THE IMPACT OF DEVELOPMENTAL AGE AND LOADING RATE ON THE PATTERNS
OF BONE FRACTURE UNDER TORSION AND BENDING USING EITHER IMMATURE
PORCINE OR OVINE FEMURS
By
Patrick E. Vaughan

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Engineering Mechanics – Master of Science
2017

ABSTRACT
THE IMPACT OF DEVELOPMENTAL AGE AND LOADING RATE ON THE PATTERNS
OF BONE FRACTURE UNDER TORSION AND BENDING USING EITHER IMMATURE
PORCINE OR OVINE FEMURS
By
Patrick E. Vaughan
The determination of whether pediatric long bone fracture is based on accidental trauma or an
abusive act is a major question in forensics. A recent clinical study has suggested that the
mechanisms of long bone fracture can be determined based on the fracture pattern. While human
pediatric bone is difficult to obtain, immature animal models, like porcine and ovine models, can
act as adequate surrogates for scientific studies. The first research topic explored in this thesis is
the influence of specimen age and loading rate on whole-bone fracture patterns. Under femoral
torsion, the spiral fracture pattern (fracture ratio) was shown to increase with porcine age and
rate of twist, bringing into question results of the clinical study. The second research topic
explored direction-specific tensile and shear test data versus specimen age and loading rate in the
immature porcine model. Results showed that both porcine age and loading rate can affect
transverse and longitudinal shear stress components, altering the torsional fracture pattern. In
another study the immature ovine femur was used in concentrated four-point bending tests, and
was shown to produce transverse fractures, while mature specimens produced compressive
wedge fractures. Preliminary evidence suggested that at higher test rates, a tensile wedge pattern
is produced for mature specimens. As impact direction is currently cited by tensile wedges,
consistent generation of compression wedges muddle this practice. The compilation of this work
demonstrates that loading rate and developmental age affect fracture patterns in immature
femora, highlighting that caution needs to be taken when analyzing pediatric long-bone fractures.

ACKNOWLEDGEMENTS

I would like to first and foremost like to thank Dr. Roger C. Haut for taking the chance on me
four years ago and for providing me with the opportunity to study under his mentorship. I
appreciate how he has always pushed me to strive for more, how he has taught me what the “re”
in research means, and how he has taught me to always keep sight of the ‘story’. I would like to
thank Dr. Feng Wei for aiding me in my time here and for always providing an ear to listen to
me. I would also like to sincerely thank Clifford Beckett for drilling the principles of hard work
into me and for teaching me some of the technical skills required by an engineer. I would like to
thank Dr. Todd Fenton for providing me with the opportunity to expand my studies in cranial
trauma and for the inter-disciplinary collaborations he provided with his team of forensic
anthropologists. Thank you to Kevin Turner and Chris Rosenbom in the Porcine Research
Laboratories at MSU and to Dr. Tammy Haut Donahue from Colorado State University for
providing me with specimens to test in this research. Finally, I would like to thank my twin
brother, Ryan F. Vaughan, for being my inspiration in this pursuit as well as my parents for
supporting me on this eventful journey. I would also like to thank all of the friends that have
supported me on this journey: Alli Harju, Alex Goots, Mari Isa, Elena Watson, Paul Snyder,
Caitlin Vogelsberg, and Jen Vollner.

iii

Copyright by
Patrick E. Vaughan
2017

iv

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................................ vii
LIST OF FIGURES ..................................................................................................................... viii
CHAPTER ONE: INTRODUCTION AND BACKGROUND .......................................................1
FEMORAL BONE COMPOSITION .......................................................................................1
FORENSIC RELEVANCE OF THE FEMUR ........................................................................2
PEDIATRIC DEVELOPMENT AND FEMUR FRACTURE ................................................3
TORSION AND PEDIATRIC FRACTURE ...........................................................................5
TORSIONAL FAILURE ...........................................................................................5
BENDING FAILURE AND FEMUR FRACTURE ................................................................7
SUMMARY AND OBJECTIVES ...........................................................................................9
REFERENCES .......................................................................................................................12
CHAPTER TWO: SPECIMEN AGE AND TORSIONAL RATE OF TWIST INFLUENCE
HELICAL FRACTURE PATTERNS OF THE IMMATURE PORCINE FEMUR .....................15
ABSTRACT ...........................................................................................................................15
INTRODUCTION ..................................................................................................................16
METHODS .............................................................................................................................18
RESULTS ...............................................................................................................................23
DISCUSSION.........................................................................................................................29
REFERENCES .......................................................................................................................35
CHAPTER THREE: THE EFFECT OF SPECIMEN AGE AND LOADING RATE ON
INTRINSIC MATERIAL PARAMETERS OF THE IMMATURE PORCINE FEMORA. .......38
ABSTRACT ...........................................................................................................................38
INTRODUCTION ..................................................................................................................39
METHODS .............................................................................................................................41
STATISTICAL METHODS .....................................................................................46
RESULTS ...............................................................................................................................47
FAILURE STRENGTH RESULTS .........................................................................47
YOUNG’S MODULUS AND SHEAR MODULUS RESULTS ...............................50
TIME TO FAILURE ...............................................................................................52
DISCUSSION.........................................................................................................................54
APPENDIX ............................................................................................................................60
REFERENCES .......................................................................................................................62
CHAPTER FOUR: AGE EFFECTS ON BENDING FRACTURE PATTERNS IN OVINE
FEMORA UNDER CONCENTRATED FOUR-POINT BENDING. .........................................65
ABSTRACT ...........................................................................................................................65
INTRODUCTION ..................................................................................................................66
v

METHODS .............................................................................................................................68
STATISTICAL METHODS .....................................................................................77
RESULTS ...............................................................................................................................77
DISCUSSION.........................................................................................................................85
APPENDIX ............................................................................................................................90
REFERENCES .......................................................................................................................96
CHAPTER FIVE: CONCLUSIONS. ...........................................................................................99
OVERVIEW ...........................................................................................................................99
CHAPTER 2 .........................................................................................................................101
CHAPTER 3 .........................................................................................................................102
CHAPTER 4 .........................................................................................................................103
APPENDIX ..........................................................................................................................107

vi

LIST OF TABLES

Table 3.1. Summary table of immature torsional data in the literature .......................................61
Table 4.1. Summary table of raw experimental data ....................................................................95

vii

LIST OF FIGURES

Figure 1.1 Depiction of bone composition from the macroscale to the microscale, adapted from
Tadano et al., 2011 ..........................................................................................................................1
Figure 1.2 Common fracture patterns and their forensic description, adapted from Kress et al.,
1996..................................................................................................................................................3
Figure 1.3 (left figure) slice location to whole bone representative. (right figure) Young age
group (left) to old age group (right) femoral cross-sections at various bone locations {A –
Anterior, M – Medial directions}, adapted from Gosman et al., 2013. ...........................................4
Figure 1.4 Torsion and its deconstruction into longitudinal and transverse shear components ...6
Figure 1.5 Shear stress element (left), description of maximum shear direction (central) and
generalized stress transformation into maximum shear plane (right) .............................................7
Figure 1.6 Typical tensile wedge pattern under three-point bending. ............................................7
Figure 1.7 Simplified reverse tensile wedge ‘compression wedge’ pattern, showing the direction
of loading and the compressive and tensile sides of the bone. Note: the pattern is most
consistently generated under four-point bending. However, large impact surfaces such as a flat
plate (Reber and Simmons, 2015) or a large curved impactor (Kress et al., 1996) have also been
shown to generate this fracture type. ...............................................................................................8
Figure 2.1 Photograph of the custom-built laser alignment fixture and the process of centering
the bone ..........................................................................................................................................19
Figure 2.2 Example of a potted bone specimen using the fast technovit liquid resin hardener
formed to the cylindrical shape of the potting cups .......................................................................20
Figure 2.3 Set-up: custom-build torsional fixture and servohydaulic testing machine ................21
Figure 2.4 Example of measuring the total fracture length using fracture segments in a single 2dimensional plane of view ..............................................................................................................22
Figure 2.5 2-dimmensional measurement technique of a mediolateral and anteroposterior view,
shown for a low-rate specimen ......................................................................................................23
Figure 2.6 Plot of anteroposterior fracture ratio with respect to twist rate and specimen age
(measured on anterior side of bone), n = 15 .................................................................................25
Figure 2.7 Plot of mediolateral fracture ratio with respect to twist rate and specimen age
(measured on medial side of bone), n = 11 ...................................................................................25
viii

Figure 2.8 Plots of the low-rate total longitudinal (element 2) fracture length versus specimen
age (AP ratio left (n=15), ML ratio right (n=11)). .......................................................................26
Figure 2.9 Plots of the high-rate total longitudinal fracture component versus specimen age (AP
ratio left (n=15), ML ratio right (n=11)). .....................................................................................27
Figure 2.10 Plots of the low-rate total angled fracture components versus specimen age (AP
ratio left (n=15), ML ratio right (n=11)). ....................................................................................27
Figure 2.11 Plots of the high-rate total angled fracture components versus specimen age (AP
ratio left (n=15), ML ratio right (n=11)). ....................................................................................28
Figure 2.12 Photographs of low-rate tests, showing the increase in angled fracture lengths in
mm for specimens (2,4,9 days) top-bottom, and its effect on the AP fracture ratio (column a).
Photographs showing the increase in length of the longitudinal fracture element in mm for
specimens (13,18,26 days) top-bottom, and its effect on the AP fracture ratio (column b) ..........30
Figure 2.13 Photographs showing changes in the fracture pattern under a high rate of twist.
Specimen age (1,6,12,18,26 days) left to right at mediolateral view.............................................31
Figure 2.14 Enlarged photographs of high-rate test specimens 1,6,12, from Figure 2.13 (top)
and a single enhanced surface view from the same specimen (bottom). Showing a jagged shallow
helical pattern for 1-day old specimen (left), a “smooth” helical pattern for a 6-day old
specimen (center), and showing a step-like helical pattern at 12 days of age (right). ..................32
Figure 3.1 Longitudinal tensile testing representation (a), transverse tensile testing
representation (b) longitudinal shear testing representation (c), transverse shear testing
representation (d) natural curvature of the bone (e). For all pictures the direction of osteons is
represented by a gray dotted line. .................................................................................................42
Figure 3.2 Photograph of tensile testing fixture (left), photograph of shear testing fixture (right)
........................................................................................................................................................43
Figure 3.3 Photograph of curvature designed clamp ...................................................................43
Figure 3.4 Young’s modulus determination for an 8-day old, low rate longitudinal tensile
specimen (left), shear modulus determination for a 7-day old, low rate longitudinal shear
specimen (right) .............................................................................................................................46
Figure 3.5 Plot of low rate failure strength values. Closed triangles are longitudinal tensile data
points (n=9), open triangles are transverse tensile data points (n=10), closed squares are
longitudinal shear data points (n=10), and open squares are transverse shear data points
(n=10). ...........................................................................................................................................48

ix

Figure 3.6 Plot of high rate failure strength values. Closed triangles are longitudinal tensile
data points (n=9), open triangles are transverse tensile data points (n=10), closed squares are
longitudinal shear data points (n=10), and open squares are transverse shear data points
(n=10) ............................................................................................................................................49
Figure 3.7 Plot of low rate shear and tensile moduli. Closed triangles are longitudinal tensile
data points (n=9), open triangles are transverse tensile data points (n=10), closed squares are
longitudinal shear data points (n=10), and open squares are transverse shear data points
(n=10). ...........................................................................................................................................50
Figure 3.8 Plot of high rate shear and tensile moduli. Closed triangles are longitudinal tensile
data points (n=9), open triangles are transverse tensile data points (n=10), closed squares are
longitudinal shear data points (n=10), and open squares are transverse shear data points
(n=10) ............................................................................................................................................51
Figure 3.9 Plot of the various test data and the time (in seconds) it took to reach bone fracture
for low rate tests.............................................................................................................................53
Figure 3.10 Plot of the various data and the time (in seconds) it took to reach bone fracture in
the high rate tests. ..........................................................................................................................53
Figure 3.11 Enlarged photographs of high-rate test specimens 1,6,12, from Figure 2.13 (top
three photos) and a single enhanced surface view from the same specimen (bottom three photos).
Showing a jagged shallow helical pattern for 1-day old specimen (left, column 1), a “smooth”
helical pattern for a 6-day old specimen (center, column 2), and showing a step-like helical
pattern at 12 days of age (right, column 3). Adapted from Figure 2.14. .......................................54
Figure 3.12 Plot of the ratio of transverse shear strength over the longitudinal shear strength
against specimen age .....................................................................................................................56
Figure 3.13 Pictorial representation of transverse crack propagation through osteons, with
crack deflections in the longitudinal direction (a), and crack bridging (b). Figure adapted from
Koester et al., 2008 ........................................................................................................................57
Figure 4.1 Photograph of the concentrated four-point bending configuration based on the
previous study by Martens et al., 1986 for old specimens. ...........................................................70
Figure 4.2 Photograph of the concentrated four-point bending configuration based on Martens
et al., 1986, for young specimens. ..................................................................................................70
Figure 4.3 Screen capture of 3D image reprocessing in Mimics. ................................................72
Figure 4.4 Screen capture of volumetric meshing of bone in 3-matic. .........................................72
Figure 4.5 Screen capture of loads and boundary condition applied to the model in Abaqus .....73

x

Figure 4.6 Graphical representation of a standard four-point bending test, taken from Rusmee
1998................................................................................................................................................74
Figure 4.7 Graphical determination of elastic modulus (left) and initial stiffness values (right) 77
Figure 4.8 High-speed capture of specimen Shelby_5_28_15_4B, showing fracture initiation
(top left) on the tensile side of the bone, to fracture propagation (bottom right) on the
compressive side of the bone..........................................................................................................79
Figure 4.9 High-speed capture of specimen Zach_5_28_15_4B, showing fracture initiation (left)
and fracture propagation (right). .................................................................................................80
Figure 4.10 High-speed capture of specimen SF3R4B, showing fracture initiation (top) and
fracture propagation (bottom). ......................................................................................................81
Figure 4.11 High-speed capture of specimen SF5R4B, showing fracture initiation (left) and
fracture propagation (right). .........................................................................................................82
Figure 4.12 Experimental high-speed capture (top) and maximum principal stress distribution,
generated with FE modeling (bottom). ..........................................................................................83
Figure 4.13 Experimental high-speed capture (top) and maximum principal stress distribution,
generated with FE modeling (bottom). ..........................................................................................84
Figure 4.14 Photograph of an impact scenario which produces reverse tensile wedges, taken
from Reber and Simmons 2015. .....................................................................................................87
Figure 4.15 Photograph of an impact scenario which produces reverse tensile wedges, taken
from Kress et al., 1996 ..................................................................................................................88
Figure 4.16 Photographs of specimen representative of variations in the fracture patterns, tested
at a high rate of 2 Hz over a 20mm haversine displacement (from left to right;
AbeL12_10_14_4B_HighRate, AbeR12_10_14_4B_HighRate, and
ClaudeL12_10_14_4B_HighRate).................................................................................................91
Figure 4.17 Photographs of specimen representative of variations in the reverse tensile wedge
pattern, tested at a low rate of 2 Hz over a 5mm haversine displacement (from left to right;
Shelby_5_28_15_4B, Ryan_5_28_15_4B, and Lindy_5_28_15_4B). ...........................................92
Figure 4.18 Photographs of specimen representative of variations in the young bone fracture
pattern, tested at a low rate of 2 Hz over a 5mm haversine displacement (from left to right;
SF1R4B, SF2R4B, and SF5R4B). ..................................................................................................93
Figure 4.19 Maximum principal stress distribution, typical 3-point bending .............................94

xi

Figure 4.20 Maximum principal stress distribution, typical 4-point bending. .............................94
Figure 4.18 Maximum principal stress distribution, Martens-type 4-point bending ....................94

xii

CHAPTER ONE: INTRODUCTION AND BACKGROUND
FEMORAL BONE COMPOSITION
Bone is an optimized geometrical structure that possesses an ideal combination of properties,
namely high stiffness, strength, fracture toughness, and low weight (Tadano et al., 2011). At the
whole bone level, the femur is composed of a tough cortical outside and a pliable trabecular
inside. The cortical bone sheathing is composed of osteons, which are generally oriented along
the long-axis of the bone. The osteons themselves are composed of collagen fibers with a
boundary of collagen fibers acting as a tough “cement line”. Between osteons exist a lamellar
interface consisting of collagen molecules and a mineralized layer of collagen fibrils that acts as
a “glue” and a sacrificial “stretch” layer (Figure 1.1).

