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TOWARDS ULTRASOUND COMPUTED TOMOGRAPHY ASSESSMENT OF BONE Ahmad M... · 2018. 6. 12. · Towards...
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TOWARDS ULTRASOUND COMPUTED
TOMOGRAPHY ASSESSMENT OF BONE
Marwan Ahmad Althomali
BSc. (Physics), MSc. (Medical Physics)
Submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy
Institute of Health and Biomedical Innovation
School of Chemistry, Physics and Mechanical Engineering
Science and Engineering Faculty
Queensland University of Technology
2018
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Keywords
Bone Stiffness
Complex Structure
Finite Element Analysis
Image Reconstruction
Osteoporosis
Phased Array Transducer
Quantitative Ultrasound
Simultaneous Iterative Reconstruction Technique
Ultrasound Attenuation
Ultrasound Computed Tomography
Mechanical Testing
Long Bones
Bone Thickness
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Abstract
Bones are significant organs with its strength and stiffness to move, support and
protect the body, and also the ability of remodelling and repair. Bone remodelling
involves the activities of osteoclasts, which remove the old and damaged bone, and
osteoblasts, which form new bone matrix. In advanced age, the imbalance between
resorption and formation of bone during remodelling process leads to a decrease in
bone mass and structure, and hence reduced bone strength, which eventually cause
bone fragility syndrome known as osteoporosis, which is a worldwide health issue in
the elderly population. After the age of 50, one-in-two women and one-in-three men
will have a fracture as a result of osteoporosis, leading to serious clinical consequences
and economic burden for health care. This calls for measures to evaluate and predict
the fracture risk factors associated with osteoporosis and prevent the morbidity and
mortality caused by this disease. Bone mineral density (BMD) is the current gold
standard factor used to diagnose osteoporosis and predict the bone fracture risk. Dual
energy X-ray absorptiometry (DXA) and quantitative computed tomography (QCT)
are the common clinical X-ray based methods used for BMD measurement. Finite
element analysis (FEA) that is based on DXA and QCT data was found to be more
efficient and better to predict bone fracture risk than DXA or QCT alone. However,
both DXA and QCT utilise ionizing radiation and have other drawbacks such as their
expensive cost and large technique for housing.
Quantitative ultrasound (QUS) is an alternative technique to X-ray based
methods due to many reasons including being non-ionizing, cost-effective, simple to
use, and useful information about bone density and mechanical properties. However,
QUS does not yield an image of bone compared to DXA and QCT. Conventional
ultrasound imaging provides 2/3D qualitative images of soft tissue; however, it failed
to obtain quantitative images and cannot be used for bone imaging. In order to use
ultrasound imaging quantitatively to estimate bone mechanical integrity and to predict
osteoporotic fracture risk, a development of an ultrasound computed tomography
(UCT) system is required.
A new proposed hypothesis is that the UCT is capable of imaging solid bodies
such as bones and providing high quality and useful quantitative information of bone
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tissues. It is also proposed that UCT may be combined with FEA and be equally
efficient to predict stiffness as conventional FEA. Moreover, it is proposed that pulse-
echo and transmission UCT may be combined and be efficient for quantitative imaging
of bones.
Hence this research mainly focuses on the development and scientific validation
of an ultrasound computed tomography system with particular emphasis on imaging
of bone replica models. Factors that were considered include quantification of complex
structure along with tissue properties, such as bone stiffness and cortical shell
thickness. The transmission ultrasound computed tomography system consists of two
phased array transducers, which are coaxially aligned in a proper holder. A robotic
arm is used for the rotation and elevation of the sample between the transducers. The
performance of the system was developed experimentally and computationally to
reduce image and parameter artefacts.
