MICROCRACKS INDUCE OSTEOBLAST ALIGNMENT AND MATURATION
ON HYDROXYAPATITE SCAFFOLDS

By

Yutian Shu

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Chemical Engineering and Materials Science

2012

ABSTRACT

MICROCRACKS INDUCE OSTEOBLAST ALIGNMENT AND MATURATION
ON HYDROXYAPATITE SCAFFOLDS

By

Yutian Shu

Physiological bone tissue is a mineral/collagen composite with a
hierarchical structure. The features in bone, such as mineral crystals, fibers,
and pores can range from the nanometer to the centimeter in size. Currently
available bone tissue scaffolds primarily address the chemical composition,
pore size, and pore size distribution. While these design parameters are
extensively investigated for mimicking bone function and inducing bone
regeneration, little is known about microcracks, which is a prevalent feature
found in fractured bone in vivo and associated with fracture healing and repair.
Since the purpose of bone tissue engineering scaffold is to enhance bone
regeneration, the coincidence of microcracks and bone densification should
not be neglected but rather be considered as a potential parameter in bone
tissue engineering scaffold design.
The purpose of this study is to test the hypothesis that microcracks
enhance bone healing. In vitro studies were designed to investigate the

osteoblast (bone forming cells) response to microcracks in dense (94%)
hydroxyapatite substrates. Microcracks were introduced using a
well-established Vickers indentation technique. The results of our study
showed that microcracks induced osteoblast alignment, enhanced osteoblast
attachment and more rapid maturation. These findings may provide insight into
fracture healing mechanism(s) as well as improve the design of bone tissue
engineering orthopedic scaffolds for more rapid bone regeneration.

Copyright by
YUTIAN SHU
2011

ACKNOWLEDGMENTS

I would like to thank my advisor, Professor Melissa Baumann for her
guidance during my pursuit of doctoral degree. She provided me opportunities
to participate in various research activities, gave me chance to meet people
with professional knowledge in related fields of endeavor. She also taught me
how to think critically, how to work with undergraduate students, and helped
me with improving my English as a second language.
I would also like to thank Professor Eldon Case for sharing his wealthy
knowledge and enlightening ideas with me, and for advice on becoming a
devoted, honest and efficient researcher. I also appreciate Professor Laura
McCabe and Professor Jeff Sakamoto for their help and suggestions on my
coursework and research.
Last but not least, I would like to thank all my lab coworkers, Chelsea
House, Craig Pearson, Fei Ren, Kaitlin Tyler, Marc Schlaud, Megan Buczkow,
Rob Friederichs, Sarah Meyer, and Xiaofeng Fan, for their assistance during
the completion of my research.

v

TABLE OF CONTENTS

LIST OF TABLES…………………………………………………………………….9
LIST OF FIGURES…………………………………………………………………10
CHAPTER 1
INTRODUCTION…………………………………………………………………….1
References………………………………………………………………………4
CHAPTER 2
BACKGROUND……………………………………………………………………...6
The composition and structure of bone……………………………………..6
Microcracking in bone…………………………………………………………..9
Bone remodeling and osteoblast function…………………………………..12
Biomaterials surface properties affecting osteoblasts……………………..14
Hydroxyapatite applications………………………………………………….17
Residual stress and microcracking…………………………………………..19
Vickers micro-indentation……………………………………………………..22
References……………………………………………………………………..30
CHAPTER 3
CELL CULTURING PROTOCOLS……………………………………………….39
Thawing………………………………………………………………………...39
Feeding…………………………………………………………………………40
Splitting…………………………………………………………………………40
Freezing………………………………………………………………………...41
Sterilize handling………………………………………………………………42
References……………………………………………………………………..44
CHAPTER 4
MICROCRACKS INDUCE OSTEOBLAST ALIGNMENT AND ACCELERATE
MATURATION ON HYDROXYAPATITE SCAFFOLDS………………………...46
Abstract…………………………………………………………………………46
Introduction and background…………………………………………………47
Materials and methods………………………………………………………..51
HA specimen preparation……………………………………………51
HA characterization…………………………………………………..52
Cell culture……………………………………………………………53
OB attachment and growth………………………………………….53
OB maturation………………………………………………………..54
CLSM imaging of OBs……………………………………………….55
Statistics………………………………………………………………………..55
Results………………………………………………………………………….56
HA characterization…………………………………………………..56
OB attachment and alignment…..…………………………………..58

vi

OB attachment…………………………………………………...58
CLSM micrographs of OB attachment at four hours…………60
Alignment angle (θ) distribution………………………………..62
Comparison of aligned and non-aligned cells………………...64
The positions of aligning cells on microcracked HA………….65
OB growth and maturation.………………………………………….67
Discussion……………………………………………………………………...70
OB attachment and growth………………………………………….70
OB shape on the CLSM micrographs………………………………72
Distribution of OB alignment angles………………………………..73
OB alignment towards the microcracked zone……………………73
Relationship between aggregated aligned cells and the size of
microcracked zone…………………………………………………...76
Microcrack boundary defined by radial/lateral cracks…………….77
OB maturation………………………………………………………..79
Conclusion……………………………………………………………………..80
References……………………………………………………………………..82
CHAPTER 5
MICROCRACKS ACCELERATE CALLCIUM RELEASE FROM
HYDROXYAPATITE………………………………………………………………..94
Introduction…………………………………………………………………….94
Materials and methods………………………………………………………..95
Results and discussion………………………………………………………..97
Conclusion……………………………………………………………………102
References……………………………………………………………………103
CHAPTER 6
CLSM OF CALCIUM PHOSPHATE PRECIPITATION FROM CRACKED
HYDROXYAPATITE………………………………………………………………107
Introduction…………………………………………………………………107
Materials and methods………………………………………………………107
Results and discussion………………………………………………………108
Conclusions…………………………………………………………………110
References……………………………………………………………………112
CHAPTER 7
OSTEOBLAST SPATIAL DISTRIBUTION AFTER 1, 2, AND 4 HOURS
ATTACHMENT……………………………………………………………………114
References……………………………………………………………………120
CHAPTER 8
SLOW GROWTH OF MICROCRACKS IN HYDROXYAPATITE INTRODUCED
BY MICROINDENTATION……………………………………………………….122
Abstract……………………………………………………………………….122
Introduction and background………………………………………………..123
Experiment procedure……………………………………………………….126
Materials and characterization methods………………………….126
Vickers indentation and crack length measurement…………….127
Results and discussion………………………………………………………128
vii

Material characterization…………………………………………..128
E, H, and Kc for HA specimens…………………………………….129
Load dependence of initial radial and lateral crack length……...130
Radial crack growth and perturbation from lateral cracks during
aging…………………………………………………………………133
Load dependent exponential growth of radial cracks………133
Perturbation from lateral crack………………………………..136
Other factors that may affect the growth of radial cracks……….139
Summary and Conclusions………………………………………………….141
Appendix A……………………………………………………………………143
References……………………………………………………………………146
CHAPTER 9
SUMMARY AND FUTURE DIRECTIONS……………………………………..154
APPENDICES
APPENDIX A BONE RESPONSE TO MECHANICAL STIMULI AND THE
LOCAL STRAIN-CUE HYPOTHESIS…………………………………………..158
APPENDIX B CALCIUM CONCENTRATION MEASUREMENT USING
ATOMIC ABSORPTION SPECTROSCOPY…………………………………..164
APPENDIX C SOLID STATE SINTERING OF HYDROXYAPTITIE AT
1360°
C…………………………………………………………………………… ..166
REFERENCES……………………………………………………………………170

viii

LIST OF TABLES
Table 2.1 Chemical compositions of bone measured by Berzelius……………..6
Table 2.2 Comparison of the mechanical properties of long bone and common
biomaterials used for bone replacement…………………………………………..8
Table 7.1 Goodness of fitting tests for cell distribution data on non-cracked
HA………………………………………………………………………………….117
Table 7.2 Goodness of fitting tests for cell distribution data on cracked HA...119
Table C-1 List of sintering profile, density, porosity and volume change……169

ix

LIST OF FIGURES
Figure 2.1 Longitude femur section showing trabecular and cortical bone.
Photo taken by Paul Crompton [2011] at University of Wales College of
Medicine. For interpretation of the references to color in this and all other
figures, the reader is referred to the electronic version of this
dissertation.…………………………………………………………………………..8
Figure 2.2 Illustration of the surface contact angle of water drop on an ideal
solid surface surrounded by gas………………………………………………….16
Figure 2.3 Elastic/plastic indention model of spherical symmetry with a
hydrostatic core near contact region with indenter, plastic deformation zone”
around the hydrostatic core, and elastic matrix…………………………………23
Figure 2.4 (A) Elastic/plastic combination at maximum load P which is a
summation of (B) reversible elastic component at load P and (C) irreversible
residual component after unloading……………………………………………...24
Figure 2.5 Elastic/plastic sharp contact indentation generates median, radial
and lateral cracks…………………………………………………………………..25
Figure 2.6 Residual component of stress field below indentation which remains
upon unloading and lateral crack of distance h below the free surface. The
dashed lines depict the median/radial crack system……………………………28
Figure 4.1 (a) Radial cracks introduced by Vickers indentation at 4.91 N; (b) A
7×7 grid with a 2 mm interval indentation pattern on HA specimens………….52
Figure 4.2 XRD spectra of as-received HA powder from vendor and pulverized
sintered HA specimen. Both powders showed representative peaks for HA
crystal and no impurity phases were detected…………………………………..56
Figure 4.3 SEM image of (a) polished non-cracked HA surface and (b) cracked
HA surface and CLSM Z-stack maximum reflection intensity projections of (c)
polished non-cracked HA surface and (d) cracked HA surface. On the cracked
HA surface, Vickers indentation impression is the center diamond shape.
Accompanying radial cracks and lateral crack spalling are pointed out by white
and black arrows, respectively……………………………………………………57
Figure 4.4 CLSM fluorescence images of OBs attached to non-cracked HA
specimens at (a) 1 hour, (b) 2 hours and (c) 4 hours, and cracked HA
specimens at (d) 1 hour, (e) 2 hours and (f) 4 hours. White arrows show
positions of Vickers indentations and cracks. The OBs were stained with

x

Rhodamine Phalloidin (Actin) and Hoescht 33342 (nucleus). The Rhodamine
Phalloidin Actin fluorescence stain was excited at 543 nm and emission was
detected through a BA560-620 nm emission filter (represented in red). The
Hoechst 33342 nucleus stain was excited with UV light at 405 nm and
emission was detected through a BA430-470 emission filter (represented in
blue)…………………………………………………………………………………59
Figure 4.5 OB attachment is increased on cracked HA specimens at 4 hours.
OBs were seeded at an initial density of 11,320 cells/cm2. OB attachments on
non-cracked and cracked HA specimens at 1, 2 and 4 hours are represented
by the relative percentage of cells seeded. Error bars represent standard error.
While no significant difference between OB attachment on non-cracked and
cracked HA specimens were detected at 1 and 2 hours, significant increase of
OB attachment by approximately 28% on cracked HA specimens was detected
at 4 hours using Student’s t-test (*p<0.05). Three specimens were used for
each condition and the experiments were tripled……………………………….59
Figure 4.6 Illustration of angle θ between cell elongation direction (cyan line)
and line connecting cell nucleus and indentation center (yellow line) on
micrographs of cracked HA. The indentation impression and radial crack
pattern are illustrated by white lines. The black crosses mark examples of cells
showing no apparent elongation direction. The OBs were stained with
Rhodamine Phalloidin (Actin) and Hoescht 33342 (nucleus). The Rhodamine
Phalloidin Actin fluorescence stain was excited at 543 nm and emission was
detected through a BA560-620 nm emission filter (represented in red). The
Hoechst 33342 nucleus stain was excited with UV light at 405 nm and
emission was detected through a BA430-470 emission filter (represented in
blue)…………………………………………………………………………………61
Figure 4.7 A schematic of cells with different elongation directions with respect
to the indentation site. Cells with θ<45° are considered as aligned cells, while
cells with θ ≥ 45° are considered as non-aligned cells………………………… 63
Figure 4.8 Probability density histograms of θ for a) non-cracked HA (N=489)
and b) cracked HA (N=587) fit to uniform distribution as shown by the thick
solid black line. N is the total number of cells considered in the probability
density histograms. The goodness of fit was tested using the
Kolmogorov-Smirnov method. The θ distribution for non-cracked HA fitted to
uniform distribution (p>0.05). The θ distribution for cracked HA did not fit to the
uniform distribution (p<0.05)………………………………………………………64
Figure 4.9 The relative fractions of aligned cells (θ<45° and non-aligned cells
)
(θ ≥ 45° and circular cells) on a) non-cracked HA and b) cracked HA at 4 hours.
Significantly more non-aligned cells than aligned cells were detected from

xi

non-cracked HA micrographs, while the opposite was observed from cracked
HA micrographs. The significance of difference was detected using Student’s
t-test (p<0.05)………………………………………………………………………65
Figure 4.10 The micrograph was partitioned into a central circle of 15 µm in
radius and 15 µm wide outer rings (a). The number of OBs with aligned
tendency (θ<45° in the center circle and outer rings (15 µm wide ) were
)
counted and normalized by the area respectively (b). Most cells with aligned
tendency (θ<45° were found in the annulus 75 to 90 µm from the indentation
)
center (b), which is around the tip of the radial cracks from Vickers indentation
(a)……………………………………………………………………………………66
Figure 4.11 OB growth is not affected by the presence of cracks on HA
specimens. OBs were seeded at an initial density of 11,320 cells/cm2. OB
growths on non-cracked and cracked HA specimens at 1, 3 and 5 days are
represented by the relative percentage of cells seeded. Error bars represent
standard errors. No significant differences between OB growths on
non-cracked and cracked HA specimens were detected (*p<0.05). Three
specimens were used for each condition and the experiments were tripled…67
Figure 4.12 OB maturation characterized by (a) AP expression and (b) AP
activity was enhanced on cracked HA specimens. OBs were seeded at initial
density of 20,000 cells/cm2. After 21 days of cell culturing, AP gene expression
was examined using RNA extracted from cell layers. Gene expression was
normalized to levels of an unmodified housekeeping gene, HPRT. AP activity
was assessed on cell layers and then measured by spectrophotometer.
Significant increases in both (a) AP gene expression and (b) AP activity were
detected using Student’s t-test (*p<0.05). Error bars represent standard errors.
Three specimens were used for each condition and the experiments were
tripled………………………………………………………………………………..68
Figure 4.13 (a) Runx2, (b) Col-I and (c) OC expressions on non-cracked and
cracked HA at 21 days. All gene expression was examined using RNA
extracted from cell layers. Gene expression was normalized to levels of an
unmodified housekeeping gene, HPRT. Significant increase in Runx2
expression on cracked HA specimens was detected using Student’s t-test (*p ≤
0.05). No significant differences in Col-I and OC expressions between
non-cracked and cracked HA specimens were detected. Error bars represent
standard errors. Three specimens were used for each condition and the
experiments were tripled…………………………………………………………..69
Figure 4.14 CLSM Z-stack maximum fluorescence intensity projections of OB
mineral depositions on (a) non-cracked and (b) cracked HA at 21 days. The
OBs were pulsed with Xylenol Orange every other day during culturing since

xii

day four. The Xylenol Orange fluorescence stain was excited at 543 nm and
emission was detected through a BA560-620 emission filter (represented in
orange)………………………………………………………………………………70
Figure 5.1 ESEM images of the same indentation impression on HA surface (a)
before immersing in distilled water, (b) 4 hours after immersion in distilled
water, and (c) 24 hours after immersion in distilled water……………………...97
Figure 5.2 The plot of calcium concentration released from non-cracked ( )
and cracked ( ) HA specimens as a function of time. Error bars represent
standard deviations. The non-cracked HA calcium release data were fit to
equation (1), which yielded a coefficient of determination R2 = 0.977. The
cracked HA calcium release data were fit to equation (2), which yielded a
coefficient of determination R2 = 0.986…………………………………………..99
Figure 6.1 CLSM Z-stack maximum fluorescence intensity projections of
calcium depositions on (a) non-cracked and (b) cracked HA in the absence of
cell culture. The OBs were pulsed with Xylenol Orange every other day during
culturing since day four. The Xylenol Orange fluorescence stain was excited at
543 nm and emission was detected through a BA560-620 emission filter
(represented in orange)…………………………………………………………108
Figure 7.1 Schematic of the measurement of osteoblast location with respect
to the indentation region on a cracked HA micrograph. The cell location is
characterized by the radial distance from indentation center, r and angle α..114
Figure 7.2 Schematic of the measurement of osteoblast location with respect
to the indentation region on a non-cracked HA micrograph. The cell location is
characterized by the radial distance from indentation center, r and angle α..115
Figure 7.3 The radial distance, r distributions (left column) and the angle, α
distributions (right column) after 1 (first row), 2 (second row) and 4 hours (third
row) of attachment on non-cracked HA. The r distributions were fit to Rayleigh
distribution (mauve solid line), and the α distributions were fit to Uniform
distribution (black solid line) using EasyFit. The radial distance r distributions
did not fit to Rayleigh distribution at all hours (p<0.01), while the angle α
distributions were uniform at all hours………………………………………….117
Figure 7.4 The radial distance, r distributions (left column) and the angle, α
distributions (right column) after 1 (first row), 2 (second row) and 4 hours (third
row) of attachment on cracked HA. The r distributions were fit to Rayleigh
distribution (mauve solid line), and the α distributions were fit to Uniform
distribution (black solid line) using EasyFit. The radial distance r distributions
did not fit to Rayleigh distribution at all hours (p<0.01), while the angle α

xiii

distributions were uniform all hours……………………………………………..118
Figure 8.1 SEM images of (a) a thermally etched surface of a 94.3% dense HA
specimen, where the average grain size calculated using line intercept method
(a total of 210 intercepts) was 7.9 µm and (b) a polished surface of a 95.4%
dense HA specimen, where uniformly distributed spherical or quasi spherical
pores with a few interconnected or entrapped pores were observed. The
diameters of the surface-breaking pores are less than 3 µm………………...128
Figure 8.2 (a) The average initial radial crack length as a function of Vickers
indentation loads. The error bars represent the standard deviations. The
collected data were fit to equation (8). The coefficient of determination R2 is
0.997. (b) The average initial lateral crack length as a function of Vickers
indentation loads. The error bars represent the standard deviations. The
collected data were fit to equation (9). The coefficient of determination R2 is
0.998……………………………………………………………………………….132
Figure 8.3 The average radial crack length as a function of time, normalized
with respect to the initial radial crack length at each load. The normalized
values were then plotted versus time with a common unit value at time zero.
The error bars represent the standard deviation. The collected data were fit to
equation (11). The coefficient of determination R2 for the 0.98 N, 1.96 N, 2.94
N, and 4.91 N loads were 0.934, 0.931, 0.987, and 0.992, respectively……134
Figure 8.4 The time constant τ obtained from the least-square fit of equation
(11) to the average radial crack length versus time data for the 0.98 N, 1.96 N,
2.94 N, and 4.91 N loads. The error bars represent the standard deviation from
each curve fitting………………………………………………………………….136
Figure 8.5 A schematic of the fully developed indentation crack system, where
cR is the half radial crack length and cL is the lateral crack size.....................137
Figure 8.6 The relative frequency of lateral cracks observed intersecting with
free surface from 15 indentations at each of the five Vickers indentation loads
(0.98 N, 1.96 N, 2.94 N, 4.91 N, and 9.81 N)…..………………………………138
L
c 0 ) over half initial
Figure 8.7 The average ratio of initial lateral crack length (
R

radial crack length ( c0 ) (

), and the average ratio of saturated lateral crack

L

R

length ( c S ) over half saturated radial crack length ( cS ) ( ) as a function of
Vickers indentation loads. The error bars represent the standard
deviations.………………………………………………………………………....139

xiv

Figure B-1 Schematic of atomic absorption spectrophotometer structure….164
Figure C-1 The logarithm of volume change increases linearly with the
logarithm of time. The data were fit to equation (3). The coefficient of
determination R2 = 0.98………………………………………………………….169

xv

CHAPTER 1
INTRODUCTION

The vertebrate skeletal system experiences cyclic forces that are
tensile, compressive and/or shear in nature during daily activities such as
walking, running and jumping, which could lead to the formation and
accumulation of microcracks in bone [Hazenberg et al. 2009]. Bone with
tolerable minor damage can be repaired and renewed through the remodeling
process in vivo which involves both bone resorption by osteoclasts (OCs) and
bone formation by osteoblasts (OBs) [Hadjidakis and Androulakis 2006]. Since
bone densification was linked to the presence of microcracks in racing horses
and/or greyhounds [Burr et al. 1985, Muir et al. 1999], we have hypothesized
that microcracks lead to enhanced OB cell maturation. Understanding how
microcracking affects OB cells could provide insight into fracture healing
mechanism(s) as well as change the design parameters for the development
of orthopedic scaffolds that promote faster bone healing.
Hydroxyapatite (HA or Ca10(PO4)6(OH)2) comprises two-thirds of the
inorganic component of physiological bone and is therefore an ideal substrate
material to assess the effect of microcracks on bone healing by examining OB
maturation [Park and Lakes 2007]. In this study, a 7Χ7 grid of microcracks
were introduced onto an HA substrate using Vickers indentation. At set time
intervals [Shu et al. 2003], OB attachment, proliferation and maturation were
evaluated using the appropriate assays along with CLSM (confocal laser

1

scanning microscopy) characterization. The response of OBs to microcracks
was investigated by comparing cell behavior (attachment, alignment, spatial
distribution, proliferation and maturation) on microcracked and
non-microcracked HA specimens.
Further, the calcium ions released from both non-cracked and cracked
HA surfaces were examined using atomic absorption spectroscopy (AAS)
based on the work of Duchyne et al. [1993], who found that changes in calcium
concentration in the microenvironment led to changes in OB response. In order
to determine if the presence of microcracks affects calcium ion release (HA
surface dissolution), non-cracked and cracked HA specimens were immersed
in distilled water at 37ºC for different time intervals. The calcium ion
concentrations in distilled water from both groups were measured using AAS.
Another focus of my research is to understand the behavior of cracks
introduced into the HA scaffold using Vickers indentation. HA is brittle in nature
and environmental crack growth has been observed by different researchers
[Benaqqa et al. 2003 and 2004, Barinov et al. 2005].
The slow growth of radial cracks introduced by Vickers indentations in
HA in ambient air was conducted for two purposes. First, slow crack growth
was examined to understand the general slow crack growth phenomenon in
HA, since HA has been widely used in various fields as will be discussed in
Chapter 2, to predict crack propagation in bone, as the propagation of cracks
has been shown to lead to catastrophic bone fracture [Fratzl 2008]. This study

2

examines the slow growth of radial cracks induced by Vickers indentation in
dense HA (94% of theoretical density) during aging in ambient air as a function
of time. We found that there is a load dependence of the radial crack growth
and this is linked to the partitioning of the residual strain energy by the lateral
crack growth.

