600 75 0.5% GTAr 0.025M Glyt
2 (n=5) 600 80 0.5% GTA 0.025M Gly
j (n=5) 600 85 0.5% GTA 0.025M Gly
mops) 1200 75 0.5% GTA 0.025M Gly
E5010) 1200 80 0.5% GTA 0.025M Gly
201:5) 1200 85 0.5% GTA 0.025M Gly

 

1 0.5% [w/v] Phosphate Buffered Glutaraldehyde Solution, pH7.4

1 0.025M Glycine, 0.05M Sodium Borate, pH8.0

S -2. 1 Equilibrium Shrinkage, e2

Equilibrium shrinkage, e2, is the value of final Shrinkage reached after cooling the

tissue back to room temperature (Figure 5.3). For both groups (cross-linked and control),

112

there was an apparent exponential relation between the temperature of the treatment and

the resulting strain (Figure 5.3). This agrees with the literature [Chen & Humphrey,

1 9980]. The results also showed that except the 85°C treated group, there was not a
significant difference between the glutaraldehyde treated and control groups in terms of
the equilibrium shrinkage achieved. This implied that the glutaraldehyde treatment did not

have a detrimental effect on the final shrinkage achieved (even yielded higher values for

the 85°C group).

8
++

 

 

 

30 -*
“921961 f
20 --
10 >— “1”] +
0 +— + -+ + 1 + ——1
70.0 72.5 75.0 77.5 80.0 82.5 85.0

Average Treatment Temperature [°C]

0 75 C, nxl, 6005 o 80 C, nxl, 6008 a 85 C, nxl, 6008 o 75 C. gta, 6008
I856.gta. 6003 080 C,gta.6008 .375 C,nxl,12008 x750,gta.12008
A80 C,nxl,12008 a80 C.gta,1ZOOs

Figure 5.3: Variation of Equilibrium Shrinkage, c; with Treatment Temperature and

Exposure Time

113

5.2.2 Recovery Ratio, R

AS explained in detail above, following heating, when the tissue was cooled back

to a lower temperature some of the initial Shrinkage, e1, recovered and the tissue slowly
converged to its equilibrium shrinkage value, c; (Figure 5.2). This is due to re-naturation,

the basic mechanism of which is the refolding of the partially unfolded tropocollagen

 

 

 

 

 

 

 

helices.
50 T
l
40 + l
” + .0. -o-
30 F
b A di—
R [%] 20 17 +
r
10 «P
0 .. 1 Non Cross-Linked: Open Symbols
GTA Cross-Linked: Filled Symbols
-10 *m‘ 'fi ‘ V" T‘"‘* 71 1 I 1
70.0 72.5 75.0 77.5 80.0 82.5 85.0

Average Treatment Temperature [°C]

0 750.nx1,6008 8 80C. nxl, 6008 a 85C.md,6008 0 750. gta, 6008 I 85C,gu.6008
x 750,nxl.12008 o 80C,gta,6008 r. 75 C.gta, 12008 880C, n10.12008 aBOC.gta, 12008

Figure 5.4: Variation of Recovery Ratio, R, with Treatment Temperature and Exposure
Time

The ratio of the amount of tissue expansion observed at room temperature to the

initial shrinkage observed at high temperature is defined here as the recovery ratio, R. The

114

results of the preliminary studies indicated that for all of the experimental groups, the
recovery of glutaraldehyde cross-linked tissues were less than their controls by ~50%
(Figure 5.4). This novel finding has very important implications for HACS procedures. To
a great extent, the tissue will be fixed at its initial shrunken state. Therefore it will be

easier for the surgeon to assess the amount of irreversible shrinkage achieved.

5.2.3 Tensile Modulus, E

Figure 5.5 summarizes the results of the tensile tests applied to the specimens after

the completion of thermal-chemical treatment. For all of the experimental groups
examined (75°CSTWW585°C, 6009mmm512005): the glutaraldehyde treated
specimens were stiffer than their controls (EGTA/ENXL>1). The increase in tensile

modulus ranged from 20% to 200% depending on the thermal treatment applied. This
important finding established the fact that the application of cross-linking agents in
conjunction with heating can be used to counteract the degradation of mechanical

properties caused by heating.