For the first time, the concept of ultrasound computed tomography based finite
element analysis (UCT-FEA) was investigated with a potential to estimate the
mechanical test stiffness of plastic rod phantoms and to compare with conventional
FEA. The results showed that UCT is able to provide quantitative ultrasound
attenuation CT images of small objects down to 0.5 mm and also proved the concept
of UCT-FEA for estimating the mechanical test stiffness of plastic samples. UCT-FEA
provided a comparable estimation of mechanical test stiffness compared to
conventional FEA. The UCT-FEA technique also applied to UCT derived attenuation
images of trabecular bone replica models, and found to be a promising tool for
estimating the mechanical integrity of a bone. The study demonstrated that UCT-FEA
based upon quantitative attenuation images provided a comparable estimation of gold
standard mechanical-test stiffness of 84% compared to µCT-FEA (R2 = 99%).
After the validation of the UCT-FEA concept on complex structures, the UCT
system was developed by combining ultrasound pulse-echo (PE) and transmission
computed tomography (T-UCT) for quantitative imaging of cortical shell of long bone
replicas. Therefore, a simple and fast UCT technique (PE-T-UCT) to extract an
average bone speed of sound (SOS) and a mean cortical shell thickness was
demonstrated. Being computationally inexpensive and utilizing standard phased array
transducers, this technique can easily be implemented from standard B-scan ultrasound
systems or from commercial UCT breast imaging systems using rotating phased array
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transducers. Also, the sample positioning errors are minimal, so a trained operator is
not required to position transducers.
Ultrasound computed tomography is a promising technique for bone imaging
and assessment. Being non-invasive, non-destructive and non-ionizing, it has a
significant potential to provide measurement of bone mechanical integrity and improve
clinical assessment and management of osteoporosis.
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Table of Contents
Keywords .................................................................................................................................. i
Abstract ................................................................................................................................... iii
Table of Contents .................................................................................................................... vi
List of Figures ....................................................................................................................... viii
List of Tables .......................................................................................................................... xii
List of Abbreviations ............................................................................................................. xiii
Symbols .................................................................................................................................. xv
Statement of Original Authorship ........................................................................................ xvii
List of Publications ................................................................................................................ xix
Acknowledgements ............................................................................................................... xxi
Chapter 1: Introduction ...................................................................................... 1
1.1 Background of the Research Problem ............................................................................ 1
1.2 Hypothesis ...................................................................................................................... 3
1.3 Aim and Obectives ......................................................................................................... 3
1.4 Significance of Research ................................................................................................ 3
1.5 Thesis Outline ................................................................................................................ 5
Chapter 2: Literature Review ............................................................................. 9
2.1 Bone Anatomy ............................................................................................................... 9
2.2 Osteoporosis ................................................................................................................. 11
2.3 Destructive Mechanical Test ........................................................................................ 11
2.4 Clinical Assessment of Osteoporotic Fracture Risk ..................................................... 12
2.5 Non-Destructive Numerical Method: Finite Element Analysis ................................... 17
2.6 Ultrasound Physics, Instrumentation and Conventional Imaging ................................ 19
2.7 Ultrasound Computed Tomography ............................................................................. 31
2.8 Summary and Knowledge Gap .................................................................................... 40
2.9 Discription of a Novel UCT System ............................................................................ 42
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of
Ultrasound Computed Tomography (UCT-FEA); A Comparison with
Conventional FEA in Simple Structures ................................................................ 51
3.1 Prelude ......................................................................................................................... 51
3.2 Abstract ........................................................................................................................ 51
3.3 Introduction .................................................................................................................. 52
3.4 Material and Methods .................................................................................................. 54
3.5 Results .......................................................................................................................... 65
3.6 Discussion .................................................................................................................... 67
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3.7 Conclusion ....................................................................................................................68
3.8 What is Novel? .............................................................................................................69
