Application of high voltage, high frequency pulsed electromagnetic field on cortical bone tissue

Application of High Voltage, High Frequency
Pulsed Electromagnetic Field on Cortical Bone
Tissue

This thesis submitted as a requirement for the degree of

Master of Engineering

Hajarossadat Asgarifar
B.Eng (Electrical)

School of Biomedical Engineering and Medical Physics
Faculty of Science and Engineering
Queensland University of Technology
Brisbane, Australia

June 2012


Statement of Originality

The work contained in this thesis has not been previously submitted to meet requirements
for an award at this or any other higher education institution. To the best of my knowledge
and belief, the thesis contains no material previously published or written by another
person except where due reference is made.

Hajarossadat Asgarifar

II

Acknowledgments

My deep foremost gratitude to the creature of the world, Allah, who all what I have
is his blessing.
Next, I express my sincere thanks and gratitude to the following generous people
whom, the completion of this work was not possible without their support, patience,
encouragement and guidance:


My supervisors, Prof Kunle Oloyede and Associate Prof Firuz Zare for their
invaluable guidance and support



The many academic and technical staff and PhD students at IHIB for their
kind consultancies and assistances, in particular, Prof Christian Langton for
ultrasound facilities and medical engineering laboratory technicians and
research portfolio staff for their technical advices and continued helps



My friends and colleagues for sharing knowledge and providing a warm
research environment



The last but not the least, to my unique family, my beloved husband, Mehran,
for his most amazing support and great advices and my gorgeous favourite
twins, Hossein and Mahdi, for their kindness and patience all through my
study



And to my dear parents for their infinite love, spiritual support and
encouragement during my life and study even when I was too far from them

III


Keywords

Pulsed Power
Cortical bone
High voltage, High frequency converter
Positive Buck-Boost Converter
Pulsed electromagnetic field
Electrical stimulation
Mechanical properties of bone
Bone functional behaviour

IV


Abstract

Over the last few decades, electric and electromagnetic fields have achieved
important role as stimulator and therapeutic facility in biology and medicine. In particular,
low magnitude, low frequency, pulsed electromagnetic field has shown significant positive
effect on bone fracture healing and some bone diseases treatment. Nevertheless, to date,
little attention has been paid to investigate the possible effect of high frequency, high

magnitude pulsed electromagnetic field (pulse power) on functional behaviour and
biomechanical properties of bone tissue.
Bone is a dynamic, complex organ, which is made of bone materials (consisting of
organic components, inorganic mineral and water) known as extracellular matrix, and bone
cells (live part). The cells give the bone the capability of self-repairing by adapting itself to
its mechanical environment. The specific bone material composite comprising of collagen
matrix reinforced with mineral apatite provides the bone with particular biomechanical
properties in an anisotropic, inhomogeneous structure.
This project hypothesized to investigate the possible effect of pulse power signals on
cortical bone characteristics through evaluating the fundamental mechanical properties of
bone material. A positive buck-boost converter was applied to generate adjustable high
voltage, high frequency pulses up to 500 V and 10 kHz.
Bone shows distinctive characteristics in different loading mode. Thus, functional
behaviour of bone in response to pulse power excitation were elucidated by using three
different conventional mechanical tests applying three-point bending load in elastic region,
tensile and compressive loading until failure. Flexural stiffness, tensile and compressive
V


strength, hysteresis and total fracture energy were determined as measure of main bone
characteristics. To assess bone structure variation due to pulse power excitation in deeper
aspect, a supplementary fractographic study was also conducted using scanning electron
micrograph from tensile fracture surfaces.
Furthermore, a non-destructive ultrasonic technique was applied for determination
and comparison of bone elasticity before and after pulse power stimulation. This method
provided the ability to evaluate the stiffness of millimetre-sized bone samples in three
orthogonal directions.
According to the results of non-destructive bending test, the flexural elasticity of
cortical bone samples appeared to remain unchanged due to pulse power excitation.
Similar results were observed in the bone stiffness for all three orthogonal directions