Figure 1.1 Depiction of bone composition from the macroscale to the microscale, adapted from
Tadano et al., 2011.

The beauty of this molecular make-up is that upon tension loosely packed interlamellar collagen
fibrils stretch apart breaking at predetermined sacrificial locations and releasing more hidden
length. This mechanism becomes advantageous by dissipating a significant amount of energy
1

allowing for small deformations between lamellae. This pre-determined failure method allows
osteons to withstand various modes of micro-deformation without the need to dissipate strain
energy by means of cracking, but instead, allows bone to dissipate energy via a reversible
mechanism (Katsamenis et al., 2013).

FORENSIC RELEVANCE OF THE FEMUR
The femur is the largest bone in the human body, and it is also the strongest bone. Femoral
fracture therefore requires a large amount of mechanical energy. Despite this, femur fractures are
common childhood injuries. Between 10 and 20 people out of 100,000 sustain femoral shaft
fractures annually (Rewers et al., 2005). The most common causes of fracture are high speed
trauma, motor-vehicle accidents, a fall from a high place, injury during an extreme or a contact
sport, and cases of child abuse (Hunter, 2005). Femoral shaft fractures are the most common
pediatric fracture site, accounting for 62% of all femur fractures (Rewers et al., 2005). These
fractures can be spiral, oblique, transverse, comminuted, or wedge-types (Shrader et al., 2011).
Femoral shaft fractures in children, however, are typically spiral and occur in 52% of cases
(Shrader et al., 2011).

2

Figure 1.2 Common fracture patterns and their forensic description, adapted from Kress et al.,
1996.

As shown in Figure 1.2, spiral fractures consist of a helical pattern around the shaft of the bone.
Oblique patterns are defined as an angled break across the bone. Transverse fractures are
described as perpendicular to the long-axis of the bone. Comminuted fractures are identified
through multiple breakages. Wedge patterns, on the other hand, resemble a Y-shape either in
line with or opposed to the direction of loading. Segmental patterns result in the bone being split
into three fragments.

PEDIATRIC DEVELOPMENT AND FEMUR FRACTURE
Specific fracture patterns are a result of the orientation and type of loading applied to the bone.
For example, it is known that torsional loading generates spiral fractures (Kress et al., 1996).
However, as bone is an anisotropic composite structure fracture propagation can also be
influenced by the material structure of the bone itself (Taylor et al., 2003). Therefore, when
considering fracture patterns in children it is imperative to consider how whole-bone geometry,
3

microstructural progression and mechanically relevant material properties change with age.
Gosman et al., 2013 has documented that in human children from neonatal to 18 years of age
young bone has greater circularity, while more mature bone becomes increasingly asymmetric
(Figure 1.3). Mechanically, this is relevant because circular cross-sectional areas tend to have
more uniform stress distributions under loading, while asymmetric cross-sections will have nonuniform stress distributions under loading. Additionally, Torzillia et al., 1982 have shown that
material properties of bone, such as the ultimate tensile strength and modulus positively correlate
with age. While the literature highlights such developmental changes with age, however, there is
limited data on how fracture patterns themselves may be affected by these changes.

Figure 1.3 (left figure) slice location to whole bone representative. (right figure) Young age
group (left) to old age group (right) femoral cross-sections at various bone locations {A –
Anterior, M – Medial directions}, adapted from Gosman et al., 2013.

4

TORSION AND PEDIATRIC FRACTURE
In the current forensic literature differentiation between an abusive and accidental trauma (AT)
in children under three years of age remains challenging. It is assumed that any trauma incurred
by children under three years of age is frequently non-accidental trauma (NAT/abuse), and that
any trauma in children less than one year is always NAT (Carty, 1993). Furthermore, spiral longbone fractures in young children are challenging cases because there are limited ‘ground truth’
studies to help forensic investigators determine whether these fractures are from an abusive act
or accidental trauma, as both situations can produce spiral fractures under torsional loads. A
recent clinical-based study, however, has proposed to document fracture ratio, defined as the
fracture length in a lateral radiograph over the diameter of the bone, to help distinguish NAT
from AT. The study associates small fracture ratios (≈1.6) with NAT and large ratios (≈2.8) with
AT (Murphy et al., 2015). Another study, using an immature canine model, indicates that fracture
ratio is increased for a high versus low rate of bone twist (Theobald et al., 2012). The authors of
this study likely assume AT occurs at a high rate of twist while NAT occurs at a low rate. While
the study of Murphy et al., 2015 did document a slightly younger age for the NAT population
than the AT population, the age effect was not statistically significant. Thus, it remains
somewhat unclear if age is a covariate of facture ratio generated under torsional loads.

TORSIONAL FAILURE
Torsion is typically defined using an isotropic cylindrical shaft, keeping one end fixed and
applying a torque to the free end. If observing a singular point on the free end of the beam 𝑎𝑏
(Figure 1.4a), this point would rotate at some angle theta 𝑎𝑏 ′ . This rotation generates shear stress
that will vary linearly from the origin, as demonstrated by the triangular stress distribution in the

5

cross-section of Figure 1.4a (Gere and Goodno, 2008). Therefore, if some arbitrary plane (abcd)
was selected, analyzed in the cross-sectional plane (Figure 1.4b), and then represented as a 2D
stress element; taking the radial direction (r) as the direction of displacement (Figure 1.4c), it can
easily be seen that both transverse and longitudinal shear stresses are generated.

𝑎

𝑏

𝑝
𝑜

𝑜

𝜽

𝑏
𝑏′

𝜏

𝜏𝑚𝑎𝑥
𝑏

𝑟

′

(𝑎)
𝑎

𝑏
𝑎

𝑏

𝑏
𝑏′

𝑜

𝑑

𝜏𝑙𝑜𝑛𝑔

𝜏

𝑏′

𝑐

𝜏𝑡𝑟𝑎𝑛𝑠

𝜏𝑡𝑟𝑎𝑛𝑠

𝑐
𝑐′
(𝑏)

𝑑

𝜏𝑙𝑜𝑛𝑔
(𝑐)

𝑐
𝑐′

Figure 1.4 Torsion and its deconstruction into longitudinal and transverse shear components.
Furthermore, if the same stress element were to be rotated forty-five degrees to align with the
direction of maximum principal stress, and were to experience the same shear-type deformation,
then there were would be an extension (tensile stress) in one direction, and a contraction
(compressive stress) in the other direction (Özkaya et al., 2017) (Figure 1.5).

6

Long Shear
𝑎

Trans Shear

𝑏
𝑜

𝜽
𝑏′

𝟒𝟓°

Figure 1.5 Shear stress element (left), description of maximum shear direction (central), and
generalized stress transformation into maximum shear plane (right).

BENDING FAILURE AND FEMUR FRACTURE
Case studies and the medical literature associate long bone failure by bending with butterfly
fractures. It is expected these occur in a tension wedge configuration, with fracture initiating as a
transverse crack at the tensile surface of the bent bone and branching toward the compressed or
impact surface (Kress, 1996, Fenton, 2012, Isa, 2015), supposedly due to shear failure on the
compressive side of the bone (Figure 1.6).

Compressive side

Tensile side
Figure 1.6 Typical tensile wedge pattern under three-point bending.

7

A wedge configuration is forensically significant because analysts often cite the presence and
orientation of butterfly fractures as diagnostic of impact direction (Kress, 1996, Fenton, 2012,
Isa, 2015). Experimental research indicates this practice is problematic as Martens et al., 1986
and Reber and Simmons, 2015 have demonstrated that under specific loading configurations,
butterfly fractures may occur in a reversed pattern on the compressive side of the bone, such that
the transverse crack is on the impact surface as opposed to the tensile surface (Figure 1.7). Most
recently, Reber and Simmons, 2015 produced a study reporting 40% of complete wedge patterns
as reverse tensile wedges, and Martens et al., 1986 demonstrated near-exclusive reverse tensile
wedge failure when loading the bone at a slow rate, under a specific, concentrated four-point
bending scenario.

Compressive side

Tensile side

Figure 1.7 Simplified reverse tensile wedge ‘compression wedge’ pattern, showing the direction
of loading and the compressive and tensile sides of the bone. Note: the pattern is most
consistently generated under four-point bending. However, large impact surfaces such as a flat
plate (Reber and Simmons, 2015) or a large curved impactor (Kress et al., 1996) have also been
shown to generate this fracture type.

8

Thus, it is forensically relevant to prove the replicability of the work of Martens et al., 1986 to
investigate if the authors configuration can exclusively produce ‘compression wedge’ failures; a
mode of failure Kress et al., 1996 has deemed unlikely to be produced consistently.
Additionally, as no research has yet been performed to test immature bone under Martens-type
loading conditions, it is also forensically relevant to investigate if there is an age-effect
associated with this reverse wedge, or ‘compressive wedge’ pattern.

SUMMARY AND OBJECTIVES
Pediatric studies are difficult to perform due to the costs involved and the relative scarcity of
bones specimens. For such reasons, most trauma-based studies have been performed on mature
bone, leaving pediatric trauma analysis to be, in large part, speculated from studies on mature
bone specimens. Since human bone is difficult to obtain immature animal models, like the
porcine or ovine models, act can act as surrogates to investigate questions on developing bone.
While animal test data is not directly applicable to the pediatric subject, researchers can
supplement knowledge acquired from such laboratory-controlled experiments to form and
standardize practices and develop a scientific basis for fracture mechanics.

Since the mechanical properties of bone may depend on age (Torzilli et al., 1982) and rate of
loading (Theobald et al., 2012) and since spiral fractures occur by the combination of tensile and
shear failure of the bone (Turner et al., 2001), altered tensile and shear properties with specimen
age and rate of loading may then in turn influence the location and direction of crack propagation
within the bone during torsion (Norman et al., 1996). The first hypothesis of the study was that
when using the immature porcine model, the previously introduced fracture ratio would increase
9

with specimen age, as osteon strength has been noted to increase with age, allowing the fracture
to fail more along the line of maximum principal stress, as opposed to through osteons, which
would result in a larger fracture ratio. The second hypothesis of the study was that the fracture
ratio would systematically increase with an increased rate of twist in the immature porcine bone
model, based on the previous work of Theobald et al., 2012.

As suggested above, the underlying failure mechanisms and resulting fracture patterns of whole
bone under torsion is not yet fully understood. As spiral fracture is considered a combination of
both transverse and longitudinal shear failure (Vashishth et al., 2005), it is theorized that a predisposed weakness to a given shear-type will be evident in the spiral fracture pattern of the bone.
In example, if bone is weaker in transverse shear than in longitudinal shear, then this type of
shear failure will become a viable alternative fracture path to the preferred mode of failure under
tension, and vice versa. Another hypothesis of the current study was that when using the
immature porcine model and testing the intrinsic material property values, the transverse and
longitudinal shear strengths would fluctuate with specimen age. If at younger ages the bone was
weaker in transverse shear than in longitudinal shear, then shearing across osteons would become
a viable failure path, resulting in lower fracture ratios and vice versa. Another hypothesis of the
current study on the intrinsic properties of bone was that when conducting tests using the
immature porcine model an increased loading rate would result in stronger property values at
lower ages, which would in turn impact the fracture ratio, as depicted by the work of Theobald et
al., 2012.

10

Finally, as suggested above, the current forensic practice of denoting impact direction based on
the transverse fracture of a butterfly wedge-type pattern may be problematic. The studies of
Reber and Simmons, 2015 and Martens et al., 1986 have demonstrated that there is a significant
prevalence of reverse tensile wedge ‘compressive wedge’ fractures produced under experimental
settings, providing evidence that these types of fracture patterns are not as unlikely as Kress et
al., 1996 infer them to be. Therefore, in another set of experiments a hypothesis was that when
using the mature ovine model, the work of Martens et al., 1986 would be replicable, and that
near-exclusive ‘compressive wedge’ patterns would be produced. Furthermore, when using the
immature ovine specimen under the Martens-type experimental set-up, the fracture pattern
produced would not be a ‘compression wedge’ and will instead be a transverse failure. The
transverse pattern would be more likely produced in the immature bone as the bone has not yet
strengthened in the medial-posterior directions from increased geometric asymmetry which takes
place with maturation, and because the osteon strength of the bone in the immature specimen
may not yet be strong enough to inhibit crack growth through osteons.

11

REFERENCES

12

REFERENCES

Carty HM. Fractures caused by child abuse. J Bone Joint Surg Br. 1993; 75(6):849-57.
Fenton TW, Kendell AE, DeLand TS, Haut RC. Determination of impact direction based on
fracture patterns in human long bones. Proceedings of the American Academy of Forensic
Sciences; Atlanta, GA. American Academy of Forensic Sciences, 2012; H72.
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Gosman JH, Hubbell ZR, Shaw CN, and Ryan TM. Development of cortical bone geometry in
the human femoral and tibial diaphysis. Anat Rec. 2013; 296: 774-787.
Hunter JB. Femoral shaft fractures in children. Injury, Int. J. Care Injured. 2005; 36: S-A86-SA93.
Isa MI, Fenton TW, DeLand TS, Haut RC. Fracture Characteristics of Fresh Human Femora
Under Controlled Three-Point Bending. Proceedings of the 67th Annual Meeting of the
American Academy of Forensic Sciences; Orlando, FL. American Academy of Forensic
Sciences, 2015; A96.
Katsamenis OL, Chong HMH, Andriotis OG, and Thurner PJ. Load-bearing in cortical bone
microstructure: Selective stiffening and heterogeneous strain distribution at the lamellar level. J
Mech Behav Biomed Mater. 2013; 17:152-165.
Kress TA. Impact biomechanics of the human body [dissertation]. Knoxville (TN): Univ. of
Tennessee, 1996.
Martens M, Van Audekercke R, DeMeester P, Mulier JC. Mechanical behavior of femoral bones
in bending loading. J Biomechanics. 1986:19(6):443-54.
Murphy R, Kelly DM, Moisan A, Thompson NB, Warner WC Jr, Beaty JH, Sawyer JR.
Transverse fractures of the femoral shaft are a better predictor of nonaccidental trauma in young
children than spiral fractures are. J Bone Joint Surg Am. 2015; 97(2):106-11.
Norman TL, Nivargikar SV, and Burr DB. Resistance to crack growth in human cortical bone is
greater in shear than in tension, J Biomech. 29(8) (1996) 1023-31.
Özkaya, Nihat, Dawn Leger, David Goldsheyder, and Margareta Nordin. Fundamentals of
Biomechanics: Equilibrium, Motion, and Deformation. 2017.
Reber SL, and Simmons T. Interpreting injury mechanisms of blunt force trauma from butterfly
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Rewers A, Hedegaard H, Lezotte D, Meng K, Battan K, Emery K, and Hammen RF. Childhood
femur fractures, associated injuries, and sociodemographic risk factors: a population-based
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Sci. Technol. Adv. Mater. 2011; 12(064708): 1-11.
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Biomech. 2003; 36: 1103-1109.
Theobald PS, Qureshi A, Jones MD. Biomechanical investigation into the torsional failure of
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Torzilli PA, Takebe K, Burstein AH, Zika JM, and Heiple KG. The material properties of
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Vashishth WT. “Damage mechanisms and failure modes of cortical bone under components of
physiological loading”. J. Orthop. Res. 2005; 23:1047-1053.