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of
Ultrasound Computed Tomography (UCT-FEA); A Comparison with µCT-
FEA in Cancellous Bone Replica ............................................................................ 73
4.1 Prelude ..........................................................................................................................73
4.2 Abstract .........................................................................................................................73
4.3 Introduction ..................................................................................................................74
4.4 Material and Methods ...................................................................................................76
4.5 Results ..........................................................................................................................83
4.6 Discussion .....................................................................................................................89
4.7 Conclusion ....................................................................................................................91
4.8 What is Novel? .............................................................................................................92
Chapter 5: Combining Ultrasound Computed Tomography Using
Transmission and Pulse-Echo for Quantitative Imaging the Cortical Shell of
Long Bone Replicas .................................................................................................. 97
5.1 Prelude ..........................................................................................................................97
5.2 Abstract .........................................................................................................................97
5.3 Introduction ..................................................................................................................97
5.4 Theory ...........................................................................................................................99
5.5 Material and Methods .................................................................................................100
5.6 Results and Discussion ...............................................................................................106
5.7 Conclusion ..................................................................................................................111
5.8 What is Novel? ...........................................................................................................111
Chapter 6: Conclusion ..................................................................................... 113
6.1 Hypothesis 1: Development of a Novel UCT System and the Capacity to Image Soild
Objects ..................................................................................................................................114
6.2 Hypothesis 2: UCT Quantitative Assessment Incorporating FEA to Estimate
Mechanical Properties ...........................................................................................................114
6.3 Hypothesis 3: Combined Ultrasound Computed Tomography Using Transmission and
Pulse-Echo ............................................................................................................................115
6.4 Limitations ..................................................................................................................115
6.5 Future Work ................................................................................................................116
Bibliography ........................................................................................................... 118
Appendix 1 .............................................................................................................. 130
Appendix 2 .............................................................................................................. 138
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List of Figures
Figure 1-1: Schematic diagram demonstrating the research outline. ........................... 7
Figure 2-1: 3D structure of bone shows the two types of bone, cortical and
cancellous [48]. ............................................................................................ 10
Figure 2-2: Sectional photographs of the human vertebra showing (a) normal
and (b) osteoporotic cancellous bone, the latter exhibiting a reduction
in bone density and loss of structural integrity [60]. .................................... 11
Figure 2-3: (left) 2D X-ray image of Roentgen's wife hand [65] and (right) 3D
CT coronal image of the hip [71]. ................................................................ 13
Figure 2-4: CT acquisition set up; a) third-generation geometry, where the X-
ray source and detectors are rotated around the object, b) fourth-
generation geometry, where the source is rotated inside a fixed
detector ring [73]. ......................................................................................... 14
Figure 2-5: MRI image of the from the distal region of the femur [94]. ................... 16
Figure 2-6: Particle wave motion: (a) shows the longitudinal particle motion;
(b) shows the transverse particle waves. Only longitudinal waves can
produce ultrasound waves that provide useful diagnostic information
[108]. ............................................................................................................ 20
Figure 2-7: Sound wave properties [109]. .................................................................. 21
Figure 2-8: Reflection and transmission of ultrasound depending on the
acoustic impedance of materials. ................................................................. 22
Figure 2-9: Diagram describing the scatter of an ultrasound beam interacting
with a small object. ...................................................................................... 24
Figure 2-10: Ultrasound transducer components [115]. ............................................. 26
Figure 2-11: Diagrams show the beam forming and time delay for firing and
receiving multiple beams [118]. ................................................................... 27
Figure 2-12: Beam focusing principle for (a) normal and (b) angled incidences
[118]. ............................................................................................................ 27
Figure 2-13: Simple RF system (transmission mode), kindly provided by Prof.
Christian Langton. ........................................................................................ 28
Figure 2-14: Simple RF system (pulse-echo mode), kindly provided by Prof.