obtained from ultrasonic technique and in the bone stiffness from the compression test.
From tensile tests, no significant changes were found in tensile strength and total strain
energy absorption of the bone samples exposed to pulse power compared with those of the
control samples. Also, the apparent microstructure of the fracture surfaces of PP-exposed
samples (including porosity and microcracks diffusion) showed no significant variation
due to pulse power stimulation. Nevertheless, the compressive strength and toughness of
millimetre-sized samples appeared to increase when the samples were exposed to 66 hours
high power pulsed electromagnetic field through screws with small contact cross-section
(increasing the pulsed electric field intensity) compare to the control samples. This can
show the different load-bearing characteristics of cortical bone tissue in response to pulse
power excitation and effectiveness of this type of stimulation on smaller-sized samples.
These overall results may address that although, the pulse power stimulation can
influence the arrangement or the quality of the collagen network causing the bone strength

VI


and toughness augmentation, it apparently did not affect the mineral phase of the cortical
bone material. The results also confirmed that the indirect application of high power pulsed
electromagnetic field at 500 V and 10 kHz through capacitive coupling method, was
athermal and did not damage the bone tissue construction.

VII


Contribution

High power pulsed electromagnetic field (Pulse Power), has been applied recently in
some fields of biology and medicine. However, the effect of pulse power on physical
characteristics of bone tissue has not yet been fully clarified. On the other hand, according

to various studies during last century, electrical stimulation using both constant and pulsed
electromagnetic field (PEMF) has had a drastic effect on bone growth and some bone
diseases healing. It was a good motivation for investigation of the possibility of applying
pulse power signals for stimulating bone.
The main contribution of the present thesis is to introduce a suitable, safe method
with controlled parameters for application of high power, pulsed electromagnetic fields on
bone tissue using capacitive coupling method. The basic biomechanical properties of
cortical bone material including stiffness, strength, toughness and brittleness have been
investigated (considering just extracellular fraction of the bone) in response to high
voltage, high frequency pulses up to 500V at 10 kHz. These have been achieved by:


The comparison and assessment of two pulse power application methods, direct
connection of bone with electrodes (which result in thermal effect and burning) and
capacitive coupling method through electrodes isolation (Chapter 4).



The determination and comparison of bone flexural elasticity before and after pulse
power excitation using the non-destructive three-point bending tests (in linear
elastic region) on both whole long bone and cortical bone strips (Chapter 4).

VIII




The study of the bone fracture behaviour in response to high voltage, high
frequency pulsed electromagnetic field using tensile test until failure point by
investigation of fracture energy, hysteresis energy and strength of the samples

exposed to pulse power compared with those of the control samples and
supplementary fractograph study via scanning electron microscopy of the fracture
surfaces (Chapter 5).



The evaluation of the compressive strength and fracture energy of the millimetresized cortical bone samples exposed to pulse power signals compared with the
control specimens (Chapter 6).



The application of ultrasonic technique as an alternative, non-destructive method
with the capability of measurement in different orthogonal directions for
determination and comparison of elastic property of cortical bone samples in
response to pulse power excitation (Chapter 7).
To author’s knowledge, this project was the first research investigating the effect of

high voltage, high frequency pulsed electromagnetic field on fundamental properties of
cortical bone structure.
Providing a basic information about the effect of pulse power excitation on bone
tissue structure, this study will contribute in further research on pulse power application on
live bone, investigating the bone growth enhancement potential of this kind of stimulation
for therapeutic purpose in musculoskeletal diseases.
Some of the results of this research were presented as accepted international
conference paper and item as below and other is going to submit as a journal paper:


H. Asgarifar, A. Oloyede, F. Zare, C. M. Langton “Evaluation of cortical bone
elasticity in response to pulse power excitation using ultrasonic technique” Ninth

IX


IASTED International Conference on Biomedical Engineering (Biomed 2012), Feb.
2012. Innsbruck, Austria


H. Asgarifar, A. Oloyede, F. Zare “Investigation of high frequency, high voltage
pulses application on bending properties of bone” EPSM-ABEC Conference, Aug
2011, Darwin Australia.