3

REFERENCES

4

REFERENCES
[Barinov et al. 2005] Barinov SM, Fadeeva IV, Fateeva LV, and Tumanov SV.
Delayed fatigue of hydroxy- and fluoro- hydroxyapatite ceramics in simulated
body fluid. Key Eng Mater 2005; 290: 366-369.
[Benaqqa et al. 2005] Benaqqa C, Chevalier J, Saadaoui M, and Fantozzi G.
Investigation crack growth process in dense hydroxyapatite using the double
torsion method. Fract Mech Ceram 2005;14: 387-397.
[Burr et al. 1985] Burr DB, Martin RB, Schaffler MB, and Radin EL. Bone
remodeling in response to fatigue microdamage. J Biomech, 1985;18:
189-200.
[Ducheyne et al. 1993] Ducheyne P, Radin S, and King L. The effect of calcium
phosphate ceramic composition and structure on in vitro behavior. I.
Dissolusion. J Biomed Mater Res 1993; 27: 25-34.
[Fratzl 2008] Fratzl P. When the cracks begin to show. Nat Mater 2008; 7:
610-612.
[Hadjidakis and Androulakis 2006] Hadjidakis DJ and Androulakis II. Bone
remodeling. Ann NY Acad Sci 2006;1092: 385-396.
[Hazenberg et al. 2009] Hazenberg JG, Hentunen TA, Heino TJ, Kurata K, Lee
TC, and Taylor D. Microdamage detection and repair in bone: Fracture
mechanics, histology, cell biology. Technol Health Care 2009; 17: 67-75.
[Muir et al. 1999] Muir P, Johnson KA, and Ruaux-Mason CP. In vivo matrix
microdamage in a naturally occurring canine fatigue fracture. Bone 1999; 25:
571-576.
[Park and Lakes 2007] Park JB and Lakes RS. (2007). Biomaterials: An
Introduction. Madison: Springer.
[Shu et al. 2003] Shu R, McMullen R, Baumann MJ, and McCabe LR.
Hydroxyapatite accelerates differentiation and suppress growth of MC3T3-E1
osteoblasts. J Biomed Mater Res A 2003; 67: 1196-1204.

5

CHAPTER 2
BACKGROUND

THE COMPOSITION AND STRUCTURE OF BONE
Bone is the major calcified tissue in vertebrates and provides
mechanical support to muscle attachment as well as protection for vulnerable
internal organs. Bone is considered as a composite material consisting of
approximately 33.3% organic and 66.7% inorganic components as shown in
Table 2.1 [Gray 2008]. The exact proportion of each component in bone may
vary as a function of bone type, and for the same bone type, the composition
can vary with age, gender, species. The organic matrix provides traction and
torsion tolerance and the inorganic mineral providing rigidity and compressive
strength [Park and Lakes 2007].
Table 2.1 Chemical compositions of bone measured by Berzelius [Gray 2008]

Chemical Composition

33.30
51.04

Carbonate of Lime

11.30

Fluoride of Calcium

2.00

Phosphate of Magnesia

1.16

Soda and Chloride of Sodium

Inorganic

Gelatine and Blood-vessels
Phosphate of Lime

Organic Matter

Relative Proportion of Bone Constituents (%)

1.20

Total

100.00

6

The main component of the organic matrix is type I collagen, which
provides a backbone for bone mineral crystal deposition. When the collagen
molecules change due to genetic abnormality, such as for the case of brittle
bone disease, the bone mineral crystals become smaller and may deposit
outside the collagen fibrils [Vetter et al. 1991, Traub et al. 1994]. While
collagen provides the basis for bone mineralization, collagen itself does not
initiate or facilitate bone mineralization [Mergenhagen et al. 1960]. Instead of
collagen, non-collagenous proteins regulates the bone matrix mineralization
[Termine et al. 1981, Endo and Glimcher 1989].
The mineral component of bone shows chemical similarity with the
mineral hydroxyapatite (HA or Ca10(PO4)6(OH)2). The Ca:P ratio in HA is 1.67:1,
but in the analysis of bone mineral, this ratio varies from 1.3:1 to 1.9:1
[Gokhale et al. 2001]. The mineral component of bone results from bone
mineralization, which is a process involving crystal nucleation and growth that
is regulated by matrix proteins. The crystal nuclei form through homogeneous
and /or heterogeneous nucleation. In homogeneous nucleation, ions in the
solution collide until reaching a critical size where they form a stable critical
nucleus. The crystal then grows as ions are added to the nucleus. At higher ion
concentrations, the accumulation of ions and/or ion clusters may favor more
nucleation. However, homogeneous nucleation is rare, requiring a much higher
energy when compared to heterogeneous nucleation. Heterogeneous
nucleation occurs on already present foreign surface where the

7

non-collagenous matrix proteins serve as nucleators and lead to discrete
mineral deposition along the collagen fibers [Gower 2011]. After the initial
crystal formation, the crystals may grow through agglomeration and
lengthening [Mitchell et al. 2001, Falini et al. 2001].
The structure of bone, when examined at the microscopic scale, has
two forms: woven and lamellar. Woven bone is composed of disoriented
collagen fibers and has isotropic mechanical properties. In contrast, lamellar
bone has oriented collagen fibers which result in anisotropic mechanical
properties. Depending on the structural organization of the woven and lamellar
bone, two bone morphologies can form: cortical (dense and/or compact) and
trabecular (spongy and/or cancellous) (Figure 2.1).

Figure 2.1 Longitude femur section showing trabecular and cortical bone. Photo taken by Paul
Crompton [2011] at University of Wales College of Medicine. For interpretation of the
references to color in this and all other figures, the reader is referred to the electronic version
of this dissertation.

8

Load bearing is the major function of bone in the body, mechanical
properties are thus of great importance in characterizing bone. The
mechanical properties of bones, such as modulus of elasticity, toughness,
tensile strength, and failure strain vary with shape, mineral content, humidity of
the environment, and mechanical testing techniques, etc. [Park and Lakes
2007]. A comparison between the Young’s modulus (GPa) and tensile strength
(MPa) of physiological bone and several commonly used bone implant
materials (longitude testing direction) is shown in Table 2.2 [Park and Lakes
2007, Carew et al. 2004].
Table 2.2 Comparison of the mechanical properties of long bone and common biomaterials
used for bone replacement [Park and Lakes 2007, Carew et al. 2004]

Materials

Tensile Strength (MPa)

Young’s Modulus (GPa)

Femur (Long Bone)

121

17.2

Al2O3

1000 to 10,000

350

735

225

Co-Cr Alloy
316 S.S.

a

b

600 (1000)

c

210

PMMA

35 to 50

3.0

Polyethylene

23 to 40

0.6 to 1.8

a 28% Cr, 2% Ni, 7% Mo, 0.3% C (max), Co balance.
b Stainless steel, 18% Cr, 14% Ni, 2 to 4% Mo, 0.03 C (max), Fe balance.
c Values in parentheses are for the cold-worked state.

MICROCRACKING IN BONE
Bone microdamage occurs in the form of microcracks in humans

9

[Blickenstaff 1966, Schaffler et al. 1995, Lee et al. 2000], thoroughbred racing
horses [Stepnik et al. 2004, Da Costa Gomez et al. 2004] and greyhounds
[Johnson et al. 2001, Muir et al. 1999] following repetitive physical activity. For
example, while the strain levels in human bone during walking reach ε = 3 x
-4

10 to 8 x 10

-4

-4

,

-3

and during running reach ε = 8 x 10 to 1.2 x 10 , this is less

than the threshold failure strain in a single cycle. However, the repetitive nature
of these activities leads to an accumulation of microdamage [Lanyon et al.
1975, Burr et al. 1996]. Unless such activity ceases or declines dramatically,
this microdamage can coalesce into macrocracks, leading to catastrophic
fracture [Blickenstaff 1966, Schaffler et al. 1989 and 1990].
The connection between bone microcracks and repetitive physical
activity was first postulated by Frost [1960], who used Fuchsin staining to
detect their presence. More recently, microcracks have been identified in bone
using increasingly sophisticated techniques including optical and confocal
laser scanning microscopy (CLSM) using Fuchsin haematoxylin [Schaffler et al.
1995, Lee et al. 2000, Da Costa Gomez et al. 2004, Muir et al. 1999] and eosin
[Johnson et al. 2001] and fluorescent staining [Zioupos and Currey 1994],
scanning electron microscopy (SEM) [Stepnik et al. 2004] and radiography
[Blickenstaff 1966].
In most cases, if the physical activity that causes damage is reduced,
catastrophic failure can be prevented because bone has the ability to
dynamically remodel following the onset of microdamage. Osteoclasts (OCs)

10

are specialized bone cells that resorb bone, while osteoblasts (OBs) generate
new bone in the vicinity of the microcracks [Burr 2002]. OC and OB activities
are increased when the syncytium, adjacent to areas of bone microdamage,
signals for remodeling to begin through increased osteocyte apoptosis. The
details of bone remodeling and the function of osteoblast will be reviewed in
the following section. This coupling between remodeling and microcracking
may paradoxically result in a lower incidence of initial catastrophic fracture
because of the ability of the microcracks to dissipate energy through crack
formation, which in turn signals bone healing.
Besides bone, microcracking in HA and other brittle materials is also
commonly observed during the release of residual stresses [Withers and
Bhadshia 2001, Marshall et al. 1983], which can be introduced into the ceramic
body during fabrication, handling, and use due to mismatch in material
properties, such as elasticity, plasticity, and thermal expansion coefficient
[Withers and Bhadshia 2001 and 2002]. The details of residual stress and
microcracking will be discussed in a later section. On one hand, the existence
of microcracks can deteriorate mechanical properties such as the Young’s
modulus and the fracture strength [Case 2002]; on the other hand, microcracks
can enhance the fracture toughness of brittle ceramics by redistributing the
stress or releasing the residual stress at the major crack tip [Shum and
Hutchinson 1990], thus preventing catastrophic fracture.

11

BONE REMODELING AND OSTEOBLAST FUNCTION
Bone continues to grow from its inception until skeletal maturity. It
responds to stresses, healing following fatigue and/or fracture through a
dynamic process called bone remodeling that occurs throughout our lifetime
[Hadjidakis and Androulakis 2006]. During bone remodeling, osteoclasts
remove bone at the bone surface and osteoblasts form new bone matrix in the
cavities left from the bone resorption. Bone mineralization begins with calcium
and phosphate precipitation following by crystallization, forming the
hydroxyapatite phase [Hadjidakis and Androulakis 2006]. Osteoblasts play an
important role in bone mineralization by promoting apatite crystal formation
and growth on the extracellular matrix (ECM) [Hessel et al. 2002]. Thus the
understanding of osteoblast function is essential for successful bone tissue
engineering.
Mature osteoblasts are highly secretory cells, and the secretory
products include mainly type I collagen and other non-collagenous proteins
such as bone sialoprotein, osteocalcin, and osteopotin [Marks and Odgren
2002]. It is hypothesized that osteoblast facilitate mineralization by producing
matrix vesicles, which provides microenvironment for hydroxyapatite
crystallization [Boskey 1998].
The interaction of osteoblasts with the substrate surface includes
attachment/adhesion, proliferation, and finally maturation phases [Anselme
2000]. Adhesion, being the first phase of cell/substrate interaction, plays an

12

important role in determining the subsequent proliferation and differentiation
stages. The adhesion of osteoblasts involves various kinds of biological
proteins, such as extracellular matrix (ECM) proteins, membrane proteins and
cytoskeleton proteins [Anselme 2000, Goldstein 2006].
Before interacting with the substrate surface, osteoblasts will first
secrete ECM proteins, which then adsorb to the substrate surface. After that,
proteins on the cell membrane then combine with the adsorbed ECM proteins,
thereby realizing the linkage to the substrate surface [Hiortso and Roos 1994].
Among all of the ECM proteins, collagen, fibronectin, vitronectin, and laminin
are known to be the proteins that influence anchorage-cell adhesions
[Cristenson et al. 2007]. The integrin family on the OB cell membrane is in
charge of cell/substrate adhesion [Anselme 2000, Goldstein 2006]. These
integrins combine with ECM proteins which contain the specific
arginine-glycine-aspartic (RGD) peptide sequence adsorbed on the substrate
surface [Grzesik and Robey 1994, Balasundaram et al. 2006].
Osteoblasts could also migrate on the substrate surface from dynamic
interactions with surrounding cells and the substrate. This involves the
formation and fixation of lamellipodium on their leading edge, generation of
energy required for movement and finally, the release of adherence at the rear
[Anselme 2000]. After adhesion, osteoblasts proliferate through mitosis and
secrete ECM matrix for later mineralization, which occurs in the last phase of
differentiation.

13

The differentiation of mature osteoblasts in vitro is a multi-stage
process, which is characterized by different phenotypes. The interaction
between biomaterials and osteoblasts can thus be assessed by examining the
characteristic phenotypical gene expressions, such as Runx2, collagen I (COL
I), alkaline phosphatase (AP), osteocalcin (OC), etc. [Aubin 2001]. Runx2 is
the transcription factor that regulates the differentiation of pluripotent
mesenchymal progenitor cells into osteoblast lineage. COL I, alkaline
phosphatase and osteocalcin are three characteristic genes that regulate the
development of osteoblast matrix secretion, differentiation and mineralization
[Aubin 2001].

BIOMATEIRAL SURFACE PROPERTIES AFFECTING OSTEOBLASTS
The effect of a biomaterial on osteoblast response is largely
dependent upon the surface characteristics of the substrate. Rather than being
a passive anchorage support for osteoblasts, the substrate surface can
interact with the cells as reflected by differential cell adhesion, alignment,
proliferation, and maturation on different biomaterial surfaces [Grinnell 1978].
The surface characteristics of a substrate material include surface chemistry,
surface topography, surface roughness, surface area, surface hydrophobicity,
and/or hydrophilicity, as well as the surface energy.
The surface chemistry primarily depends on the chemical composition
of the surface and may significantly differ from the bulk chemistry. By modifying
the surface chemical composition, the cell/substrate interaction could be

14

influenced [Romand et al. 1995, Alves et al. 2008, Hench and Ethridge 1982].
For example, using self-assembling methods, several model studies, in which
the surfaces of materials were chemically modeled, showed that terminal
amine and carboxylic acid groups could improve adhesion while surfaces with
polyethylene glycol subunits inhibited cell adhesion [Tegoulia and Cooper
2000].
The surface topography of materials has been shown to restrict sites
of cell adhesion and dictate cell orientation [Wiemann et al. 2007]. A
century-old study found that the substrate topography of spider webs dictated
the orientation of adherent cells [Harrison 1912]. In a study carried out Martin
Wiemann et al. [2007] revealed that osteoblast orientation was influenced on
the micro scale, showing that osteoblast-like cells could be contact-guided by
parallel grooves. Other studies found that grooves of ~0.5 microns deep and
4~20 microns wide were ideal for cell alignment [Ismail et al. 2007].
The hydrophobicity of a material surface can be characterized by the
contact angle (θ) of a water drop on the surface (Figure 2.2) [Hench and
Ethridge 1982]. Generally speaking, water drop has a higher contact angle on
a hydrophobic surface, and a smaller angle on a hydrophilic surface. Studies
on 13 different kinds of polymers demonstrated significantly larger cell
spreading on hydrophilic surfaces compared with hydrophobic surfaces
[Schakenraad et al. 1986]. Polar chemical functional groups (hydrophilic) were
found to improve cell adhesion while non-polar ones (hydrophobic) hinder cell

15

adhesion [Tegoulia and Cooper 2000, Scotchford et al. 1998]. MacDonald et al.
[2004] applied thermal and chemical methods to modify the surface properties
of a Ti-6Al-4V alloy in a way that the hydrophobicity of the alloy surfaces was
artificially altered by changing the surface area and roughness. Surfaces with a
larger surface area and roughness were found to be more hydrophilic. Both a
significant increase in fibronectin and MG63 cell attachment were observed on
more hydrophilic surfaces [MacDonald et al. 2004].
Surface bonds (external surfaces and grain boundaries) are different
from the bulk in that the atomic bonds at surfaces are unsaturated [Park and
Lakes 2007, Hench and Ethridge 1982]. From a thermodynamic point of view,
the unsaturated surface atoms are at a higher free energy (G) [Hench and
Ethridge 1982]. When two different phases are in contact, they tend to
minimize their interfacial energy which corresponds to a minimum free energy
of the system [Hillert 2008]. In the case of a free surface (or external surface),
the free energy could be calculated from the contact angle (θ) of a specific
liquid drop on the surface (Figure 2.2).

Figure 2.2 Illustration of the surface contact angle of water drop on an ideal solid surface
surrounded by gas [Hench and Ethridge 1982].

The contact angle is defined by analyzing the force on a liquid drop
when it was placed on a solid surface and surrounded by gas as shown in

16

equation 1 (apply to ideal surface) [Hench and Ethridge 1982]. The three
phases, solid (s), liquid (l), and gas (g) are immiscible.

γ SL = γ SL + γ LG cos θ

(1)

where γSG is the interfacial tension between solid and gas phases; γSL is the
interfacial tension between solid and liquid phase; γLG is the interfacial tension
between liquid and gas phases; θ is the contact angle shown in Figure 2.2.
The increase in cell adhesion corresponds to an increase in surface area and
surface energy [He et al. 2004, Webster and Ejiofor 2004, Webster et al.
1999].

HYDROXYAPATITE APPLICATIONS
The presence of HA in natural teeth and bone makes it a good
candidate biomaterial for hard tissue substitution [Park and Lakes 2007]. The
HA surface can adsorb functional biomolecules, and the change of surface
electronic state due to biomolecule adsorption enables HA thin films to be used
as biosensors [Masanobu et al. 2005]. HA coatings on metal implants promote
earlier and stronger bonding between the host bone and the implant, as well as
increase uniform bone growth at the bone-implant interface [Furlong and
Osborn 1991, Geesink et al. 1988]. Porous ceramic implants based on HA
have also been designed for space filling osteogenesis [Dong et al. 2001,
Damien et al. 2003]. Dense HA, fabricated using spark plasma sintering,
showed an improvement in the bone-like apatite crystal growth [Nakahira et al.
2002]. Fang et al. [1995] fabricated transparent HA, using microwave sintering,

17

for use as observation windows for percutaneous devices used by Aoki et al.
[1987].
The use of HA as a catalyst support has also been extensively
explored. Mori et al. [2003] created a novel heterogeneous Lewis acid catalyst
for Diels-Alder and Aldol reactions utilizing HA for the hybrid-catalyst, which
presented high activity for useful carbon-carbon bond forming reactions as well
as high reusability. Mori et al. [2004] in a later study, created an HA supported
palladium nano-cluster for selective alcohol oxidation using molecular oxygen,
which could effectively promote alcohol oxidation under atmospheric oxygen
pressures. Venugopal and Scurrell [2003] used HA as a support for gold
catalyst which was exceedingly active for water gas shift reaction at low
temperatures.
Nagai and Nishino [1988] proposed the use of porous HA for a CO2
sensor based on the changes in electrical conductivity induced in HA by CO2.
One year later, Owada et al. [1989] found that the logarithm of the electrical
conductivity of their yttrium substituted calcium HA sensor decreased linearly,
as the relative humidity increased from 30% to 65%, suggesting the application
of HA as a humidity sensor. Measurements of the dielectric and current-voltage
properties of an HA thin film in the frequency range from 1 KHz to 1MHz
showed HA may be used as an insulating material for electronic circuits and as
dielectric layers in microwave applications for biomedical devices [Hontsu et al.
1997].

18

HA has also been employed in the removal of heavy metals from the
environment. Raicevic et al. [2004] demonstrated theoretically and
experimentally that heavy metals in polluted soils could be immobilized by
addition of HA to soils. HA organofunctionalized with silylating agents
(H3CO)3SiR also showed the ability to remove heavy cations from aqueous
solution [Silva et al. 2006].