Christian Langton. ........................................................................................ 29
Figure 2-15: Diagram depicting the creation of B-scan from A-scan. ....................... 30
Figure 2-16: (left) 2D B-scan image, and (right) 3D ultrasound image showing
my daughter at 19 weeks of gestation. ......................................................... 31
Figure 2-17: Architectures of ultrasound tomographic systems. a) Two linear
opposite transducer arrays rotating mechanically around the object. b)
Ring shaped array enclosing the object [125]. ............................................. 32
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Figure 2-18: (right) Projection profiles of point source taken at 8 angles
(views): (left) 2D sinogram represents a set of projection profiles, r
(horizontal axis) and φ (vertical axis) are the location in the projection
and rotation angle respectively [130]. .......................................................... 34
Figure 2-19: Backprojection reconstructs an image by taking each view and
smearing it along the path it was originally acquired. The obtained
image is a blurry version of the correct image [131]. .................................. 35
Figure 2-20: Filtered back-projection reconstructs an image by filtering each
view before back-projection which removes the blurring of the simple
back-projected image [131]. ........................................................................ 35
Figure 2-21: Cylindrical aperture for first experimental 3D setup of UCT [145]. .... 39
Figure 2-22: Robotic arm (left), NX100 controller and programming pendant
(right). .......................................................................................................... 42
Figure 2-23: Olympus Omniscan MX........................................................................ 43
Figure 2-24: TomoView user interface showing menus, toolbars and different
representation views of the data imaging..................................................... 44
Figure 2-25: Sketch of the UCT setup utilizing one Omniscan device...................... 46
Figure 2-26: Sketch of the UCT setup utilizing two Omniscan devices. ................... 47
Figure 3-1: (a) Photograph of the rod samples with varying rod diameter (from
left to right) of 0.5, 1.5, 2.5, 3.5, 4.5, and 5.5 mm. (b) Sketch of the
5.5 mm rod sample design showing the rod diameter, distance from
centre to centre and total scan area, measurements are in mm. ................... 55
Figure 3-2: a): Sketch of the UCT system set-up. b): Photograph of the
experimental set-up showing the sample attached to the robotic arm
and positioned between the two transducers. ............................................... 56
Figure 3-3: a) uncorrected sinogram is asymmetric with the rotation axis (y-
axis) being off-centred by three times of the transducer element width,
b) corrected and symmetric sinogram. The red solid line indicates the
symmetric centre line, c) 2D UCT image before correction, and d) 2D
UCT image after correction. For subfigure (a) and (b), x-axis is
measurement index (angle) and y-axis is sensor pair index. For c and
d, the colourmaps display the attenuation map in dB m-1, x- and y-axes
are in pixels unit. .......................................................................................... 58
Figure 3-4: The reconstructed 2D UCT images of 1.5 mm rod sample from
different number of projections; a) 360 projections, b) 180 projections,
c) 91 projections, d) 46 projections, e) 23 projections and f) 11
projections. ................................................................................................... 59
Figure 3-5: a) Raw 2D UCT image (attenuation map in dB m-1), b) binary 2D
UCT image, c) 3D STL file, axes are in mm unit. The STL files were
imported into SolidWorks v2014 (Dassault Systems, Waltham, MA,
USA) as mesh files in order to save them into solid part format
(SLDPRT), which was then used as the input geometry for the finite
element analysis simulation in Ansys. ......................................................... 60
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Figure 3-6: The binary images of 1.5 mm rod sample using different threshold
values, a) 1800 dB m-1, b) 1900 dB m-1 and c) 2000 dB m-1. ...................... 61
Figure 3-7: Photograph of the six strips that have been used in the three-point
bending test to measure Young’s Modulus of the bulk material, each
3.75 mm thick, 12 mm wide, and 100 mm long. ......................................... 62
Figure 3-8: a) FE model of the rod sample with 5.5 mm diameter rod, b) shows
the applied displacement (in z-direction). .................................................... 63
Figure 3-9: Mesh size convergence in the 2.5 rod sample with element sizes of
2 mm, 1 mm and 0.5 mm. ............................................................................ 64
Figure 3-10: Set-up of the mechanical test of a rod sample using an Instron
5848 MicroTester testing machine with a 500 N load cell. ......................... 65
Figure 3-11: The reconstructed 2D UCT images. (a) 0.5 mm rods thickness, (b)
1.5 mm rods thickness, (c) 2.5 mm rods thickness, (d) 3.5 mm rods
thickness, (e) 4.5 mm rods thickness and (f) 5.5 mm rods thickness.
The colour bars in the images display the attenuation map in dB m-1.