X


Table of Contents

Statement of Originality .................................................................................. II
Acknowledgments .......................................................................................... III
Keywords ........................................................................................................ IV
Abstract ............................................................................................................. V
Contribution ................................................................................................ VIII
Table of Contents ........................................................................................... XI
List of Figures ........................................................................................... XVIII
List of Tables .............................................................................................. XXV
List of Abbreviations and Symbols........................................................ XXVII
Chapter 1: Introduction ................................................................................. 1
Chapter 2: Physical Behaviour and Electrical Stimulation of Bone.......... 8
2.1

Introduction................................................................................................ 9

2.2

Hierarchical architecture of bone............................................................. 10

2.3

Cortical bone structure ............................................................................. 12

2.3.1 Bone cells................................................................................................. 12
2.3.2 Extracellular matrix (ECM) architecture ................................................. 15
Collagen fibrils arrangement ....................................................... 17
Mineral crystals structure............................................................. 18
The water content......................................................................... 19
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2.4

Contribution of the bone constitutes at different hierarchical levels on its

mechanical competence .............................................................................................. 20
2.4.1 The bone basic elements (molecular level) ............................................. 22
Collagen fibrils ............................................................................ 22
The mineral crystals ..................................................................... 24
The bone water content ................................................................ 24
2.4.2 The mineralized collagen fibrils (nanoscale level) .................................. 26
2.4.3 The arrays of the collagen fibrils (mesoscale level) ................................ 26
2.4.4 The organization of the fibril arrays in lamellae and osteon (microscale
level) ........................................................................................................ 27

2.5

Bioelectric phenomena in bone ............................................................... 28

2.5.1 The origin of the stress generated potential (SGP) in bone ..................... 29
2.5.2 Electrical stimulation of bone with low intensity electromagnetic field . 31
Application of direct contact method for bone tissue stimulation31
Application of the pulsed electromagnetic field stimulation on bone
tissue ...................................................................................................... 33
Inductive coupling............................................................................................. 34
Capacitive coupling........................................................................................... 36
2.5.3 Influential factors in electrical stimulation methods ............................... 38
2.5.4 Some of the hypothesized mechanisms involved in bone generation due
to pulsed electromagnetic field ................................................................ 40
2.5.5 The effect of low intensity pulsed electromagnetic field on biomechanical
properties of bone .................................................................................... 41
2.5.6 Application of high intensity pulsed electromagnetic field on bone ....... 42
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Chapter 3: Pulse Power Generator Based on Positive Buck-Boost Converter
44
3.1

Introduction.............................................................................................. 45

3.2

Topology of pulse power generator ......................................................... 47

3.2.1 General configuration of positive Buck-Boost Converter ....................... 47
3.2.2 Switching Modes ..................................................................................... 49
First state: charging inductor (S1: on, S2: on) ............................. 49
Second state: circulating the inductor current (S1: off, S2: on) ... 49
Third state: charging the capacitor and load supplying (S1: off, S2: off)
............................................................................................................... 50
3.3

The pulse power generators applied in this study.................................... 52

3.4

Load modeling ......................................................................................... 55

Chapter 4: Physical Characterisation of Bone Exposed to Pulse Power in
Bending

57

4.1

Introduction.............................................................................................. 58

4.2

Factors influencing experimental measurement ...................................... 59

4.3

Materials and Methods ............................................................................ 62

4.3.1 Sample preparation .................................................................................. 62
4.3.2 Three-point bending test .......................................................................... 63
4.3.3 Data collection and calculation ................................................................ 65
4.3.4 Pulse Power excitation............................................................................. 68
4.4

Experimental procedure and Results ....................................................... 69