RESIDUAL STRESS AND MICROCRACKING
Residual stress can be introduced from the mismatch of material
properties such as elasticity, plasticity, and thermal expansion coefficient within
a system of interest [Bhadeshia 2002]. Residual stress can be classified into
Type I (macroscopic), Type II (microscopic) and Type III (atomic scale)
stresses according to the dimension it exhibits at equilibrium with the
surroundings [Withers and Bhadshia 2001]. Common examples of Type I
stresses are those that arise from a misfit of components in an assembly,
different thermal stresses experienced by different parts, and non-uniform
plastic deformation in machining processes such as grinding [Withers and
Bhadshia 2001, Hoshide et al. 2001]. Common examples of microscopic
residual stresses are the stresses that exist between different phases within a
composite and/or resulting from phase transformation [Lawn et al. 1993].
Residual stresses that arise from point defects and/or dislocations are
generally balances at atomic scales [Withers and Bhadshia 2001].
As residual stresses can develop easily and have an important

19

influence on a materials performances and lifetime, the nature, distribution and
role of residual stress in initiating and driving crack growth in brittle materials
has been extensively studied in different systems.
Fu and Evans [1981] investigated the influence of grain size on the
formation of secondary cracks in the vicinity of a primary crack in single phase
polycrystals by calculating residual stress introduced by thermal expansion
anisotropy. By considering a microstructure configuration that renders the
maximum compressive stress along the primary crack opening direction as
well as the maximum opening tensile stress at the secondary crack initiation
sites, Fu and Evans [1981] calculated the critical grain size (lc) for the initiation
of secondary cracks, and found that the increase in fracture toughness
between lc and lcs (critical grain size for spontaneous cracking) corresponded
with experimental fracture energy of Al2O3, Nb2O5 and TiO2 as a function of
grain size.
When examining toughness for two-phase ceramics, Lawn et al. [1993]
considered the insertion of compressed second-phase particles in the matrix
and divided the bridging stress into two regions according to the crack opening
scale within the matrix. They found a transitional crack length that
corresponded to a minimum toughness and a mechanism change of how the
second phase particles affected matrix microcracking. Below that transitional
crack length, compressed second-phase particles provide tensile stress to the
surrounding matrix for the initiation of cracks, while above the transitional crack

20

length, the second-phase particles act as frictional barriers for grain sliding
[Lawn et al. 1993]. The model proposed by Lawn et al. [1993] was well
supported by the data from Al2O3/Al2TiO5 composite.
Cao et al. [1988] examined the nature and distribution of residual
stresses in systems consisting of two brittle ceramics bonded with a ductile
metallic strip during cooling. They found that the maximum residual tensile
stresses at the ceramic/metal interface. The residual tensile stresses were
determined by the elastic mismatch resulted from differential thermal
expansion coefficient (αmetal > αceramic) during cooling process. The elastic
mismatch gave rises of cracking when considering an elastic field. The exact
cracking or fracture resistance sites at the ceramic/metal interface, or within
the brittle ceramic, varies with the thermal mismatch between the metal and
the ceramic, the yield strength and the thickness of the metal layer. The
prediction of cracking nonetheless relied on the interpretation of the intensity
and distribution of the residual stress [Cao et al. 1988].
This demonstrates the importance of analyzing residual stress in
determining microcracking in brittle materials, since materials tend to release
residual stresses to get to a lower energy state. Microcracking is what
accompanies residual stress release observed in brittle materials [Withers
2001 and Marshall 1982].
Available techniques that provide quantitative or qualitative information
about residual stress were divided into destructive and non-destructive tests

21

[James and Lu 1996]. Destructive methods are mostly mechanical approaches
such as hole drilling, ring core, layer removal, and sectioning, where a change
in stresses between the new stress state and the old residual stress state was
calculated [James and Lu 1996]. Non-destructive methods such as X-ray
diffraction and neutron diffraction generally are based on the influence of
residual stress on the materials’ physical properties [James and Lu 1996].
Vickers indentation can itself be an approach to investigate residual
stresses that are introduced through grinding and machining damage [Hoshide
et al. 2001, Marshall et al. 1982]. Raman luminescence microscopy was used
by Banini et al. [2001] in evaluating the residual component under Vickers
indentation impression and their direct measurement of residual stress field
was shown in accordance with predictions from theoretical analytical models.

VICKERS MICRO-INDENTATION
Vickers micro-indentation of brittle solids provides useful information
for evaluating machining damage [Marshall et al. 1982] and grinding [Hoshide
et al. 2001] as well as estimating residual stress [Jang 2009]. It is thus
necessary to understand the nature and distribution of stresses in the vicinity
of Vickers indentation and the cracking systems involved in the indentation
process in order to use the Vickers indentation technique in our studies.
Vickers indentation with an included angle of 136° coul d be described
by an elastic/plastic deformation mode [Chiang et al. 1982]. In a
comprehensive review on indentation fracture by Lawn and Wilshaw [1975],

22

the simplified model of stress field about Vickers indentations is illustrated in
Figure 2.3. The material in contact with the indenter was assumed to form a
hydrostatic core which pushed the surrounding material and resulted in the
formation of a plastic zone, both of which were assumed to exhibit a spherical
symmetry, and beyond the plastic zone, an elastic matrix [Lawn and Wilshaw
1975]. According to this model, a residual stress field could be developed from
the formation of permanent deformation zone during the loading process
without recovering after unloading [Lawn and Wilshaw 1975].

Figure 2.3 Elastic/plastic indention model of spherical symmetry with a “hydrostatic core” near
contact region with indenter, “plastic deformation zone” around the “hydrostatic core”, and
“elastic matrix” [Lawn and Wilshaw 1975].

Lawn et al. [1980] divided the stress field into a reversible elastic
component and an irreversible residual component illustrated in Figure 2.4.
Marshall and Lawn [1979] provided a more detailed explanation of the
combination of symmetric tensile stress field and asymmetric compressive
stress field in the formation of elastic component during loading. Chiang et al.
[1981] described the plastic zone volume ∆V using maximum load P and the

23

indentation volume V.

Figure 2.4 (A) Elastic/plastic combination at maximum load P which is a summation of (B)
reversible elastic component at load P and (C) irreversible residual component after unloading
[Lawn 1980].

Stress analysis of both the elastic and plastic zone could provide
useful information for the formation and evolution of cracks during the loading
and unloading cycles of Vickers indentation [Chiang et al. 1981]. By analyzing
the stress field at the boundary between the plastic deformation zone and the
elastic matrix, Chiang et al. [1981] concluded that the initiation of cracks close
to the boundary was due to a maximized tension, a diminishing of tension in
the elastic matrix, and the compressive nature of the residual plastic
deformation zone.

24

During a complete cycle of loading and unloading in Vickers
indentation, median, radial, and lateral cracks may form as illustrated in Figure
2.5 [Chiang et al. 1981].

Figure 2.5 Elastic/plastic sharp contact indentation generates median, radial and lateral cracks
[Chiang et al. 1981].

Lawn et al. [1980] and Marshall et al. [1982] examined propagation of
both median/radial and lateral crack systems by analyzing the role of the
elastic and the residual components of the stress field during indentation. The
two crack systems were classified according to their orientations with respect
to the loading plane, where the median/radial cracks were found to lay within
the loading plane while the lateral cracks in planes parallel to the surface
[Lawn et al. 1980].
As depicted by Figure 2.5, cracking occurs mostly within the elastic
field outside the plastic deformation zone, and the intensity of the elastic field

25

was maximized at maximum loading P and recovered during the removal of
the indenter [Chiang et al. 1981, Lawn et al. 1980]. The irreversible residual
plastic deformation zone was created during loading and stayed below the
indentation impression after unloading as a compressed semi-sphere within
the elastic matrix. Thus, during loading the propagation of the median crack
was enhanced by the downward tensile stress and the propagation of the
radial crack was prevented by the asymmetric compressive stress within the
elastic field (Figure 2.4B). Upon unloading, the residual plastic zone remained
to influence the crack evolution, particularly to drive the radial crack growth
[Lawn et al. 1980].
Both the elastic and residual components were incorporated in the
calculation of fracture toughness, denoted by Kc, during loading and unloading,
and compared with experimental observations by Lawn et al. [1980]. They
concluded that the residual plastic deformation zone played a dominant role in
determining the final crack configuration, which was characterized by an
equilibrium crack length upon unloading in an inert ambient environment
especially at a lower H/E (hardness to Young’s modulus) ratio. The
relationship between equilibrium radial crack length cR and maximum
indentation load P is described by equation 2,
R
c R = {§r (cotψ ) 2 / 3 [( E / H )1/ 2 / K C ]}2 / 3 P 2 / 3

where

R
§r

is a constant,

ψ

(2)

is the half angle for Vickers indentation, and E,

H, KC are Youngs’ modulus, hardness, and fracture toughness, respectively. E,

26

H, and KC can be considered invariant for a system at equilibrium with its
surroundings [Lawn et al. 1980].
Analysis on the evolution of a lateral crack system based on the
summation stress field of an elastic component and a residual component
(illustrated by Figure 2.6) also showed that the residual plastic deformation
zone provided the driving force for lateral crack propagation. This is similar to
the case of radial crack propagation except that the relationship between the
L

lateral crack length c and the maximum indentation load P was described by
equation 3 [Marshall et al. 1982]. Observations from experimental
measurements in various ceramics showed that lateral cracks mostly resided
at the plastic deformation zone radius [Marshall 1982]. Similar to radial crack
propagation, the dominant role of residual component was also magnified at
lower H/E ratio [Marshall et al. 1982].

cL = {(ζ L / A1/ 2 )(cotψ )5/ 6[(E / H )3/ 4 / KC H 1/ 4 ]}1/ 2 P5/ 8 (3)
where

ζL

and A are constants [Marshall et al. 1982].

27

Figure 2.6 Residual component of stress field below indentation which remains upon
unloading and lateral crack of distance h below the free surface. The dashed lines depict the
median/radial crack system [Marshall et al. 1982].

The fact that both radial and lateral cracks evolve upon unloading as
discussed above [Lawn et al. 1980, Marshall et al. 1982] indicates that the
energy stored in the residual plastic deformation zone has two outlets, which
may add complexity in interpreting the slow growth of radial cracks based on
the relaxation of residual stresses. It is necessary to measure the residual
stresses in the compressive deformation zone and/or at the tensile crack tip
arises in order to understand the slow growth behavior of indentation-induced
radial cracks in hydroxyapatite. The methods for measuring this residual stress
were discussed in the previous section.
For most ceramics and/or glasses, a general trend of diminishing
strength with time was observed in ambient air, the molecular mechanism of
which was investigated by Michalske et al. [1983] considered a chemical
concerted reaction driven by the strain energy at the crack tip. However, the

28

environment effect on slow crack growth in HA is not addressed in the current
study.

29

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30

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38

CHAPTER 3
CELL CULTURING PROTOCOLS

Basic cell culturing steps include: thawing, feeding, splitting, counting,
and freezing. The MC3T3-E1 cell line used in this study was from the
McCabe's lab on campus. In the current study, the cell passage number was
21~23 to guarantee consistent and comparable cell behavior between control
and experimental groups. The passage number reflects the age of cells, in
other words, the subculture time of the cells. With the increase in passage
number, the cell population doubling time increases.

THAWING
The cells are stored in 1.8 ml cryogenic vials in liquid nitrogen, the
boiling temperature of which is 77 K (-196° or -321° F) at atmospheric
C
pressure. The handling of frozen cells thus requires the use of temperature
resistant gloves to avoid frost damage to the skin.
The rule of thumb for cell preservation is fast thaw (< 5 minutes) and
slow freeze. Leaving cells in cryogenic vials for long times leads to cell death.
Cells can be thawed either by rubbing between warm hands or placing in a
warm water bath. After thawing, the cells should be distributed evenly in 3-5
culture dishes with warm complete media (CM). The CM refers to α-MEM
(alpha minimum essential media, Invitrogen, Carlsbad, CA) supplemented with
10% FBS (fetal bovine serum, Atlanta Biologicals, Lawrenceville, GA).

39

Depending on the passage number of the cells and the actual experimental
design, the number of culture dishes for thawing may vary. The cell plates
should be rocked slowly from side to side, and front to back, for an even
distribution of cells across the plate and to avoid piling up at specific spots. The
plates should not be rotated as the cells could be brought to the plate edges
due to centrifuge force rather than distribute uniformly.

FEEDING
After thawing, cells are kept in an incubator (37° 5% CO2 and 95%
C,
air) for 24 hours which allows the cells reattaching to plate surface. Feeding
refers to the process of replacing the complete media. The old media in the
culture dishes were aspirated away using a vacuum system. This step
removes the dead cells that failed to reattach during the thawing step. The
warmed-up complete media is then added to the culture dishes. After feeding,
cells are moved back to the incubator. Depending on the experiment design,
cells are fed every 1 to 3 days.

SPLITTING
Splitting refers to the step during which cells are removed from the
substrate surface either for subculture or for specific studies. Usually, cells are
fed with CM 24 hours prior to splitting. To determine when to split, cells should
be checked on a daily basis. When about 25 cells are visible in the field of view
using the 10x transmitted light microscope, the cells are ready for splitting. If

40

the cells start to fill the field of view and appear to touch each other
(confluency), the cells should not be used for studies, as subcloning may have
already take place, which leads to changes in cell behavior [Bellows et al.
2004].
To split cells, the old media is first aspirated from the culture dishes the
same way as in the feeding step. After removing the media, 0.5%
Trypsin-EDTA (Trypsin-ethylenediaminetetraacetic acid, Invitrogen, Carlsbad,
CA) is added to the plate, enough to cover the surface (e.g. 1 to 2 ml for 100
mm petri dish). This step detaches cells from the plate. For better results, the
plates are rocked from side to side, as well as back and forth. However, this
step should not last for more than 2 minutes as the Trypsin-EDTA could
damage the cells. 1 to 2 ml of complete media is then added to the plates, and
the plate surface is washed several times to gather most of the detached cells.
The cell suspensions are then pipetted into 50 ml centrifuge tubes. The empty
plate is brought to the transmitted light microscope to check if most of the cells
are attached. The above steps are repeated if necessary. The total number of
cells gathered in the suspension is counted using a hemacytometer. After
counting, the cells could be subcultured with lower density in more plates,
used for specific studies, or frozen for future use.

FREEZING
When there are excess cells left from studies, or when the desired
passage number is reached, cells could be frozen for future use. The typical

41

number of cells frozen in a 1.8 ml cryogenic vial is around 1 million. The
preceding freezing steps are similar to splitting, which includes aspirating away
the old media, trypsinizing, washing, and pipetting the cell suspension and
followed by cell counting. After cell counting, the cells are centrifuged at 3000
rpm for 10 minutes. A white colored cell pallet should be visible after separating
the cells from the media. After dumping the waste media from centrifuging, the
cells should be re-suspended in the freezing media, the amount of which is
dependent on the cell number. The freezing media is a mixture of 90%
complete media and 10% DMSO (dimethyl sulfoxane, Sigma Aldrich), which is
a cryoprotectant that protects cells from damage caused by low temperature.
For each cryogenic vial, about 1.5 ml of freezing media is added.
In contrast to thawing, the most important thing to remember is to
freeze slowly. The cryogenic vials are in a -80° freez er overnight and are then
C
moved into the liquid nitrogen tank. If the same vial of cells will be used within
2 weeks, they can also be stored in the -80° freezer. H owever, for longer term
C
storage, cells should be kept in the liquid nitrogen tank.

STERILE HANDLING
All the cell handling described above should be conducted in a
sterilized environment to prevent possible contamination. Sterilization during
cell culture mainly includes the following aspects: First, the biosafety cabinets
should be maintained in a sterile condition at all time. The biosafety cabinets
are where all cell handling takes place. The UV light inside the cabinets should

42

always be on when not in use. Prior to use, the inner surface of the cabinets
should be sprayed with 70% alcohol or isopropanol. The culture dishes,
centrifuge tubes, cryogenic vials, and six-well plates should not be open
outside of the cabinet hood. All the tools that will be used during cell culture
should be sterilized either by autoclave (if applicable) and sprayed with 70%
alcohol or isopropanol before entering the hood. Pipette tips should be
autoclaved before using.
The incubator used for cell culturing should be cleaned and the
removable parts autoclaved. The HEPA filter in the incubator is regularly
replaced according to the HEPA replacement signal approximately every six
months. The water bath in the incubator is filled with autoclaved distilled water.
Supplements of aqua blue and a copper penny is added to help keeping out
bacteria and/or yeast infections.

43

REFERENCES

44

REFERENCES
[Bellows et al. 2004] Bellows CG, Sodek J, Yao KL, Aubin JE. Phenotypic
differences in subclones and long-term cultures of clonally derived rat bone
cell lines.

45

CHAPTER 4
MICROCRACKS INDUCE OSTEOBLAST ALIGNMENT AND ACCELERATE
MATURATION ON HYDROXYAPATITE SCAFFOLDS

ABSTRACT
The response of MC3T3-E1 mouse osteoblasts (OBs) to microcracks
was investigated by comparing cell behavior on microcracked and
non-microcracked hydroxyapatite (HA or Ca10(PO4)6(OH)2) specimens. Four
hours after seeding, OB attachment was significantly greater on the
microcracked HA specimens compared to non-cracked HA specimens
(p<0.05). Confocal laser scanning microscope (CLSM) micrographs taken at
this time demonstrated that the cells were randomly oriented on non-cracked
HA specimens but preferentially aligned in the direction of the microcracks on
the microcracked HA. OB proliferation was not influenced by the presence of
microcracks. In contrast, OB maturation was enhanced on the microcracked
HA, as shown by the significant increase (p<0.05) in alkaline phosphate (AP)
activity and Runx2 and alkaline phosphatase gene expression at 21 days.
CLSM images taken at 21 days indicate that mineral/bone deposition is
concentrated at the indentation site on cracked HA specimens. Our findings
suggest that microcracks induce OB recruitment, matrix synthesis and bone
formation/healing at crack sites.

46

INTRODUCTION AND BACKGROUND
Fatigue fracture is common in greyhounds [Muir et al. 1999], horses
[Estberg et al. 1996] and human athletes, especially runners [Brukner et al.
1996, Burr 1997] due to the repeated, cyclically applied stresses. In an in vivo
study of racing greyhounds, Muir et al. [1999] found linear microcracks in the
fatigue fracture of the central tarsal bone. Microcracking in bone is a common
form of fatigue injury [Muir et al. 1999, Zarrinkalam et al. 2005, Taylor and Lee
1998, O’Brien et al. 2003, Hazenberg et al. 2009] where the tip-to-tip lengths of
the resulting linear microcracks range from approximately 50 to 300 µm [Taylor
and Lee 1998, Schaffler et al. 1989, Burr et al. 1990, Burr and Martin 1993,
Mori and Burr 1993, Lee 1995, Lee et al. 1998].
From the mechanical standpoint, the formation of microcracks in the
vicinity of the fatigue fracture [Muir et al. 1999, Zarrinkalam et al. 2005, Radtke
et al. 2003, Burr et al. 1990] may prevent catastrophic bone failure by
dissipating the strain energy at the advancing crack tip, thereby improving the
overall bone toughness [An et al. 2011, Taylor and Prendergast 1995].
Microcracks also play an important physiological role in triggering bone healing
and/or bone remodeling when the bone is adapting to an externally applied
stress [Burr et al. 1985, Muir et al. 1999, Lee 1995, Martin and Burr 1989,
Martin 1992, Mori and Burr 1993, Prendergast and Taylor 1994, Taylor 1997].
Although fatigue microcracks in bone have been shown to stimulate bone
healing and/or remodeling, stress fractures occur if the microcracks

47

accumulate at a rate faster than the rate of bone repair [O’Brien et al. 2003].
Bone remodeling is an interactive process between osteoclasts (OCs)
and osteoblasts (OBs), where the former resorb existing bone and the latter
form new bone [Hadjidakis and Androulakis 2006, Huiskes et al. 1987, Cowin
and Hegedus 1976, Verborgt et al. 2000]. A desirable bone implant fosters
faster bone formation and thus heals faster. This response is largely
dependent on the interaction between the OBs and the implant substrate
surface [Anselm 2000]. Enhanced in vivo bone remodeling in the vicinity of
microcracks gives rise to our hypothesis that OBs prefer microcracks over
intact, non-cracked HA scaffolds because the OB response to the microcracks
mimics the natural fracture repair cascade events in physiologic bone.
HA, the main inorganic component of bone, is a widely used bone
implant material [Smith et al. 2006a and 2006b, Shu et al. 2003, Hossain et al.
2005]. The interconnections among the microstructural-physical properties and
the biological properties of HA and bone is a critical area of research. In terms
of microstructural-physical properties, our group has examined the porosity
dependence of a broad range of physical properties of HA [Hoepfner and Case
2002 and 2003, Ren et al. 2009, Fan et al. submitted Part I and Part II 2011,
Singh et al. 2005 and 2006] along with microcracking and fracture in HA
[Hoepfner and Case 2004, Fan et al. submitted 2011, Case et al. 2005]. In
terms of the biological properties, the interactions between OBs and HA has
also been investigated, including OB attachment, growth and differentiation

48

[Smith et al. 2006a and 2006b, Shu et al. 2003, Hossain et al. 2005] and gene
expression [Xie et al. 2004].
Our collective understanding of HA and in particular, microcracking in
HA, enables us to investigate the mechanism(s) by which OBs respond to
microcracks in HA bone tissue engineering scaffolds. An improved
understanding of the crack-cell interface, whether a function of the changes in
the localized physical/chemical properties of the scaffold, could in turn lead to
improved bio-functionality of the HA scaffolds and a greater insight into the
mechanism(s) involved in fracture healing.
Early interactions of OBs with substrate surfaces include sequential
attachment/adhesion, growth/proliferation and maturation/differentiation
stages [Anselme 2000]. The attachment/adhesion of OBs, the first stage of
cell/substrate interaction, is the initial step in determining the long-term viability
and function of OBs. Rather than directly interacting with the naked substrate,
cells secrete extracellular matrix (ECM) proteins that are adsorbed by the
substrate surface. The cell attachment/adhesion phase is then achieved by the
interaction of cell membrane proteins with the ECM proteins [Anselm 2000].
The ECM can alter cell shape and alignment through adhesive interactions
with the cell cytoskeleton, which then in turn affects the arrangement of the
ECM by exerting contracting forces [Numaguchi et al. 2003, Ingber and
Folkman 1989, Singhvi et al. 1994, Huang et al. 1998, Parker et al. 2002].
Alterations in cell shape and alignment affect cell growth, motility,

49

differentiation and apoptosis [Ingber 2002]. Thus, knowledge of these
parameters is essential in evaluating cell/substrate interactions.
Cell alignment, cell shape and cell migration, guided by the substrate
surface topography, were called contact guidance by Weiss [Weiss 1941].
Observations of cells guided by surface topography date back to 1912 when
Harrison observed cell growth along the fibers of spider webs [Harrison 1912].
The surface topographies that have been shown to guide cells range in scale
from the nano- (1 to 100 nm) to micro- (0.1 to 100 µm) scale [Curtis and
Wilkinson 1998].
OB alignment is extensively studied by researchers because the
anisotropic mechanical properties of bone are a function of the bone
cell/collagen matrix alignment [Weiner et al. 1999, Ziv et al. 1996, Ascenzi and
Benvenuti 1986]. Alignment of OBs and cell-produced collagen matrix was
observed on anisotropic surface features, mostly parallel ridges and/or
grooves introduced by electron beam/laser/Langmuir-Blodgett lithography at
both the nano- and micro- scale [Lenhert et al. 2005, Zhu et al. 2005, Puckett
et al. 2008, Yang et al. 2008]. In cases where grooves/ridges are introduced by
abrasion [Calzado-Martin et al. 2011], both surface roughness and cracks
have been shown to result [Couto et al. 1994]. However, for Vickers
indentation, the cracking is controlled and localized, producing divots rather
than ridges.
While parallel ridges and/or grooves have been shown to alter the

50

entire substrate surface [Lenhert et al. 2005, Zhu et al. 2005, Puckett et al.
2008, Yang et al. 2008], Vickers indentation introduces a localized
microcracked site (less than 100 µm in radius in this study. Vickers indentation
cracks were thus introduced to HA substrate surfaces to test if OB alignment
may prompt enhanced bone formation at and around the sites of localized
microcracks in bone [Burr and Martin 1993, Mori and Burr 1993, Stafford et al.
1994].
In this chapter, OB attachment, alignment, growth and maturation were
investigated on Vickers indentation microcracked HA to identify cellular
responses to and benefits of introducing microcracks to biomimetic bone
scaffolds.