Axes are in pixel units. ................................................................................. 66
Figure 3-12: Estimation of the experimental mechanical test stiffness by (a)
conventional FEA (left) and (b) UCT-FEA (right). The range of all
data sets were normalised to unity. 1.5 mm (○), 2.5 mm (□), 3.5 mm
(∆), 4.5 mm (ⅹ), 5.5 mm (◊). ........................................................................ 67
Figure 3-13: Summery of the UCT-FEA study in Chapter 3. .................................... 69
Figure 4-1: The FEA simulation process consists of dividing the structure into
regular-shaped finite-elements (a), onto which constraints and loads
(indicated with the yellow arrow on the top) are applied (b). ...................... 76
Figure 4-2: Photograph of the cancellous bone replicas: iliac crest (IC1 and
IC2), calcaneus (CAB1 and CAB2), femoral head (FR1 and FR2) and
lumbar spine (LS1 and LS2). ....................................................................... 77
Figure 4-3: Left: Sketch of the UCT system set-up. Right: Photograph of the
experimental set-up showing the sample attached to the robotic arm
and positioned between the two phased-array transducers. ......................... 79
Figure 4-4: a) a typical 2D attenuation map obtained by the UCT, the x and y
axis represent the pixel number, the colour bar denotes the attenuation
values in [dB m-1]. b) 2D binary image after applying the threshold. c)
reconstructed 3D ultrasound model after stacking all 2D images. The
axes are in [mm]. .......................................................................................... 80
Figure 4-5: File conversion flow-chart diagram from STL to SLDPRT,
required for input into Ansys software. ....................................................... 81
Figure 4-6: Mesh size convergence in the CAB1 sample with element sizes of
5 mm, 3 mm and 1 mm. ............................................................................... 82
Figure 4-7: Set-up of the mechanical test of a cancellous bone replica sample
using an Instron 5848 Micro Tester testing machine with a 500 N load
cell. ............................................................................................................... 83
Figure 4-8: 2D UCT images of the same slice but with different digitizing
frequency: 25 MHz, 50 MHz and 100 MHz (from top to bottom). The
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image size is 256x256 pixels (48x48 mm2). The colour bar represents
the attenuation values in [dB m-1]. ............................................................... 84
Figure 4-9: 3D UCT models of the 3D-printed samples; a) CAB1, b) CAB2, c)
LS1, d) LS2, e) IC1, f) IC2, g) FR1 and h) FR2. ......................................... 85
Figure 4-10: Estimation of the experimental mechanical test stiffness by µCT-
FEA (a) and UCT-FEA (b). LS1 and LS2 (x), CAB1 and CAB2 (□),
IC1 and IC2 (○), FR1 and FR2 (Δ). ............................................................. 86
Figure 4-11: Correlation between bone replicas density and (a) mechanical test
stiffness, (b) µCT-FEA stiffness, (c) UCT-FEA stiffness. LS1 and
LS2 (x), CAB1 and CAB2 (□), IC1 and IC2 (○), FR1 and FR2 (Δ). .......... 86
Figure 4-12: SVF measurement for all the bone replicas samples obtained from
µCT-FEA and UCT-FEA, showing that the UCT-FEA overestimates
the SVF for all the samples but CAB1 and CAB2 have a noticeably
higher overestimation of the SVF compared to the other samples. ............. 87
Figure 4-13: Cross-section area images for CAB1 (top) and FR1 (bottom),
black = microCT and UCT overlap, dark grey = UCT only, light grey
= microCT only and white = no microCT or UCT. ..................................... 88
Figure 4-14: Cross-sectional area measurement along the z axis for two UCT-
FEA models, CAB1 (top) and FR1 (bottom). .............................................. 90
Figure 4-15: Summery of the UCT-FEA study in Chapter 4. .................................... 92
Figure 5-1: Photograph of the Perspex cylinder samples; P25 and P35 with 25
and 35 mm diameters respectively, and the plastic bone samples; PB1,
PB2 and PB3. ............................................................................................. 101
Figure 5-2: Schematic representation of the UCT system. The robotic arm is
used to position the transducers such that the sample is approximately
centered between the transducers in the xy plane and positioned at the
correct z position for imaging. The robotic arm also rotates the
transducers during acquisition. .................................................................. 103
Figure 5-3: Ultrasound signal detected (right) through a hollow 35 mm
diameter Perspex cylinder (left). Ultrasound waves are emitted from
the left transducer and detected on the right transducer. As each wave
propagates from the transmitting transducer it experiences different
propagation speeds. Each wave can also experience different path
lengths if there is significant refraction occurring. The combination of
both effects result in a time delay registered at the receiving
transducer compared to propagation through water alone. Each
transducer element signal is normalized to the maximum value
separately for clarity. ................................................................................. 107
Figure 5-4: From left to right: The sample dimensions from optical
micrographs, PE-UCT reconstructions, PE-T-CT reconstruction, T-
UCT reconstruction. From top to bottom: P25, P35, PB1, PB2, PB3.