4.4.1 Pulse power excitation with voltage up to 180V and 100 Hz frequency. 69
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Whole bone stimulation with Pulses of 180 V at 100 Hz ............ 70
Bone strips stimulation with pulses of 180 V at 100 Hz ............. 71
4.4.2 Pulse power excitation with pulses up to 450 V magnitude at 10 kHz
frequency ................................................................................................. 73
Pulses up to 450 V at 340 Hz ....................................................... 73
Pulses up to 450 V at 10 kHz ....................................................... 75
4.5

Discussion ................................................................................................ 77

Chapter 5: Effect of Pulse Power Exposure on Functional Behaviour of
Cortical Bone in Tension .......................................................................................... 80
5.1

Introduction.............................................................................................. 81

5.1.1 Fractographic study ................................................................................. 83

5.2

Materials and Methods ............................................................................ 84

5.2.1 Practical consideration for tensile testing ................................................ 84
5.2.2 Sample preparation .................................................................................. 85
5.2.3 Pulse Power excitation............................................................................. 88
5.2.4 Uniaxial quasi-static tensile test .............................................................. 90
5.2.5 Scanning electron fractograph ................................................................. 91
Sample preparation for SEM procedure ...................................... 91
5.3

Experimental procedure and Results ....................................................... 92

5.3.1 Dumbbell shape tensile test samples with round junction versus those
with sharp junction .................................................................................. 92
5.3.2 Hysteresis energy absorption for PP-exposed samples versus the control
samples .................................................................................................... 94
5.3.3 Tensile toughness and strength measurement.......................................... 96
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5.3.4 Fractographic examination using SEM ................................................... 98
5.4

Discussion .............................................................................................. 105

Chapter 6: Effect of Pulse Power Excitation on Basic Mechanical Properties of
Cortical Bone in Compression ............................................................................... 110
6.1

Introduction............................................................................................ 111

6.2

Materials and Methods .......................................................................... 112

6.2.1 Sample preparation ................................................................................ 112
6.2.2 Experimental Procedure......................................................................... 113
Bone samples stimulation with pulse power signals ................. 113
Compressive testing ................................................................... 115
6.3

Toughness and strength measurement (results) ..................................... 116

6.4

Discussion .............................................................................................. 120

Chapter 7: Evaluation of Cortical Bone Elasticity in Response to Pulse Power
Excitation Using Ultrasonic Technique ................................................................ 122
7.1

Introduction............................................................................................ 123

7.2

The theoretical consideration................................................................. 125

7.3

Materials and Methods .......................................................................... 127

7.3.1 Sample preparation ................................................................................ 127
7.3.2 Density measurement............................................................................. 128
7.3.3 Experimental Procedure......................................................................... 129
Ultrasound velocity measurement ............................................. 129
Pulse Power excitation ............................................................... 132

XV


7.4

Results ................................................................................................... 133

7.5

Discussion .............................................................................................. 135

Chapter 8: Effect of Pulse Power Stimulation on Functional and Physical
Characteristics of Cortical Bone (Discussion and Conclusion) .......................... 138
8.1

Introduction............................................................................................ 139

8.2

Research procedure description and justification .................................. 141

8.2.1 Introduction of a suitable pulse power application set up and evaluation
of the flexural elasticity of cortical bone through non-destructive 3-point
bending test ............................................................................................ 142
8.2.2 The effect of pulse power exposure on the tensile strength and total
fracture energy accompanying the microstructure analysis of the test
bone fracture surfaces ............................................................................ 143
8.2.3 The effect of the pulse power excitation on the compressive strength and
toughness of the small sized samples .................................................... 144
8.2.4 Application of ultrasonic technique to evaluate the effect of pulse power
on bone elasticity ................................................................................... 144
8.3

The effect of pulse power stimulation on functional behaviour of cortical bone

tissue 145
8.3.1 Results Interpretation ............................................................................. 145
8.3.2 Final results ............................................................................................ 152
8.4