14

CHAPTER TWO: SPECIMEN AGE AND TORSIONAL RATE OF TWIST INFLUENCE
HELICAL FRACTURE PATTERNS OF THE IMMATURE PORCINE FEMUR
ABSTRACT
In the current forensic literature differentiation between abusive (NAT) and accidental trauma
(AT) in children under three years of age remains challenging. Currently, it is assumed that any
trauma incurred by children under three years of age is frequently non-accidental trauma (NAT),
and that any trauma in children less than one year is always NAT. Furthermore, spiral long-bone
fractures in young children are challenging cases because there are limited ‘ground truth’ data to
help forensic investigators determine abuse from accidental trauma of torsional long-bone
fracture. A recent case study separates pediatric abusive trauma from accidental trauma based on
fracture pattern in which the length of torsional fracture divided by bone diameter, namely
fracture ratio, was found to be low in cases of abuse (≈1.6) and higher in cases of documented
accidental injury (≈2.8). In the case study, there was a reported difference in the mean ages
between accidental and abuse populations, where NAT possessed slightly younger victims. This
age effect while noted, was not statistically significant in the case study. In the current study, the
immature porcine femoral model has been used to study the effects of age and rate of twist on a
redefined fracture ratio. Results of the study showed that both specimen age and rate of twist
were significant factors influencing fracture ratio in the immature porcine long bone specimen.
At younger ages the fracture ratio was low, and it was seen to statistically increase with
specimen age in both the low rate and high rate tests. Correspondingly, at lower rates the fracture
pattern transitioned from a high-angle fracture in the young group to a combination of both lowangle and longitudinal failure segments in the older group, when measured with respect to the
longitudinal axis. At higher rates the fracture pattern rapidly transitioned from low-angle failure

15

to very low angle tensile failure with longitudinal elements, and specimen comminution occurred
as specimen age increased. Notably, the fracture ratio was consistently higher for all ages when
tested at high rates of twist.

INTRODUCTION
Femur fractures are the second most common long bone injury in child abuse cases, after the
humerus (Baldwin et al., 2011), with spiral fractures being the most frequently occurring fracture
pattern in children younger than 15 months of age (Kemp et al., 2008, Worlock et al., 1986).
Spiral fractures, which suggest a twisting action, currently incite forensic practitioners to suspect
non-accidental trauma in children younger than 3 years of age (Carty et al., 1993). This is
especially true for children who are not yet walking, as spiral fractures may well occur more
often accidentally in the femur once the child begins to walk (Baldwin et al., 2011, Flaherty et
al., 2014). For example, a child could trip down a flight of stairs resulting in a twist of the leg, or
the child could fall into a split-legged position while running (Baldwin et al., 2011). Often it is
the job of the forensic practitioner to comment if the injury is accidental or due to an abusive act
by gathering testimony, studying familial history, assessing the time to report the injury, and
utilizing relevant biomechanical data in case evaluations. These types of injury parameters, as
described by Pierce et al., 2005, can be utilized to objectively comment on the probability that an
injury was the result of an abusive action on a case by case basis.

Forensic anthropologists and biomechanists currently have no way of discerning between
accidental injury and an injury resulting from an abusive act, as both produce spiral fractures
under torsional loading. This is problematic for medicolegal investigators. Potentially, a recent

16

case study suggests a method to separate abusive from accidental trauma based on the long bone
fracture pattern (Murphy et al., 2015). The quantitative tool, developed in the study, is called the
fracture ratio and it is defined as the length of torsional fracture in a radiological view of the
bone divided by bone diameter. The study shows that patterns of bone fracture generally have a
low fracture ratio for cases found to be due to abusive acts, as opposed to a high fracture ratio in
cases of documented accidental injury (Murphy et al., 2015). A potential limitation of the study
may be that there was a slight but statistically insignificant age effect biasing the results, as the
abuse population of victims was slightly younger. Secondly, the material properties of bone, such
as the ultimate tensile strength and modulus, have been shown to positively correlate with age
(Torzilli et al., 1982). This may then influence the pattern of torsional fracture, as a spiral
fracture occurs from the combination of tensile and shear failure of the bone (Turner et al.,
2001). A long bone under torsional loading experiences maximum shear stresses on planes
perpendicular and parallel to its longitudinal axis, while maximum tensile stresses are generated
45 degrees to the long-axis of the bone. This in turn influences the location and direction of crack
propagation within the bone that produces a spiral fracture under torsional loads (Norman et al.,
1996). Another potential limitation of the Murphy et al., 2015 study was that there was not a
stratification of the speed of each traumatic event, especially those separating the abuse from
accidental groups. A study by Theobald et al., 2012, using 7-day old calf femurs, has shown that
an increase in the rate of twist generates a corresponding increase in fracture ratio (decrease in
fracture angle).

Due to the lack of infant and child cadavers for controlled biomechanical experiments,
investigators have largely had to use surrogate animal models. Pearce et al., 2007, for example,

17

has shown similarities in bone mineral density of porcine bone to that of human bone.
Similarities have also been documented in the femoral cross-sectional area between humans and
pigs (Pearce et al., 2007). Our laboratory has also used the immature porcine model in studies of
cranial fracture (Baumer et al., 2009, Deland et al., 2016, Vaughan et al., 2016). This is because
Baumer et al., 2010 has shown a direct correlation in bending rigidity of the infant human
parietal bone in months to that of the infant porcine bone in days of age. Cheong et al., 2017
recently has also recently suggested that one week in development of the porcine femur is
approximately equivalent to 1 year of development of the human femur.

In the current study immature porcine femurs were used to study the effects of age and rate of
twist on bone fracture ratio. A hypothesis of the study was that the fracture ratio would increase
with age, since the tensile strength of bone has been shown to increase with age in humans (Vinz
et al., 1975). Second, it was also hypothesized that fracture ratio would increase with rate of
twist in the immature porcine bone model, based on the previous work of Theobald et al., 2012

METHODS
Fifteen pairs of porcine femur specimens aged 1-26 days old were collected from a local farm
and frozen within 12 hours of death at -20°C. Prior to testing the specimens were thawed at
ambient temperature for 24 hours. After the tissues thawed, the femurs were dissected, cleaned
of soft tissue and immediately wrapped in a gauze-soaked phosphate buffered solution (PBS) to
prevent the bones from drying and changing their material properties (Kim et al., 2004). Each
specimen was inserted into a custom-built, laser alignment fixture (Figure 2.1).

18

Figure 2.1 Photograph of the custom-built laser alignment fixture and the process of centering
the bone.

A liquid resin hardener purchased from technovit (J-61Lb, J-61pb, Jorgensen Laboratories Inc.,
Loveland, CO) was used to pot the bones in cylindrical cups to provide a gripping surface during
these torsion experiments (Figure 2.2). After potting, the specimens were maintained in a
refrigerator at 0°C while wrapped with saline-moistened gauze until testing. All tests were
performed within 24 hours of thawing.

19

Figure 2.2 Example of a potted bone specimen using the fast technovit liquid resin hardener
formed to the cylindrical shape of the potting cups.

Each specimen was twisted until observable failure in a servo-hydraulic testing machine (model
1331, Instron Corporation; Norwood, MA), using a custom-built torsion fixture (Figure 2.3). The
linear actuator of the servo-hydraulic testing machine provided linear displacement to a rack and
pinion assembly to provide controlled torsion of each specimen. To secure the specimen in the
fixture, set screws were inserted through the potting cups into holes in the potting material
(Figures 2.2 and 2.3). In preliminary tests it was decided to maintain an average gauge or test
length of 3 times the smallest mid-shaft bone diameter for each specimen, regardless of specimen
age. The test length was selected to provide the maximal exposed bone length, while retaining a
sufficient length of potting to secure the specimen in the test fixture.

Specimens were rotated until failure under external rotation for each leg pair, recording the
torque and the angle of rotation at a sampling rate of 10,000 Hz. The angle of rotation was

20

measured with a rotary encoder (model BHW 16.05A72000-BP-A, Baumer Electric, Frauenfield,
Switzerland) attached to the moving cup, while the torque was recorded using a 200 in-lb.
torsion transducer (model TRT-200, Transducer Techniques; Temecula, CA) attached to the
fixed cup.

In this study the left femur of each pair was twisted to failure at a rate of 3 degree/sec, while the
right femur was twisted at a rate of 90 degree/sec. The fracture ratio was defined as total fracture
length / bone diameter (Figure 2.4). Additionally, while not the target focus of the study, a
composite fracture angle was also measured and recorded with respect to the longitudinal axis to
more easily compare the current results to angles reported in a previous study.

Figure 2.3 Set-up: custom-built torsion fixture and servohydraulic hydraulic testing machine.
21

Figure 2.4 Example of measuring the total fracture length using fracture segments in a single 2dimensional plane of view.

The total fracture length was defined as the summation of each fracture segment in a single plane
of view, and the bone diameter was the smallest diameter of the bone measured pre-failure in the
same 2-dimensional plane.

Photographs of each failed specimen were taken in both the anteroposterior and mediolateral
planes of the bone (Figure 2.5). A reference scale was placed in the same plane as the specimen
diameter and fracture ratio to measure these parameters directly from the photographs.

22

Figure 2.5 2-dimmensional measurement technique of a mediolateral and anteroposterior view,
shown for a low-rate specimen.

Statistical tests to compare differences in some test parameters between groups were performed
using a two-way ANOVA in Minitab 16 (State College, PA). The parameters examined here
were the effects of specimen age and rate of twist on fracture ratio. This statistical test was
utilized for the low and high rates of twist when compared against specimen age. A linear
regression analysis was performed on the above parameters as well as the total angled (e.g.
segment 1 and segment 3 in Figure 2.4) and longitudinal (e.g. segment 2 in Figure 2.4)
components of the fracture surface versus specimen age using SPSS (SPSS Inc., Chicago, IL) to
determine if the slopes and intercepts of the regression lines were significantly different from
zero. If the slope of the lines was not significantly different from zero, an average value was
computed and a one-sample t-test was performed between test groups using Minitab 16 (State
College, PA). All statistical analyses used a criterion alpha level of 0.05.

RESULTS
Fifteen specimens were tested, ranging from 1-26 days of age. From the youngest to oldest
specimen the total bone length increased from approximately 20 to 60 mm, and the bone

23

diameter increased from approximately 6 to 9 mm. The average exposed bone length after
potting was 3.0 Âą 0.2 times the smallest bone diameter for each specimen in the current study.
Spiral fracture patterns were produced in all specimens. Fracture comminution was only
observed in some of the high rate of twist experiments.

It was noted that the fracture ratio increased with specimen age in both mediolateral and
anteroposterior planes, with the low rate of twist yielding a consistently lower fracture ratio than
the high rate of twist (Figure 2.6 and 2.7). A polynomial curve was fit to the dataset to highlight
the rapid increase in the fracture ratio from (1-9 days), plateauing after about 10 days of age.
Mediolateral specimens showed incomplete fracture patterns in the low and high rate pairings
(did not fracture completely across the bone diameter) for specimen ages 2,5,9, and 13, so these
pairs were eliminated from the mediolateral data set. This reduced the sample size to 11 paired
specimens. Specimen age and rate of twist were significant factors influencing the
anteroposterior fracture ratio with p=0.031 and p=0.0001, respectively (Figure 2.6). Specimen
age and rate of twist were also significant factors influencing the mediolateral fracture ratio with
p=0.026 and p=0.0001, respectively (Figure 2.7).

24

Figure 2.6 Plot of anteroposterior fracture ratio with respect to twist rate and specimen age
(measured on anterior side of bone), n = 15.

Figure 2.7 Plot of mediolateral fracture ratio with respect to twist rate and specimen age
(measured on medial side of bone), n = 11.

25

Upon a detailed inspection of the fracture segments, the total length of longitudinal, segment
type-2, fracture and the total length of angled, segment 1 and 3-type fracture, followed consistent
trends. In low rate experiments for specimens 1 to 9 days of age, there was no observable
segment type-2 failure in either the ML or AP views. For specimens aged 10 to 26 days of age in
the AP view, the length of segment type-2 failure increased with age (Figure 2.8). In the AP
view, the linear regression slope and intercept was significantly different than zero for the old
group (p=0.033). In the ML view the length of longitudinal fractures remained constant,
becoming visible after 10 days of age, with no significant age effect 3.48 Âą 0.49 mm.

Figure 2.8 Plots of the low-rate total longitudinal (element 2) fracture length versus specimen
age (AP ratio left (n=15), ML ratio right (n=11)).

In the higher rate experiments the longitudinal component of fracture appeared earlier with age,
between approximately 3 and 5 days for ML and AP views, respectively (Figure 2.9). For all
non-zero length of longitudinal fracturing there was no significant age effect observed in both
views 4.62 Âą 0.69 mm and 4.29 Âą 1.96 mm for ML and AP, respectively.

26

Figure 2.9 Plots of the high-rate total longitudinal fracture component versus specimen age (AP
ratio left (n=15), ML ratio right (n=11)).

In contrast, the length of the angled failure components, taken as fracture lines that propagated at
some angle theta to the longitudinal axis, increased rapidly for early ages, reaching a critical
value between 10 and 12 days of age, where the total angled fracture component became
relatively constant for the low-rate experiments (Figure 2.10). This was true in both the ML and
AP views.

Figure 2.10 Plots of the low-rate total angled fracture components versus specimen age (AP
ratio left (n=15), ML ratio right (n=11)).
27

In low-rate tests the linear regression slope was only significantly different than zero at younger
ages, with (p=0.008) and (p=0.030) for AP and ML views respectively.

Interestingly, the high-rate of twist experiments revealed a significant age effect, with (p =
0.025) and (p=0.002) over all ages tested in AP and ML views, respectively. The measured
length of the angled fracture segments was shown to increase with specimen age (Figure 2.11).
Additionally, for the higher rate of twist experiments there was a noted increase in the number of
fracture lines in addition to the main break, with specimen age. These additional fracture lines
were not measured by fracture ratio, but are instead additional evidence of a high-speed bone
fracture event for older bone specimens.

Figure 2.11 Plots of the high-rate total angled fracture components versus specimen age (AP
ratio left (n=15), ML ratio right (n=11)).