It is reported that after subfailure levels of strain damage, the stiffness of the
tissues drops significantly [Panjabi, et al., 1996]. The detrimental effects of thermotherapy
on mechanical properties is well-established and is a function of the severity of the
treatment [Panjabi, et al., 1996; Schaefer, et al., 1997; Berend, et al., 1996; Vangness, et
al., 1997; Hecht, et al., 1999]. The combined effect of strain damage and thermotherapy
reduce the stiffness to approximately 10-15% of its normal value. This combination of

strain damage and heating is identical to the conditions that exist at the time of the

115

application of thermotherapy to a dislocation injured shoulder capsule. The stiffness
increase achieved by chemical therapy as shown here is therefore very important for the
eflicacy of HACS procedures. These results prove the feasibility of utilizing chemical

therapy as an adj uvant therapy to thermotherapy.

80 7 Very Significant.
1 P=0.009

1* _./L__\
70 . '

60 I Not Significant
IfiAW‘\

 

1:] gta
Significant. P=0.017 EJ nxl

 

 

Not Significant

._A_..\

 

(a)
D

If

Tensile Modulus [MPa]
.5
O

I Quite Significant.
I P=0.090

 

N
O

 

..L
o

   

 

 

 

 

 

 

 

 

 

 

 

 

 

80C,1200$ 750,12008 750.6005 80C,6008
Heating Condition

0

I

850.6008

Figure 5.5: Variation of Modulus Ratio, E with Treatment Temperature and Exposure
Time

5.3 Cytotoxicity
The results of the preliminary in-vitro experiments showed that the proposed

combined thermal-chemical treatment was superior to thermotherapy alone. Using this

method, 50% reduction in recovery and up to 200% increase in tensile modulus were

116

achieved. The next step was to confirm these findings in a living system to address the
issues such as cytotoxicity and long term efficacy of the suggested cross-linking protocol.
These studies were performed in collaboration with Dr. Steven Amoczky of the College of

Veterinary Medicine at MSU.

The first step of the cytotoxicity studies was the tissue culture tests performed with
patellar tendon fibroblast cells. The control groups of these cells were exposed to culture
media and PBS only. The experimental cell populations were subjected to different
concentrations of glutaraldehyde for different exposure times. Some groups underwent
blocking agent treatment after glutaraldehyde exposure. Then an MTT assay (Product No.
M5655, Sigma Chemical Co., Saint Louis, MO) was used to determine the changes in the
metabolic activity of the cells as a function of cross-linking agent concentration, exposure
time and blocking agent type. The MTT assay is based on the cleavage of the yellow
tetrazolium salt MTT to purple formazan crystals by metabolic active cells. The

solubilized formazan product is quantified using standard microplate absorbance readers.

Six to seven tissue culture wells were used for each experimental group and 50,000

fibroblast cells were used in each well. All of the chemicals and the PBS used in the

experiments were filtered (filter pore size = 0.2um) for sterilization and heated to 37°C to
eliminate heat shock on the cells. Through an automatic optical density reader opearated at
540 nm, the emission from the formazan crystals at each well (which is a measure of
metabolic activity of the cells) was measured and the resuls are presented below in Figure
5.6. Unfortunately, these results indicated that even at these low concentrations, the
cytotoxic effects of glutaraldehyde was very significant and that in order to apply

chemical enhancement methods as an adj uvant therapy, a better approach would be to

117

examine the feasibility of using (mechanically less effective) non-cytotoxic agents.
However, one important point that should not be disregarded is that even 20 minutes

exposure to saline solution killed 45% of the cells.

1001

804 f 1;
701 y
601
501
401
301

 

Cell Survival (96)

2° * 13 07 12.81

o. .. .. .. a .. L1. 1
10m‘nutes 20m'nutes 20m'nutes 101nhutes 201mm 10mm 20mm
in Blocker in Blocker inPBS in GTA in GTA in GTA+10 ln GTA+20
nintaesin nimbsin
Blodter Blocker

 

Figure 5.6: Results of Cytotoxicity Tests with Rabbit Patellar Tendon Fibroblasts

5.4 Other Studies

Similar cross-linking experiments were performed (following the same
experimental protocol described in Section 5.1) by replacing glutaraldehyde with either 1-
ethyl-3 -(3-dimethylaminopropyl)-carbodiimide (EDC) or hexamethylene diisocyanate
(HMDC) in the saline solution but the resultant mechanical property enhancement was not

Significant. An alternative process; photo-crosslinking of the tendon specimens

118

preconditioned by immersion in a sucrose solution (90g/L) followed by methylene blue or

riboflavin solution immersion and exposure to UV light was also tried without success.