MATERIALS AND METHODS
HA specimen preparation
Following established procedures, HA powders (Taihei, Osaka, Japan)
with a particle size of 4-6 µm were uniaxially pressed at 28 MPa for one minute
in a 32-mm diameter steel pellet die. The green HA specimens were then
sintered in air at 1360°C for 4 hours. The sintered specimens were then
polished to a 0.5 µm finish using diamond paste to obtain a flat, uniform
surface. Microcracks were introduced to the polished surfaces using Vickers
indentation with a Shimadzu micro-hardness tester at 4.9 N with a loading time
of 5 seconds in ambient air at room temperature. Indents were introduced in a
7×7 grid with a 2 mm interval as shown schematically in Figure 4.1.

51

2a
2c

a

Indentation impression
Top View
b
Radial crack
Lateral crack
Side View
Indentation impression

Plastically deformed zone

b

Figure 4.1 (a) Radial cracks introduced by Vickers indentation at 4.91 N; (b) A 7×7 grid with a 2
mm interval indentation pattern on HA specimens.

HA characterization
The phase purity of HA, both as-received powder and pulverized
powder from sintered HA specimen was determined by X-ray diffraction (XRD)
using Bruker D2 Phaser diffractometer equipped with Cu X-ray radiation
operating at 30 kV, 10 mA and at sweep rates of 0.5° 2θ /min. The sample
placed in a PMMA sample holder was rotated at 5°
/min. The surface
morphology of both cracked and non-cracked HA surfaces were imaged using
scanning electron microscope (SEM) (JEOL-6400V SEM, JEOL Ltd., Japan)

52

and confocal laser scanning microscope (CLSM) (Zeiss LSM 5 Pascal, Carl
Zeiss, Inc., Thornwood, NY).

Cell culture
OB cells were seeded at a density of 11,320/cm2 for the evaluation of
cell attachment and growth. For cell maturation studies cells were seeded at a
concentration of 20,000/cm2. Cells were fed every other day with α-MEM
media supplemented with 10% fetal bovine serum (FBS), 100 units Penicillin
and 100 µg Streptomycin. The media was further supplemented with 2 mM
inorganic phosphate and 2.5 µg/mL ascorbic acid to promote differentiation
when cells reached confluence. Following lab protocols [Shu et al. 2003], cells
were cultured in a humidified atmosphere containing 95% air and 5% CO2 at
37 °C.

OB attachment and growth
For attachment and growth trials, three microcracked and three
non-cracked HA specimens were used per time point. Cell attachment was
evaluated at 1, 2 and 4 hours while cell growth was evaluated at 1, 3 and 5
days. Each experiment was repeated three times. In the cell attachment and
growth studies, cells were fixed and stained with Hoechst 33342, and cell
numbers counted using Cell Profiler. The relative fractions of attachment and
growth were calculated by normalizing the cell density at each time period with
the initial seeding density.

53

OB maturation
Cells were cultured on cracked and non-cracked HA discs for 21 days.
Each experiment contained triplicate HA disks of each condition. To assess the
level of maturation in the culture, staining was carried out to assess
extracellular matrix and mineralization. AP staining was performed by
incubating the OBs for 30 minutes at 37° with 0.5 mg/ ml naphthol AS-MX
C
phosphate disodium salt with 1 mg/mL Fast Red TR salt in a 10.2 M Tris buffer,
pH 8.4. AP quantization was performed by solubilizing the precipitated salt in
100% TCA, diluting 1:10, and reading at 540 nm as previously described
[McCabe et al. 1996].
For molecular analyses of maturation and gene expression, RNA was
isolated from OBs harvested from non-cracked and microcracked HA at 21
days, using Tri Reagent (Molecular Research Center, Inc., Cincinnati, OH).
RNA integrity was assessed by formaldehyde-agarose gel electrophoresis.
cDNA was synthesized by reverse transcription with Superscript II Reverse
Transcriptase Kit and oligo dT(12-18) primers (Invitrogen, Carlsbad, CA) and
amplified by real-time PCR with iQ SYBR Green Supermix (Biorad, Hercules,
CA) and gene-specific primers synthesized by Integrated DNA Technologies
(Coralville, IA). Hypoxanthine guanine phosphoribosyl transferase (HPRT)
mRNA levels do not fluctuate between conditions and were used as an internal
control. Other primers used are previously described [Botolin et al. 2006, Motyl
et al. 2011].

54

CLSM imaging of OBs
OBs on cracked and non-cracked HA specimens were stained with
Rhodamine Phalloidin actin stain and Hoechst nucleus stain at 1, 2 and 4
hours. The OB morphology and spatial distribution were imaged using CLSM
(Olympus FluoView, Tokyo, Japan). In order to view the cell orientation in all
directions with respect to the center of the microcracked region, the fluorescent
micrographs of microcracked HA specimens were taken in a way such that the
microcracked region was close to the center of the field of view. At four hours,
a total of 30 micrographs were collected for both the control (non-cracked) and
the experimental (cracked groups), with at least 500 cells analyzed per
condition.
Xylenol Orange powder (Sigma-Aldrich Co., St. Louis, MO) was
dissolved in distilled water to make a 20 mM stock solution which was added to
differential media for detecting calcium formation [Wang et al. 2006].
Mineralization was assessed by pulsing the culture with 20 µM Xylenol Orange
and then visualizing the disk using CLSM (Olympus FluoView, Tokyo, Japan).

STATISTICS
Student’s t-test was used to test the statistical significance of the
differences where a value of p < 0.05 was considered significant.

55

RESULTS
HA characterization
The XRD analysis of as-received HA powder and pulverized sintered
HA specimen showed that both HA powders were crystalline with characteristic
peaks matching with the standard JCPDS 9-432 (Joint Committee on Powder
Diffraction Standards, Swarthmore, PA). No phases other than HA were
detected (Figure 4.2).

Figure 4.2 XRD spectra of as-received HA powder from vendor and pulverized sintered HA
specimen. Both powders showed representative peaks for HA crystal and no impurity phases
were detected.

Both the SEM and CLSM images of non-cracked HA showed a smooth
surface with uniformly distributed, isolated, surface-breaking pores

56

approximately 3 µm in diameter (Figure 4.3a and 4.3c). The SEM image of the
cracked HA specimens clearly showed both the indentation impressions and
chipping at the vicinity of the indentation impression (Figure 4.3b). The CLSM
image of cracked HA showed clear radial cracks (2c ≈ 180µm) aligned parallel
to the indentation diagonal as well as quarter plate like lateral cracks (Figure
4.3d).

Figure 4.3 SEM image of (a) polished non-cracked HA surface and (b) cracked HA surface and
CLSM Z-stack maximum reflection intensity projections of (c) polished non-cracked HA surface
and (d) cracked HA surface. On the cracked HA surface, Vickers indentation impression is the
center diamond shape. Accompanying radial cracks and lateral crack spalling are pointed out
by white and black arrows, respectively.

In a fully developed crack system, microdamage from Vickers
indentation contains lateral and radial cracks as well as the centrally located
indentation impression as shown in Figure 4.1a. Materials and their

57

microstructural properties such as porosity and grain size may affect the
evolvement of the radial/lateral cracks [Osterstock et al. 1996, Tancret and
Overstock 2003]. In a given material, the occurrence and development of
radial/lateral cracks is load dependent (Chapter 8). The relative frequency for
lateral cracks to occur is approximately 95% at 4.91 N in the HA specimens in
this study (Chapter 8). The average size of the lateral cracks, b, and the half
radial crack length, a, were 67.3 ± 17.5 µm and 90.6 ± 4.9 µm, respectively
(Figure 4.1a).

OB attachment and alignment
OB attachment
At one and two hours post seeding, OBs were still somewhat rounded
and not fully attached, but by four hours the cells began to elongate (Figure
4.4). The cell nuclei stained with Hoechst 33342 appeared blue, and the cell
membranes stained with Rhodamine Phalloidin Actin stain appeared red
(Figure 4.4). A significant increase of OB attachment onto cracked HA
specimens was observed at four hours (p<0.05), but not at one and two hours
(Figure 4.5).

58

Figure 4.4 CLSM fluorescence images of OBs attached to non-cracked HA specimens at (a) 1
hour, (b) 2 hours and (c) 4 hours, and cracked HA specimens at (d) 1 hour, (e) 2 hours and (f) 4
hours. White arrows show positions of Vickers indentations and cracks. The OBs were stained
with Rhodamine Phalloidin (Actin) and Hoescht 33342 (nucleus). The Rhodamine Phalloidin
Actin fluorescence stain was excited at 543 nm and emission was detected through a
BA560-620 nm emission filter (represented in red). The Hoechst 33342 nucleus stain was
excited with UV light at 405 nm and emission was detected through a BA430-470 emission

% Cells seeded

filter (represented in blue).

100

non-cracked
cracked

*

50

0
1

2
Hours

4

Figure 4.5 OB attachment is increased on cracked HA specimens at 4 hours. OBs were
2

seeded at an initial density of 11,320 cells/cm . OB attachments on non-cracked and cracked
HA specimens at 1, 2 and 4 hours are represented by the relative percentage of cells seeded.
Error bars represent standard error. While no significant difference between OB attachment on
non-cracked and cracked HA specimens were detected at 1 and 2 hours, significant increase
of OB attachment by approximately 28% on cracked HA specimens was detected at 4 hours

59

using Student’s t-test (*p<0.05). Three specimens were used for each condition and the
experiments were tripled.

CLSM micrographs of OB attachment at four hours
Figure 4.6 is a representative CLSM fluorescent micrograph of cells
attached on cracked HA at four hours post-seeding. The alignment of the
elongated cells towards the indentation center is described by the alignment
angle, θ, as shown in Figure 4.6. The alignment angle, θ, was defined by two
lines: one line (horizontal, yellow line in Figure 4.6) was drawn from the
nucleus of each OB to the indentation center of the cracked samples. The
other line (vertical, cyan line in Figure 4.6) was drawn through the nucleus and
the longest part of the cell. For the few circular cells, having no apparent
elongation (marked by black crosses on Figure 4.6), no alignment angle could
be defined.

60

Figure 4.6 Illustration of angle θ between cell elongation direction (cyan line) and line
connecting cell nucleus and indentation center (yellow line) on micrographs of cracked HA.
The indentation impression and radial crack pattern are illustrated by white lines. The black
crosses mark examples of cells showing no apparent elongation direction. The OBs were
stained with Rhodamine Phalloidin (Actin) and Hoescht 33342 (nucleus). The Rhodamine
Phalloidin Actin fluorescence stain was excited at 543 nm and emission was detected through
a BA560-620 nm emission filter (represented in red). The Hoechst 33342 nucleus stain was
excited with UV light at 405 nm and emission was detected through a BA430-470 emission
filter (represented in blue).

Thus, the circular cells were excluded from the quantitative angular
distribution analysis. Yang also excluded these circular cells in a quantitative
analysis of OB alignment on grooved substrates [Yang et al. 2008]. A careful
examination of the non-cracked HA micrographs showed that 45 out of 534
cells appeared circular with no apparent elongation direction, while in the
microcracked HA micrographs, 17 out of 604 cells showed no obvious
elongation direction. Thus, approximately 92% and 97% of the cells were
elongated on the non-cracked and microcracked HA micrographs,
respectively.

61

Alignment angle (θ) distribution
For the CLSM micrographs of the HA specimens, the alignment angle,
θ, for the elongated cells, the coordinates of the crack center, O (X0, Y0) and
the cell nucleus center C (X, Y) were determined via the software package
→

Datathief [Tummers 2005]. The vector

OC = ( X − X 0 , Y − Y0 ) then

gave the relative position of each cell with respect to the indentation center.
For each cell, the elongation direction was described by another vector,
→

EF = ( X 2 − X 1 , Y2 − Y1 ) , where E (X1, Y1) and F (X2, Y2) are two
points along the elongated cell filaments. The angle, θ, can then be calculated
from equation (1),
→

→

→

→

θ = arc cos θ = arc (OC • EF ) ( OC EF )

(1)

For the non-cracked (control) HA specimens, no Vickers indentations
were made. Thus, in order to define the angle of alignment for cells on
non-cracked HA, artificial origins of polar coordinate system were
superimposed on the CLSM micrographs of the non-cracked HA specimens.
These artificial origins were superimposed near the center of micrographs for
non-cracked HA specimens, similar to the positions of the indentation centers
on micrographs of cracked HA.
The alignment angle, θ, of cells can range from 0° to 90° with respect
to the microcracked region centered at the indentation center, as shown
schematically in Figure 4.7. Since no alignment angle θ could be determined

62

for the few cells with no apparent elongation direction, these cells were
excluded from the θ distribution analysis.
θ = 90°

θ = 45°

θ = 0°

Figure 4.7 A schematic of cells with different elongation directions with respect to the
indentation site. Cells with θ < 45° are considered as aligned cells, while cells with θ ≥ 45° are
considered as non-aligned cells.

A total of 489 elongated cells from non-cracked HA micrographs and
587 elongated cells from microcracked HA micrographs were considered for
the analysis of θ distribution. Figure 8 shows the probability density histograms
of θ (probability versus θ) for the elongated cells measured from the CLSM
micrographs of both the non-cracked and the cracked HA.
The distributions of the angle θ were then compared to a uniform
distribution described by equation (2),

f (θ ) =

1
,a < θ < b
(b − a)

(2)

where a and b are the two parameters for a uniform distribution and give the
range of angle θ. The goodness of fit was determined using the
Kolmogorov-Smirnov method [Massey 1951]. The uniform distribution of angle
θ corresponds to the random cell orientations with respect to the origin of the
polar coordinate system [Curray 1956, Fisher et al. 1985]. The θ distribution for
OBs from the non-cracked HA micrographs is consistent with the uniform
distribution (p>0.05) (Figure 4.8a), whereas the θ distribution for OBs from the

63

microcracked HA micrographs was found to be significantly different from the
uniform distribution (p<0.05) (Figure 4.8b).

0.08

Probability

a

0.06
0.04
0.02
0

0

20

40

60

80

60

80

θ°
b

Probability

0.08
0.06
0.04
0.02
0

0

20

40

θ°
Figure 4.8 Probability density histograms of θ for a) non-cracked HA (N=489) and b) cracked
HA (N=587) fit to uniform distribution as shown by the thick solid black line. N is the total
number of cells considered in the probability density histograms. The goodness of fit was
tested using the Kolmogorov-Smirnov method. The θ distribution for non-cracked HA fitted to
uniform distribution (p>0.05). The θ distribution for cracked HA did not fit to the uniform
distribution (p<0.05).

Comparison of aligned and non-aligned cells
When θ is less than 45° the midpoint of the [0° 90° inte rval, cells with
,
,
]
θ < 45° are considered to be aligned towards the microcra cked region (Figure
4.7). To determine whether the OBs on the microcracked HA specimens
aligned in the direction of the microcracked zone, centered at the indentation
impression center, the cells were divided into three groups according to both
their alignment angle and shape: (i) aligned cells (θ < 45° (ii) non-aligned
),

64

cells (θ ≥ 45° and (iii) circular, cells for which alignment was i ndeterminate.
)
The relative fraction of aligned cells (θ < 45° and non-aligned cells ( θ ≥ 45°
)
)
were then calculated and compared. From the micrographs of non-cracked HA
specimens, the relative fraction of aligned cells (θ < 45° was significantly less
)
(p<0.05) than the relative fraction of non-aligned cells (θ ≥ 45° and circular
cells) as shown in Figure 4.9a. However, from the micrographs of cracked HA,
the relative fraction of aligned cells (θ < 45° was significantly more (p<0.05)
)
than non-aligned cells (θ ≥ 45° and circular cells) as shown in Figure 4.9b.
b
70

Relative Fraction(%)

Relative Fraction(%)

a
Non-cracked

35

0
Aligning

Non-aligning

70

Cracked

35

0
Aligning

Non-aligning

Figure 4.9 The relative fractions of aligned cells (θ<45°) and non-aligned cells ( θ ≥ 45° and
circular cells) on a) non-cracked HA and b) cracked HA at 4 hours. Significantly more
non-aligned cells than aligned cells were detected from non-cracked HA micrographs, while
the opposite was observed from cracked HA micrographs. The significance of difference was
detected using Student’s t-test (p<0.05).

The positions of aligning cells on microcracked HA
The location of the aligned cells (θ < 45° was characterized by the
)
distance (r) between each cell nucleus and the indentation center, which was
→

obtained by calculating the length of vector
described in earlier using equation (3),

65

OC = ( X − X 0 , Y − Y0 )

→

r = OC = ( X − X 0 ) 2 + (Y − Y0 ) 2

(3)

The micrographs of the microcracked HA surface were then partitioned
into a circle centered at the indentation site, with increasing, concentric 15
µm-wide annuli as shown schematically in Figure 4.10a. The area for the
central circle and each annulus was calculated from the 15 µm central circle
radius and the 15 µm increments in radius, such that the center circle has an
area of 706.85 µm2, and the nth (n=1, 2, …) annulus has an area of
π[15(n+1)]2-π(15n)2 (µm2). The number of aligned cells within the central circle
and each ring was then normalized by the circle/annulus area to give the cell
density as a function of distance away from the indentation center as shown in
Figure 4.10b.
a

b

Figure 4.10 The micrograph was partitioned into a central circle of 15 µm in radius and 15 µm
wide outer rings (a). The number of OBs with aligned tendency (θ<45° in the center circle and
)
outer rings (15 µm wide) were counted and normalized by the area respectively (b). Most cells
with aligned tendency (θ<45° were found in the annulus 75 to 90 µm from the indentation
)
center (b), which is around the tip of the radial cracks from Vickers indentation (a).

The surface microcracked zone introduced using Vickers indentation

66

contains the indentation impression, lateral cracks and radial cracks. The
average lateral crack size and the half radial crack length were approximately
67.3 ± 17.5 µm and 90.6 ± 4.9 µm, respectively. The boundary region of the
microcracked zone as determined by both lateral and radial cracks is thus an
annulus approximately 67.3µm to 90.6 µm away from the indentation center.
The highest density of aligned cells was found in the ring located 75 µm to 90
µm from the indentation center (Figure 4.10b). This concentric ring was similar
in size to the boundary region of the microcracked zone determined by the
lateral and radial cracks.

OB growth and maturation
Cell growth was measured to determine if increases in attachment led
to more cell growth. However, no significant differences in OB number were
detected between microcracked and non-cracked specimens at one, three and
five days post-seeding (Figure 4.11), suggesting that OB expansion was
similar on both surfaces, despite early differences in surface

% Cells seeded

recognition/attachment.

800

non-cracked
cracked

400

0
1

3
Days

67

5

Figure 4.11 OB growth is not affected by the presence of cracks on HA specimens. OBs were
2

seeded at an initial density of 11,320 cells/cm . OB growths on non-cracked and cracked HA
specimens at 1, 3 and 5 days are represented by the relative percentage of cells seeded. Error
bars represent standard errors. No significant differences between OB growths on
non-cracked and cracked HA specimens were detected (*p<0.05). Three specimens were
used for each condition and the experiments were tripled.

Alterations in surface structure and cell attachment can also impact the
maturation of OBs, the effect of microcracking on OB phenotype markers were
thus investigated. Cells were harvested at 21 days post-seeding, a time when
OBs are in a mid to full stage of maturation. First, alkaline phosphatase activity
and expression, markers of mid-to-late stage extracellular matrix maturation
[Lian et al. 1998, Owen et al. 1990, Quarles et al. 1992] were measured. Cells
on the microcracked surface had greater alkaline phosphatase RNA levels and
correspondingly greater alkaline phosphatase activity compared to
non-cracked surfaces (Figure 4.12).
a

b

*

1.5

*

2

Absorbance

AP/HPRT

3

1
0

0.75

0

Non-Cracked

Cracked

Non-cracked

Cracked

Figure 4.12 OB maturation characterized by (a) AP expression and (b) AP activity was
2

enhanced on cracked HA specimens. OBs were seeded at initial density of 20,000 cells/cm .
After 21 days of cell culturing, AP gene expression was examined using RNA extracted from
cell layers. Gene expression was normalized to levels of an unmodified housekeeping gene,
HPRT. AP activity was assessed on cell layers and then measured by spectrophotometer.
Significant increases in both (a) AP gene expression and (b) AP activity were detected using
Student’s t-test (*p<0.05). Error bars represent standard errors. Three specimens were used
for each condition and the experiments were tripled.