28

DISCUSSION
The current study was performed to determine if the parameters of age and rate of twist would
influence the fracture pattern of immature porcine femora under torsional loading. The study
generated biomechanical data supporting this first hypothesis. It was shown that the fracture ratio
began low and significantly increased with specimen age. Additionally, the study supported the
second hypothesis that fracture ratio was significantly greater in the high rate of twist
experiments than in the low rate tests, which had been suggested by the previous work of
Theobald et al.

Interestingly at low rates of twist as age increased the length of the type-1 and type-3 angled
segments increased, with the angle of the fracture decreasing to 30 degrees from the long axis of
the bone (Figure 2.12a). At an age of 10 days and beyond, the fracture pattern began to fail with
an increasing length of segment type-2 failure (Figure 2.12b). The length of segment type-2
failure was proportionally smaller than the combined type-1 and type-3 failure, which is
supported by Norman et al., 1996 who demonstrated that cracks are more likely to grow in
tension than in shear, even when the longitudinal shear stresses are significantly high enough to
cause fracture (Jepsen et al., 1999).

29

(a)

(b)

Figure 2.12 Photographs of low-rate tests, showing the increase in angled fracture lengths in
mm for specimens (2,4,9 days) top-bottom, and its effect on the AP fracture ratio (column a).
Photographs showing the increase in length of the longitudinal fracture element in mm for
specimens (13,18,26 days) top-bottom, and its effect on the AP fracture ratio (column b).

In the higher rate experiments the overall fracture pattern transitioned from low-angle failure
(approximately 35 degrees), to very low angle failure (approximately 25 degrees), with
longitudinal elements and increased comminution as specimen age increased (figure 2.13).

30

Figure 2.13 Photographs showing changes in the fracture pattern under a high rate of twist.
Specimen age (1,6,12,18,26 days) left to right at mediolateral view.

Upon closer inspection of the bone for the higher rate experiments, the helical fracture pattern
appeared to vary with specimen age and failed under differing mechanisms. At one day of age
the helical fracture appeared more jagged, suggesting that the fracture was continuously shearing
through osteons. At as early as six days the helical pattern became smooth with no apparent
deflections. After 10 days of age the helical pattern became more step-like, failing successively
in the longitudinal direction, directly increasing the crack length and fracture ratio (Figure 2.14).

31

Figure 2.14 Enlarged photographs of high-rate test specimens 1,6,12, from Figure 2.13 (top)
and a single enhanced surface view from the same specimen (bottom). Showing a jagged shallow
helical pattern for 1-day old specimen (left), a “smooth” helical pattern for a 6-day old
specimen (center), and showing a step-like helical pattern at 12 days of age (right).

The studies by Turner et al.,2001 and Saha, 1977 previously indicate that cortical bone is weak
in both tension and shear, particularly in the longitudinal shear plane. Additionally, using
compact bone tissue from the adult human femurs of different ages, Vinz et al., 1975 has shown
that the tensile strength of bone increases with age. This increase in tensile strength has been
correlated with an increased number of osteons in the bone with increasing age (Evans et al.,
1967, Frassica et al., 1997). Furthermore, a high number of osteons has been shown to help
inhibit crack propagation (Norman et al., 1996). This could imply that as the bone properties
strengthen with age, due to an increase in the number of osteons, relatively more shear failure
occurs between osteons as opposed to through osteons. This hypothesis, to help explain the
increase in longitudinal shear failure with age, will need further investigation.

32

For an infant porcine femur twisted at a low rate, 10 days appears to be a critical age where
below this threshold the fracture is transverse shear and tensile fracture dominate, whereas past
this threshold age longitudinal shear becomes a more significant failure mode, as evidenced in
Figures 2.8, 2.9, 2.10, 2.11, 2.12a. and 2.12b. This possible semi-maturation age of
approximately 10 days for a porcine bone (tested under low-rate) was also shown to be a critical
age in previous studies from our laboratory that investigated the patterns of porcine cranial
fracture in relation to porcine growth and development (Baumer et al., 2010, Powell et al., 2012).
In contrast, for the high rate of twist experiments this transition occurred much earlier between 3
and 5 days of age, more likely due to relative stiffness increases, as the bone responded to the
faster loading.

In contrast to the study by Murphy et al., 2015, that the fracture ratio can be utilized to
differentiate between accidental and abusive acts, the current study may suggest that age and
speed of twisting may have influenced the results of this clinical-based study. Using the
immature porcine model, the current study has also shown that the newly defined fracture ratio is
increased with rate of twist. It might be suggested then that accidental traumas, especially those
from automobile accidents, may generate a high fracture ratio due to a potentially high rate of
twist. While not mentioned in the Murphy et al., 2015 study, based on a personal communication
between the authors of the current study and those of Murphy et al., 2015, all the known
accidental cases in that study were motor vehicle accidents or falls from heights. As a result,
these cases may have potentially involved high rates of twist that, based on the results of the
current study, produce a high fracture ratio, therefore leading to the correlation between the high
fracture ratio and accidental trauma. Furthermore, the current study showed age was an

33

influencing parameter on the fracture ratio. While age was not shown to be a significant
statistical factor in the Murphy et al., 2015 study, explaining the lower fracture ratio for abuse
cases, the power of the Murphy et al., 2015 study was not clearly defined. As such the current
study, while limited to using the infant porcine model, might suggest additional clinical studies
utilizing more specimens and stratification by rate of loading may be needed before fracture ratio
alone should be utilized for the determination of accidental versus abusive pediatric trauma.

In summary the current study has documented that fracture ratio was significantly dependent on
both specimen age and rate of twist, using the infant porcine femur model, with low rates of twist
consistently producing lower fracture ratios than those shown under high rates of twist. While
both an accidental and abusive act may produce spiral fractures, the results of the current study
cannot aid in the interpretation of intent. This study does, however, provide experimental
‘ground-truth data’ that may help forensic biomechanists and anthropologists draw conclusions
surrounding the circumstances of an injury that may help in the evaluation of truth in testimony
during criminal litigations.

34

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37

CHAPTER THREE: THE EFFECT OF SPECIMEN AGE AND LOADING RATE ON
INTRINSIC MATERIAL PARAMTERS OF THE IMAMTURE PORCINE FEMORA
ABSTRACT
The underlying failure mechanisms and resulting fracture patterns of whole bone under torsion is
not fully understood. From torsional testing conducted previously by this lab, it was discovered
that the spiral fracture’s surface changes with specimen age and rate of twist, and that this
change in the fracture pattern is measurable via a fracture ratio, where the spiral fracture length is
divided by the bone diameter when measured under a single radiographic view. Under close
examination the fracture surface was seen to transition from a jagged surface (high angle failure)
at a young age, to a smooth break, and then to a step-like fracture surface (low angle failure), as
measured from the longitudinal axis of the bone. It was theorized that a pre-disposed weakness to
a given shear-type, namely low fracture strength of the bone under longitudinal or transverse
shear, is what causes deviation in the spiral fracture surface from an idealized ‘smooth’ fracture
surface resulting from failure under tension. For example, if bone is weaker in transverse shear
than in longitudinal shear, then this type of shear failure will become a viable alternative fracture
path to the preferred mode of failure under tension, and vice versa. Results of this study indicated
that at low rates the longitudinal shear strength from birth was initially stronger than the
transverse shear strength, becoming weaker than the transverse shear strength after
approximately 7 days of development. A similar trend was also noted at a high rate of loading,
with approximately 4.5 days of development acting as the critical transition age for failure
strength of the bone. This information supports the notion that there are three modes of spiral
bone fracture. Below the critical transition ages reported above for each respective rate of testing,
a combined transverse shear and tensile failure mode is likely to occur, resulting in a low fracture

38

ratio due to increased transverse failure through osteons. At and perhaps a few days before and
after the critical age, which from herein will be defined as the critical region where the transverse
and longitudinal shear strengths are approximately equal, a purely tensile mode of failure is
likely to be seen in the spiral failure, generating a smooth fracture surface, increasing the fracture
ratio. After the reported critical age, a combined tensile and longitudinal mode of failure is likely
to be generated, further increasing the fracture ratio due to increased failure between osteons
cement lines.

INTRODUCTION
The underlying failure mechanisms and resulting fracture patterns of whole bone under torsion is
not fully understood. Currently forensic biomechanists and anthropologists only report is that a
spiral fracture pattern is evidence that the bone was twisted, and in which direction the bone had
been twisted (Kress et al., 1996). This may not provide evidence whether the injury was due to
an accident or an abuse-type scenario. The only comment forensic practitioners often are willing
to make is that for children under the age of walking to acquire a spiral fracture of the femur is
by non-accidental trauma or abuse (Carty, 1993, Pierce et al., 2004).

As bone is an anisotropic material, it has differing properties in different directions. This is
largely a result of its underlying microstructure (Pierce et al., 2004). The femur is composed of
longitudinally-oriented osteons which are composed of a stretchable fibrous protein collagen and
a brittle mineral phase hydroxyapatite, which results in a very strong and tough material (Tadano
et al., 2011). Osteons are interconnected by a cement lining and a weak lamellar interface
(Katsamenis et al., 2012). For purposes of this thesis the longitudinal direction will be taken as

39

the long-axis of the femur, and the transverse direction will be taken as perpendicular to the
long-axis.

Indirect measures of the aggregate properties of the osteon and lamellar interface can be found
through material testing techniques, such as tensile and shear tests. In bone the longitudinal
tensile strength and the transverse shear strength can be considered as indirect measures of the
aggregate strength of the bone. The transverse tensile strength and the longitudinal shear strength
of the bone can be considered as indirect measures of the cement-lining and matrix interface
between osteons. Understanding how these properties are influenced by both specimen age and
loading rate are pivotal in the understanding of whole bone failure mechanisms, like twistingfracture.

As noted by Turner et al., 2001, shear strength is typically reported as the torsional shear strength
of whole bone while there is limited data on ‘pure’ shear values in either the longitudinal or
transverse directions. Furthermore, there is limited data presented on immature bone, as more
mature ‘adult’ bone is typically available for study. It has been generally assumed in the
literature that immature bone will produce fracture patterns and fail under similar mechanisms to
those of mature bone, with limited supporting data at this time.

The aim of the current study was to collect ‘pure’ shear and tension data from immature porcine
femora in both the longitudinal and transverse directions over a range of ages and two rates of
loading that parallels the study in Chapter 2. As spiral fracture is considered a combination of
both transverse and longitudinal shear failure (Vashishth et al., 2005), it is theorized that a pre-

40

dispositional weakness to a given shear-type will be evident in the spiral fracture pattern of the
bone as a function of specimen age and rate of loading. For example, if bone is weaker in
transverse shear than in longitudinal shear then this type of shear failure will become a viable
alternative fracture path to the preferred mode of failure under tension, and vice versa.

METHODS
Forty paired porcine specimens aged 1-24 days old were collected from the MSU swine research
facilities and frozen within 12 hours of death at -20°C. All specimens that were collected
perished of natural causes. Prior to testing specimens were brought to room-temperature and
dissected from the limb, cleaned of excess muscular tissue, and immediately wrapped in salinemoistened gauze to prevent drying-out of the bone. The mid-section of the right and left leg pairs
was then removed with a bone saw from the anterior plane of the bone. The anterior plane was
selected, as Chapter 2 Figure 2.6 showed that the greatest rate effect occurred on the anterior
plane. Specimens were then wet-cut by hand into tensile and shear testing shapes (Figure 3.1).
After shaping and prior to testing specimens were maintained in a refrigerator at 0°C while
wrapped in saline-soaked gauze. Prior to testing, the specimens were brought back to ambient
temperature. Tests were performed within 48 hours of initial thawing.

41

(a)

(b)

(c)

(d)

(e)

Figure 3.1 Longitudinal tensile testing representation (a), transverse tensile testing
representation (b) longitudinal shear testing representation (c), transverse shear testing
representation (d) natural curvature of the bone (e). For all pictures the direction of osteons is
represented by a gray dotted line.

Each specimen was tested until failure in a servo-hydraulic testing machine (model 1331, Instron
Corporation; Norwood, MA) using a custom-built tensile and shear test fixture (Figure 3.2). The
linear actuator provided a measurable vertical displacement which resulted in controlled shear or
tensile deformation. To help reduce bending forces on the bone from direct clamping of a curved
surface, a small curvature was set into the clamp itself to mimic the natural curvature of the bone
surface (Figure 3.3).

42

Figure 3.2 Photograph of tensile testing fixture (left), photograph of the shear testing fixture
(right)

Curved Surface

Figure 3.3 Photograph of the curvature designed into the clamp

43

As the load-displacement rate in tension and shear could not be directly resolved from the tests
performed in Chapter 2, it was decided to match the failure time of the tensile test specimen in
both directions to that of the failure time recorded at 3 degree/sec and 90 degree/sec under
torsion. This was selected because bone is claimed to fail in torsion primarily under tension, as
opposed to shear (Kress et al.,1996, Turner et al., 2001), and shear failure under torsion is
theorized to only act as a secondary alternative failure mode for crack energy dissipation of
propagating helical cracks. In preliminary tests the rate of displacement that fit this criterion was
a low rate of 0.065 mm/sec to match failure time at 3 degree/sec, and a high displacement rate of
1.61 mm/sec to match the failure time at 90 degree/sec.

Force-time data was collected with a 100 lb load cell (model 1500ASK-100, Interface;
Scottsdale, AZ) at a sampling rate of 5000 Hz for the high rate tests, and a sampling rate of 2500
Hz for the low rate tests. A pre-load of 2N was applied for both tests to take slack out of a joint
which was added to the fixture to reduce bending loads and promote ‘pure’ axial loading of the
specimens. The pre-load of 2N was then held for three seconds before a haversine load at the
previously given rates was applied for a total displacement of 1 mm and 2 mm in the low and
high rate tests, respectively.

Traditional engineering mechanics equations were utilized in the study (Sukla, 2014). The
ultimate tensile strength of the bone was calculated using the expression
𝜎=

𝐹𝑓𝑎𝑖𝑙
𝑤∗𝑡

44

(3.1)

where 𝜎 is the ultimate tensile strength in megapascals, 𝐹𝑓𝑎𝑖𝑙 is the failure force required to break
the specimen in Newtons, 𝑤 is the width of the test specimen in millimeters, and 𝑡 is the cortical
bone thickness in millimeters. The tensile strain was calculated using the expression
∆𝑥

𝜀𝑡𝑒𝑛𝑠𝑖𝑙𝑒 =

𝐿𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒

(3.2)

where 𝜀𝑡𝑒𝑛𝑠𝑖𝑙𝑒 is the tensile strain in either the longitudinal or transverse directions, ∆𝑥 is the
measured displacement of the Instron machine in millimeters, and 𝐿𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 is the effective
length of the test section of the specimen in millimeters. The Young’s modulus was calculated
using the expression
𝜎

𝐸=

𝜀𝑡𝑒𝑛𝑠𝑖𝑙𝑒

(3.3)

where E is the Young’s modulus of elasticity in megapascals. The modulus was taken as a linear
regression over the elastic portion of the stress-strain curve (Figure 3.4 left).