119

Chapter 6: Conclusions

Over the last decade, sub-ablative thermotherapy has found ever-increasing
application in orthopedic and ophthalmologic surgery. The therapy aims at altering the
configuration of the strain-damaged, pathological or congenitally anomalous soft tissue in
order to re-establish stability and function. The basic mechanism of this therapy is the
heat-induced denaturation of the underlying collagenous network of the Soft tissues. Heat-
induced denaturation causes microstructural transformation of the collagen molecule and
produces a thermal stress field along the direction of the collagen fiber orientation. The

thermal stress field formed changes the configuration of the tissue proper.

The initial wide-Spread use and short-term clinical success of these therapies are
being questioned by the recent availability of the long-term clinical results in the literature
[Anderson, et al., 2002]. The reports reveal the unpredictability of the outcome of the
therapy and suggest more careful patient selection (for instance, the direction of the
instability -anterior, posterior or multidirectional- is thought to be an important factor in
determining the outcome of thermotherapy applied for the treatment of shoulder
instability). There are also other major factors that contribute to the phenomena; such as
the non-standard, unoptimized clinical practice of using a variety of heating modalities,

patterns and techniques.

120

A thorough and careful examination of the literature revealed that most of the
seemingly contradicting results in the literature can be explained and the unpredictability
of the clinical outcome can be minimized by understanding the macroscale tissue response
to the heat-induced microstructural transformations and by developing models, and
simulation tools to be used in the analysis of the clinically important parameters and the
design of optimized heating protocols. Therefore, the research presented here was aimed
at establishing the scientific basis and developing the tools to increase the safety and
efficacy of the Sub-Ablative Hermetherapy procedures applied to treat instabilities of

the knee, ankle and shoulder joints and in the elimination of discogenic pain in the spine.

Proceeding the Introduction Section, where the background was presented, this
thesis was divided into four main parts. In the first part, constitutive equations describing
the heat-induced mechanical response of collagenous tissues were established by means of
in-vitro experimentation with a model soft tissue. In the second part, the sub-ablative
thermal damage created in the soft tissue by clinically applied heating modalities was
examined using numerical simulations (through finite element analysis). In a similar
fashion, in the third part of the thesis the heat-induced mechanical response of collagenous
tissues were simulated. In the last part, feasibility of applying adjuvant, chemical

enhancement methods to thermotherapy were examined.

The clinical relevance of the study presented in this thesis was explained in the
Introduction Section (Chapter 1). The advantages and disadvantages of Sub-Ablative
Thermotherapy in treating joint instability were presented and it was concluded in this
section that detailed basic science studies were required to increase the efficacy of this

therapy.

121

In the first main part of the thesis (Chapter 2), heat-induced mechanical response
of the collagenous tissues was characterized by means of in-vitro experimentation using a
model soft tissue; New Zealand white rabbit patellar tendon. Through thermal (isothermal
heating and DSC studies) and thermomechanical analyses, the resultant gross mechanical
response of the tissue to thermal stimuli was examined. Three distinct heat-induced

response regimes were identified. These regimes are:

1. Irreversible Elongation: Elongation up to 0.5% strain accompanied by an
increase in tensile modulus (E ~ 125% of the native tendon calculated at the reference

state).

2. Irreversible Shrinkage: Decrease in the overall length of the sample in the
dominant direction of fiber orientation accompanied by an exponential decrease in tensile

modulus (with respect to the native value) and disappearance of viscoelastic response.

3. Reversible Shrinkage: Defined by thermoelastic response where shrinkage was
completely reversible. Upon returning to room temperature, the tissue regained its pre-
heating length. In this regime, there was no decrease in tensile modulus with fm'ther

heating.

The first regime in the heat-induced collagenous tissue response (Irreversible
Elongation regime, which corresponds to a slight elongation of the sample with improving
mechanical properties) may be usefirl in developing new soft tissue thermal treatments
aimed at increasing the tissue mechanical properties with minimal thermal strain
formation. It may also be used in designing curing protocols for artificial collagen

scaffolds used either as drug carriers or tissue substitutes.