68

Further analysis of other gene expression levels indicated an increase
in Runx-2 (a transcription factor important for OB lineage selection and
maturation). Collagen I (a major bone extracellular matrix protein) RNA levels
displayed a tendency to increase on HA surfaces but the data was variable and
statistical significance could not be reached. Interestingly, no significant
changes were observed in osteocalcin expression (a marker of late-stage OB
maturation) (Figure 4.13) [Lian et al. 1998, Owen et al. 1990, Quarles et al.
1992].
b
3

1.8

*
ColI/HPRT

Runx2/HPRT

a

2
1

1.2
0.6
0

0
Non-Cracked

Non-Cracked

Cracked

Cracked

OC/HPRT

c 1.2
0.8
0.4
0
Non-Cracked

Cracked

Figure 4.13 (a) Runx2, (b) Col-I and (c) OC expressions on non-cracked and cracked HA at 21
days. All gene expression was examined using RNA extracted from cell layers. Gene
expression was normalized to levels of an unmodified housekeeping gene, HPRT. Significant
increase in Runx2 expression on cracked HA specimens was detected using Student’s t-test
(*p ≤ 0.05). No significant differences in Col-I and OC expressions between non-cracked and
cracked HA specimens were detected. Error bars represent standard errors. Three specimens
were used for each condition and the experiments were tripled.

69

To determine if the identified phenotypic changes could impact OB
bone formation on the cracked HA surface, we imaged OB mineralization on
cracked and non-cracked HA at 21 days by CLSM. Surface analyses indicated
that significantly more mineral deposition occurred on the cracked HA. The
deposited minerals, which contained calcium stained by Xylenol Orange, were
shown as orange dots in Figure 4.14. Non-cracked HA (Figure 4.14a)
displayed mineral deposition that was scattered uniformly across the surface.
In contrast, there was a zone of concentrated mineral deposition at the
indentation site on the cracked HA (Figure 4.14b). This concentrated
deposition was not apparent in parallel studies on HA scaffolds without cells
(data not shown), suggesting that HA cracking stimulates osteoblast bone
formation to repair of surface indentations and smooth the surface.

Figure 4.14 CLSM Z-stack maximum fluorescence intensity projections of OB mineral
depositions on (a) non-cracked and (b) cracked HA at 21 days. The OBs were pulsed with
Xylenol Orange every other day during culturing since day four. The Xylenol Orange
fluorescence stain was excited at 543 nm and emission was detected through a BA560-620
emission filter (represented in orange).

DISCUSSION

70

OB attachment and growth
The interaction of OBs with the substrate surface includes cell
attachment or adhesion, cell growth or proliferation, and finally cell
differentiation or maturation phases [Anselme 2000]. Attachment or adhesion,
being the first phase of OB/substrate interaction, plays an important role in
determining the subsequent proliferation and differentiation stages [Anselme
2000]. In this study, the presence of microcracks was observed to increase OB
attachment four hours after seeding but not at one or two hours (Figure 4.5).
Observed differences between times may be related to the release rate of
calcium from the free surface of the HA, the details of which are still under
investigation by the authors.
The increase in OB attachment in vitro is usually taken as a strong
indication for improved biocompatibility of the bone implant substrate [Gough
et al. 2004, Balasundaram et al. 2006, Webster et al. 2000, Cai et al. 2006, Lim
et al. 2004, Kopecek et al. 2008]. The improvement in observed OB
attachment is likely a result of contributions from modification in substrate
surface characteristics, such as the surface roughness/area [Gough et al.
2004, Webster et al. 2000 and Cai et al. 2006], the surface chemistry [Shu et al.
2003, Lim et al. 2004, MacDonald et al. 2004, Scotchford et al. 1998], the
surface hydrophilicity and the surface free energy [Boyan et al. 2003, Zhao et
al. 2005 and 2007, Olivares-Navarrete et al. 2007].
While OB attachment was observed to increase on cracked HA

71

specimens (Figure 4.5), no enhancement in OB growth was observed (Figure
4.11), which showed that an increase in OB attachment did not necessarily
lead to more OB growth. In a study conducted by Smith et al. OB attachment
and growth also showed a similar trend, such that when OB attachment
increased, OB growth did not show obvious differences or was even
suppressed at longer times [Smith et al. 2006 a]. In another study by Shu et. al.
[2003], OB growth was suppressed on HA when compared to plastic culture
dishes, but an enhanced OB maturation (increased AP activity) on HA was
observed, which is also found in the current study.

OB shape on the CLSM micrographs
We observed two main cell shape phenotypes at 4 hours post-seeding:
circular and elongated. The circular cells result from three different cell
behaviors: (1) cells not strongly adhered to the surface, as observed at one
and/or two hours post seeding; (2) cells with focal adhesions in all directions
[Tranquillo et al. 1999]; and/or (3) cells detaching from the surface during
apoptosis [Grossman et al. 2002, Numaguchi et al. 2003]. Cell apoptosis is not
a major concern in the current study, because HA has been shown to be an
excellent substrate for OB culturing [Shu et al. 2003] and as a bone implant
material [Hench 1991].
Cells elongate during cell attachment, an essential step for cell motility.
Thus, in this study, the preferred elongation direction observed on cracked HA
specimens may indicate cell movement towards or away from the

72

microcracked zone. On the other hand, cell elongation also reflects the cell’s
response to the substrate surface, such that the formation of cytoskeletal focal
adhesions is guided by the substrate physical/chemical properties in order to
optimize cell functions on the substrate [Weiner et al. 1999, Ziv et al. 1996,
Ascenzi et al. 1986, Lenhert et al. 2005, Zhu et al. 2005, Puckett et al. 2008,
Yang et al. 2008 and Lee et al. 2006]. In this study, the observed cell
elongation towards the microcracked zone was noted specifically at the crack
boundaries. Thus, it is likely that the introduction of microcracks disturbed the
local physical/chemical environment, which in turn altered the cell elongation
direction when the cells were attaching in the vicinity of the microcracked zone.

Distribution of OB alignment angles
The uniform distribution of cell alignment angles, θ, on non-cracked
HA specimens indicated that the OBs were randomly oriented and showed no
preferential alignment towards the superimposed polar coordinate origins. The
random orientation of the elongation axes for the cells also implies a random
movement of cells on the non-cracked HA surfaces, which is consistent with
observations of random cell movement on isotropic substrate surfaces by
Tranquillo [1999] and Selmeczi et al. [2005]. The non-uniform distribution of
the cell alignment angles (θ) on microcracked HA (Figure 4.8b) showed that
the presence of the microcracks introduced by Vickers indentation affected the
cell orientation.

73

OB alignment towards the microcracked zone
Based on our findings, OBs were more extensively aligned on
microcracked HA specimens compared to non-cracked HA specimens, which
indicates that the microcracked zone likely influences cell alignment. The
elongated OBs that were aligned towards the indentation center may in turn
lead to the alignment of the ECM, which interacts with cells through adhesive
forces [Numaguchi et al. 2003, Ingber et al. 1989, Singhvi et al. 1994, Huang
et al. 1998, Parker et al. 2002]. Alignment of OBs and/or mineralized ECM has
been observed by researchers culturing OBs on substrate surfaces with
anisotropic topographies, both at the nano- and the micro-scale [Zhu et al.
2005, Puckett et al. 2008, Lenhert et al. 2005, Yang et al. 2008]. The alignment
of OBs on substrates with surface grooves was described by qualitative
observations of representative micrographs by both Zhu and Puckett; however,
no quantification of the cell alignment was conducted in their studies [Zhu et al.
2005, Puckett et al. 2008].
On the other hand, Lenhert and Yang provided a quantitative
characterization of OB shape and alignment on the grooved surfaces, where
the OB orientation angles were defined by the grooves and the elongation
direction of the cells [Lenhert et al. 2005, Yang et al. 2008]. The cells with
orientation angles less than 30° were considered to be a ligned in Lenhert’s
study [Lenhert et al. 2005]; while in Yang’s study, cells with orientation angles
less than 10° were considered aligned [Yang et al. 2008 ].

74

Though the standards for defining alignment varied among
researchers, the quantitative descriptions of cell alignment along surface
grooves all showed significant differences between the proportions of aligned
cells on grooved (experimental) and smooth (control) substrate surfaces
[Lenhert et al. 2005, Yang et al. 2008]. On the grooved surfaces introduced by
lithography techniques, 42% of cells aligned within 30° of the grooves in
Lenhert’s study [Lenhert et al. 2005], and more than 60% cells aligned within
10° of the grooves in Young’s study [Young et al. 2008 ], while cells showed no
preferred orientation on the control substrate surfaces. In cases where
grooves/ridges are introduced by abrasion [Calzado-Martin et al. 2011], it is not
possible to entirely separate whether the enhanced cell activity is due to the
grooves/ridges or the microcracks associated with the abrasion [Couto et al.
1994].
It is important to address the difference between OB alignment
towards the localized microcrack zone observed in this study and OB
alignment along parallel ridges and/or grooves observed by others [Lenhert et
al. 2005, Zhu et al. 2005, Puckett et al. 2008, Yang et al. 2008]. In these OB
alignment studies, the focus was on mimicking the anisotropic nature of bone;
while in this study, the interest was to determine whether alignment indicated
enhanced bone formation around microcracks [Burr and Martin 1993, Mori and
Burr 1993, Stafford et al. 1994].
It should be noted that when microcracking occurs in vivo, OBs do not

75

necessarily have direct contact with the microcracked sites, but may be
generated and migrate from the undamaged bone before mineralizing in the
vicinity of the microcracks [Stafford et al. 1994]. The microcracked zone
introduced using Vickers indentation is localized microdamage, mimicking the
localized damage found from repetitive use injury in humans and animals [Burr
and Martin1993, Mori and Burr 1993, Stafford et al. 1994].
In the other studies, cells remained in contact with the parallel
ridges/grooves because the ridges or grooves covered the whole surface
[Clark et al. 1990 and 1991, Lenhert et al. 2005, Zhu et al. 2005, Puckett et al.
2008, Yang et al. 2008]; while in our study, the cells were in contact with not
only the surface microcracks, but also the surrounding un-cracked regions
when seeded on the cracked HA (Figure 4.6). It is therefore important to
address not only the shape and alignment of cells as discussed above, but
also the locations of the aligned cells on the microcracked HA specimens with
respect to the localized microcracked zone.

Relationship between aggregated aligned cells and the size of
microcracked zone
The majority of the aligned cells were found at the annulus boundary
region of the microcracked zone rather than accumulating at the indentation
impression. So as not to confuse the Vickers indentation impressions with
surface breaking pores, it is useful to note that the indentation impressions in
this study have an average diagonal of 44.8 ± 1.4 µm and ~9 µm deep, too

76

shallow to support bone ingrowth [Engh et al.1987, Karageorgiou and Kaplan
2005]. Therefore, it is reasonable that the majority of aligned cells are present
at the indentation impression when we assess cell attachment and
proliferation.
Bone ingrowth has been shown to occur with pore sizes >100 µm
[Engh et al.1987, Karageorgiou and Kaplan 2005], which is comparable to the
diameter of the Haversian bone osteons noted by Burg et al. [2000]. The size
of the Vickers indentation impression (~45µm) in this study was significantly
smaller than the pore size capable of inducing bone ingrowth documented in
the literature (100 - 400 µm) [Hulbert et al. 1970, Bobyn et al. 1980, Martens et
al. 1980]. Further, although interconnected pores approximately 50 µm in
diameter [Klawitter et al. 1976, Itala et al. 2001] were also reported to induce
bone ingrowth, the Vickers indentations in this study were not interconnected
but isolated from each other. Because the Vickers indentation impression is a
shallow divot rather than a real pore, the OB alignment towards the
microcracked zone was not likely influenced by the Vickers indentations, but
instead by the radial and lateral cracks.

Microcrack boundary defined by radial/lateral cracks
In this study, the length of the radial cracks (181.2 ± 9.8 µm) induced
by Vickers indentations was within the range of linear microcracks found in
bone (50 to 300 µm) [Taylor et al. 1998, Schaffler et al. 1989, Burr et al. 1990,
Burr and Martin 1993, Morri and Burr 1993, Lee 1995, Lee et al. 1998]. These

77

radial cracks thus can be considered as a reasonable model for fatigue
microcracking in bone. When microcracking occurs in bone, as well as in
engineering ceramics that are not completely dense, the crack propagation
can be arrested by pores via crack tip blunting, an important energy absorption
mechanism [Kruzic et al. 2003, Deng et al. 2004]. Cracks could also be
deflected by the anisotropic collagen matrix in bone [Kruzic et al. 2003],
particularly in the transverse directions [Taylor and Lee 1998].
In the HA specimens used in this study, the radial cracks from the
Vickers indentations showed enhanced growth within the first hour following
indentation, due to the release of residual strain energy from the plastic
deformation zone beneath the indentation impression (Chapter 8). The radial
crack length then reaches a plateau due to the exhaustion of the residual strain
energy (Chapter 8). The radial crack extension in HA is also likely to be
disrupted by the surface breaking pores via crack tip blunting [Deng et al. 2004]
and/or deflected by grain boundaries [Faber et al. 1983, Suresh et al. 1983].
Thus, crack tip blunting is a likely mechanism inhibiting crack propagation in
both bone and HA, which acts to redistribute localized strain energy at the
crack tip, inhibiting further crack propagation.
Radial crack tips however only account for part of the microcracked
zone introduced by Vickers indentations. The presence of lateral cracks should
also be considered, because OBs were observed to align around the entire
periphery, rather than merely clustering at the crack tips. Lateral crack chipping

78

from Vickers indentations has been widely used to investigate the abrasive
wear, erosive wear, and the surface material removal process in a variety of
brittle materials [Ahn et al. 2003, Srinivasam et al. 1990, Thiruvengadaswamy
et al. 1993, Swain et al. 1976, Zhang et al. 2000]. Lateral crack chipping in
bone, on the other hand, has not been documented. However, in clinical cases
[Matic et al. 2004, Suzuki et al. 2009] involving trauma from collisions and
sudden falls, bone chipping may occur when a large physical force is applied
over a small area of bone. Thus, lateral crack chipping could potentially serve
as a model for bone chipping, which differs from fatigue microcracking as
modeled by radial cracks.
The observed OB alignment at the periphery of the microcracked zone
suggests two possible bone healing processes by examining both the radial
and lateral cracks. The first is that crack tip blunting may be activated at the
radial crack tips. This resembles bone healing in the case of fatigue
microcracking in vivo observed by Muir et al. [1999], Zarrinkalam et al. [2005],
Taylor and Lee [1998], O’Brien et al. [2003] and Hazenberg et al. [2009]. The
second is the possible inhibition of lateral crack chipping that could occur in
bone in vivo, a concept that has yet to be addressed in the literature.

OB maturation
In this study we found that microcracked HA further enhanced AP gene
expression (Figure 4.12a, AP activity (Figure 4.12b) and Runx-2 expression
(Figure 4.13a). Collagen I levels also exhibited an increasing trend (Figure

79

4.13b) but interestingly we did not observe a corresponding increase in
osteocalcin (Figure 4.13c). This could indicate that HA and microcracking
specifically enhance a subset of maturation associated genes that are
associated with osteoblast maturation (Runx-2 and AP) and bone matrix
synthesis (AP and Col-I) which are required for bone healing to begin. It is also
possible that at a later time point, we would observe a microcrack-induced
increase in more advanced maturation markers such as osteocalcin.
Since the main purpose of fabricating a bone tissue engineering
implant is to enhance bone healing in the long term, OB maturation is an
important reference in judging the biofunctionality of scaffolds. The increase in
OB attachment and corresponding enhancement of OB maturation on cracked
HA in vitro observed in the current study showed that the introduction of
microcracks has the potential to enhance bone healing in vivo.

CONCLUSION
The current study is based on the knowledge of both the physical
properties of HA and accumulated OB behaviors established by our group in
previous studies [Hoepfner and Case 2002, 2003, and 2004, Ren et al. 2009,
Fan et al. submitted Part I and II 2011, Singh et al. 2005 and 2006, Fan et al.
submitted 2011, Case et al. 2005, Smith et al. 2006, Shu et al. 2003, Hossain
et al. 2005, Xie et al. 2004]. The HA used in this study had a well-controlled
density (~94%) and uniformly distributed spherical and/or quasi-spherical
isolated surface breaking pores (2-3 µm in diameter). Vickers indentation was

80

used to model localized microcracking.
The effect of microcracking on OB attachment and maturation has
been demonstrated by increased cell attachment, alkaline phosphatase activity,
and gene expression in in vitro cell studies. OB shape and alignment in the
local vicinity of a microcrack was also affected at four hours post-seeding. The
observed preferential alignment of OBs to the microcracked zone, especially at
the circular boundary region, may in turn lead to enhanced OB maturation and
localized mineralization as evidenced by CLSM images showing concentrated
mineralization at the indentation center. These observations suggest two
possible bone healing mechanisms: crack tip blunting at the radial crack tips
and bone chipping inhibition at the lateral crack boundaries.
Though the exact mechanism as to how these cracks affect OB
attachment and maturation is still not clear, the benefits of such cracks, in
terms of enhanced OB maturation, brings a new dimension to designing
scaffolds for bone tissue engineering. Future studies will address the detailed
mechanism(s) by studying the local chemical environment in the crack vicinity
and by examining the protein conformations at the cracked sites which are
hypothesized to present a higher surface energy state. While radial cracks,
resembling fatigue microcracking in vivo, have been widely observed, future
studies will look for evidence of lateral crack chipping in bone, because lateral
crack chipping may also trigger bone healing by guiding OB shape and
alignment as observed in this study.

81

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CHAPTER 5
LOCAL SURFACE DAMAGE ACCELERATES
DISSOLUTION IN DISTILLED WATER

HYDROXYAPATITE

INTRODUCTION
Hydroxyapatite (HA or Ca10(PO4)6(OH)2) is widely used to supplement
bone/dental grafts [LeGeros 2002, Wetzell et al. 1995, Yoshikawa et al. 2000],
as a scaffold for bone tissue engineering [Karageorgiou and Kaplan 2005, Wei
and Ma 2004, Hollister et al. 2002], and as a structural support material for
catalysts, heavy metal removal, and sensors [Mori et al. 2003 and 2004,
Venugopal and Scurrell 2003, Nagai and Nishino 1988, Owada et al. 1989].
During material handling and application, localized damage such as scratches
and cracks can be generated, which may alter the local chemical/mechanical
environment and the dissolution behavior of the material [Li et al. 2009]. The
dissolution behavior of HA is important as it releases free calcium ions which
affects the biofunctionality of HA. Increases in local calcium ion concentration,
released as a result of the biological dissolution of implanted calcium
phosphate coatings, was shown to influence mineralization in vitro [Morgan et
al. 1996]. In Chang et al.’s [2000] study, supplementing with calcium ions was
shown to promote bone cell mineralization. In another in vitro study by Yang et
al. [2004], elevated extracellular calcium ion levels were also observed to
induce cell to matrix mineralization. The biological dissolution of
hydroxyapatite giving rise to an increased calcium ion concentration is thus
likely associated with the biological response of bone cells in vitro [Ducheyne

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et al. 1993]. Besides calcium, phosphate ions, released as the HA dissolves,
have also been shown to play a role in regulating osteoblast differentiation
[Beck 2003] and apoptosis [Meleti et al. 2000].
The dissolution behavior of HA along with its mechanical stability in
aqueous environments is well documented in the literature [Fazan and
Marquis 2000, Zhang et al. 2003]. However, far less attention has been paid to
HA dissolution around localized surface damage such as scratches and/or
cracks, which are associated with local residual stresses. These residual
stresses were found to affect the dissolution of HA coatings as shown by Han
et al. [2001]. Also, in studies by Reis et al. [1994] and Raynaud et al. [1998],
the degradation of HA was found to accelerate when the HA was subjected to
cyclic tensile stresses.
In the current study, local surface damage was introduced to HA using
the well-established Vickers indentation method, which generates consistent
indentation impressions and radial/lateral crack patterns at each loading
condition. The surface morphology evolution during dissolution of locally
damaged HA was imaged using environment scanning electron microscopy
(ESEM). The dissolution behavior of HA in distilled water, with and without
indenting, were compared by measuring the calcium ion concentration over
immersion periods ranging from 1 hour to 7 days.

MATERIALS AND METHODS
Hydroxyapatite (HA) specimens were made from fine powders (Taihei

95

Chemical Industry, Osaka, Japan) with a vendor specified particle size of 4 to 6
µm. Powders were uniaxially pressed at 27.7 MPa for 1 minute in a 32 mm
diameter steel pellet die. The green powder compacts were then sintered at
1360ºC for 4 hours in an electrical resistance furnace (CM Inc., Model
#0100277, Bloomfield, NJ) at a ramp rate of 10ºC/minute during both heating
and cooling. The sintered specimen surfaces were polished using diamond
paste of grit size down to 0.5 µm prior microindentation.
Vickers indentation was used to introduce local damage to the
specimen surfaces using Shimadzu microhardness tester (HMV2000, Kyoto,
Japan) at a peak indentation load of 4.91 N. The loading time at the peak load
was 5 seconds and both the loading and unloading rates were 70 µm/s. The
indentations were made in a 7Χ7 grid pattern at 2-mm intervals as described in
the previous chapter.
Both the polished specimens (control group) and indented specimens
(experiment group) were immersed in distilled water and maintained at 37ºC
which mimics the normal body temperature. The immersion periods (1 hr, 1.5
hr, 2 hr, 3 hr, 4 hr, 6 hr, 8 hr, 13 hr, 18 hr, 1 day, 2 days, 3 days, 4 days, 5 days,
and 7days) ranged from 1 hour to 7 days. The dissolution of one
representative indentation impression and its accompanying radial/lateral
cracks were imaged using ESEM at 0, 4, and 24 hours.
HA dissolution was characterized by measuring the calcium ion (Ca2+)
concentration in distilled water sampled at each time interval using atomic

96

absorption spectrophotometry (AAS, model 3110, PerkinElmer, Massachusetts,
0.01 mg/L) where the emission light wavelength for Ca2+ is 422.7 nm.