Discussion and Conclusion .................................................................... 152

8.5

Research limitations............................................................................... 155

8.6

Future work and recommendation ......................................................... 156

XVI

References ...................................................................................................... 158

XVII


List of Figures

Figure ‎2.1 Hierarchical structure of bone (a) Cortical and cancellous bone (b) Osteon
consist of haversian canal (c) Lamellae (d) Collagen fibers (e) Collagen
molecules and mineral crystals23 .................................................................. 11
Figure ‎2.2 Cross-section of a bone showing both cortical and cancellous bone
structure26 ..................................................................................................... 12
Figure ‎2.3 Response pattern of the bone cells to extrinsic/intrinsic applied load27... 15
Figure ‎2.4 Multi scale of bone architecture (a) Amino acid building block (the
smallest scale of bone) (b) Tropocollgen molecules made from three
polypeptide chains of over 1000 amino acid residues (c) Mineralized
collagen fibrils consisting of mineral crystallites embedded within and
between collagen fibrils (d) Fibrillar arrays, the arrangement of the
mineralized collagen fibrils (e) Different organizations of fibrillar arrays in
different bone types (f) The osteon which surrounds and protects the blood
vessels (g) Bone tissue level (h) Whole bone level21 .................................. 16
Figure ‎2.5 (a) Triple-helical structure of collagen molecule (tropocollagen molecule)
(b) The arrangement of the collagen molecules in the collagen fibrils , (the
staggered arrays of tropocollagen molecules assembles in collagen fibrils
which themselves organize into arrays. The neighboring collagen molecules
have the gap (G) of 40 nm and the overlap (O) of 27 nm relative to each
other29.) ......................................................................................................... 18

XVIII


Figure ‎2.6 Mineralization of the collagen fibrils during bone synthesis

33

.............. 19

Figure ‎2.7 Strain generated potential created on a femur under mechanical
deformation10 ................................................................................................ 30
Figure ‎2.8 Four stimulatory techniques for application of electric current to the
tissue by direct contact of the electrodes (A) The cathode in the target site
and the anode on the skin (B) The cathode in target site and the anode in
some distance with the cathode implanted in soft tissue (C) Non-invasive
stimulation placing the electrodes on the skin (D) Both electrodes implanted
in the soft tissue, away from the target site

87

............................................. 32

Figure ‎2.9 Inductive coupling set up over a tibia fracture94 ...................................... 34
Figure ‎2.10 Capacitive coupling set up over the fracture site94 ................................. 36
Figure ‎3.1 Conversion of low power, long time input waveform to high power, short
time output waveform by a pulse power generator ...................................... 45
Figure ‎3.2 Typical diagram for pulse power generators ............................................ 46
Figure ‎3.3 A combination of current and voltage sources as a pulse power
generator135 ................................................................................................... 47
Figure ‎3.4 Circuit diagram of positive buck-boost converter .................................... 48

Figure ‎3.5 First switching state, charging the inductor ............................................. 49
Figure ‎3.6 Second switching state, circulating the inductor current.......................... 50
Figure ‎3.7 Third switching state, charging the capacitor........................................... 51
Figure ‎3.8 Power delivery through the load switch ................................................... 51
Figure ‎3.9 Pulse power generator A (PGA) with NEC microcontroller.................... 53