The scale is the same for all images which are 60 mm by 60 mm in
size and the tick marks are 15 mm apart. ................................................... 108
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List of Tables
Table 2-1: Acoustic impedance values of different tissue materials. ......................... 23
Table 3-1: The UCT diameter for the samples compared to the actual measured
diameter from the test pieces. ...................................................................... 66
Table 5-1: Tabulated results of the PE-UCT measured bone diameter and PE-
T-UCT measured SOS and shell thickness. Actual values refer to
measurements from either optical micrographs or SOS measurements
of bulk material. Bottom numbers in each cell are the measured values
minus the reference values (if applicable). Standard deviations (𝜎) are
also shown when appropriate. Blue = measured value overestimated
cf. actual value and red = measured value underestimated cf. actual
value ........................................................................................................... 110
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List of Abbreviations
2D Two Dimensional
3D Three Dimensional
ART Algebraic Reconstruction Technique
BMD Bone Mineral Density
BUA Broadband Ultrasound Attenuation
CQUT Compound Quantitative Ultrasonic Tomography
CT Computed Tomography
DAQ Data Acquisition
DXA Dual-Energy X-ray Absorptiometry
FBP Filtered Back Projection
FEM Finite Element Analysis
HR High Resolution
HR-MRI High-Resolution Magnetic Resonance Imaging
MR Magnetic Resonance
MRI Magnetic Resonance Imaging
µCT Micro-Computed Tomography
PA Phased Array
PE Pulse-Echo
PET Positron Emission Tomography
PE-UCT Pulse-Echo Ultrasound Computed Tomography
PVDE Polyvinylidene Difluoride
PZT Lead Zirconate Titanate
QCT Quantitative Computed Tomography
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QUS Quantitative Ultrasound
RC Reflection Coefficient
RF Radio-Frequency
ROI Region of Interest
SIRT Simultaneous Iterative Reconstruction Technique
SOS Speed of Sound
SPECT Single Photon Emission Computed Tomography
SVF Solid Volume Fraction
TC Transmission Coefficient
TOF Time of Flight
T-UCT Transmission Ultrasound Computed Tomography
UCT Ultrasound Computed Tomography
UT Ultrasound Technology
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Symbols
𝐴 Amplitude V
𝑑 Length m
𝐷 Sample outer diameter m
𝐸 Young’s modulus MPa
f Frequency Hz
F Force N
h Depth m
I0 Intensity of incident beam W m-2
I Intensity of propagated beam W m-2
𝑡 Time s
∆𝑡 Apparent delay time s
𝑇 Thickness m
𝑇′ Reduced thickness m
𝑣 Velocity m s-1
w Width m
x Distance m
Z Acoustic impedance Kg sm-2
z Displacement m
α Attenuation coefficient dB m-1
β Ultrasound attenuation dB
λ Wavelength m
µ/ρ Mass attenuation coefficient cm2 g-1
σ Areal density g m-2
Towards Ultrasound Computed Tomography Assessment of Bone xvi
Towards Ultrasound Computed Tomography Assessment of Bone xvii
Statement of Original Authorship
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.