RESULTS AND DISCUSSION
ESEM of indentation damage during HA dissolution
ESEM was used to capture the HA surface dissolution in and around
the indentations and accompanying cracks (0 immersion time) and following
immersion in distilled water for 4 and again for 24 hours. Figure 5.1 shows the
morphological evolution of the same indentation impression prior to water
immersion as well as 4 and 24 hours after immersion.

Figure 5.1 ESEM images of the same indentation impression on HA surface (a) before
immersing in distilled water, (b) 4 hours after immersion in distilled water, and (c) 24 hours after
immersion in distilled water.

97

Figure 5.1a depicts the indentation impression, radial cracks (white
arrow) and lateral crack (black arrow) prior to distilled water immersion. The
indentation impression is characterized by sharp edges and a readily
distinguishable diagonal cross formed from the rectangular pyramid shape of
the Vickers indenter tip. Two pairs of radial cracks extended along the indent
impression in a diagonal direction (white arrows). One instance of
quarter-plate lateral crack spalling was observed in the upper right region
(black arrow). Surrounding the indentation impression, and the radial/lateral
cracks, were isolated spherical and quasi-spherical pores, uniformly
distributed across the surface. The occasional pore cluster was also present
(white circles).
After immersion in distilled water for 4 hours (Figure 5.1b), the
indentation impression edges became less distinct when compared to no
immersion time (Figure 5.1a). The surface radial cracks appeared to open up
in the indentation impression rather than opening at the indentation diagonals
as shown in Figure 5.1a. Also, more lateral crack spalling appeared in the
upper left, upper right, and lower left regions as indicated by the black arrows.
The isolated pore clusters prior to water immersion (white circles, Figure 5.1a)
have now coalesced, forming larger surface cavities (white circles, Figure
5.1b).
Following 24 hours of immersion in distilled water (Figure 5.1c), the
indentation impression lost its distinguishable diamond shape. The radial crack

98

openings which appeared in the indentation impression at 4 hours (Figure 5.1b)
disappeared by 24 hours (Figure 5.1c). On the other hand, lateral cracks
became more apparent on the surface and appeared to coalesce with some of
the surface pore clusters (Figure 5.1c) that appeared at early immersion times
(Figure 5.1a and b).

AAS measurements of HA dissolution and surface area increase
The concentration of calcium ions released into distilled water from
both non-cracked and cracked HA as a function of time are shown in Figure
5.2.

Figure 5.2 The calcium ion concentrations released from non-cracked (

) and cracked (

HA specimens as a function of time. Error bars represent standard deviations. Both the
non-cracked HA calcium release data and the cracked HA calcium release data were fit to
2

2

equation (1), which yielded a coefficient of determination R = 0.994 and R = 0.996,
respectively.

Figure 5.2 shows that the calcium ions released from both

99

)

non-cracked HA ( ) and cracked HA ( ) increased exponentially with
immersion time in distilled water. The data from both the non-cracked and the
cracked HA specimens were fit to equation (1) via a least squares technique,

C = Cs − (Cs − C0 ) exp(−t / τ )

(1)

where C is the calcium ion concentration released into distilled water from
cracked HA, t is the immersing time, Cs corresponds to the plateau value of
calcium concentration at t→∞, C0 corresponds to the calcium concentration in
distilled water at t=0, and τ is a time constant that inversely correlates to the
changing rate of calcium ion concentration.
The least squares fit for non-cracked HA yields Cs = 14.38 ± 0.26 mg/L,
C0-Cs = -13.64±0.31 mg/L (such that C0 is approximately 0.74 mg/L), and τ =
23.74 ± 0.003 hours, with a coefficient of determination, R2 of 0.994. The least
squares fit of the cracked HA data yields Cs = 15.32 ± 0.18 mg/L, C0-Cs =
-15.11±0.30 mg/L (such that C0 is around 0.21 mg/L), and τ =12.01 ± 0.004
hours, with a coefficient of determination, R2 of 0.996.
From Figure 5.1, the concentration of calcium ions released from
cracked HA becomes significantly higher than from non-cracked HA at four
hours. The calcium release rate from the cracked HA surface is faster than that
from non-cracked HA surfaces as indicated by the time constant τ, which is
inversely correlated to the calcium ion release rate, such that the smaller the
value of τ, the faster the release rate. For non-cracked HA, τ = 23.74 ± 0.003
hours, which is about twice the value for the time constant for the cracked HA,

100

where τ =12.01 ± 0.004 hours. Both the higher calcium concentration and the
faster calcium release rate from the cracked HA surface shows that the
dissolution of the HA surface was enhanced by the presence of microcracks
and possibly the increase in surface area from pore dissolution.
Besides the changes in HA dissolution behavior, the introduction of
Vickers indentations can also lead to surface area increases. This increased
surface area resulting from Vickers indentation can be calculated using
equation (2),
∆A ≈ d2/1.8544-d2/2

(2)

where ∆A is the surface area increase, and d is the indentation diagonal
[ASTM E384-11]. The surface increase from each indentation is thus In the
current study, the indentation diagonal d is approximately 45 μm, and the
increase in surface area from each indentation is calculated to be 79.5μm2.
Keeping in mind that pore coalescence is a constant for both the cracked and
the non-cracked HA, the total increase in surface area from the 7Χ7
indentation grid is thus approximately 3,894.6 μm2 which when compared to
the non-cracked surface (2.9 cm2), represents only a 1.3 x 10-3% increase.
Calcium ion signaling is known to control OB growth and differentiation
[Zayzafoon 2006]. Accompanying the release of calcium ions, HA dissolution
releases inorganic phosphate ions, which have also been found to signal OB
differentiation [Beck 2003]. In our study, this increase in calcium ion
concentration is associated with a negligible increase in overall surface area.

101

Therefore, the enhanced cell activity described previously can be said to result
from the presence of the cracks (leading to enhanced Ca and likely P ion
release) and not from the slight added surface area or surface features. To
verify this hypothesis, future studies should examine OB attachment on
microcracked (Vickers indented) and non-microcracked alumina specimens of
comparable surface finish, density and grain size. Alumina should be used
because any enhanced cell activity would only arise from the presence of the
cracks and not from a chemical effect as alumina has been shown by multiple
groups to be inert with respect to osteoblast activity [Malik et al. 1992, Marti
2000, Fischer et al. 2005].

CONCLUSION
Calcium ion release in distilled water from HA is increased by the
presence of microcracks as shown by both a higher calcium concentration in
the early hours and a faster calcium release rate when compared to
non-cracked HA. It is likely that the observed enhanced OB response to
microcracked specimens in the previous chapter is related in part to the
calcium ion concentration changes in the microenvironment at the presence of
the microcracks, and not to the negligible increase in surface area.

102

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CHAPTER 6
CALCIUM PHOSPHATE PRECIPITATION ON HYDROXYAPATE IN THE
ABSENCE OF CELL CULTURE
INTRODUCTION
In chapter 4, mineral deposition on both non-cracked and cracked HA
was observed after cell culturing for 21 days. However, since the dissolution
of HA and the release of calcium ions were observed in the previous chapter
and calcium phosphate crystals can grow on HA surface [Nancollas and
Tomazic 1974], one may wonder how the mineral nodules may form in the
absence of bone forming cell. In other words, it is necessary to find out how
the calcium phosphate precipitation would occur on hydroxyapatite surfaces
in the absence of cells. Thus, in order to compare with mineral deposition by
the cells observed at 21 days in chapter 4, a parallel study was done on
non-cracked and cracked HA surfaces in the absence of cells.

MATERIALS AND METHODS
Non-cracked (control) and cracked HA (experiment) specimens are
prepared as described in previous chapters. Both control and experiment
groups were pulsed with 20 µM Xylenol Orange [Stuart and Smith 1992] in
differential media. The time interval and duration of the Xylenol orange pulse
are the same as described in Chapter 4. In the presence of OB culture
(Chapter 4), Xylenol orange was pulsed every other day starting from day four
(cells reach confluency and start differentiation), ended on day 20 and were

107

imaged on day 21. In this parallel study, we did not have to wait until day four
since no cells were present. However, the amount of fluorescent Xylenol
orange stain should still be consistent with what had been used in Chapter 4.
The Xylenol orange was thus pulsed every other day starting on day one until
day 17 and calcium deposition was imaged on day 18.

RESULTS AND DISCUSSION
Figure 6.1 shows the CLSM micrographs of calcium deposition on
non-cracked (Figure 6.1a) and cracked (Figure 6.1b) HA surfaces. The orange
dots represent the free calcium that has re-deposited onto the substrate
surfaces

b

a

Figure 6.1 CLSM Z-stack maximum fluorescence intensity projections of calcium depositions
on (a) non-cracked and (b) cracked HA in the absence of cell culture. The OBs were pulsed
with Xylenol Orange every other day during culturing since day four. The Xylenol Orange
fluorescence stain was excited at 543 nm and emission was detected through a BA560-620
emission filter (represented in orange).

Figure 6.1 shows that even in the absence of osteoblasts, calcium
phosphate can precipitate from the HA surfaces. Moreover, comparing to
non-cracked HA surface (Figure 6.1a), the radial cracks and edges of

108

indentation impression on the cracked HA surface (Figure 6.1b) are outlined by
more orange dots which correspond to more calcium precipitaion localized at
the radial cracks and indentation edges based on a qualitative observation.
The vicinity of indentation on cracked HA surface shows similar calcium
deposition as non-cracked HA surface.
However, the localized calcium precipitation in the absence of OBs
(Figure 6.1b) is different from the localized mineral deposition by the OBs
(Figure 4.14b). In Figure 6.1b, where no cells were involved, the orange dots
were concentrated at radial cracks and indentation edges, but none in the
indentation center. In Figure 4.14b, where cells were involved, the
concentrated orange dots were filling in the indentation impression rather than
lying along the radial cracks or indentation edges.
In the absence of cells (Figure 6.1b), calcium precipitation is correlated
with the active surface features such as radial cracks and edges. In the case of
OB culture (Figure 4.14b), however, calcium deposition depends on the
cellular matrix secreted by the bone forming cells [Hessel et al. 2002].
The reason why no calcium precipitation was observed along the
radial cracks at the presence of cells can be explained by considering the
relative size of radial cracks and the bone forming cells. The radial crack
opening is a few nanometers [Burghard et al. 2004] and thus likely to be
covered by the osteoblasts (10 ~ 20 µm) and secreted extracellular matrix in
the early attachment and proliferation stages. Since the fluorescent Xylenol

109

orange was only applied upon cell confluence, it is likely that the mineralized
cellular matrix rather than the free HA surface was stained. Different from the
radial cracks, the indentation impression is about 45 µm, which serves as a
natural concave well for the OBs. The ECM secreted by the “trapped” cells
could have altered conformation comparing to the cellular matrix on the flat
surface. The possible alteration in ECM matrix may in turn lead to the localized
mineralization in the indentation impression observed in Figure 4.14b.

CONCLUSIONS
In this study, calcium phosphate precipitation on the HA surfaces were
observed in the absence of osteoblasts. Moreover, the radial cracks and the
edges of the indentation impression on the cracked HA surface showed more
active calcium precipitation as compared to the non-cracked regions.
Different from the observed calcium phosphate deposition along the
cracks and indentation edges, the matrix mineralization in the presence of cells
in Chapter 4 was localized in the indentation impression. This observed
difference is likely due to the relative sizes of radial crack opening, the
osteoblast cells, and the indentation impression. In the absence of cells, the
calcium precipitation from the free HA surface was stained; while at the
presence of cells, the calcium precipitation from the HA surface was
overwhelmed by the mineralization of the cellular matrix.
The CLSM imaging method used in this chapter did not provide a
quantitative measurement of calcium ion concentration as measured using

110

AAS in the previous chapter. However, it could potentially be used to identify
localized calcium precipitation from the cell-free cracked HA surface at early
times.

111

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[Nancollas and Tomazic 1974] Nancollas GH and Tomazic B. Growth of
calcium phosphate on hydroxyapatite crystals, effect of supersaturation and
ionic medium. J Phys Chem 1974; 78: 2218–2225.
[Stuart and Smith 1992] Stuart AJ and Smith DA. Use of the fluorochromes
Xylenol orange, calcium green, and tetracycline to document bone deposition
and remodeling in healing fractures in chickens. Avian Disease 1992; 36:
447-449.

113

CHAPTER 7
OSTEOBLAST SPATIAL DISTRIBUTION AFTER 1, 2 AND 4 HOURS
ATTACHMENT

In this chapter, osteoblast distribution on non-cracked and cracked HA
were discussed and compared. The distribution data were collected from
fluorescent micrographs. The micrographs of cracked HA were taken in a way
such that the indentations were located in the center of the image in order to
include cells from all directions. A polar coordinate system was set up on each
micrograph by choosing the indentation center as the origin and an arbitrary
half radial crack direction as the 0º axis as shown schematically in Figure 7.1.
The cell location is depicted by the blue nucleus and characterized by the
radial distance r and angle α (Figure 7.1).

r
α

Figure 7.1 Schematic of the measurement of osteoblast location with respect to the indentation
region on a cracked HA micrograph. The cell location is characterized by the radial distance
from indentation center, r and angle α.

The distribution of cells on non-cracked HA surfaces was also

114

examined in the same way. Since no indentations were made on non-cracked
HA, the origin was chosen as the center of the micrograph, which allows the
measurement of cells in all directions.

r
α

Figure 7.2 Schematic of the measurement of osteoblast location with respect to the indentation
region on a non-cracked HA micrograph. The cell location is characterized by the radial
distance from indentation center, r and angle α.

The cells on both non-cracked and cracked HA specimens were
imaged after 1, 2 and 4 hours attachment. In order to have a large enough cell
population for a statistical cell distribution analysis, data from 90 images were
pooled together. The data pooling is valid considering that both cell and cell
culture conditions were well controlled and specimen surfaces properties are
comparable.
The cell distribution was considered in a polar coordinate system,
where the indentation center (cracked) or image center (non-cracked) was
chosen as the origin and the arbitrary indentation diagonal as the 0° axis. If the
cells are randomly distributed about the origin, the radial distribution and

115

angular distribution should fit with Rayleigh and Uniform distribution,
respectively [Kuruoglu et al. 2004].
Equation (1) gives the probability density function of one-parameter
Rayleigh distribution:

f (r ; σ ) =

r

1 r
exp(− ( ) 2 ) ,
2 σ
σ2

(r 0)

(1)

where r is the distance from origin, and σ is a continuous scale parameter
[EasyFit]. The probability density function of Uniform distribution is:

f (α ) =

1
,a < α < b
(b − a)

(2)

where θ is the angle from the polar coordinates [EasyFit].
Figure 7.3 shows the radial distance and angular distribution for cell on
non-cracked HA at 1, 2, and 4 hours. The radial distance distributions were fit
to Rayleigh distribution model (equation 1) and the angular distributions were
fit to uniform model (equation 2). The goodness of fitting for cell distributions
on non-cracked HA is listed in Table 7.1.

116

Figure 7.3 The radial distance, r distributions (left column) and the angle, α distributions (right
column) after 1 (first row), 2 (second row) and 4 hours (third row) of attachment on
non-cracked HA. The r distributions were fit to Rayleigh distribution (mauve solid line), and the
α distributions were fit to Uniform distribution (black solid line) using EasyFit. The radial
distance r distributions did not fit to Rayleigh distribution at all hours (p<0.01), while the angle α
distributions were uniform at all hours.
Table 7.1 Goodness of fitting tests for cell distribution data on non-cracked HA
α=0.01

Radial distance data fit to Rayleigh

Angle

distribution

distribution

Chi-Square

Kolmogorov-Smirnov

1 hour

p=2.1130E-7

Fit

2 hour

p=4.6263E-8

Fit

4 hour

p=4.4409E-16

Fit

Goodness of fitting

data

fit

to

Uniform

test

Figure 7.4 shows the radial distance and angular distribution for cell on

117

cracked HA at 1, 2 and 4 hours. The radial distance distributions were fit to
Rayleigh distribution model (equation 1) and the angular distributions were fit
to uniform model (equation 2). The goodness of fitting for cell distributions on
cracked HA is listed in Table 2.

Figure 7.4 The radial distance, r distributions (left column) and the angle, α distributions (right
column) after 1 (first row), 2 (second row) and 4 hours (third row) of attachment on cracked HA.
The r distributions were fit to Rayleigh distribution (mauve solid line), and the α distributions
were fit to Uniform distribution (black solid line) using EasyFit. The radial distance r
distributions did not fit to Rayleigh distribution at all hours (p<0.01), while the angle α
distributions were uniform all hours.

118

Table 7.2 Goodness of fitting tests for cell distribution data on cracked HA
α=0.01

Radial

distance

fit

to

Rayleigh

Angle

fit

to

distribution

distribution

Chi-Square

Kolmogorov-Smirnov

1 hour

p=3.9891E-8

Fit

2 hour

p=6.6613E-16

Fit

4 hour

p=0

Uniform

Fit

Goodness of fitting
test

The spatial distribution for cells on both non-cracked and cracked HA
showed uniform angular distribution. However, the radial distance distributions
disagreed with the Rayleigh distribution, which showed that the cells were not
randomly distributed on the HA surface. It is reasonable since cells are not
isolated from each other but could communicate with each other through
membrane proteins such as integrin and cadherin [Anselm 2000].
A closer examination of the p value from the Chi-square tests for
Rayleigh distribution showed two trends: first, for both control and
experimental groups, the p value decreases with increasing time, which
indicates that the deviation of cell distribution from random distribution
increases with time; second, at a given time, the p value obtained from cracked
HA data is at least one magnitude smaller than the p value from non-cracked
HA data, which indicates that cell distribution on cracked HA is more deviated
from random distribution comparing to cells on non-cracked HA.

119

REFERENCES

120

REFERENCES
[Anselme 2000] Anselme K. Osteoblast adhesion on biomaterials. Biomaterials
2000; 21-667-681.
[Kuruoglu and Zerubia 2004] Kuruoglu EE and Zerubia J. Modeling SAR
images with a generalization of the Rayleigh distribution. IEEE Trans Image
Proc 2004; 13: 527-533.

121

CHAPTER 8
SLOW GROWTH OF MICROCRACKS IN HYDROXYAPATITE DURING
AGING

ABSTRACT
Hydroxyapatite (Ca10(PO4)6(OH)2 or HA) is a brittle material that is
subject to environmentally assisted slow crack growth. While most slow crack
growth studies are carried out after aging, this study examines the slow growth
of radial cracks induced by Vickers indentation in dense HA (94% of theoretical
density) during aging in ambient air, where the observed crack growth is
consistent with a process in which residual stress drives crack growth. For
indentation loads of 0.98 N, 1.96 N, 2.94 N, and 4.91 N, the average radial
crack length increased exponentially with time for indentation loads of 0.98 N,
1.96 N, 2.94 N, and 4.91 N, with crack lengths saturating within one hour
following indentation. However, no radial crack growth was observed for 9.81
N loads. The load dependence of radial crack growth is proposed to be linked
to the partitioning of residual strain energy by the lateral crack growth, which
has not been reported in the literature.

122

INTRODUCTION AND BACKGROUND
Hydroxyapatite (Ca10(PO4)6(OH)2 or HA) has been widely applied as a
catalytic substrate [Mori et al. 2003 and 2004, Venugopal and Scurrell 2003],
CO2 gas and humidity sensors [Nagai and Nishino 1988, Owada et al. 1989],
insulating materials for electric circuits, dielectric layers for microwave
applications [Hontsu et al. 1997], substrates for heavy metal removal [Silva et
al. 2006, Raicevic et al. 2005], and for hard biological tissue replacement [Park
and Lakes 2007]. During the in-service lifetime, fabrication and handling of
brittle materials, both residual stresses and cracks can be introduced by
structural mismatch, thermal expansion anisotropy, as well as by interactions
among contacting parts [Withers and Bhadshia 2001]. Slow crack growth may
lead to catastrophic failure, which in turn limits a component’s useful life
[Michalske and Freiman 1983, Connally and Brown 1992, Tomozawa 1996,
West and Hench 1998].
Slow crack growth behavior in HA and other brittle ceramics is usually
described in terms of a V-KI relationship where V refers to the crack velocity
and KI, the mode I stress intensity factor (equation 1) [Wiederhorn 1974].