122

Independent of the stress state, for all of the experimental conditions examined,
formation of thermal strain and the variation of the mechanical properties with
accumulated thermal damage were shown to collapse on respective master curves. An
Arrhenius damage integral representation of soft tissue thermal history was shown to be
adequate even when mechanical stress was present. It was postulated that the effects of
thermal and mechanical history (in the load and temperature ranges examined) could be
separated and the constitutive equations describing the heat-induced tissue response could
be derived. It was suggested that the delay seen in the denaturation response of the
collagenous tissue with increasing mechanical load was caused by a decrease in the
activation entropy of denaturation, but that the denaturation enthalpy remained

unchanged.

It was shown that the mechanical success (restoring the function) of sub-ablative
thermotherapy (in the treatment of joint instability) was dependent on two major
parameters. These were: the kinematic stability achieved by re-establishing the
kinematical equilibrium of the joint (in terms of the locations and directions of the forces
carried) and the structural stability of the tissues comprising the joint (in terms of their
strength and resistance to deformation). The results of this research suggested that even
though kinematic stability might be restored by thermotherapy (and that the mechanically
deformed, elongated tissue could be brought back to its pre-injury length by heating),
structural stability of the tissue was compromised (due to degradation of mechanical
properties). This finding has very important clinical implications (at least during the short
post-operative period before the onset of the healing response); the existence of a trade-off

between the kinematic and the mechanical stability of the joint. It was shown that

123

overheating can be as ineffective as underheating and that there existed an optimum point
(from a mechanistic perspective) in between. For instance, upon heating, two distinctly
diflerent final states of a tendon tissue could be reached: 8% shrinkage (from its native
length) of the tissue resulting in a state where the tissue exhibited 50% of its initial tensile
modulus or 16% shrinkage with a tissue that retained only 25% of its initial tensile
modulus (data taken from Figure 2.23). Here, the important questions to be answered are:
“Is this (thermally treated) tissue going to be able to carry the same physiological forces it
used to carry before the injury without rupturing or stretching beyond its physiological
length?” and “In which one of those states presented above is the tissue more likely to be
both stable and functional?”. In terms of maximization of the thermal stress developed in
the heat-treated tissue, the mechanical optimum was shown to correspond to 12%
shrinkage in a uniformly heated, dense, oriented collagenous tissue (such as tendon and
ligament). This result established the first step in answering the questions presented

above.

The results presented here and the conclusions drawn are valid for a uniformly
heated, dense, oriented collagenous soft tissue. In clinical application of thermotherapy
however, there are additional factors to be considered. These are the thermal and
thermomechanical strain gradients formed due to non-uniform heating of the tissue as well
as due to the non-uniformity of the tissue structure (spatial variation of collagen fiber
orientation and gross tissue geometry). Within a locally heated tissue, the thermal damage
field is not uniform. There are also distinct differences among the thermal damage fields
created by hydrothermal, radiofiequency or laser heating due to the differences in their

modes of action. Hydrothermal heating is mainly a surface heat transfer phenomena; heat

124

penetrates into the tissue by convection due to the circulation of high temperature liquid at
the tissue-liquid interface. The mechanism of radiofrequency heating, on the other hand, is
based on increased mechanical friction (and therefore increased heat generation) among
the polar molecules, which are forced to oscillate by the rapid changes in the magnetic
field created by the high frequency alternative current passing through the medium. In the
case of laser heating, the light energy absorbed by different chromophores (depending on
the wavelength of light, starting with certain amino acids in the UV range, ~193nm, all the
way to water absorption in the IR range, ~2.96p.m) inside the tissue and released as heat.
Additional factors affecting the thermal damage field within the tissue are related to the

the applicator (probe) geometry design, power setting and application patterns.

Therefore, in the second part of the thesis, the sub-ablative thermal damage created
in the tissue by different heating modalities was examined through finite element analysis
and the effects of different parameters (such as power setting, probe sweep speed and
surface convection) were examined. In the FEA of thermal damage penetration, it was

assumed that all of the tissue properties except heat capacity was constant.

Through FEA it was shown that there were significant differences among the
g clinically applied heating modalities. Heating imposed by bipolar radiofiequency is
mainly superficial (confined within the top layers of the tissue so long as the treatment
temperatures are sub-ablative). However, in monopolar radiofi'equency heating, the
alternating current flows directly through the tissue between the active electrode (located
at the tip of the radiofrequency probe) and the ground electrode (which is placed over the
abdomen of the patient in the clinical setting and underneath the target tissue during in-

vitro experimentation).