QUT Verified Signature
Towards Ultrasound Computed Tomography Assessment of Bone xviii
Towards Ultrasound Computed Tomography Assessment of Bone xix
List of Publications
• Althomali, M.A.M., Wille, M.-L., Shortell, M.P., and Langton, C.M.,
Estimation of mechanical stiffness by finite element analysis of
ultrasound computed tomography (UCT-FEA); a comparison with X-
ray µCT based FEA in cancellous bone replica models. Applied
Acoustics, 2018. 133: p. 8-15.
https://doi-org.ezp01.library.qut.edu.au/10.1016/j.apacoust.2017.12.002
• Shortell, M.P., Althomali, M.A.M., Wille, M.-L., and Langton, C.M.,
Combining Ultrasound Pulse-Echo and Transmission Computed
Tomography for Quantitative Imaging the Cortical Shell of Long-Bone
Replicas. Frontiers in Materials, 2017. 4(40).
https://doi.org/10.3389/fmats.2017.00040
• Althomali, M.A., Wille, M-L., Koponen, J., Shortell, M.P., and Langton,
C.M., Estimation of Mechanical Stiffness by Finite Element Analysis of
Ultrasound Computed Tomography (UCT-FEA); a Comparison with
Conventional FEA in Simplistic Structures. Submitted to the journal
Ultrasonics on 14th December 2017.
Towards Ultrasound Computed Tomography Assessment of Bone xx
Chapter 1: Introduction xxi
Acknowledgements
First and foremost, I thank Almighty God for giving me the strength and ability
to complete my thesis and blessing me with many wonderful people who helped and
support me during the PhD journey.
I would like to extend my deepest gratitude to my previous principle supervisor
Professor Christian Langton for his guidance, support and advice throughout this
research. This project would not be accomplished without your help.
I am very grateful to my current principal supervisor Dr Marie-Luise Wille for
valuable suggestions and insightful comments. Your encouragement is much
appreciated.
Thanks to my associate supervisors: Dr Devakar Epari for advices and
suggestions related to FEA, Professor Wageeh Boles for encouragement and useful
discussions. The excellent help from Dr Matthew Shortell for binarizing and
converting UCT images to STL files and Janne Koponen for UCT image
reconstruction codes is gratefully acknowledged.
I must also send warm thanks to my beloved parents for their constant
encouragement and support to achieve my goal. Mum and Dad, acknowledging you is
the least of what I can do to show my appreciation. I would also like to extend my
sincere appreciation to my brothers and beloved sister. I am very delighted and lucky
to have such a family.
Lots of thanks go to my wife for her great patience and endless encouragement.
Without her support and help, this project would not have been possible. Thank you
very much Ebtisam!
I would like to take the chance to thank my friends and desk neighbours at IHBI:
Ezzat, Saeed, Majdi, Ali, Mohammed and Yasser. Thank you all for insightful
discussions and constant encouragement.
Chapter 1: Introduction 1
Chapter 1: Introduction
This chapter outlines the background (section 1.1) and hypothesis of the research
(section 1.2), and its aims and objectives (section 1.3). Section 1.4 describes the
significance and scope of this research and provides definitions of terms used. Finally,
section 1.5 includes an outline of the remaining chapters of the thesis.
1.1 BACKGROUND OF THE RESEARCH PROBLEM
Medical imaging is an indispensable tool for medical professionals, yielding
clinically useful data about the human body both in terms of general anatomy and
clinical research, and in particular, the diagnosis of pathological conditions and the
assessment of treatments [1, 2]. Medical imaging refers to the methods and processes
involved in creating and visualizing the areas of the human anatomy not visible to the
naked eye [3, 4]. A clear anatomical image helps identify and distinguish a region of
interest (diseased tissue) from the surrounding healthy and normal tissues [3, 5, 6]. The
era of modern medical imaging was launched in 1895 when Wilhelm Conrad Roentgen
discovered the X-ray [7]. This discovery paved the way for sophisticated imaging
methods, such as X-ray computed tomography (CT), nuclear medicine, magnetic
resonance imaging (MRI) and ultrasound [4, 8].
The discovery of diagnostic ultrasound is attributed to Ian Donald in the 1950s
and was based on Sonar (Sound Navigation and Ranging) application [9, 10].