For shear tests the ultimate shear strength of the bone was calculated using the expression
𝜏=

𝐹𝑓𝑎𝑖𝑙

(3.4)

ℎ∗𝑡

where 𝜏 was the ultimate shear strength in megapascals in either the longitudinal or transverse
direction, ℎ was the notch height of the specimen in millimeters, and 𝑡 was the cortical bone
thickness in millimeters. The shear strain was taken as
𝜀𝑠ℎ𝑒𝑎𝑟 =

∆𝑥
ℎ

(3.5)

where 𝜀𝑠ℎ𝑒𝑎𝑟 was the shear strain, ∆𝑥 was the measured displacement of the Instron in
millimeters, and ℎ was the effective length of the specimen minus the notch dimensions in
millimeters. The shear modulus was given by the expression
𝐺=

𝜏
𝜀𝑠ℎ𝑒𝑎𝑟

45

(3.6)

where 𝐺 is the shear modulus in megapascals. The shear modulus was taken as a linear
regression over the elastic portion of the stress-strain curve, as performed for the Young’s
modulus (Figure 3.4 right).

Figure 3.4 Young’s modulus determination for an 8-day old, low rate longitudinal tensile
specimen (left), shear modulus determination for a 7-day old, low rate longitudinal shear
specimen (right).

STATISTICAL METHODS
A two-way ANOVA was performed in Minitab 18 (State College, PA) to compare the effects of
specimen age (1-24) and specimen loading rate (low and high) on various factors such as
ultimate strength, tensile and shear moduli, time to failure, and failure strain. A linear regression
analysis was performed on all parameters to determine if the slope and intercepts were
significantly different from zero. If the slopes of the lines were not significantly different from

46

zero, and average value was computed for the dataset, and a one-sample t-test was performed to
produce the confidence range of that data, using Minitab 18 (State College, PA). All statistical
analyses used an alpha-criterion of 0.05.

RESULTS
Forty specimen pairs were tested at both low and high loading rates, ranging from 1-24 days of
age. 10 specimens were tested at low and high rates for longitudinal tensile tests, transverse
tensile tests, longitudinal shear tests, and transverse shear tests. A sample size of (n=10) was
recorded for each test, excluding the longitudinal tensile test where (n=9) as a paired specimen
broke while loading into the clamps.

FAILURE STRENGTH RESULTS
It was noted in low rate tests that the longitudinal shear strength decreased with specimen age.
Interestingly, the longitudinal shear strength from birth was initially stronger than the transverse
shear strength, becoming weaker than the transverse shear strength after 7 days of development.
For these low rate tests 7 days appeared to be a critical age, where the transverse and longitudinal
shear strengths were equal (Figure 3.5). A similar trend was also noted in high rate tests where
4.5 days of development appeared to be the critical age (Figure 3.6).

47

Figure 3.5 Plot of low rate failure strength values. Closed triangles are longitudinal tensile data
points (n=9), open triangles are transverse tensile data points (n=10), closed squares are
longitudinal shear data points (n=10), and open squares are transverse shear data points
(n=10).

48

Figure 3.6 Plot of high rate failure strength values. Closed triangles are longitudinal tensile
data points (n=9), open triangles are transverse tensile data points (n=10), closed squares are
longitudinal shear data points (n=10), and open squares are transverse shear data points
(n=10).

The longitudinal shear strength had an age (p = 0.0001) and rate effect (p = 0.012) with the high
rate tests yielding lower longitudinal shear strength values than the low rate tests. For both high
and low rates the longitudinal shear strength decreased with increasing age. The transverse shear
strength also had an age effect (p = 0.014), but no discernable rate effect. The transverse shear

49

strength was shown to increase with increasing specimen age. The longitudinal tensile strength
and the transverse shear strength were neither rate nor age dependent.

YOUNG’S MODULUS AND SHEAR MODULUS RESULTS

Figure 3.7 Plot of low rate shear and tensile moduli. Closed triangles are longitudinal tensile
data points (n=9), open triangles are transverse tensile data points (n=10), closed squares are
longitudinal shear data points (n=10), and open squares are transverse shear data points
(n=10).

50

Figure 3.8 Plot of high rate shear and tensile moduli. Closed triangles are longitudinal tensile
data points (n=9), open triangles are transverse tensile data points (n=10), closed squares are
longitudinal shear data points (n=10), and open squares are transverse shear data points
(n=10).

Similar trends to that of the failure strength were also noted for the shear and tensile moduli of
the bone at the two rates (Figure 3.7 and Figure 3.8). The longitudinal shear modulus had an age
effect (p = 0.003), but there was no statistically significant difference between the low and high
rate data. For both high and low rate tests the longitudinal shear modulus decreased with
increasing age. The transverse shear modulus had both an age (p = 0.035) and a rate effect (p =
0.045) with the high rate transverse shear moduli possessing a higher value for all ages when
51

compared to the low rate data. The transverse shear modulus was shown to increase with
increasing specimen age. The longitudinal tensile modulus was also both age (p = 0.025) and
rate-sensitive (p = 0.018) with the high rate Young’s modulus yielding higher values for all ages
compared to the low rate test data. The longitudinal tensile modulus increased with increasing
specimen age. The transverse tensile modulus was only age-dependent (p = 0.004). The
transverse Young’s modulus increased with increasing specimen age.

TIME TO FAILURE
The low rate test of 0.065 mm/sec over a 1mm displacement and the high rate test of 1.61
mm/sec over a 2mm displacement in these experiments were selected to be loading rates
representative of the 3 degree/sec and 90 degree/sec torsional tests, based upon recorded time at
bone fracture. All low rate and high rate test data fell within a range that was not statistically
different from the torsional tests, except for the transverse shear tests. At the same failure rate as
the longitudinal shear, longitudinal tensile, and transverse tensile tests, it took significantly more
time for the transverse shear tests to achieve total failure (Figure 3.9 and Figure 3.10).

52

12

A

Time (s)

10

B

8
6

B/C

C

B/C

4
2
0

Long Shear

Long Tens

Torsion

Trans shear

Trans Tens

Type
Figure 3.9 Plot of the various test data and the time (in seconds) it took to reach bone fracture
for low rate tests.

1.2
1.0

Time (s)

0.8

B

0.6
0.4

A

0.2
0.0

Long Shear

A

A

Long Tens

Torsion

Type

A
Trans shear

Trans Tens

Figure 3.10 Plot of the various data and the time (in seconds) it took to reach bone fracture in
the high rate tests.

53

DISCUSSION
The current study was performed to assess the effects of specimen age and loading rate on the
intrinsic material properties of the immature porcine femur in both the longitudinal and
transverse directions. From torsional testing conducted in Chapter 2 of this thesis, it was
discovered that the spiral fracture surface changed with specimen age, transitioning from a low
fracture ratio (large-angle failure from long-axis) to a high fracture ratio (low-angle failure from
long-axis). The fracture surface transitioned from a jagged surface at a young age, to a smooth
break, and then to a step-like fracture surface with increasing age of specimen (Figure 3.11).

Figure 3.11 Enlarged photographs of high-rate test specimens 1,6,12, from Figure 2.13 (top
three photos) and a single enhanced surface view from the same specimen (bottom three photos).
Showing a jagged shallow helical pattern for 1-day old specimen (left, column 1), a “smooth”
helical pattern for a 6-day old specimen (center, column 2), and showing a step-like helical
pattern at 12 days of age (right, column 3). Adapted from Figure 2.14.

54

It was therefore theorized that a pre-disposed weakness to a given shear-type or tensile-type
would be evident in the spiral fracture pattern of the bone, and that this weakness would allow
the crack to either propagate transversely though osteons, or longitudinal along osteons, as an
alternative crack path from the preferred mode of failure along the line of maximum tension.
Therefore, if bone is weaker in transverse shear than in longitudinal shear, then transverse shear
failure through osteons will become a viable alternative fracture path to the preferred mode of
failure under tension, reducing the fracture ratio (increasing the angle of fracture from the longaxis and vice versa if longitudinal shear is the viable alternative fracture pathway, resulting in an
increase in the fracture ratio (decreasing the angle of fracture from the long-axis). The study
generated biomechanical data supporting this hypothesis.

Treating the transverse and longitudinal shear strength as a ratio of the fitted curves from Figures
3.5 and 3.6, the point where the shear strengths are equal (a ratio value of one) was
approximately 4.5 days for high-rate tests and approximately 7 days for low-rate tests (Figure
3.12). Taken as the mean critical transition point, it is likely that a few days before and after the
critical value will possess similar fracture properties, and is defined here as the critical region.
While not a direct finding of Chapter 2, composite fracture angles were measured of the spiral
fractures produced for all ages, for convenience when comparing the fracture ratio to the fracture
angles that are commonly reported in the literature. In this critical region it appeared the bone
failed purely in tension at an angle of approximately 45 degrees. This is the most commonly
reported mode of spiral fracture (Porta et al., 2005). Prior to this critical range the transverse
shear strength is weaker than the longitudinal shear strength, allowing for deviations from the
mechanically preferred mode of failure by tension, and allowing energy to be dissipated by crack

55

failure through osteons (resulting in a low fracture ratio/high fracture angle). After this critical
region the longitudinal shear strength was weaker than the transverse shear strength, allowing for
deviations from the mechanically preferred mode of failure in tension, and allowing energy to be
dissipated by crack failure along the cement line, longitudinally (resulting in a high fracture
ratio/low fracture angle).

Figure 3.12 Plot of the ratio of transverse shear strength over the longitudinal shear strength
against specimen age.

Nalla et al., 2005 used notched human bone specimens to demonstrate that bone is tougher in the
transverse direction than in the longitudinal direction. When bone fails under transverse shear,
not only does it break through osteons, but the crack is also deflected along cement lines as it
56

propagates generating a highly torturous crack (Koester et al., 2008, Nalla et al., 2005 and
Vashishth et al., 2005). This pattern-type in the transverse orientation is best shown by Koester et
al., 2008 (Figure 3.13a).

(a)

(b)

Figure 3.13 Pictorial representation of transverse crack propagation through osteons, with
crack deflections in the longitudinal direction (a), and crack bridging (b). Figure adapted from
Koester et al., 2008.

Interestingly, in Figure 3.11 (left, column 1) the 1-day old specimen showed this type of crack
propagation along the line of maximum principal stress. The failure description provided by
Cheong et al., 2008 provides evidence to support that while the spiral fracture depicted in the
figure is generated primarily because of failure under tension due to the angled failure, that there
are clear signs that transverse shear is also a contributing factor to this spiral fracture pattern.

When bone is weak in the longitudinal direction, microcracks are produced along the osteons,
creating crack bridges as shown by Koester et al., 2008 (Figure 3.13b). Agreeing with Turner et
al., 2001, and as seen in Figure 3.11 (right, column 3) and 2.12b, the longitudinal shear direction
is weak. The weakening of the cement lining observed in Figures 3.5 and 3.6 is most likely the

57

result of Haversian remodeling, which as Norman et al., 1996 has noted reduces bone strength,
perhaps primarily longitudinal shear strength.

The current literature has contradicting data on torsional failure for immature long bones. Like
the studies of Chapter 2, Cheong et al., 2008, and Taylor et al., 2003, have also noted
longitudinal fracture components (Table 1). Additionally, as in the Chapter 2, Theobald et al.,
2012 finds that high rate tests produce lower angle fractures (higher ratios) than those in low-rate
tests (low ratios), when measured from the long-axis. Contradictory to the Chapter 2 and to that
of Theobald et al., 2012, Cheong et al., 2008 produces composite fracture angles that are lower at
higher rotational rates. Additionally, Taylor et al., 2003, reports a large-angle fracture under
cyclic fatigue, which for the purposes of comparison, can be considered a very low rate test.
Based upon this study of Chapter 3, the varying results of the literature may be explained when
considering specimen age as it relates to the intrinsic material property values. For example, as
specimen age was not reported by Taylor et al., 2003, it is possible that young and old specimens
were mixed in the test population. This would explain why one photo reported in the study is of a
55-degree tensile failure (a suspected younger specimen), while another photo in the study has
tensile and longitudinal components of fracture (a suspected older specimen).

In summary the current study attempted to document which mechanical properties were
dependent on specimen age and loading rate using the immature porcine femoral model, and its
potential effect on the torsional fracture ratio. The study has documented that alternating
transverse and longitudinal shear properties may help to provide a mechanical reasoning for
interpreting changes in the helical fracture pattern under torsional loading. As may be shown by

58

Figures 3.5 and 3.6, it is speculated that combined tensile and transverse shear failure results in
lower fracture ratios under torsional loading (high fracture angles from long-axis), which can be
a result of either young specimen age, and/or a low rate of twist. In turn, combined tensile and
longitudinal shear failure results in higher fracture ratios under torsional loading (low fracture
angles from long-axis), which can be attributed to an older specimen or a younger specimen
failed at a high rate of twist. The current study is limited and could easily be expanded upon for
future work. A wide spectrum of test ages from immature to mature bone can provide a better
understanding of how bone properties change during maturation and development. Additionally,
multiple displacement rates should be stratified like in the work of Theobald et al., 2012. Such
an effect would have more clinical relevance if ever transitioned into a human study.
Furthermore, this study neglected curvature effects of the bone specimen. A larger bone model
such as from an ovine or bovine femur would eliminate this issue and would be closer to a
human surrogate model. However, while the current study is limited in scope, it may still provide
useful ‘ground-truth’ data from which immature bone failure mechanisms can be better
understood.