125

Other factors that can be examined using the Simulation tool developed in Chapter
2 include the effects of the laser wavelength, beam diameter, power setting, pulse width
and fi'equency and laser probe speed. In the clinical setting, lasers are usually pulsed in
order to decrease the risk of creating hot spots in the target tissue. Due to this pulsating
behavior, the thermal damage accumulated in the tissue is not uniform but rather in the
form of high damage “islan ” surrounded by low damage regions (as seen in Figure 7,
Insert 6). The effect of this type of heating on the mechanical properties and the healing

response of the tissue proper have not yet been examined.

In the third part of this thesis, a computer simulation tool for the heat-induced
mechanical response of collagenous tissues was developed. In developing the algorithm
for this simulation, it was postulated that the gross response of a multi-dimensional dense
collagenous tissue could be predicted from the mechanical response of the representative
elementary volumes of a lower dimension. For instance, the response of the tissue
Simulated in two-dimensions was a combined outcome of the representative elementary
volumes whose characteristic responses were dominantly in one dimension (along their
dominant collagen fiber orientation). By the use of this algorithm, the efiects of thermal
damage accumulation, the shape of the thermal lesion formed and the final mechanical
configuration and the state of collagenous tissue could be modeled. This algorithm is the
product of a novel approach and can be used to predict the heat induced responses of
collagenous tissues having very complex geometries subjected to very complex heating
conditions. Future studies should focus on quantifying the applicability range of this
algorithm. The limited experiments performed indicated that the validity was confined to

small displacements.

126

It is interesting that even though soft tissue thermal therapy is being applied rather
widely to treat shoulder, knee and ankle instabilities and even discogenic pain, the real
mechanism responsible for re-establishing joint stability is not fully understood.
According to some researchers, collagen denaturation and the resultant mechanical
tightening is the major factor, but others claim that it is the heat-stimulated biological
repair mechanisms that “do the job”. Additionally, it is stated as a major concern that the
temperatures required to initiate collagen denaturation are fatal for the cells. It is obvious
that the lack of viable cells at the Site of thermal injury delays the healing response of the
tissue. However, before reaching a verdict, the desirability of a fast healing response
should also be questioned. A very fast healing response could render the heat-treatment
ineffective if the heat-treated (and thus modified) tissue is immediately replaced with new
tissue or remodeled. On the other hand, if an accelerated response is desired, pulsating
lasers or radiofrequency heating applied in a grid pattern could serve this purpose by
leaving safe zones for cells surrounded by thermally treated zones. These zones would
serve as safe heavens for the cells to survive through the procedure and facilitate their

migration to the “damaged” regions to start modeling immediately after thermotherapy.

Thermal therapy is currently applied to cause tissue shrinkage, thus producing
joint stabilization. However, heating causes significant reduction in the mechanical
properties of the tissue (tensile modulus and failure strength). Consequently, adjunct
methods that could retain the benefits of thermal therapy while minimizing or eliminating
the degradation of mechanical properties are of interest. In the last part of this thesis, the
feasibility of adapting a thermal-chemical therapy protocol was examined. This combined

method was offered as a means of maintaining optimum joint stability without

127

compromising mechanical integrity of the tissue. Results of in-vitro experiments
performed on an animal model (New Zealand rabbit patellar tendon) demonstrated the
positive impact of combining chemical treatment with thermotherapy. The contribution of
the chemical treatment using glutaraldehyde as a cross-linking agent may be summarized
briefly as a reduction of strain recovery by as much as 50% and an increase in the tensile
modulus by as much as 100% when compared to thermotherapy alone. However,
preliminary tissue culture tests performed on patellar tendon fibroblasts showed that with
increasing glutaraldehyde concentration, the potential cytotoxicity of the chemical
treatment increased. This indicated an apparent trade-off between the efficiency of the
chemical treatment protocol applied and its cytotoxicity. Future research should focus on
defining optimal thermo-chemical means to produce safe and efficacious HACS
procedures that produce the desired tissue Shrinkage with enhanced mechanical properties

through sub-ablative thermotherapy with non-cytotoxic cross-linking agents.