XIX


Figure ‎3.10 Pulse power generator B (PGB) with Digital Signal Controller (DSP) . 54
Figure ‎3.11 High-voltage high frequency pulses with 500V at 10 kHz generated by
GPB .............................................................................................................. 55
Figure ‎3.12 Topology of pulse generator B with load modeling ............................... 56
Figure ‎4.1 Two types of bending tests and the compression-tension relationship of
forces along the surfaces of the loaded specimens[3] .................................. 60
Figure ‎4.2 Three-cycle bending load in linear elastic region on the bone strip sample64
Figure ‎4.3 A small drop on the first cycle of bending test in elastic region that was
removed on the further cycles ...................................................................... 65
Figure ‎4.4 Three point bending test142 ....................................................................... 66
Figure ‎4.5 Assumed elliptical cross-section for whole bone ..................................... 67
Figure ‎4.6 Cross-sectional area of whole long bone in ANSYS for determination the
area moment of inertia .................................................................................. 67
Figure ‎4.7 Bone strip obtained from the cortical diaphysis ....................................... 68
Figure ‎4.8 Variation of Young’s modulus of the ovine metatarsus exposed to 180V
and 100 Hz pulses over 5 days (PP-exposed sample) compared to that of the
control sample .............................................................................................. 71
Figure ‎4.9 Sketch of experimental set-up for pulse power stimulation of the cortical
bone strip sample .......................................................................................... 72
Figure ‎4.10 Variation of the Young's modulus of femoral cortical strips exposed to
180V at 100 Hz pulse power over 9 days compared with that of the same

samples without pulse power excitation ....................................................... 73

XX


Figure ‎4.11 The pulse power waveform with 450V magnitude and 10 kHz frequency
applied on cortical bone samples.................................................................. 76
Figure ‎4.12 Elastic properties of the cortical bone samples exposed to pulse power
(450 V at 10 kHz) before and after excitation compared with those values of
the control samples ....................................................................................... 76
Figure ‎5.1Typical macroscopic tensile test fracture (A) ductile shear fracture (B)
moderately ductile fracture (C) brittle fracture 155 ....................................... 84
Figure ‎5.2Dumbbell shape specimen with round junction (GL, GW and GT are gage
length, gage width and gage thickness respectively) ................................... 85
Figure ‎5.3 Sketch of partitioned tibia used for tensile test specimen preparation ..... 87
Figure ‎5.4 Dumbbell shape specimen with sharp junction (GL, GW and GT are gage
length, gage width and gage thickness respectively) ................................... 87
Figure ‎5.5 Top view of a sketch of experimental set up for Pulse Power excitation of
the bone tensile test specimens between two isolated aluminium strips ...... 89
Figure ‎5.6 Tensile testing of the cortical bone specimen .......................................... 90
Figure ‎5.7 Cortical bone samples mounted on the SEM stubs, place for gold coating91
Figure ‎5.8 Tensile Stress-Strain responses until failure of dumbbell shape samples
with round junction (
sharp junction (

) versus those of dumbbell shape samples with
).................................................................................. 93

Figure ‎5.9 Comparison of the strength and toughness of dumbbell shaped samples
with round junction and those of samples with sharp junction .................... 93

XXI


Figure ‎5.10 Hysteresis loops in tensile loading-unloading cycle for a bone specimen
exposed to pulse power before and after 145 hours excitation .................... 94
Figure ‎5.11 Hysteresis loops in the tensile loading-unloading cycle for a control
bone sample before and after 145 hours being in similar environmental
condition as PP-exposed samples ................................................................. 95
Figure ‎5.12 Mean hysteresis energy of the control samples versus the samples
exposed to pulse power before and after 145 hours excitation .................... 96
Figure ‎5.13 Tensile stress-strain graphs of the cortical bone samples in four groups
up to failure .................................................................................................. 97
Figure ‎5.14 SEM micrographs from the top and side views of the control samples
(unexposed to pulse power) with their corresponding stress-strain graphs 100
Figure ‎5.15 SEM micrographs from top and side views of cortical bone samples
exposed to 500Vand 10 kHz pulse power for 145 hours with their
corresponding stress-strain graphs ............................................................. 101
Figure ‎5.16 SEM micrographs from top and side views of the cortical bone samples
exposed to pulse power, A and B for28 hours, C and D for 35 hours with
their equivalent stress-strain graphs ........................................................... 102
Figure ‎5.17 Details of scanning electron micrographs of fracture surface in higher
magnification (A) Dimpled, irregular appearance of fracture surface (B)
Microcrack diffusion (C) Microvoids (D) Crack bridging by collagen fibrils104
Figure ‎5.18 Higher magnification of scanning micrographs of the fracture surfaces
of the representative samples from each group (A) Control sample (B)