59

APPENDIX

60

Table 3.1. Summary table of immature torsional data in the literature

study low rate (deg/sec) composite fracture angle (deg)
Theobald
0.5
43
Cheong
19.6
34.5
Bertocci
0.17
x
Taylor cyclic failure (3 Hz)
55
Current Study
3
45.1
Current Study
3
36.87
Current Study
3
35.47

fracture pattern
high rate (deg/sec) composite fracture angle (deg)
fracture pattern
specimen age specimen tested
angled segment
90
31
angled segment
7 days
Bovine
angled & vertical segments
196
41.5
angled segments & comminution 5 months
Ovine
x
90
x
x
3 months
Porcine
angled & vertical segments
x
x
x
x
Bovine
angled segment
90
31.67
angled segment
2 days
Porcine
angled & vertical segments
90
30
angled segments & comminution 14 days
Porcine
angled & vertical segments
90
28.93
angled segments & comminution 22 days
Porcine

61

REFERENCES

62

REFERENCES

Bertocci G, Thompson A, and Pierce MC. Femur fracture biomechanics and morphology
associated with torsional and bending loading conditions in an in vitro immature porcine model.
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Carty HM. Fractures caused by child abuse, J Bone Joint Surg Br. 75(6) (1993) 849-57.
Cheong VS, Karunaratne A, Amis AA, and Bull AMJ. Strain rate dependency of fractures of
immature bone. J Mech Behav Biomed Mater. 2017; 66:68-76.
Katsamenis OL, Andriotis OG, and Thurner P. Load-bearing in cortical bone microstructure:
Selective stiffening and the heterogenoeus strain distribution at the lamellar level. J Mech Behav
Biomed Mater. 2012; 17:152-165.
Koester KJ, Ager JW, and Ritchie RO. The true toughness of human cortical bone measured with
realistically short cracks. Nat Mater. 2008; 7:672-677.
Kress TA. Impact biomechanics of the human body [dissertation]. Knoxville (TN): Univ. of
Tennessee, 1996.
Nalla RK, Stö lken JS, Kinney JH, and Ritchie RO. Fracture in human cortical bone: local
fracture criteria and toughening mechanisms. J Biomech. 2005; 38:1517-1525.
Norman TL, Nivargikar SV, and Burr DB. Resistance to crack growth in human cortical bone is
greater in shear than in tension, J Biomech 29(8) (1996) 1023-31.
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children: a biomechanical approach with illustrative cases. Child Abuse Negl. 2004; 28(5):50524.
Porta D.J. (2005) Biomechanics of Impact Injury. In: Rich J., Dean D.E., Powers R.H. (eds)
Forensic Medicine of the Lower Extremity. Forensic Science and Medicine. Humana Press
Shukla A, and Dally JM. 2014. Experimental solid mechanics.
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Turner CH, Wang T, Burr DB. Shear strength and fatigue properties of human cortical bone
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CHAPTER FOUR: AGE EFFECTS ON BENDING FRACTURE PATTERNS IN OVINE
FEMORA UNDER CONCENTRATED FOUR-POINT BENDING
ABSTRACT
Most research regarding bending of long bones focuses on a 3-point bending model. Under 3point bending the bone typically fails directly under the point of loading, initiating as a
transverse crack on the tensile surface of the bone. This transverse crack then branches out into a
Y-shape pattern at approximately the midline of the bone with the two-branching fracture lines
reaching out to either side of the loading point on the compressive side of the bone. This socalled tensile wedge is so prevalent that forensic practitioners commonly cite this fracture pattern
as an indication of impact direction. The practice is problematic, however, as there appears to be
a sub-class of bending that can produce reverse tensile wedges (compression wedges). Martens et
al., 1986 performed a four-point loading test configuration where the lower supports are set to
60% of the bone length, and the inner-loading probes are set to 10% of the bone length. This is
considered a concentrated loading scenario, as the inner loading probes under four-point bending
are typically set between 40-50% of the bone length (Diab et al., 2006, Lanyon et al., 1979, and
Quinn et al., 2009). Under these concentrated conditions Martens et al., 1986 documented that
85% of the human femora tested failed in the middle of the bone in a Y-shape. However, the Yshape fracture pattern possessed a transverse fracture on the loading side of the bone, with the
branching fractures connecting to the non-loading side of the bone, which is opposite to that
produced and most commonly reported under a three-point bending configuration. The current
study tested twenty ovine femora with (n=10) femora classified as mature (1-2 years of age) and
another group (n=10) femora classified as immature (1 day – 1 week old). Within the mature
testing group 7 specimens were tested at low rate and 3 were tested at high rate. All young

65

specimens were tested at a low rate. In general, old specimens under the Martens et al., 1986
loading conditions produced near-exclusive reverse tensile wedge fractures, while younger
specimen commonly produced transverse fractures. Additionally, stress distributions were
created for specimen-specific models from the young and old ovine femur groups. This was
done by rendering a volumetric model from CT-scans, in mimics, and then applying
experimentally-defined loading and boundary conditions to the model in Abaqus. The two
models produced reasonable stress distributions that might help explain the fracture patterns
generated in these experiments. The study demonstrated that specimen age affects the resultant
fracture pattern under a concentrated, four-point bending test, and attempts to provide an
explanation for the patterns using a basic finite element approach.

INTRODUCTION
Most research in forensic biomechanics of long bones is based on a 3-point bending model. The
side of the bone that undergoes loading generates compressive stresses while the opposite side of
the bone is in tension (Pierce et al.,2004, Gardener et al., 2010). Under 3-point bending the bone
typically fails directly under the point of loading where the bending moment is highest, initiating
as a transverse crack on the tensile surface of the bone. This transverse crack then branches out
into a Y-shape pattern at approximately the midline of the bone, with the two-branching fracture
lines reaching out to either side of the loading point on the compressive surface of the bone
(Reber and Simmons, 2015). This wedge-shaped pattern of fracture is described as shear failure
of the bone on its compressive side (Ebacher et al., 2007)

66

In forensic terminology these wedge-shaped fracture patterns are known as butterfly fractures.
The tensile wedge is commonly used by forensic practitioners as an indication of impact
direction (Kress et al., 1996, Porta et al., 2005, and Isa et al., 2015). This practice is problematic,
however, as there are cases, and studies where reverse tensile wedges (also known in the
literature as compression wedges) are produced. Reverse tensile wedges are defined as a
transverse fracture on the compressive side of the bone with branching failure on the tensile side
of the bone. In 1986, Levine et al. first noted these types of wedge fractures as common in
automobile accidents where impacts to the tibia by car bumpers often produced reverse wedges
in the fractured long bone. Kress et al., 1996, whom first recommended tensile wedges to be
good indicators of impact direction, also noted reverse tensile wedges in some leg impact studies,
deeming the pattern “an extremely uncommon pattern for long bones”, and one to be generally
ignored. However, Martens et al., 1986 demonstrated nearly exclusive reverse tensile wedge
fractures when loading human femur bones at a low rate, under a rather concentrated four-point
bending scenario. More recently Reber and Simmons, 2015 report 40% complete wedge patterns
as reverse tensile wedges using the sheep femur. It has therefore become clear in the literature
that the reverse tensile wedge is not a failure mode to be ignored, but its mechanism has not been
well studied.

As stated by Passalacqua and Fenton et al., 2012, it is imperative that forensic practitioners
“move beyond our reliance on experience as the only way to inform us in the analysis of
trauma”, and that there is a great “need to establish baseline parameters on how bones break in
numerous scenarios”, moving towards a “science of trauma that involves hypothesis testing”. It

67

is therefore forensically relevant to determine how this reverse tensile wedge might have been
consistently produced under a Martens-type concentrated 4-point loading configuration.

Vaughan et al., 2016 has recently demonstrated in torsion tests on long bones that there are age
and rate of loading effects influencing the generated spiral fracture patterns. It may therefore be
important to determine what effects, if any, specimen age and rate of loading may have on the
production of potential reverse tensile wedge produced under the 4-pt test configuration of
Martens et al., 1986.

In the current study mature and immature ovine femurs were used to study the effects of age and
rate of loading on the generation of reverse tensile wedges. The objectives of the study were to
execute controlled, concentrated Martens-type 4-point bending tests on ovine femora to identify
fracture patterns in association with specimen age and rate of loading. Furthermore, a simplified
finite element (FE) modeling effort was conducted to understand the mechanism of reverse
tensile wedges types of long bone fracture versus tensile wedges (Vaughan et al., 2017).

METHODS
Twenty ovine femora were tested with (n=10) femora classified as mature (1-2 years of age), and
another group (n=10) of immature (1 day – 1 week old) femora. The specimens were collected
by Colorado State University, dissected and cleaned of excess soft tissues, immediately wrapped
in saline-soaked gauze to prevent dry-out of the bone (Wieberg et al., 2008), and frozen at -20°C
before being shipped on ice from Colorado State to Michigan State University. Once received,

68

specimens were immediately transferred to a freezer at a temperature of -20°C. All specimens for
this study were from animals sacrificed for another research study.

A custom-built four-point bending fixture (Figures 4.1 and 4.2) was used to test freely supported
ovine femora under a Martens-type concentrated 4-point bending configuration. In this test the
two outer supports were set to 60% of the specimen bone length, and the testing distance of the
inner loading-probes was set to 10% of the specimen length (Figure 4.1). It was important for
both loading points to contact the bone at the same time to produce accurate results (Beaupied et
al., 2007). To achieve this, the load fulcrum was set in place with a pin. A small pre-load of
approximately 2 Newtons was applied to the bone to ensure initial contact of the loading probes
with the bone shaft. Furthermore, specimen supports needed to be fairly-smooth and rounded to
minimize stress concentrations at the point of contact (Beaupied et al., 2007). This was achieved
by setting an external diameter to the inner probes of 6.4 mm and 5.40 mm (Figure 4.1 and 4.2
respectively), and by setting a smooth inner groove to the free-rotating supports of 11mm length,
2.60 mm width, and a 2 mm radial depth at its deepest (Figure 4.1). The free-rotating supports
for the fixture in Figure 4.2 were set to a 5mm width, and a 1.8mm radial depth at its deepest.

69

Figure 4.1 Photograph of the concentrated four-point bending configuration based on the
previous study by Martens et al., 1986 for old specimens.

Figure 4.2 Photograph of the concentrated four-point bending configuration based on Martens
et al., 1986, for young specimens.

70

Each specimen was loaded until failure in a servo-hydraulic testing machine (model 1331,
Instron Corporation; Norwood, MA). All specimens were failed at a rate of 2 Hz with a 5 mm
haversine wave, except for three of the old specimens which were used as a pilot study for these
experiments and loaded at a rate of 2 Hz with a 20 mm haversine wave. Force-time data was
collected using a 500-lb force transducer (model 1010AF-500, Interface; Scottsdale, AZ) for
young specimens. For old specimens a 2500-lb load cell (model 1010-AF-2.5K-B, Interface;
Scottsdale, AZ) was utilized. All bones were loaded on the posterior side of the bone (Figure
4.2). The experiments were filmed with a high-speed camera at 40,000 fps to capture the fracture
initiation and propagation. After fracture, they were photographed to document gross fracture
morphology.

Prior to mechanical tests a whole-bone CT scan was taken of one bone specimen from each of
the old and young groups. These 3D images were processed using volumetric techniques in
Mimics (Mimic Technologies Inc., Seattle WA) (Figure 4.3), given a tetrahedral mesh in 3-matic
(Materialise, Leuven, Belgium) (Figure 4.4), and imported into ABAQUS 6.11 (Dassault
Systemes, Waltham, MA) where loads and boundary conditions were applied to simulate the
above-mentioned 4-point bending tests (Figure 4.5). A representative bone specimen was
selected for both the young and old groups, and material property values were set to those
determined from the current experiments, as described below and given in Table 1. A basic
impact was simulated by placing vertical displacement constraints at the supports, static-loading
at the loading points, and preventing out-of-plane motion (Figure 4.5).

71

Figure 4.3 Screen capture of 3D image reprocessing in Mimics.

Figure 4.4 Screen capture of volumetric meshing of bone in 3-matic.

72

Figure 4.5 Screen capture of loads and boundary condition applied to the model in Abaqus.

Classical beam theory was utilized in the study to determine the material bone properties of
representative young and old specimens (Rusme 1998). Under generalized four-point bending
theory it is assumed that between the point loads there is a constant applied bending moment,
with no developed shear stresses. Between the outer supports and the inner probes, the bending
moment gradually increases and there are shear stresses developed (Figure 4.6). While Martenstype concentrated four-point bending has of yet no standardized mechanical description, the
generalized case will be utilized to obtain approximated values.

73

Figure 4.6 Graphical representation of a standard four-point bending test, taken from Rusmee
1998.

The bending moment of inertia for each bone was assumed to be elliptical and was calculated
using the expression
𝐼=

𝜋
4

𝜋

(𝑎𝑜 𝑏𝑜 3 ) − 4 (𝑎𝑖 𝑏𝑖 3 )

(4.1)

where 𝐼 is the bending moment of inertia in millimeters to the fourth power, 𝑎𝑜 is the average
anterior-posterior outer diameter in millimeters, 𝑏𝑜 is the average medial-lateral outer diameter in
millimeters, 𝑎𝑖 is the average anterior-posterior inner diameter in millimeters, and 𝑏𝑖 is the
average medial-lateral inner diameter in millimeters. The moment arm was defined using the
expression
74

𝑥𝑚 =

𝐿𝑜 −𝐿𝑖

(4.2)

2

where 𝑥𝑚 is the moment arm in millimeters, 𝐿𝑜 is the distance between outer supports in
millimeters, and 𝐿𝑖 is the distance between loading points in millimeters. The maximum bending
moment is given as
𝑀=

𝐹𝑚𝑎𝑥 𝑒𝑙𝑎𝑠𝑡𝑖𝑐
2

∗ 𝑥𝑚

(4.3)

where 𝑀 is the maximum bending moment in Newton-millimeter, 𝐹𝑚𝑎𝑥 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 is the maximum
elastic force in Newtons based on the linear regression, and 𝑥𝑚 has been previously defined. The
estimated bone tensile elastic modulus was calculated with the expression (Christoforo et al.,
2012)
𝐸=

𝐹𝑚𝑎𝑥 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 ∗(3∗𝐿𝑜 2 −4∗𝐿𝑖 2 )∗𝐿𝑖
∆𝑥∗4∗𝐼

(4.4)

where 𝐸 is the estimated bone tensile elastic modulus in megapascals, ∆𝑥 is the displacement of
the bone based on the displacement recorded from the machine actuator in millimeters,
𝐹𝑚𝑎𝑥 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 is the maximum elastic force in Newtons based on the linear regression, and all other
terms have been previously defined. The bending failure stress was calculated by the expression
𝜎𝑏𝑒𝑛𝑑𝑖𝑛𝑔 =

𝐹𝑚𝑎𝑥 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 ∗𝑥𝑚 ∗𝑎𝑜
2∗𝐼

(4.5)

where 𝜎𝑏𝑒𝑛𝑑𝑖𝑛𝑔 is bending stress in megapascals, and all other terms have been previously
defined. The energy absorbed by the bone to failure was expressed as
𝐸𝑖𝑛𝑝𝑢𝑡 =

𝐹𝑚𝑎𝑥 𝑒𝑙𝑎𝑠𝑡𝑖𝑐
2

∗ ∆𝑥

(4.6)

where 𝐸 is the energy of the bone in Joules after converting the displacement (∆𝑥) from
millimeters to meters. The initial stiffness of the bone is expressed as
𝑘=

𝐹𝑚𝑎𝑥 𝑒𝑙𝑎𝑠𝑡𝑖𝑐
∆𝑥

75

(4.7)

where 𝑘 is the initial stiffness of the bone in Newton/millimeters, 𝐹𝑚𝑎𝑥 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 is the force change
in the elastic regime of the bone, and ∆𝑥 is the displacement of the beam at the inner probe.
Elastic modulus values and initial stiffness values were taken as linear regression over the elastic
region of the plots of stress/strain and force/displacement respectively (Figure 4.7). It is
important to note that the initial non-linear region in the data, below about 1.5% strain and below
approximately 0.5mm displacement (Figure 4.7), is a result of the loading points adjusting
themselves with the pivoting fulcrum to the bone’s asymmetric surface for equal loading. The
fulcrum prior to testing was visually lowered to the bones surface for alignment purposes, and
the small 2N pre-load was applied to prevent slipping of the bone on the point supports during
testing. Once the test initiated, the fulcrum initially adjusted, and this action coincided with the
initial non-linear section of the data. Once there was an equal load under each of the points, the
bone responded linearly, and this explains why the initial section of the data is excluded from the
elastic linear regression fitting. For the most part this action was hypothesized and not
experimentally validated in the current study.

76

Figure 4.7 Graphical determination of elastic modulus (left) and initial stiffness values (right).
STATISTICAL METHODS
A general linear ANOVA was performed in Minitab 18 (State College, PA) to compare the effect
of initial bone stiffness, elastic modulus, bone displacement to failure, and failure forces against
specimen age (young/old). All statistical analyses used an alpha-criterion of 0.05.