Application of heat and cold for treatment purposes is not novel, but developing
the means of controlling and localizing its effects is. In summary, through the research

presented in this thesis:

I. Constitutive equations governing the heat-induced mechanical response of

dense, oriented, uniformly heated collagenous tissues were defined.

2. An Arrhenius damage integral representation of thermal damage was shown to

be adequate irrespective of the stress-state of the collagenous tissue.

3. Through experimental analysis, it was shown for the collagenous tissues that

there are three distinct heat-induced mechanical response regimes.

128

4. It was shown that irrespective of the stress-state, heat-induced shrinkage

response and tensile modulus variation follow universal curves.

5. It was concluded that for sub-ablative thermotherapy procedures aimed at
treating joint instability, there is a trade-off between the kinematic stability of the joint
established by shrinking the lax capsuloligamentous tissues and the mechanical stability

of the joint tissue compromised by the degradation of the mechanical properties.

6. Existance of a mechanical optimum for thermal treatment corresponding to the
maximum thermal stress created in the uniformly denatured, dense collagenous tissue was

demonstrated and was Shown to correspond to an equilibrium shrinkage of approximately

12%.

7. Clinically applied heating modalities used in sub-ablative thermotherapy were

shown to create distinctly different thermal damage fields within the target tissue.

8. Discrepansies and contradictions among the in-vitro experimental results and
the clinical reports in the literature were shown to be caused mostly by different heating

modalities used and different levels of denaturation reached in the target tissue.

9. Non-uniform thermal damage fields created by low frequency pulsed lasers
could prove useful in accelerating the repair of the treated tissue by leaving low damage
zones between high damage zones (where fibroblasts may survive), if such a response is

desired.

10. A hybrid simulation algorithm comprised of in-vitro experimentation and finite

element analysis was developed to simulate the heat-induced responses of collagenous

129

tissues in multi-dirnensions. This simulation tool is believed to be very useful in pre-

treatment therapy planning and optimization of therapies.

11. It was shown that chemical enhancement techniques are feasible candidates for
developing adjuvant therapies for sub-ablative thermotherapy in minimizing the adverse

mechanical effects of the said therapies.

12. The thermal and chemical treatment protocols developed here have the
potential to be applied to the manufacture of artificial tissues and protein based drug

carriers.

This thesis laid the foundation for modeling the heat-induced mechanical
responses of collagenous tissues through development of novel in-vitro experimentation
and simulation techniques. It also reached out to explore different avenues in adapting

engineering techniques to medical problems, however it Should be regarded as a beginning

rather than an end.

130

Chapter 7: Directions for Future Research

The thermomechanical response simulation algorithm developed in this thesis was
based on the correlations derived from the results of one-dimensional, in-vitro mechanical
experimentation with rabbit patellar tendon tissues. In order to be able to accurately
simulate the heat-induced mechanical response of a collagenous tissue, the analyses
established here should be extended to multi-dimensions and should take into
consideration the non-homogeneous nature of the tissues. This requires multi—dimensional
mechanical testing combined with real-time strain measurement and structural
information. The strain measurement may be performed using optical methods (such as
particle tracing) which trace the displacements of predetermined points on the tissue
surface while the tissue is heated in a controlled fashion. Coupled to this system, optical
(birefiingence and/or optical coherence tomography (OCT)) or magnetic resonance
imaging techniques can also be utilized to collect structural information (before the
experiment in order to determine the collagen fiber orientations as well as the heat-
induced structural variations during the experiment). Data collected from these
thermomechanical experiments may then be used to detemrine the anisotropic constitutive
relationships in multi dimensions as a function of the thermal damage accumulated. These

experiments can also be modified to examine the effects of various factors on the heat-

131

induced response characteristics of collagenous tissues (which are not examined in the
research presented here) such as the tissue hydration level, adj uvant chemical cross-
linking and permanent mechanical damage (microstructural mechanical damage induced
prior to experimentation in order to simulate a mechanical injury). It is believed that both
tissue hydration level and pre-existing microstructural mechanical damage affect the heat-

induced response of the collagenous tissues.

The same setup mentioned above, may also be modified for experimentation with
clinically applied heating modalities (such as monopolar/bipolar radiofrequency and
Ho:YAG laser). A setup involving multiple CCD cameras may be utilized to determine
the configuration change of the sample tissue specimen when it is subjected to localized
heating. OCT, birefringence or MRI data collected during experiments can also be used to
verify the thermal damage penetration values predicted by the FEA software developed as

a part of this thesis.