XXII

Samples exposed to pulse power for 28 hours (C) Sample exposed to pulse
power for 35 hours (D) Sample exposed to pulse power for 145 hours ..... 105
Figure ‎6.1 Position and directions of the rectangular specimen obtained from the
tibial cortical dyaphysis .............................................................................. 113
Figure ‎6.2 Sketch of experimental set-up for pulse power stimulation of millimetresized cortical bone samples ........................................................................ 115
Figure ‎6.3 Compressive testing of cortical bone specimen ..................................... 116
Figure ‎6.4 Compressive stress-strain responses for the control specimens (
verse those for the samples exposed to pulse power (

)

) .............. 117

Figure ‎6.5 The total strain fracture energy of the samples exposed to 500V, 10 KHz
electromagnetic field compared to that of the control samples .................. 118
Figure ‎6.6 The strength of the samples exposed to 500V, 10 KHz electromagnetic
field compared to that of the control samples ............................................ 118
Figure ‎6.7 Comparison of the stiffness of the samples exposed to pulse power with
that of the control samples.......................................................................... 119
Figure ‎7.1 Ultrasound wave propagation in a bone specimen142 ............................. 125
Figure ‎7.2 Ultrasound velocity measurement set up inside water tank ................... 130
Figure ‎7.3 Ultrasound wave propagation trough the sample and time delay
measurement on Lab view Signal Express ................................................. 131
Figure ‎8.1 The elastic modulus of the normal specimens compared with the samples
exposed to pulse power for 144 hours obtained from ultrasonic technique146

XXIII


Figure ‎8.2 Comparison of the flexural elastic modulus of the control and the PPexposed samples before and after pulse power stimulation ....................... 147

Figure ‎8.3 Comparison of the bone mineral density of the control and PP-exposed
samples before and after pulse power excitation........................................ 148
Figure ‎8.4 Comparison of the hysteresis energy dissipated by the control and the PPexposed samples before and after excitation .............................................. 149
Figure ‎8.5 Comparison of the tensile strength and total failure strain energy of the
samples exposed to pulse power for 145 hours with those of the control
samples ....................................................................................................... 150
Figure ‎8.6 The strength and total fracture energy absorption of the samples exposed
to pulse power for 66 hours compared with those parameters of the control
samples ....................................................................................................... 151
Figure ‎8.7 Comparison of the Young’s modulus of the samples exposed to pulse
power with that of the control samples obtained from compression tests.. 152

XXIV


List of Tables

Table ‎4.1 Comparison of the area moment of inertia of the whole bone samples
obtained from ANSYS and calculation ........................................................ 68
Table ‎4.2 Mean value± standard deviation for Young’s modulus of cortical bone
before and after pulse power excitation (450V at 340Hz) in three days ...... 75
Table ‎5.1 Mean value ±standard deviation for the toughness and strength of the
tensile bone samples in four treated groups ................................................. 98
Table ‎7.1 Comparison between the conventional mechanical tastings and the
ultrasonic technique161, 162 .......................................................................... 124
Table ‎7.2 Mean values ± standard deviation for the specimens’ dimensions .......... 127
Table ‎7.3 Mean density ± standard deviation for cortical bone specimens before and
after pulse power excitation ....................................................................... 129
Table ‎7.4 Mean value± standard deviation for ultrasound velocity and Young’s
modulus of PP-exposed samples before and after pulse power excitation in

longitudinal, radial and tangential directions respectively ......................... 134
Table ‎7.5 Mean value± standard deviation for ultrasound velocity and Young’s
modulus of control samples before and after pulse power excitation period
in longitudinal, radial and tangential directions respectively ..................... 134

XXV