RESULTS
Twenty ovine femora were tested with (n=10) femora classified as mature (1-2 years of age), and
(n=10) femora classified as immature (1 day – 1 week old). Within the mature testing group, 7
specimens were tested at low rate and 3 were tested at high rate. All young specimens were
tested at a low rate. Of the old specimens tested at a low rate, 6/7 produced a reverse tensile
wedge pattern, while 1/7 produced an oblique pattern (Appendix 1). In the group of old
specimens tested at a high rate 1/3 produced a tensile wedge pattern, and 2/3 produced oblique

77

patterns. In the young group of specimens 6/10 produced transverse fractures, while 4/10
produced partial tensile wedges (Appendix 1).

The stiffness’s of the three groups of bones (old high rate, old low rate, and young low rate) were
significantly different (p=0.0001), with the old high rate specimens having the greatest initial
stiffness at 3404 Âą 895 N/mm, the old low rate specimens generating an initial bone stiffness of
2771 Âą 269 N/mm, and the young low rate specimens generating an initial bone stiffness of
230.30 Âą 111.30 N/mm. The elastic modulus based on the terminal linear range of response, was
also a statistically significant parameter (p=0.0001). The older specimens were not statistically
different from one another between test rates, however, the older specimens had a significantly
higher modulus value of 3.41 Âą 0.71 GPa compared to that of the young low-rate test specimens
0.77 Âą 0.31 GPa. The failure strength of the bone was not statistically different between the
young and old test groups. The bone’s failure strength under bending was 107.85 ± 26.47 MPa.

In the old group of specimens, reverse tensile wedge fractures were captured on a high-speed
camera. The fracture was shown to initiate on the non-loading (tensile side) of the bone with
fracture initiation generated simultaneously in the areas between the loading point and support
point at an angle theta. The fracture then propagated along the long-axis of the bone, meeting and
finally propagating as a transverse crack on the loading side (compressive side) of the bone
(Figure 4.8).

78

Figure 4.8 High-speed capture of specimen Shelby_5_28_15_4B, showing fracture initiation
(top left) on the tensile side of the bone, to fracture propagation (bottom right) on the
compressive side of the bone.

The oblique fractures were also captured using the high-speed camera. It was shown again that
these fractures initiated at approximately the outer support on the distal end of the bone and
propagated towards the loading probe. Interestingly, a fracture line along the long-axis of the
bone was recorded, like that seen in the compressive wedge failure (Figure 4.9).

79

Figure 4.9 High-speed capture of specimen Zach_5_28_15_4B, showing fracture initiation (left)
and fracture propagation (right).
In the young group of specimens, transverse failure and partial tensile wedge fractures were
generated in these experiments. The transverse failure was shown to initiate on the tensile side of
the bone directly between the two loading points, with the fracture propagating up towards one
of the loading points (Figure 4.10). The partial tensile wedge failure pattern was shown to initiate
between the two loading points, branching into a typical Y-pattern. However, only one side of
the branch connected to the compressive side of the bone (Figure 4.11).

80

Figure 4.10 High-speed capture of specimen SF3R4B, showing fracture initiation (top) and
fracture propagation (bottom).

81

Figure 4.11 High-speed capture of specimen SF5R4B, showing fracture initiation (left) and
fracture propagation (right).

Analysis of the specimen-specific maximum principal stresses under finite element modeling
showed the potential stress distribution observed over the bones surface when loaded under a
Martens-type configuration. The old group of specimens was represented by
Shelby_5_28_15_4B. The model showed high tensile stresses near the support points which were
shown to exist at some angle theta. Interestingly, there was a mixture of large compressive and
tensile stresses generated directly under the applied loading points. These longitudinally-oriented
tensile stresses under the loading points may explain the generation of a transverse fracture on
the loading surface. Under the assumption that fracture lines are generated perpendicular to high
principal (tensile) stresses (Chen, 2007), the experimental results appear to be comparable to the
stress distribution generated under FE modeling (Figure 4.12). It is important to note however,
that the data generated under FE modeling was only intended to illustrate what a relative stress
distribution under these experimental loading conditions may look like prior to actual bone
fracture.

82

Figure 4.12 Experimental high-speed capture (top) and maximum principal stress distribution,
generated with FE modeling (bottom).

The young group was represented by specimen SF3L4B. The model showed high tensile stresses
generated within the loading region, with high compressive stresses generated at the loading
surface. Under the assumption that fracture lines are generated perpendicular to high principal
(tensile) stresses (Chen, 2007), the experimental results appear to be comparable to the stress
distribution generated under FE modeling (Figure 4.13). It is important to note as before, that the
83

data generated under FE modeling was only intended to illustrate what a relative stress
distribution under these experimental loading conditions may look like prior to actual bone
fracture.

Figure 4.13 Experimental high-speed capture (top) and maximum principal stress distribution,
generated with FE modeling (bottom).

84

DISCUSSION
The aim of the current study was to perform a Martens-type 4-point bending test on both young
and old specimens, to evaluate if the resultant fracture pattern differed with specimen age.
Biomechanical data was generated, demonstrating that the fracture pattern was significantly
different between the young and old testing group. The second aim of the study was to
investigate what the potential principal (tensile) stress distribution looked like under the
experimentally tested Martens-type loading. For comparison purposes models were also
generated for a typical 3-point bending configuration and under a typical 4-point bending
configuration.

In Appendix 1, finite element models were generated under the two typically reported loading
scenarios in the forensic literature of three-point bending and four-point bending (with a loading
point at midpoint of the bone, and loading-points oriented at 40% of the bone length
respectively), and under the Martens-type configurations using the mature bone model
Shelby_5_28_15_4B. All parameters were kept the same between models. As seen in Figure
4.19 of Appendix 1, under three-point loading high tensile stresses were generated directly under
the point of impact on the non-loading side of the bone, with large compressive and some tensile
stresses generated directly under the loading point on the loading side of the bone. Under typical
three-point bending, a tensile wedge pattern of fracture is expected under such a stressdistribution. It is currently believed that the tensile wedge pattern is formed because a transverse
fracture results from the high tensile stresses, and then two branching shear failures are then
formed within the zone of compression. This result parallels with the forensic literature (Kress et
al., 1996, Porta, 2005, and Isa et al., 2015). As seen in Figure 4.20 in Appendix 1, under typical

85

four-point bending large tensile stresses are seen at both the supports on the non-loading side,
and just outside the loading points on the loading side. Visually mapping fracture patterns as
normal to the maximum tensile stresses, two sets of almost cubic-shaped fracture patterns are
generated. In the forensic literature, typical four-point bending is associated with a segmented
fracture pattern (Turek, 1994, and Kress et al., 1996), and this pattern tends to agree with the
stress-distribution generated by the model. Martens-type loading then appears to be a special
combination of both the three-point and four-point loading models. As seen in Appendix 1,
Figure 4.21, large tensile stresses are generated between the supporting points and the loading
points at some angle theta, like what is generated under the four-point model. However, as the
loading points are concentrated at only 10% of the bone length, directly under the loading points
there is a large concentration of compressive stress, like what is seen in the three-point bending
model, with some local tensile stresses also generated directly underneath the right loading point.
These large compressive stresses appear to act as a barrier against transverse crack propagation,
and instead allow the fracture to propagate longitudinally along the cement line of the bone,
which is known to be a weak crack path (Zimmerman et al, 2009 and Nalla et al., 2005), and is
also the path that appears to be dictated by the tensile stress distribution. Interestingly, this path
may also be dictated by longitudinal shear stress within the zone of compression. Finally, once
the two opposing crack lines meet longitudinally, the pattern completes with a transverse fracture
at an area of high tensile stress, generated directly underneath the right loading point in this
instance.

As reverse tension wedges (compression wedges), require a large concentrated load spanning
approximately 10% of the specimen length, this may explain why reverse tension wedges have

86

previously not been consistently produced within the forensic literature. The most common
loading-scenario tested, three-point bending, is too small of a concentrated load to produce the
reverse tension wedge (compression wedge) pattern, and the typical four-point bending scenario
has loads so widely dispersed, that they tend to act as two individual and simultaneous impacts,
as opposed to a singular concentrated impact. This line of reasoning may then explain why the
experiments of Reber and Simmons, 2015, generated a reverse tension wedge pattern while
impacting bone with a large flat plate (Figure 4.14), and why Kress et al. managed to produce the
pattern while impacting with a 10-cm steel impact pipe (Figure 4.15). Inadvertently, these
experiments may have generated a large concentrated loading scenario, like what would be
generated under Martens-type four-point bending. Further indicating that this fracture pattern
may be more common than previously thought, as large flat impacts, or impacts by a curved
surface could be representative of impacts by the bumper of a car, as first suggested by Levine et
al., 1986 on tibial impacts by a car’s bumper.

Figure 4.14 Photograph of an impact scenario which produces reverse tensile wedges, taken
from Reber and Simmons 2015.

87

Figure 4.15 Photograph of an impact scenario which produces reverse tensile wedges, taken
from Kress et al., 1996.

Interestingly, the reverse tensile wedge pattern was not generated for young specimen tested in
the study. Instead, 60% of the specimen generated transverse fractures under low-speed
conditions, with 40% of specimen tested generating incipient tensile wedge patterns as indicated
in Figure 4.13 (top). These results appear to agree with a study by Cheong et al., 2017, whom
investigated the effects of low, medium, and fast rates of loading on immature 5-month-old lamb
tibiae using a 4-point bending configuration. The authors produced transverse failures in 100%
of low-rate testing, with 3/8 transverse fractures produced in medium and high rate testing, 4/8
oblique fractures in the medium and high-rate tests, and 1/8 tensile wedge failure in the medium
and high rate tests (Cheong et al., 2017). However, it is unclear what percentage of the specimen
length the supports and loading points were held in the Cheong et al., 2017 study. Therefore, it is
not clear if the results of the study are comparable to those performed using the concentrated,
four-point Martens-type loading scenario of this current study.

88

A potential explanation for the transverse fracture generated under four-point bending at younger
ages, is that as noted by Gosman et al., 2013, bone possesses a relatively circular geometry at
younger ages, and becomes increasingly asymmetric at older ages. As is suggested by the stress
distribution of the three-point bending model of old bone (Figure 4.19 in Appendix 1), and by the
four-point bending model of young bone (Figure 4.13 (bottom)), the bones relatively uniform
and circular geometry at younger ages may influence the uniformity of tensile stresses generated
on the non-loading side of the bone. Uniformly generated tensile stresses of the young group
may in turn allow for transverse fractures to be easily produced, due to the large propensity for
fracture transversely across the bone. Conversely, due to the asymmetric geometry of the bone at
older ages under concentrated four-point bending (Appendix 1, Figure 4.21), less uniformly
distributed tensile stresses are generated under the loading points on the non-loading side of the
bone, allowing for greater tensile stresses to be built up on the outer more curved sections of the
bone by the supports. Thus, producing the reverse tensile wedge generated in the current study.

While more testing needs to be performed to verify potential rate effects under Martens-type
four-point loading, it may be suggested from the Cheong et al., 2017 study, and from the old
specimen tested here at a high loading rate, that tensile wedge fracture patterns may be produced
at higher loading rates under Martens-type conditions. The reverse tensile wedge pattern
produced here, may only be representative of low rate loading. This potential rate-effect will
need to be investigated further in future work.

89

APPENDIX

90

Figure 4.16 Photographs of specimen representative of variations in the fracture patterns, tested
at a high rate of 2 Hz over a 20mm haversine displacement (from left to right;
AbeL12_10_14_4B_HighRate, AbeR12_10_14_4B_HighRate, and
ClaudeL12_10_14_4B_HighRate).

91

Figure 4.17 Photographs of specimen representative of variations in the reverse tensile wedge
pattern, tested at a low rate of 2 Hz over a 5mm haversine displacement (from left to right;
Shelby_5_28_15_4B, Ryan_5_28_15_4B, and Lindy_5_28_15_4B).

92

Figure 4.18 Photographs of specimen representative of variations in the young bone fracture
pattern, tested at a low rate of 2 Hz over a 5mm haversine displacement (from left to right;
SF1R4B, SF2R4B, and SF5R4B).

93

Figure 4.19 Maximum principal stress distribution, typical 3-point bending

Figure 4.20 Maximum principal stress distribution, typical 4-point bending.

Figure 4.21 Maximum principal stress distribution, Martens-type 4-point bending.

94

Table 4.1. Summary table of raw experimental data
Specimen Name

Group

Wedge Type

Units
SF1L4B
SF2L4B
SF3L4B
SF4L4B
SF5L4B
SF1R4B
SF2R4B
SF3R4B
SF4R4B
SF5R4B

young/old
young
young
young
young
young
young
young
young
young
young

fracture pattern
Tensile
Transverse
Tensile
Transverse
Tensile
Transverse
Transverse
Transverse
Transverse
Tensile

mm
106.17
82.77
94.57
103.14
90.76
107.00
75.27
94.10
104.37
94.10

mm
10.62
8.28
9.46
10.31
9.08
10.70
7.53
9.41
10.44
9.41

mm
63.70
49.66
56.74
61.88
54.46
64.20
45.16
56.46
62.62
56.46

Young Bone Low Rate Means young

Bone Length Inner Length (Li) outter length (Lo) Innertia

Max Load Displacement Input Energy Initial Stiffness Failure Stress Elastic Modulus ML OD AP OD ML ID AP ID ML Thickness AP Thickness

mm^4
4678
4149
4410
5934
4664
4007
5088
4771
5314
5936

N
410
865
777
369
575
465
795
723
408
463

mm
3.64
2.72
3.10
4.39
4.87
3.80
2.32
3.16
4.23
4.09

mJ
1038
1310
1610
877
1695
1149
937
1423
1163
1074

N/mm
171
339
373
87
211
160
369
332
142
119

Mpa
99
140
147
63
87
110
105
129
75
69

Gpa
0.75
1.13
1.25
0.40
0.49
0.97
0.75
1.04
0.54
0.41

mm
9.55
8.73
8.85
9.99
9.01
8.89
8.96
9.02
9.41
9.36

mm
9.13
9.67
9.07
9.95
10.30
8.83
10.00
9.33
9.72
10.28

mm
6.63
5.59
4.97
7.05
6.15
5.95
5.16
5.62
6.05
5.42

mm
6.85
6.59
5.47
6.75
6.86
5.23
5.20
4.35
6.02
5.48

mm
1.46
1.57
1.94
1.47
1.43
1.47
1.90
1.70
1.68
1.97

mm
1.14
1.54
1.80
1.60
1.72
1.80
2.40
2.49
1.85
2.40

-

95.23

9.52

57.14

4915

585

3.63

1228

230

102

0.74

9.18 9.63 5.86 5.88

1.66

1.87

oblique
Tensile
oblique

207.15
207.23
205.23

20.72
20.72
20.52

124.29
124.34
123.14

179009
167422
172367

4290
3958
3595

1.46
1.24
2.39

2675
1449
3231

3433
4284
2495

91
144
68

3.79
4.41
1.96

22.9 24.72 15.56 18.3
22.62 24.19 15.52 17.87
22.29 26.94 15.63 20.66

3.67
3.55
3.33

3.21
3.16
3.14

old

-

206.54

20.65

123.92

173162

3948

1.70

2452

3404

101

3.08

22.60 25.28 15.57 18.94

3.52

3.17

old
old
old
old
old
old
old

Reverse Tensile
Reverse Tensile
Reverse Tensile
Reverse Tensile
Reverse Tensile
Reverse Tensile
oblique