After these studies are completed, the next challenge would be to apply the

technology developed to the clinical setting.

132

Appendix A: Eshelby’s Method

In Eshelby's Method [Eshelby, 1957], it is assumed that the stresses created in a

continuum (Figure Al), 9?, due to a phase transformation (in this case denaturation) in a

subregion, N can be calculated using the stress-free transformation strains, 5; , formed in

Nwhen N is isolated from 9?.

   

 

 

 

 

 

 

 

{T7 1 mu 11.1.] r
a
e = 8° 5
Transformation Strain
a C: 5 8T

Figure A. 1: Eshelby’s Method for Stress-free Transformation of an Ellipsoidal Region
[Clyne & Withers, 1993]

These transformation strains are related to the resultant potential stress field,

T .
01:1 ’by'

T T T

o - e A.1
ij ijkl kl

133

T

where the material constants, C. 1’ are those of the transformed state (in this case the
l

denatured tissue). In Eshelby's Method this stress field is relaxed later combining the

regions gland N and letting them assume their final stress states.

"'\
‘V 1. Original (ReferenCe) Configuration
yrs-ix...“ R 1’ Configuration 1'

\_ Deformed (Present) Configuration

\, ’j ; /-’ Configuration wj"

Transformation to
| Original Configuration

\---l-v-./ R.

q V \ Original (Reference) Configuration
'I' I . With Surface Tractions

/"‘T“”\ Configuration ”'1'

 

.,
l Assembly
~ 9
\g \ x“ R
\
\
( 81 "Vi \ Configuration at 170
\\ . \‘fj R. / Configuration '1'
J L Relaxation
,1- ‘fivjd—m _’_ I- _K—‘\~c\\-\ R
.._\\
‘ \
(/ \\
(i R‘ \Conliguralion as taco
‘1‘ -- -‘~~--\ I Configuration "k”
\\ S I ' l/
’ k \k /

Figure A.2: Transformation Stresses and Determination of the Final Configuration

134

In Chapter 4 of this thesis, following the same rationale used to deve10p Eshelby's
Method [Eshelby, 1957], it is assumed that the global effects of the transformation stresses
created in a sub-region, R*, enclosed by a region R can be calculated from the stress-free
transformations of the sub-region R* when it is completely isolated (Figure A.2).
According to this algorithm, if a stress field is formed in subregion R*, (defined by a

surface, 3;, and volume, Vi, in its reference configuration) possibly due to structural

transformations (such as denaturation), one way to solve the resultant stress field is to start
by completely isolating the subregion R* from region R and allowing it to undergo stress-
free transformations. In this isolated, transformed state (configuration “j”), the sub-region

R * is assumed to be defined by the surface S] and the volume V} which are different from

66",
1

those at the reference configuration (configuration ). Later, surface tractions are applied

to bring the subregion R* back to its original configuration defined by the surface, 3;, and
volume, V;. Note that the surface tractions applied are functions of the stress-free

deformation sub-region R* undergoes and the material properties of sub-region R * in the
transformed state. Next step is the assembly step where the subregion R* and the region R

are united again and equal and opposite traction forces are applied on the surface Si,

causing deformation of region R. This step corresponds to a new reference state (where
t=0) since the shape of the subregion R* has not been allowed to change yet. In order to
determine the final configuration of the region R (which now completely encloses the sub-
region, R*) the constraints on the surface between R and R* are removed and the steady
state (equilibrium) solution to the equations of elasticity infinity is sought through

transient analysis.

135

Appendix B: User Subroutines

Below a typical user subroutine coupled to the main body of the MARC FEA code
is presented. The first subroutine (plotv) is used to calculate the Arrhenius Damage
Integral for each node in the mesh during transient analysis. The second subroutine (flux)

is used to define a moving Gaussian heat source.