V = AK In

(1)

where A is a constant and n is a propagation exponent which characterizes the
material’s resistance to mechanical fatigue. For HA, the n value is lower than
30, and thus is considered as materials with high susceptibility to slow crack
growth [Choi et al. 2006]. Both indirect static/dynamic fatigue tests [Raynaud et

123

al. 1998, Barinov et al. 2003, Schell et al. 2010] and direct measurements of
crack velocity via double torsion tests [Benaqqa et al. 2004 and 2005] have
been used to explore the V-KI behavior of brittle materials. The slow crack
growth exponent, n, obtained from either indirect or direct methods, describes
a materials' resistance to delayed mechanical fatigue [Wiederhorn 1974]. For
HA, the n value is lower than 30, and is considered as materials with high
susceptibility to slow crack growth [Choi et al. 2006].
The relative ease in controlling the load, loading time, and indentation
location has led to Vickers indentation cracks as crack growth models for
studies of slow crack growth [Dwivedi and Green 1995, Salomonson et al.
1996], thermal shock/thermal fatigue [Anderson and Rowcliffe 1996, Lee et al.
2002], thermally-induced crack healing [Chlup et al. 2008, Wilson and Case
1997 and 1999], cracking/delamination in coatings [Galmen et al. 1991,
Ibrahim et al. 2007], contact flaws introduced during processing or handling of
brittle materials [Lawn and Wilshaw 1975, Lawn et al. 1993], and in vitro cell
responses to microcracks in bioceramics [Smith 2007, Shu submitted 2011].
In general, during Vickers indentation, the residual stress from plastic
deformation left upon unloading is responsible for the development of both the
radial and the lateral crack systems [Lawn et al. 1980, Marshall et al. 1982].
The detailed role of residual stresses in crack formation and propagation
during Vickers indentation is described in Appendix A of this chapter. The
relationship between equilibrium radial crack length cR and the maximum

124

indentation load, F, is described by equation (2),

{

}

c R = §R (cotψ ) 2 / 3 [( E / H )1/ 2 / K C ]
r
where

R
§r

2/3

F 2/3

(2)

is a dimensionless constant independent of indenter and
R

)
specimen ( §r =0.032), ψ (68° is the half angle for Vickers indenter tip, the
Young’s modulus, E, hardness, H, and fracture toughness, KC can all be
considered invariant for a system at equilibrium with its surroundings [Lawn et
al. 1980]. A similar relationship between equilibrium lateral crack length cL and
the maximum indentation load, F, is described by equation (3),

{

}

c L = (ζ L / G 1 / 2 )(cot ψ ) 5 / 6 [( E / H ) 3 / 4 / K c H 1 / 4 ]
where

ζL

1/ 2

F 5/8

(3)

is a dimensionless constant independent of indenter and specimen

( ζ L =0.025), G is a dimensionless geometrical constant and has a value of 3/4
when the lateral crack length is less than the radial crack length (quarter plate)
[Marshall et al. 1982].
Radial cracks received most attention as model cracks, and the crack
velocities are typically measured after the release of residual stresses via the
aging process [Ritter et al. 1971, Marshall and Lawn 1980, Chantikul et al.
1981]. However, the literature does not address crack growth behavior during
the aging process.
This study focuses on slow crack growth during aging in ambient air
for Vickers indentation induced radial cracks in 94% dense HA. Radial crack
lengths were measured after indentation and during room temperature aging in
air at loads of 0.98 N to 9.81 N. The occurrence and relative size of lateral

125

cracks at all loads are also evaluated to assess the perturbation from lateral
cracks during the slow growth of radial cracks.

EXPERIMENTAL PROCEDURE
Materials and characterization methods
HA powders (Taihei Chemical Industry, Osaka, Japan) with
vendor-specified particle size of 4 to 6 µm were uniaxially pressed at 27.65
MPa for one minute in a 32 mm diameter steel pellet die. The specimens were
then sintered in an electrical resistance furnace (CM Inc., Model #0100277,
Bloomfield, NJ) at 1360oC for 4 hours in air at a ramp rate of 10oC per minute
during both heating and cooling. The sintered specimens were polished using
diamond paste of grit size down to 0.5 µm before microindentation.
Specimen mass and dimensions were measured using an electronic
analytical balance (Denver Instrument Company, Arvada, CO; accuracy,
±0.001 gram) and an electronic digital caliper (Davis Calibration, Carol Stream,
IL; accuracy, ±0.01 mm) respectively. Bulk densities were calculated from the
mass and dimension measurements.
One polished specimen was thermally etched in air at 1360oC for 1
hour in the same furnace used for sintering the indented specimens. Following
thermal etching, the specimen was coated with a 21 nm thick film of Au using a
gold sputter coater (EMSSCOPE SC500, Ashford, Kent, Great Britain). The
microstructure (grain size and porosity) was examined using a scanning
electron microscope (JEOL-6400V SEM, JEOL Ltd., Japan) using an

126

accelerating voltage of 20 kV and a working distance of 39 mm.
For chemical and phase composition characterization, X-ray diffraction
(XRD) analysis was performed on both the as-received HA powders and
pulverized powder from sintered HA specimens, as described in detail in
Chapter 4.

Vickers indentation and crack length measurement.
Radial and lateral cracks on polished surfaces were introduced by
Vickers indentations in ambient air using Shimadzu microhardness tester
(HMV2000, Kyoto, Japan) at five loads (0.98 N, 1.96 N, 2.94 N, 4.91 N and
9.81 N). For each load, a total of 15 indentations were made with a loading
time of 5 seconds. The hardness, H, and fracture toughness, KC, of HA
specimens included in this study were determined from the measurements of
indentation diagonal and initial radial crack length.
The indentation impression centers were placed at least five times of
the radial crack length (2cR) apart to minimize possible interactions between
adjacent radial cracks. The radial crack lengths (2cR) were measured at
approximately fifteen minute intervals during the first, third, and fifth hours
following indentation, using an optical microscope mounted on the Shimadzu
microhardness tester. The lateral cracks lengths (cL) visible on the polished
specimen surfaces were measured in the same way as the radial cracks.

127

RESULTS AND DISCUSSION
Material characterization
The sintered HA specimens reached an average of 94% of theoretical
density (3.16 g/cm3) [Anthony et al. 2000]. The average grain size of sintered
HA specimen is approximately 7.9 µm as determined by linear intercept
method (a total of 210 intercepts) on micrographs of polished specimen
surfaces using a stereographic projection factor of 1.5 (Figure 8.1a) [Fulrath
and Pask et al. 1968]. The polished HA surfaces has uniformly distributed
spherical or quasi-spherical isolated pores with diameters ~3 µm (Figure 8.1b).
From a previous study [Shu submitted 2011], the XRD analysis of as-received
HA powder and pulverized sintered HA specimen showed only the crystalline
HA phase was present (JCPDS 9-432, Joint Committee on Powder Diffraction
Standards, Swarthmore, PA).

Figure 8.1 SEM images of (a) a thermally etched surface of a 94.3% dense HA specimen,
where the average grain size calculated using line intercept method (a total of 210 intercepts)
was 7.9 µm and (b) a polished surface of a 95.4% dense HA specimen, where uniformly
distributed spherical or quasi spherical pores with a few interconnected or entrapped pores
were observed. The diameters of the surface-breaking pores are less than 3 µm.

128

E, H, and Kc for HA specimens
The porosity dependence of Young’s modulus, E, can be
described by equation (4),
E = E0 exp(-bEP)

(4)

where E0 is the Young’s modulus for theoretically dense specimen, bE is a
dimensionless material-dependent constant, and P is porosity [Spriggs 1961].
In Fan et al.[submitted 2011] and Ren et al.’s [2009] studies of HA with porosity
ranging from 0.05 to 0.62, the Young’s modulus data measured at different
porosity, a least-squares fit to equation (4) yielded E0 = 133.3 GPa, bE = 3.8
and a coefficient of determination, R2=0.974. Using equation (4) and E0 and bE
values from Fan and Ren et al.’s studies yields E = 106.1 GPa for the HA
specimens (P = 0.06) included in this study.
The Vickers hardness was calculated using equation (5) [ASTM C
1327-03],
H = 1.8544F/d2

(5)

where F is the maximum indentation load and d is the Vickers indentation
diagonal. The average H of HA specimens used in this study was 4.50 ± 0.19
GPa.
The hardness of ceramics is also a function of porosity as described
by equation (6),
H = H0 exp(-bHP)

129

(6)

where H0 is the hardness for theoretically dense specimen, bH is a
dimensionless constant dependent on material properties, and P is porosity
[Rice 1996]. The hardness values calculated from Hoepfner’s and Dey’s data
using equation (6) are 4.17 GPa and 4.16 GPa respectively, which are similar
to the H=4.50 ± 0.19 GPa for HA in this study.
The fracture toughness was obtained from equation (7) [Lawn et al.
1980, Antis et al. 2006],

KC = δ (

H −1 / 2 F
)
R
E
c0

(7)

where the empirically determined constant δ = 0.016, independent of material
R

properties. F is the maximum indentation load and c0 is the initial half radial
crack length. Using equation (7), and E = 106.1 GPa and H = 4.50 ± 0.19 GPa
(as described above) yielded the average KC = 0.484 ± 0.26 MPa·m1/2 for HA
specimens in this study. The KC of HA coatings (P = 0.11) measured by Dey et
al. was approximately 0.6 MPa·m1/2, which is slightly higher than the KC of bulk
HA specimens in this study [Dea and Mukhopadhyay 2011].

Load dependence of initial radial and lateral crack lengths
The average of 30 initial radial crack lengths at each of the loads (0.98
N, 1.96 N, 2.94 N, 4.91 N and 9.81 N) was fit via a least-squares technique to
equation (8) (Figure 8.2a) which is a simplified form of equation (2),

l0 = B R F 2 / 3

130

(8)

where l0 is the average initial radial crack length ( l 0

R
= 2c0 ), BR is a

constant that depends on material properties, and F is the indentation load
(Figure 8.2a) [Lawn et al. 1980]. The initial radial crack length, l0,
increases when the load, F, increases as described by equation (8),
where a value of BR = 65.2 ± 1.1 µm·N-2/3 was obtained by the least
squares fit, with the coefficient of determination, R2 = 0.997.
The constant BR in equation (8), which depends on materials
properties, can also be calculated from the knowledge of E, H, and KC
determined for HA specimens used in this study (section 4.2). The
calculated BR value is approximately 62.3 µm·N-2/3, which is a factor of
0.04 lower than the value of 65.2 ± 1.1 µm·N-2/3 obtained for BR from the
least square fitting of initial radial crack length versus indentation load
data to equation (8). The measurement of radial crack length thus yielded
a constant that was close to the constant determined by the material
properties (E, H, and KC).
Similarly, the initial lateral crack lengths measured at all loads
(0.98 N, 1.96 N, 2.94 N, 4.91 N and 9.81 N) were least-squares fit to
equation (9) (Figure 8.2b) which is a simplified form of equation (3),
L
c0 = B L F 5 / 8

where

L
c0

(9)

is the average initial lateral crack length, BL is a constant

depending on material properties and indenter geometry when referring to
equation (3) such that

131

{

}

B L = (ζ L / G 1 / 2 )(cot ψ ) 5 / 6 [( E / H ) 3 / 4 / K c H 1 / 4 ]

1/ 2

, F is the indentation

load (Figure 8.2b) [Marshall et al. 1982]. The initial lateral crack length,
L
c 0 increases when the load, F, increases as described by equation (9),

where a value of BL = 24.9 ± 0.6 µm·N-5/8 was obtained by the least
squares fit, with the coefficient of determination, R2 = 0.998.

Figure 8.2 (a) The average initial radial crack length as a function of Vickers indentation loads.
The error bars represent the standard deviations. The collected data were fit to equation (8).
2

The coefficient of determination R is 0.997. (b) The average initial lateral crack length as a
function of Vickers indentation loads. The error bars represent the standard deviations. The
2

collected data were fit to equation (9). The coefficient of determination R is 0.998.

Using the E, H, and Kc values for the HA specimens used in this study,

132

the BL value is calculated to be 8.8 µm·N-5/8, which is a factor of 0.65 lower
than the value of for BL obtained from the least square fitting of the initial lateral
crack length versus indentation loads data to equation (9). In contrast to radial
cracks (section 4.3.1), the measurement of lateral crack length yielded a
constant that largely deviated from the constant determined by materials
properties (E, H, and Kc).
Up to this point only the load dependence of initial radial and lateral
crack lengths was considered. The cracks evolve with time and the evolution
as well as the final stage of both radial/lateral crack systems will now be
considered, since in choosing model crack, one must consider not only the
crack initiation itself but rather the temporal development of the crack during
aging in specific environments, such as ambient air or aqueous environment
[Dwivedi and Green 1995, Salomonson et al. 1996]. In the following section,
the slow growth of radial cracks and the perturbation from lateral cracks during
aging in ambient air at room temperature are discussed.

Radial crack growth and perturbation from lateral cracks during aging
Load dependent exponential growth of radial cracks
The radial crack lengths, l, increased significantly within the first hour
following indentation and reached a plateau for indentation loads at 0.98 N,
1.96 N, 2.94 N, and 4.91 N (Figure 8.3). The physical radial crack growth
process, for the release of residual strain energy after Vickers indentation
(Chapter 8 - Appendix A) resembles the evolution processes of many physical

133

systems. In those systems, there is a physical quantity that decreases
exponentially with time, such as the electric charge in the case of capacitor
discharging, number of particles in the case of radioactive decay [Halliday et al.
1997], thermal energy in the case of Newtonian free cooling [Burmeister 1993],
or the vibrational energy in the case of internal friction damping in solids
[Reed-Hill 2009]. For the four physical systems listed above, the evolution of
all physical quantities is such that the time rate change of each physical
quantity is a linear function of the physical quantity itself. If we relate this to our
current observation with radial cracks, we may consider the growth rate of
radial cracks as a linear function of the radial crack length.

Figure 8.3 The average radial crack length as a function of time, normalized with respect to the
initial radial crack length at each load. The normalized values were then plotted versus time
with a common unit value at time zero. The error bars represent the standard deviation. The
2

collected data were fit to equation (11). The coefficient of determination R for the 0.98 N, 1.96
N, 2.94 N, and 4.91 N loads were 0.934, 0.931, 0.987, and 0.992, respectively.
•

When the time rate of change of a dependent variable, y , is linear with
respect to its value, y, the time dependence of y is described by equation (10)

134

[Apostol 1962].
•

y (t ) = Cy (t ) + D

(10)

where C (nonzero) and D are constants.
If we apply equation (10) to the slow radial crack growth problem
(Figure 8.3), the variable y is replaced by radial crack length, l (l=2cR). The
boundary conditions are l=l0 at t=0, and l=lS at t→∞, where l0 and lS are the
initial and saturated (steady state) crack length respectively. In this case l0 is
obtained by direct measurement of the initial radial crack length (Figure 8.2a)
and lS is determined from the plot of radial crack length versus time (Figure 8.3).
Applying the boundary conditions, the solution of equation (10) yields an
exponential relationship between l and t, as given by equation (11).

l = l s − (l s − l0 ) exp( −t / τ )

(11)

where τ is a time constant that is inversely related to the time rate of change of
crack length, i.e., larger the τ value, slower the crack growth. The observed
exponential radial crack growth is probably a combined result from the residual
strain energy dissipation and the existence of water in the ambient air, as the
presence of water may reduce the energy barrier required for the formation of
new fracture surfaces [Michalske and Freiman 1983].
While the exponential growths of radial cracks were observed for the
lower four loads (0.98 N, 1.96 N, 2.94 N, and 4.91 N), no radial crack growth
was observed for the highest load, 9.81 N, which indicates that the exponential
growth of radial cracks is load dependent. A closer examination of τ for the four

135

indentation loads that induced exponential radial crack growth did not yield a
specific pattern as shown by Figure 8.4, which indicates that the crack growth
rate may not be load dependent.

Figure 8.4 The time constant τ obtained from the least-square fit of equation (11) to the
average radial crack length versus time data for the 0.98 N, 1.96 N, 2.94 N, and 4.91 N loads.
The error bars represent the standard deviation from each curve fitting.

It is important to note that the exponential growth model was deduced
by considering radial crack growth as a result of the release of residual strain
energy. In the Vickers indentation system, however, lateral cracks may also
occur in parallel with radial cracks and share the same residual strain energy
reservoir for growth. Thus, the perturbation from lateral cracks may contribute
to the lack of radial crack growth at 9.81 N and influence the radial crack
growth rate at the four lower loads.

Perturbation from lateral crack
Ideally, after Vickers indentation, a completely evolved crack system
has two radial cracks aligned with the indentation impression diagonals and

136

four lateral cracks in the subsurface region near the hemispherically deformed
zone, intercepting the specimen surface in quarter sections divided by radial
cracks (shown schematically in Figure 8.5) [Lawn et al. 1980]. Lateral cracks
that have initiated but not fully evolved are subsurface and difficult to observe
until they intercept the free surface of the specimen.

cL

cR

R

Figure 8.5 A schematic of the fully developed indentation crack system, where c is the half
L

radial crack length and c is the lateral crack size.

In this study, 30 individual radial cracks were observed for each load
(two radial cracks from each of the 15 indentation sites for a given load).
However, instead of 60 lateral cracks (four from each indentation site), the
number of observed lateral cracks were 37 at 0.98 N, 47 at 1.96 N, 58 at 2.94
N, 57 at 4.91 N, and 59 at 9.81 N, respectively (Figure 8.6). Thus, while the
radial crack systems were completely evolved at all loads, the lateral cracks
were less likely to intersect the specimen surface at lower loads, although they
may have initiated near the hemispherical deformation zone. However, with
increasing load, there is an increasing likelihood of a fully developed lateral

137

Frequency of lateral
crack occurence

crack system (Figure 8.6).

60
40
20
0
0.98 1.96 2.94 4.91 9.81
Load (N)

Figure 8.6 The relative frequency of lateral cracks observed intersecting with free surface from
15 indentations at each of the five Vickers indentation loads (0.98 N, 1.96 N, 2.94 N, 4.91 N,
and 9.81 N).

For all indentation loads, significant increases from initial lateral crack
lengths to saturated lateral crack lengths were detected using paired student’s
t-test (p < 0.01) [Bethea et al. 1985]. The ratio of
calculated and compared at all loads, where
and radial crack lengths, while

csL and csR

L
c0

L
R
c0 / c0

and

R
c0

and

csL / csR

are

are initial lateral

are saturated lateral and initial

crack lengths, respectively.
As shown in Figure 8.7, both the relative initial crack length
and the relative saturated crack length
load. Also, the saturated

csL / csR

csL / csR

L
R
c0 / c0

increased with increasing

ratio were lower than the initial

L
R
c0 / c0

ratio for the four lower loads, and the contrary trend was observed for the
highest load (9.81 N), which strongly indicates that the energy partitioning by
lateral cracks increases with increasing load and lateral crack growth becomes
dominant at higher load.

138

L

Figure 8.7 The average ratio of initial lateral crack length ( c 0 ) over half initial radial crack
R

length ( c 0 ) (

L

), and the average ratio of saturated lateral crack length ( c S ) over half
R

saturated radial crack length ( c S ) (

) as a function of Vickers indentation loads. The error

bars represent the standard deviations.

Under the assumption that the stored strain energy is partitioned
between radial and lateral cracks, the load dependence of the radial cracks
growth (section 4.4.1) thus is directly related to the evolvement of the lateral
cracks (Figure 8.6 and 8.7). As load increases, the total plastic strain energy
increases, however, the relative fraction of residual strain energy available for
driving radial cracks growth may decrease due to the increasing share of
companying lateral crack. This explains the absence of radial crack growth
with time at 9.81 N, in which case the residual strain energy was likely
consumed mostly by the lateral crack growths.

Other factors that may affect the growth of radial cracks
In addition to perturbation from lateral cracks, other factors such as

139

microcracking, porosity as well as grain size and shape, can affect the growth
of indentation cracks. Any material with lower atomic symmetry than cubic is
subject to microcracking due to TEA [Case et al. 2005]. Since HA is not cubic
(the unit cell of HA (a = b = 9.432 Å, c = 6.881 Å) [Kay et al. 1964], HA is a
noncubic material. Microcracking in single phase HA has been confirmed by
Case et al [2005]. Pre-existing microcracks from TEA may in turn affect the
indentation crack behavior via crack branching [Nie et al. 2009, Zhang et al.
2003] and by lowering the local [Swan 1990] as well as the global [Sridhar et al.
1994] elastic modulus.
Since isolated quasi-spherical pores are present in the HA substrates
used in this study (Figure 8.2), it is necessary to keep in mind that porosity also
influences crack behavior. In a study of SiC, Deng et. al. identified that the
reinforcement of porous ceramics through crack tip blunting [Deng et al. 2004],
where crack propagation in a dense body showed a sharp crack-tip, but
showed a blunt crack-tip in porous ceramic body.
The mean grain size of HA specimens in this study is approximately
7.9 µm, which is smaller than the dimensions of the smallest indentation
impression (19 µm at 0.98 N). However, when the grain size and indentation
size become comparable, local grain failure can disrupt the radial/lateral crack
pattern [Shivakuma and Crews 1987]. Also, though not observed in the current
study, the variation in grain shape and orientation may affect the fracture
pattern of Vickers indentation, since grain boundaries can deflect crack

140

propagation [Faber and Evans 1983, Suresh 1983].
Ambient environment may also affect the slow crack growth behavior.
Environmentally assisted crack growth refers to an enhancement in crack
growth that takes place due to a stress-enhanced chemical reaction at the
highly strained region near a crack tip [Michalske and Freiman 1983,
Wiederhorn 1968, Freiman et al. 2009]. In particular, when exposed to water,
HA exhibits higher susceptibility to slow crack growth than in air as indicated by
n values of 10 ± 4, 11.3, 11 measured in water, which are lower than the n
values measured in ambient air (n = 22.5 ± 2, 19.8, 23) [Raynaud et al. 1998,
Barinov and Shevchenko 1995, Barinov et al. 2003].