219.00
222.00
232.00
209.15
208.89
208.85
208.63

21.90
22.20
23.20
20.92
20.89
20.89
20.86

131.40
133.20
139.20
125.49
125.33
125.31
125.18

164953
163700
204692
190617
135157
177877
168015

3649
4054
5073
5280
3399
3469
4354

1.86
1.82
2.85
2.07
1.47
1.25
1.99

3090
3215
5524
5863
2291
2095
3325

2447
2601
2557
3040
2638
3029
3083

110
116
142
128
116
98
120

3.25
3.87
2.82
3.18
4.05
3.70
3.07

22.9
22.31
24.37
23.63
22.08
23.81
22.91

17.73
18.34
18.98
18.07
17.44
19.2
17.82

3.28
3.49
3.4
3.27
2.93
3.02
3.3

3.1
3.19
3.07
3.58
2.73
2.78
3.2

old

-

215.50

21.55

129.30

171484

4183

1.90

3629

2771

119

3.34

23.14 24.41 16.66 18.23

3.24

3.09

AbeL12_10_14_4B_High Rate
AbeR12_10_14_4B_High Rate
ClaudeL12_10_14_4B_High Rate

old
old
old

Old Bone High Rate Means
BettyL12_10_4B
DorisL12_10_14_4B
ErnestL12_10_14
Lindy_5_28_15_4B
Ryan_5_28_15_4B
Shelby_5_28_15_4B
Zach_5_28_15_4B

Old Bone Low Rate Means

95

23.93
24.72
25.12
25.23
22.9
24.76
24.22

16.34
15.33
17.57
17.09
16.22
17.77
16.31

REFERENCES

96

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Gosman JH, and Shaw CN. Development of cortical bone geometry in the human femoral and
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CHAPTER FIVE: CONCLUSIONS
OVERVIEW
From the study of Murphy et al., 2015, questions arose regarding the authors proposed fracture
ratio as a means of interpreting the spiral fracture pattern under abusive and accidental-type
injury scenarios. It became evident that the authors case-based study may have been indirectly
influenced by specimen age. In the case-based study of Murphy et al., 2015 the mean age for
abuse victims was, on average, lower than the mean age of the accidental victims. While noted in
the study, however, age was not a statistically significant factor. The work of Theobald et al.,
2012 also raised further questions about the Murphy et al., 2015 study, as the authors
demonstrated that an increased loading rate significantly decreased the spiral fracture angle.
While the Theobald et al., 2012 study did not consider varying specimen age, it provided a
significant indicator that the Murphy et al., 2015 study may have been biased due to the types of
loading scenarios classified as accidental and abuse. A correspondence with the authors in the
Murphy et al., 2015 study uncovered that many accidental injuries of the femur were the result of
motor-vehicle accidents or falls from heights, which likely produce high rates of loading
scenarios. Experimental results using the porcine femora under torsion in the current study have
demonstrated that both specimen age and loading rate are influential factors on the fracture ratio.
Therefore, in future work, it is paramount that these factors be considered when evaluating spiral
fracture patterns.

Potential age and rate effects were not just limited to torsional fracture patterns, but also
appeared to influence bending fracture patterns in the literature as well. Martens et al., 1986
demonstrate near-exclusive reverse tensile wedge patterns (compressive wedge patterns) in

99

studies using the human femur. Cheong et al., 2017, while not testing under Martens-type
loading conditions, was able to produce exclusive transverse fractures under typical four-point
bending in 5-month-old sheep. Interestingly, as the loading rate was increased in the study, the
pattern of fracture changed into the oblique fracture pattern, and even a tensile wedge pattern
was produced for younger aged specimens. It therefore became forensically relevant not only to
test how/why the compression wedge was produced under Martens-type loading of long bones,
but also to see what effects, if any, specimen age and loading rate might have under this special
loading configuration.

The first hypothesis of this thesis work was that material parameters would change with
developmental age in the porcine model, and that these will in turn influence the resultant
fracture pattern in the femur. This was investigated by performing direction-specific tensile and
shear tests over a range of immature specimens. Testing of these parameters against development
in days was performed to demonstrate how the longitudinal and transverse parameters change
throughout early development of the immature, porcine femur. The goal was to utilize these
aggregate material parameters to aid in an interpretation at the mechanical level, addressing the
question of why the gross-scale fracture pattern was altered with specimen age under torsional
loading, when tested at the whole-bone level using the immature porcine model.

The second hypothesis of the current research was to address how the material properties are
impacted by loading rate in the transverse and longitudinal directions. The goal once more was to
utilize these aggregate material parameters to aid in the interpretation at the mechanical level,

100

addressing the question of why the gross-scale fracture pattern is altering with loading rate under
torsion, when tested at the whole-bone level using the immature porcine model.

The final hypothesis of the current research was that Martens-type loading is a special loading
scenario that also is influenced by specimen age and loading rate. The goal of this study was to
provide pilot work demonstrating that under Martens-type loading, young specimens would not
generate compression wedge failures, and that the compressive wedge pattern would be
produced under low-rate loading in mature specimen.

CHAPTER 2
Chapter 2 was an experimental study which tested whole, intact immature porcine femora of
varying developmental age under rate-controlled torsional loading. The purpose of this study was
to test the validity of the fracture ratio proposed by Murphy et al., 2015, while additionally
addressing what effects developmental age and loading rate may have on the fracture pattern
(fracture ratio). Results of this study showed that both specimen age and rate of twist were
significant factors influencing fracture ratio in immature specimen. Interestingly, at lower rates,
the pattern of fracture transitioned from a high-angle fracture in the young group, to a
combination of both low-angle and horizontal failure segments in the older group when
measured from the longitudinal axis. At higher rates the fracture pattern rapidly transitioned from
low-angle failure, to very low angle tensile failure, with horizontal elements and increased
comminution as specimen age increased. In summary, the study documented that fracture ratio
was significantly dependent on both specimen age and rate of twist, using the infant porcine
femur model, with low rates of twist consistently producing lower fracture ratios than those

101

shown under high rates of twist. While both an accidental and abusive act may produce spiral
fractures, the results of the current study would not help determine intent. This study does,
however, provide experimental ‘ground-truth’ data that may help forensic biomechanists and
anthropologists draw conclusions surrounding the circumstances of an injury, which in turn may
help in the evaluation of ‘truth of testimony’ during criminal litigations. As such the current
study, while limited to using the infant porcine model, might suggest additional clinical studies
utilizing more specimens over a pediatric age range with a stratification by loading rate, may be
needed before fracture ratio alone should be utilized for the determination of accidental versus
abusive pediatric trauma.

CHAPTER 3
Chapter 3 was an experimental study which tested cortical bone segments of the immature
porcine femur, shaped into notched and dog-bone specimens oriented in the longitudinal and
transverse directions along the bone. The purpose of this study was to test the effects of
specimen age and loading rate against calculated material parameters under tensile and shear
testing. Results of the study indicated that at both low and high rates of loading, the longitudinal
shear strength decreased with specimen age. Interestingly, the longitudinal shear strength from
birth was initially stronger than the transverse shear strength, becoming weaker than the
transverse shear strength at a critical age of approximately 7 days of development for low rate
tests, and approximately 4.5 days of development for high rate tests. Prior to this critical age in
development, the transverse shear strength is weaker than the longitudinal shear strength,
allowing for deviations from the mechanically preferred mode of failure under tension, allowing
energy to be dissipated via crack failure through osteons (resulting in a low fracture ratio/high
fracture angle). After this critical age the longitudinal shear strength became weaker than the
102

transverse shear strength, allowing for deviations from the mechanically preferred mode of
failure under tension, by allowing energy to be dissipated by crack failure along the cement
interface between osteon, longitudinally (resulting in a high fracture ratio/low fracture angle).
This information supported the notion that three are three types of spiral fracture modes. Below
the critical age, a combined transverse shear and tensile failure mode, within the critical age, a
purely tensile mode of failure due to equal parts longitudinal and transverse shear failure along
the line of maximum principal stress, and after the critical region, a combined tensile and
longitudinal mode of failure. Future work towards mechanistically explaining why the torsional
spiral fracture pattern changes with specimen age and rate first and foremost should utilize a
larger bone model, as curvature effects with specimen age may have influenced the results of the
study. Furthermore, biological studies such as osteon population density and mineral density
should be studied in comparison with specimen age, as these parameters influence the basic
structural characteristics of bone as it develops into a maturity. Finally, tensile tests should be
conducted at incremental angles from 0 to 90 degrees to test if the weakest composite plane in
tension is altering with specimen age and loading rate. It would be useful to create a theoretical
model using equations from linear elasticity to validate such work.

CHAPTER 4
Chapter 4 was an experimental study which tested whole and intact sheep femora under
concentrated four-point bending to simulate the loading conditions of Martens et al., 2015 using
mature and immature specimens. Additionally, a basic finite element model was developed to
investigate what the potential principal (tensile) stress distribution looks like under the
experimentally tested Martens-type loading, compared to the stress distributions formed under a

103

typical 3-point bending configuration and under a typical 4-point bending configuration.
Computational models were generated to match specimen geometry by creating volumetric
meshes based on CT images of a young and older test specimen. The two-fold purpose of this
work was to first, to determine the effect of age on the pattern of femur fracture using a Martenstype loading configuration. Secondly the study was to investigate how the stress distribution
generated under the Martens-type loading condition differed from the traditional 3-point and 4point bending tests used in traditional studies in the biomechanical and forensic fields. Results of
the study indicated that in mature specimens tested under a Martens-type bending configuration,
there is a near-exclusive production of compression wedge fracture patterns when tested at low
rates. Furthermore, immature specimens tested at low rates under a Martens-type configuration
appeared to commonly produce transverse fracture patterns, or incipient tensile wedge patterns.
Interestingly, in this pilot study the preliminary results from mature bone specimens tested under
Martens-type loading at high rates demonstrated that non-compressive wedge patterns (oblique
and tensile wedge patterns) can be produced. These data suggested that the compressive-wedge
pattern may be rate-sensitive, as well as age-sensitive. The experimental portion of this study
demonstrated that specimen age does indeed affect the resultant fracture pattern under
concentrated, four-point bending, and provides preliminary framework indicating that loading
rate may also influence the fracture pattern under Martens-type conditions.

From the computational work of this study, specimen-specific models appeared to correspond
well with their experimental counterparts for both young and old specimens. Interestingly, when
testing mature bones at low loading rates the stress distribution was shown to markedly change
between 3-point bending, 4-point bending, and Martens-type bending scenarios. These modeling

104

studies demonstrated that each loading type generated unique stress patterns. Typical 3-point
bending produced high tensile stresses under the point of impact on the non-loading side of the
bone, in addition to large compressive stress on the loading side of the bone, correlating well
with the typical tensile wedge fracture pattern, assuming wedge fractures due to shear in the
compression side of the bone as suggested in the biomechanical literature. Typical 4-point
bending produced large tensile stresses just outside each of the loading points on the loading side
of the bone, in addition to large tensile stresses observed just outside each of the supports on the
non-loading side of the bone. This stress distribution indicated possibly two zones of failure that
likely may correlate well to the typical segmental fragment pattern associated with standard 4point bending. Most notedly, the Martens-type loading appeared to act as a unique, and novel
combination of both 4-point and 3-point bending stress distributions. For Martens-type bending,
large tensile stresses were noted just outside the outer supports like that shown in typical 4-point
bending, with large compressive stresses generated under the inner loading probes, typical to that
observed under three-point bending. Interestingly, there are also small tensile stresses generated
underneath the inner probe loading points on the surface of the bone. The stress distribution
appeared to correlate well with the compression wedge fracture pattern.

While more testing needs to be performed to verify potential rate effects under Martens-type
four-point loading, it may be suggested from the Cheong et al., 2017 study of immature
specimen, and from the limited number of mature specimen tested in the current work under a
high loading rate, that both younger and older specimens may be more inclined to produce the
typical tensile wedge fracture pattern under Martens-type loading. In future work it should be
paramount to stratify the four standardized fracture patterns of tensile/compression wedges,

105

segmental fragments, and transverse fractures by developmental age of occurrence, under what
loading speeds they can be generated, and at what percentage of loaded bone length the four
patterns can be generated under four-point bending and/or 3-point bending.

106

APPENDIX

107

PUBLICATIONS

Vaughan P, Vogelsberg C, Vollner J, Fenton, Haut R: The Role of Interface Shape on the Impact
Characteristics and Cranial Fracture Patterns Using the Immature Porcine Head Model. J Forensic Sci
2016; 61(5)1190-7
Vaughan P, Orth MW, Haut RC, Karcher DM: A method of determining bending properties of poultry
long bones using beam analysis and micro-CT data. J Poultry Sciences 2016; 95(1):207-12
Vaughan P, Wei F, Haut R: The Effect of Specimen Age and Speed of Torsion on Fracture Patterns of
the Immature Porcine Femur. J Biomech Eng, In Review

PRESENTATIONS

Vaughan P, Wei F, and Haut R: Age effects on bending fracture patterns in ovine femora. Proceedings of
the 69th annual scientific meeting of the American Academy of Forensic Sciences, New Orleans,
Louisiana, D3:629, 2017
Vaughan P, Wei F, and Haut R: Specimen age affects the fracture pattern of immature porcine femurs
under torsional loading. Proceedings of the 68th annual scientific meeting of the American Academy of
Forensic Sciences, Las Vegas, Nevada, D3:453, 2016

ABSTRACTS

Goots A, Isa M, Fenton TW, Watson E, Vaughan P, Wei F, and Haut R: Estimating points of impact in
multiple blunt force cranial trauma: lessons from experimental impacts. Proceedings of the 70th annual
scientific meeting of the American Academy of Forensic Sciences, Seattle, Washington, 2018, In Review

Isa M, Fenton TW, Goots A, Watson E, Vaughan P, Wei F, and Haut R: Initiation and propagation of
fractures in blunt impacts to minimally-constrained human cadaver heads. Proceedings of the 70th annual
scientific meeting of the American Academy of Forensic Sciences, Seattle, Washington, 2018, In Review

Watson E, Fenton TW, Isa M, Goots A, Watson E, Vaughan P, Wei F, and Haut R: The influence of
implement shape on fracture pattern and defect size in experimental blunt cranial impacts. Proceedings of
the 70th annual scientific meeting of the American Academy of Forensic Sciences, Seattle, Washington,
2018, In Review

108

Isa M, Fenton TW, Vaughan P, and Haut R: Understanding the role of contact area in adult cranial
fracture variation. Proceedings of the 68th annual scientific meeting of the American Academy of
Forensic Sciences, Las Vegas, Nevada, A78:131, 2016

Vollner J, Vogelsberg CM, Vaughan P, Fenton TW, Clark SC, and Haut R: The interpretation of human
pediatric cranial fracture patterns using experimentally generated porcine ground-truth data. Proceedings
of the 68th annual scientific meeting of the American Academy of Forensic Sciences, Las Vegas, Nevada,
A76:128, 2016

Fenton TW, Isa M, Vaughan P, and Haut R: Experimental and computational validations of the initiation
and propagation of cranial fractures in the adult skull. Proceedings of the 67th annual scientific meeting
of the American Academy of Forensic Sciences, Orlando, Florida, A100:180, 2015

Vogelsberg CM, Vaughan P, Fenton TW, and Haut R: A forensic pathology tool to predict pediatric
skull fracture patterns: Part V. Proceedings of the 67th annual scientific meeting of the American
Academy of Forensic Sciences, Orlando, Florida, A99:178, 2015

109