B.l Subroutine Plotv:

 

subroutine plotv(v,s,sp,etot,eplas,ecreep,t,m,nn,layer,ndi,
* nshear,jpltcd,vhistory)

implicit real*8 (a-h,o-z)

save incort,v1,dt

dimension s(*),etot(*),eplas(*),ecreep(*),sp(*),vl (100000,8),
* dt(l00000,8),incort(100000,8)

include 'fliome/uz/aksanalp/marc/creeps'

include '/home/uz/aksanalp/marc/concom'

real*8 incort,v1,dt,damagep,tempal

save incort,v1,dt

136

tempal=t
if (inc.eq.0) then
v=0.0
v1 (m,nn)=v
incort(m,nn)=0
return
endif
if (tempal.lt.3 l 1) then
v1(m,nn)=0
v=v1(m,nn)
return
else
damagep=(198. 1498-67 5 84.0/tempal)
if (damagep.gt.0) then
v1 (m,nn)=v] (m,nn)+AB S(timinc)*EXP(ABS(1 .O‘damagep»
else if (damagep.lt.0) then
v1 (m,nn)=v] (m,nn)+AB S(timinc)/EXP(ABS(1 .O*damagep))
else if (damagep.eq.0) then

v1 (m,nn)=v1(m,nn)+ABS(timinc)

137

endif

v=v 1 (mm)

return

endif

end

 

B.2 Subroutine Flux:

 

subroutine flux(f,temflu,mibody,time)

implicit real*8 (a-h,o-z)

save maxtemprLincrementinfo

dimension mibody(1),temflu(6),maxtemprt(10000,l O),
"‘ incrementinfo(10000)

include '/home/uz/aksanalp/marc/creeps'

include 'home/uz/aksanalp/marc/concom'
settemperature=75 .O+273. l 5

settemperaturehys=2.5

waittime=1 .O

138

if (time.le.waittime) then
vel=0.0
else
vel=0.002
endif
EMAX=40.0
ro= l .1 7E-3
if (inc.eq.0) then
do 2 J=O,10
do 1 I=0,10000
maxtemprt(I,J)=0.0
incrementinfo(I)=0.0
continue
continue
endif
incrementinfo(inc)=ncycle
if (ABS(temflu(5)).lt.1.22E-3) then
if (time.le.waittime) then

if (temflu(4).ge.0.0) then

139

if (ABS(temflu(4)).lt.50.0E-6) then
maxtemprt(inc,ncycle)=temflu(3)
endif
endif
else
if (temflu(4).ge.0.0) then
if (ABS(temflu(4)—vel*(time-waittime)).lt.50.0E-6) then
maxtemprt(inc,ncycle)=temfiu(3)
endif
endif
endif
endif
if (inc.gt.0) then
if (ncycle.eq.1) then
temperamrediff=settemperature-maxtemprt((inc-1 ),
* incrementinfo(inc-1))
else
temperamredifisettemperature-maxtemprfi inc,(ncycle-1 ))

endif

140

endif
if (temperaturediff. gt.settemperaturehys) then
coordx=temflu(4)-vel*(time-waittime)
coord=coordx"‘*2+temflu(5)**2+temflu(6)**2
f=EMAX*ro/(12.57*(coord**2))
else
f=0.0
endif
return

end

 

141

Appendix C: Determination of Glutaraldehyde Penetration

C.l: Experimental Protocol

The samples are flash frozen in liquid nitrogen and cross-sectional samples at

thicknesses of 25, 50, 100, 150 um are cut using a cryotome.

The samples are kept hydrated by placing them in tissue culture wells that are

filled with saline solution.

The wells are drained and filled with 1.5 ml of 0.25 mg/ml S-FAM, SE and 1.5 ml

of 0.15M sodium bicarbonate solution.

After 1 hour, the reaction is terminated by draining the wells and filling them with

3ml of 1.5M Hydroxylamine hydrochloride.

After 1 hour, the samples are washed twice with saline solution and mounted on

microslides using a non-fluorescing mounting medium.

The tissue sample mounted on a microslide is excited at 495 nm and the emission

at 520nm is captured by a high sensitivity CCD camera.

At 35 times magnification the tissue is scanned along the axis of cross-linking
agent penetration and successive fluorescence and normal transmitted light images are

collected at 0.5mm increments.

The images are merged and the fluorescence intensity variation along the width of

the tendon is measured using the ImagePro sofiware. The background emission is

142

suntracted and the intensity is normalized with respect to maximum fluorescence

measured.

C.2: Sample Merged Images

 

Figure C.l: Transmitted Light Microscopy Across the Width of the Tendon Specimen

 

Figure C.2: Fluorescent Light Microscopy (520nm) Across the Width of the Same Tendon
Specimen

143

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