SUMMARY AND CONCLUSIONS
This paper addresses the slow growth behavior for Vickers indentation
induced radial/lateral cracks in hydroxyapatite during the aging process in
ambient air at room temperature. For each of the five applied indentation loads
F, the residual strain energy was released through radial and/or lateral crack
propagation during the first hour of aging in air.
The radial cracks grew exponentially (equation 11) at four indentation
loads (0.98 N, 1.96 N, 2.94 N, 4.91 N) (Figure 8.3). No specific trend was
observed for radial crack growth rate as characterized by the time constant τ
for the four indentation loads (0.98 N, 1.96 N, 2.94 N and 4.91 N) selected in
this study (Figure 8.4).
However, the radial cracks did not grow at F = 9.81 N, likely due to a

141

load dependent change in the partitioning of strain energy from the
hemispherically deformed zone to the radial and lateral cracks, with the result
being that post-indentation lateral crack growth became dominant at higher
load levels. With increasing indentation load, we observed an increase in both
(1) the frequency of occurrence of the lateral cracks (Figure 8.6) and (2) the
relative lateral/radial crack ratio (Figure 8.7), both of which reflect the increase
in the relative “share” of the residual strain energy with the radial crack system.
This study suggests that the slow growth of radial cracks is a load
dependent process, which has not been reported previously in the literature.
Using measurements of the time dependent radial and lateral cracks lengths
along with a simple model of the energy partitioning, we propose that the load
dependence of radial crack growth is linked to this partitioning of residual strain
energy.
If lateral crack growth very suppressed, then the extension of radial
crack length due to adding in a humid or aqueous environment may occur for
all loads. However, indentation-induced residual stress and the emergence of
both a median/radial crack system and a lateral crack system add complexity
to Vickers indentation induced radial crack growth behavior [Lawn et al. 1980,
Marshall et al. 1982].
Thus, when using Vickers indentation radial crack as the model crack
as mentioned in the introduction section, both the environmental assisted slow
growth of radial crack and the disturbance from lateral cracks should be

142

treated carefully. Also, it is important to note that when there are concentrated
residual stress introduced into a brittle material body, crack propagation may
take place in the form of both radial cracks (cracking) and/or lateral cracks
(chipping, spalling or flaking) [Ahr et al. 2003, Srinivasam et al. 1990, Swain
and Lawn 1976].

APPENDIX A THE ROLE OF RESIDUAL STRESS IN CRACK
FORMATION/PROPAGATION DURING VICKERS INDENTATION
This study focuses on the time and load dependence of Vickers radial
and lateral cracks as they evolve during post-indentaion aging in humid air.
Vickers indentation tips with an included angle of 136° were described by
Chiang et al. [1982] as generating an elastic/plastic deformation mode. During
a complete cycle of loading and unloading of a Vickers indentation, median,
radial and lateral cracks may form. The two crack systems were classified
according to their orientations with respect to the loading plane, where
median/radial cracks lay within the loading plane while lateral cracks lay in
planes parallel to the surface [Lawn et al. 1980]. During loading, downward
tensile stress favors the propagation of the median crack, and the radial/lateral
crack propagation was prevented by the asymmetric compressive stress within
the elastic field. Upon unloading, the residual plastic zone remained, driving
radial/lateral crack growth [Lawn et al. 1980]. Both radial and lateral cracks
were observed upon unloading in the current study at all indentation loads
(0.98 N, 1.96 N, 2.94 N, 4. 91 N, 9.81 N).

143

Since in the current study, the growth of radial/lateral cracks were
observed when no external stresses were applied, it is then curious that where
the driving energy may come from and how many energy sources there might
be. In a comprehensive review of indentation fracture, Lawn and Wilshaw
proposed a simplified model of the stress field about Vickers indentations
[Lawn and Wilshaw 1975]. The material directly in contact with the indenter tip
was assumed to form a “hydrostatic core” which exerts pressure on the
surrounding material and results in the formation of a “plastic zone”, where
both the plastic zone and the hydrostatic core were assumed to be spherically
symmetric. Beyond the “plastic zone” was the “elastic matrix” [Lawn and
Wilshaw 1975]. An irreversible residual plastic deformation zone was created
during loading and persisted after unloading beneath the indentation
impression as a compressed semi-sphere within the elastic matrix [Lawn et al.
1980]. The stored residual strain energy in that hemispherical deformation
zone is thus what is left to provide the driving energy for the observed growth
of both radial and lateral cracks in this study.
The role of residual stress in driving the observed crack growth should
not be confused with the role of water discussed in section 2. Residual
stresses from the plastic deformation zone under Vickers indentation is acting
like an energy reservoir for the growth of both radial and lateral cracks upon
unloading. However, the existence of water does not provide energy but rather
lower the energy barrier required for the advance of radial cracks tips. Also,

144

note that only cracks on the free surface are exposed to water, thus water may
assist the growth of radial cracks but could not affect the subsurface
propagation of lateral cracks.
The role of residual stress in driving both radial/lateral cracks upon
unloading showed that there must be a partitioning between the stored strain
energy between radial and lateral cracks as pointed out multiple times in the
paper.

145

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CHAPTER 9
SUMMARY AND FUTURE DIRECTIONS

This project is illustrated by anecdotal data showing that in the
fractured bones of racing horses and/or greyhound, microcracks coincided
with bone densification. The formation of microcracks not only dissipates
excessive energy and prevents catastrophic fracture, but may also induce
bone remodeling. Though microcracks are a widely-recognized defect in
engineering ceramics, it may also be a beneficial feature in bone scaffold
design in terms of stimulating bone formation. The current project is thus
designed to investigate the osteoblast (bone forming cell) response to
microcracks.
In this project, microcracks were introduced into hydroxyapatite
scaffold using Vickers indentation. The temporal development of osteoblasts
on non-cracked (control) and cracked (experiment) were compared. The
presence of microcracks was shown to induce OB alignment and enhance OB
attachment as well as maturation, which indicates that microcracks are able to
signal faster bone formation in vitro.
The underlying mechanism for the observed OB response to
microcracks may be attributed to the increase in calcium ion concentration
(Chapter 5) and the alteration in the extracellular matrix (Chapter 6 and
Appendix A) due to the presence of microcracks. It is likely that at the early
attachment phase, the calcium ion increase in the local environment guides

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cell migration towards the cracks. The radial crack tips as well as the lateral
crack spalling may be then sensed by the arriving cells, which results in varied
conformation of their extracellular matrix. The alteration of the arriving cells
may further affect other approaching cells and leads to the observed OB
alignment around the crack boundary.
With extended time, the cells on the HA surface become confluent and
proceed into the differentiation stage. The cells and their ECM that fill in the
indentation impression is likely to have a different conformation and present a
different mechanical strain field as compared to the cells and ECM on the flat
surfaces. According to the local strain-cue model (Appendix A) [Cox 2010],
local variations in the mechanical strain field may contribute to the localized
mineral deposition observed in the CLSM micrographs shown in Chapter 4.
In order to prove the above hypothesized mechanisms, future studies
should be done to verify the following two aspects: First, osteoblast migration
in response to calcium gradients in the local environment should be assessed
by introducing calcium source, such as soluble calcium phosphate during cell
culturing; second, alteration in the strain field within the cell and ECM localized
at the microcrack region should be measured using computational methods. A
live cell imaging could be carried out to monitor the cell migration, which may
provide an experimental basis for establishing a strain-cue model to simulate
the cellular response to the presence of microcracks.
In the current study, microcracks were introduced using Vickers

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indentations as described in Chapter 4. Though Vickers indentations can be
well controlled, the radial and lateral crack patterns, as well as the indentation
impression, comprise a complex surface feature. Thus, other machining
methods that can separate radial cracks, lateral cracks, and the indentation
impression could be used. One possible choice is to use the Sonic Mill, which
enables the introduction of slots or any other surface features of interests onto
substrate surfaces. The flexibility of Sonic Mill could be applied to introduce
desired surface features to investigate cellular responses in future studies.
Comparing to Vickers indentation, slots introduced using Sonic Mill will not
present sharp tips as radial cracks and their sizes (length and opening) will be
considerably larger than cracks introduced using Vickers indentation.
Besides probing into the underlying mechanism, future studies could
also be done to investigate the practical value of introducing microcracks to
artificial scaffolds that are already on the market, to study the in vivo bone
healing process in animal models.

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APPENDICES

157

APPENDIX A
BONE RESPONSE TO MECHANICAL STIMULI AND THE LOCAL
STRAIN-CUE HYPOTHESIS
The adaptability of bone to mechanical stress/strain had long aroused
people’s interests. Wolff’s law which stated that the distribution of bone mass
was determined by the distribution of mechanical stress was proposed in 1892
[Wolff 1892]. Twenty years later, Thomson [1961] emphasized the importance
of mechanical strain rather than stress in directly stimulating bone growth
[Thompson 1961]. Frost [1964] further pointed out there was a minimum strain
threshold to be met for bone adaption to happen in 1964. Liskova and Hert
[1971] made an important leap by demonstrating dynamic strains rather than
static strains that induced bone increase in 1971. After that, the importance of
peak strain and loading waveform frequency (the number of cycles per second)
to bone adaptation were proved by Rubin and Lanyon [1985 and 1994] around
1980s. Turner et al [1995] further confirmed the importance effects of strain
rate and loading frequency in modifying bone growth. Following the discovery
of the importance of dynamic/cyclic loading, a saturation of bone mass
increase was demonstrated after a short loading period by Rubin and Lanyon
[1984] using avian ulna, and by Umemura et al [1997] using rat tibia. Further
more, bone adaptation was more driven by “abnormal” loading conditions
rather than “normal” daily activities as proposed by Lanyon [1992], which
showed the possibility of accommodation of bone to routine activities within a
certain range on a cellular level.

158

Extensive studies had also been carried out to investigate the
dependence of bone adaptation on strain type, magnitude, frequency, and
distribution. The bone adaptation studies have been carried out both in vitro
and in vivo and at both macro and micro levels by different researchers.
In order to carry out experiments that could simulate bone growth in
vivo, the quantification of strain experience by bone is a must. Fritton and
Rubin [2001] had reviewed the peak strain and strain rate measured in
different species and different activities, which could vary from less than 1000
microstrain to 5000 microstrain. However, this gives only the information of
normal functional strain, the driving force for bone adaption as proposed by
Lanyon [1992] (i.e., the abnormal loading superimposed on normal functional
strain) is not determined. Lots of studies found a correlation between strain
magnitude and frequency, such that the minimum strain magnitude required to
induce bone growth decreases with an increase of frequency. For example, in
Rubin et al’s study with the isolated avian ulna model, a mechanical load of
500 microstrain had no effect on osteogenesis at 1 Hz, while obviously
enhanced osteogenesis at 10 Hz and above [Rubin and McLeod 1994].
Robling and Turner [2009] found that at 1 Hz, the minimum strain needed to
initiate bone formation is 1820 microstrain, but dropped to 1180 microstrain at
5 Hz, and dropped to only 650 microstrain at 10 Hz.
The mechanical stimuli occur in vivo include compression, tension,
fluid shear components. Each of the above components and/or combinations

159

of them has been extensively studied by different researchers using various
techniques. Dong et al [2001] analyzed the alkaline phosphatase activities by
subjecting osteoblast seeded on a porous hydroxyapatite scaffold under a set
of low pressures, which were 760 mmHg (normal atmospheric pressure), 500
mmHg, 250 mmHg, 100 mmHg, 50 mmHg, and 10 mmHg for durations of 4
weeks and 8 weeks. They found that the 100 mmHg showed highest ALP
acitivity, and ALP activity was higher at 4 weeks than 8 weeks in all groups.
Song et al [2007] studied the proliferation of human bone marrow
mesenchymal cells (hMSCs) by applying cyclic longitudinal mechanical stretch
with different magnitude, frequency, and duration. At a fixed strain 10% and
duration of 15 minutes, 1.0 Hz showed highest relative proliferation
(normalized with control 0 Hz) compared with 0.01 Hz, 0.1 Hz, 0.5 Hz, and 1.5
Hz. At a fixed frequency 1.0 Hz, proliferation of hMSCs was enhanced at 5%
strain for 15, 30, and 60 minutes, was enhanced at 10% strain for 15 and 30
minutes, was enhanced at 15% for 30 and 50 minutes, and longer durations of
12 hours and 24 hours blocked proliferation. Shivaram et al [2010] applied a
maximum shear stress of 1 Pa using a sinusoidal wave form at 1 Hz to
MC3T3-E1 osteoblasts, and showed an up-regulation of 103 known genes and
expressed sequence tags (ESTs) and down-regulation of 67 known genes and
ESTs.
Techniques could be applied to simulate mechanical input in vivo such
as compressive, tensile, and shear strain were reviewed in great detail by

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Brown [2000]. Compressive stresses could be achieved by using hydrostatic
pressure and/or direct platen abutment; tensile stresses could be applied using
uniaxial tension, substrate bending and out-of-plane or in-plane circular
substrate distention (Flexercell uses vacuum to realize substrate deformation);
shear stress could be introduced using cone and plate flow chamber and/or
parallel plate flow chamber [Brown 2000]. Other techniques that combine
substrate distension and fluid shear were also developed. One approach used
by Benbrahim et al [1994] was to grow cultures on the inner wall of highly
distensible tubes, where the shear stress was pressure gradient dependent,
and substrate distension was internal pressure dependent.
To fully understand the reason behind bone adaptation to mechanical
stimuli, people had long intended to explore the story at cellular level. Ehrlich
and Lanyon [2002] gave a detailed review on mechanical strain and bone cell
function. They mainly discussed the release of prostanoids, nitric oxide, and
insulin-like growth factors (IGFs) during bone adaptation to mechanical
stiumuli, which suggested the involvement of cation channels and intracellular
calcium increase in bone cell repose to mechanical stimuli [Ehrlich and Lanyon
2002, Klein-Nulend et al 1998, Zaman 1999 and Ralston 1997]. Iqbal and Zidi
[2005] discussed molecular regulation of mechanotransduction on a more
general base regardless of cell types, which summarized the role of integrin in
interacting with environment, mediating the increase of intracellular Ca2+ levels
and activating MAP kinase cascades that led to ERK1/2 phosphorylation,

161

which then activated the AP-I family of transcription factors for pro-growth
response involving up-regulation of the genes c-fos, IFG-I, cyclooxygenase,
and osteocalcin. Nesbitt et al [2009] found that mechanical loading of bone cell
could stimulate Wnt/β-catenin signaling, which could result in the generation of
new bone mass.
While the above mechanical stimuli are global and have high strain
rate (>1s-1), Cox [2010] brought up a strain-cue theory which hypothesized that
the cell migration and cell network formation was cued by localized strain
(nearest 100 cells) generated in the host media (host cell and extracellular
matrix). Cox built his strain-cue model by considering the invasion of cells to a
densely packed host media, such that when accommodating the new invading
cell, the host media must displace and thus lead to changes in the local strain
field. The invading cells tend to migrate in the direction perpendicular to the
tensile direction. Cox model considers only the variation of the strain field but
not the diffusion distance of chemical signals.
The simulated strain rate from Cox’s model is 10-4 s-1 during loading
and 10-5 to 10-6 s-1 during unloading, which are much lower than the strain
rates used in conventional mechanical stimuli studies. The localized as well as
low strain rate generated by the host media during accommodating invading
cells may be referred to explain our observation of localized mineralization in
the indentation center as discussed in chapter 4.
However, the diffusion of chemical signals, in our case calcium should

162

not be neglected. At the early cell attachment phase, the ECM matrix and host
cells are not closely packed and thus the local strain-cue may not be effective
until the cells reach confluency at later times.

163

APPENDIX B
CALCIUM
CONCENTRATION
ABSORPTION SPECTROSCOPY

MEASUREMENT

USING

ATOMIC

Atomic absorption spectroscopy (AAS) is a chemical analysis method
first proposed by Walsh in 1955 [Walsh 1955]. As shown in Figure B-1, the
atomic absorption spectrophotometer consists of four major parts: the light
source, the flame or atomizer, the monochrometer and the detector.

Figure B-1 Schematic of atomic absorption spectrophotometer structure.

The light source is a hollow cathode lamp, where the cathode is made
from either the element to be measured or its alloy. The lamp emits light that
could be absorbed by the to-be-measured atoms in the sample. Thus in the
case of calcium measurement, a calcium cathode lamp is used as the light
source, which generate a light wavelength of 422.7 nm.
In the sample compartment, the sample is atomized by heat
dissociation. The heat can be generated either from a chemical flame or an
electrical furnace. In our case, an oxygen rich flame (2000 to 3000 ºC) is used
to dissociate the sample into free atoms. The free atoms can absorb the
radiant energy of their specific resonance wavelength. The light absorbance
after passing through the flame is proportional to the number of free atoms in

164

the flame. The concentration of the target element, in this case calcium can be
obtained by measuring the light absorbance.
The monochrometer selects the wavelength to analyze the target
element. The analysis wavelength for calcium is 422.7 nm. The detector then
converts light into electrical signals.
Prior to the measurement of calcium concentration in the sample
solutions, a concentration versus absorbance curve was plotted using
standard calcium solutions. The standard solutions are made by diluting the
stock calcium solution (1g/L) in distilled water. The concentrations of standard
calcium solutions are 1, 3 and 10 mg/L, respectively. Each standard solution is
aspirated into the sample compartment and the absorbance of light is
determined. Distilled water is also aspirated as the blank background with 0
calcium concentration. From the above data, a calibration curve of calcium
concentration versus absorbance is plotted. After plotting the standard curve,
the calcium concentration in the unknown sample solutions can then be
measured by aspirating them into the AA flame.

165

APPENDIX C
SOLID STATE SINTERING OF HYDROXYAPATITE AT 1360°
C

In a cooperative study with Fan et al., the porosity dependence of
Weibull modulus and strength of brittle ceramics was investigated [Fan et al.
submitted 2011]. Hydroxyapatite was chosen as the model ceramic due to its
wide application and availability in our research group. In order to obtain a
wide range of HA porosity, Fan tried different sintering profiles by changing
sintering temperature and time. While HA specimens in the lower (>90%) and
higher porosity (<80%) ranges were obtained with consistency in color, the
intermediate porosity range specimens were found to show pink-colored spot
and tend to break at the interface between different color regions. The
un-uniform color is likely caused by uneven heating gradient experienced by
the powder compact. However, the detailed cause and mechanism for the
occurrence of pink spots remain unclear. We solved the color problem by
employing a thick powder bed (at least 3 mm thick) and by maintaining
sintering boat in the center of the furnace chamber. In this appendix, the
porosity and/or density evolution of HA sintered at a fixed temperature 1360°
C
with time is presented and discussed, which provided a map for determining
sintering profile for desired densities.
Sintering is defined as “the process that transforms powder compacts
into solid, dense body upon heating” [Barsoum 2003]. Sintering could happen
with and without liquid phases, which are referred as liquid-phase and solid

166

state sintering respectively. The driving force for sintering is surface energy
reduction globally and curvature differences that lead to partial pressure
differences locally (equation 1) [Barsoum, 2003].

Pcurv = Pflat (1 +

2Ω MX γ sv
)
rkT

(1)

where Pcurv and Pflat are partial pressures above the curved surface and the flat
surface respectively,

MX

is the volume of a formula unit, γsv is the solid/vapor

surface energy, r is the radius of a sphere (negative for concave surfaces and
positive for convex surfaces), k (= 1.3806503 × 10-23 m2 kg s-2K-1) is the
Boltzmann constant such that, and T is the temperature. According to equation
(1) and the signs given to concave (-) and convex (+) surfaces, the partial
pressure is the highest above a convex surface, followed by flat surface, and
lowest above a concave surface.
There are five mass transfer mechanisms: evaporation-condensation,
surface diffusion, volume diffusion, grain boundary diffusion, and viscous flow
[Barsoum 2003]. The diffusion sink is always the “neck area”, while the
diffusion source could be the surfaces or grain boundaries. Depending on the
diffusion path in the powder compacts, coarsening (surface to neck area) or
densification (grain boundary to neck area) could take place during sintering
[Barsoum 2003].
When coarsening and densification take place, shrinkage, grain, and
pore sizes of the sintered body could evolve depending on the initial particle
sizes, sintering temperature and time. The volume change of a powder

167

compact after sintering could be described by equation (2).

∆V
= A(T )t n (1 / r ) m
V0

(2)

where ∆V is the volume change after sintering, V0 is the initial volume of the
green powder compact, A(T) is temperature dependent function, t is sintering
time, the observed n often ranges from 0.1 to 0.5, r is the initial particle size, m
varies from 1 to 2.
For a given particle size and a fixed sintering temperature, Equation 2
could be simplified and rewritten as equation (3).

ln(

ρ
∆V
) = ln(1 − 0 ) = C + n ln t
ρt
V0

(3)

where ρ0 and ρt are initial and final densities of the specimen, C is a constant
depending on temperature and particle size.
The green HA specimens fabricated the same way as described in
chapter 4 were sintered at 1360oC for 1, 5, 12, 20, 23, 27, and 30 minutes
respectively. A powder bed about ~3 mm thick was employed both beneath
and on top of the specimens. The sintering boat was always kept in the center
bottom of the furnace chamber. The density of HA specimens were calculated
from density and dimensions measurement as described in previous chapters.
The sintering profiles (temperature, time and ramp rate) and the
calculated values of density/porosity as well as volume change are given in
Table C-1. The average density/porosity is calculated from three specimens.

168

Table C-1 List of sintering profile, density, porosity and volume change
∆V/V0

Temperature

Time

Average

Porosity

Ramp

(ºC)

(min)

Density(%)(N*=3)

(%)

(ºC/min)

Green

0

40

60

1360

1

72.16

27.84

10

1360

5

76.59

23.41

1360

12

82.69

1360

20

1360
1360

ln(∆V/V0)

lnt

0.445676

-0.80816

0

10

0.477739

-0.73869

1.609438

17.31

10

0.516266

-0.66113

2.484907

84.52

15.48

10

0.526739

-0.64105

2.995732

27

87

13

10

0.54023

-0.61576

3.295837

30

88.5

11.5

10

0.548023

-0.60144

3.401197

0

The last two columns ln(∆V/V0) and lnt in Table C-1 are plotted as
shown in Figure C-1. The data were fit to equation (3) via least squares
technique, which yielded C=0.8175 and n = 0.0608±0.0042.

Figure C-1 The logarithm of volume change increases linearly with the logarithm of time. The
2

data were fit to equation (3). The coefficient of determination R = 0.98.

For the HA powders used in our group, any desired density could be
obtained fairly well by referring to the relationship between volume change and
sintering time as shown in Figure C-1.

169

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