Ultrasound has become a fundamental technique of medical imaging which can be
implemented for different purposes especially diagnosis and therapy. After X-ray
imaging, ultrasound is the most widely used imaging technique in medicine, being
used in more than 25% of all medical imaging procedures [9, 11, 12]. This technique
has the advantages of being radiation-free, non-destructive [13], inexpensive and
easily portable [14]. In addition, it is readily accessible which is very useful for the
assessment of musculoskeletal tissues. Moreover, ultrasound allows real-time
imaging; hence, it is beneficial for interventional procedures including injections and
biopsies. These features have contributed to significant developments in the ultrasound
field such as tissue characterization and tomographic images creation [8, 12, 15].
Chapter 1: Introduction 2
Quantitative ultrasound (QUS) based on the transmission mode, is a non-
imaging technique that is extensively used for bone assessment, especially for the
diagnosis of osteoporosis disease in cancellous bone, for which QUS is considered an
alternative method for dual-energy X-ray absorptiometry (DXA). QUS is an ultrasonic
mechanical wave which makes it preferable for such assessments, since it enables the
use of ultrasound parameters (for example velocity and attenuation) to assess the
structure and mechanical properties of bone [16, 17].
Qualitative 2D images of the human body can be readily achieved using
ultrasound scanning, referred to as B-mode (brightness-mode). The creation of 3D
images can also be obtained by combining multiple 2D B-mode images from different
positions [18]. 3D imaging can also be enables by matrix array transducers, allowing
for native 3D imaging [19]. The conventional 3D ultrasound uses a low-cost and non-
ionizing beam. It has its drawbacks, however, such as being relatively time consuming
and producing images with low resolution (blurring) due to registration inaccuracies
and, analogous to conventional 2D sonography. It is also operator dependent, so it is
limited by sonographer experience and skills that results in a huge difference in the
accuracy of diagnosis [20-23]. Ultrasound computed tomography (UCT) has become
the first option to resolve such issues [24].
UCT is a novel technique which allows for the creation of 3D images and
quantitative analysis. The fixed and automated setup of UCT makes it operator
independent and results in images with high resolution [25-28]; this is especially useful
for soft tissue diagnostics, such as breast cancer in women [21, 29, 30] but is also used
for imaging of the skeleton [31]. Compared to the intensive work of using UCT for
assessing soft tissue, researchers paid little attention to the use of UCT for bone
mechanical integrity assessment.
Destructive mechanical testing is the gold standard to predict bone strength in
vitro. However, only numerical simulations can be used to compute and predict bone
strength in vivo. Finite element analysis (FEA) is a numerical technique where the
geometry is based on the derived 3D images of the bone, and was first introduced to
assess the mechanical integrity of bone over 40 years ago. Combinations of FEA and
in-vivo bone imaging data have significantly improved the estimation of bone
mechanical behaviour compared to imaging alone [32-35]. To our knowledge, the
Chapter 1: Introduction 3
combination of UCT and FEA has not previously been reported, so we anticipate that
UCT can be combined with FEA to predict the stiffness of bone.
The goal of this research project is to develop and scientifically validate an
ultrasound computed tomography system with particular emphasis on imaging bone
replica samples and its mechanical integrity assessment. Factors that will be
considered include quantification of internal structure along with tissue properties,
such as bone stiffness and cortical thickness of long bones.
1.2 HYPOTHESIS
The primary hypothesis is that UCT is capable of imaging solid bodies such as
bones and providing high quality and useful quantitative information of bone tissues.
The secondary hypothesis is that UCT may be combined with FEA and be
equally efficient to predict stiffness as conventional FEA that is based on designed 3D
models or derived 3D images.
The third hypothesis is that the pulse-echo and transmission UCT may be
combined and be efficient for quantitative imaging of bones.
1.3 AIM AND OBECTIVES
The aim of this project is to provide a scientific validation of an UCT system for
bone imaging and fracture risk assessment, incorporating FEA.
The scientific performance, including image and parameter artefact reduction,
of the recently developed UCT system will be optimised through a combination of
computational enhancements and experimental studies.
The combined twin-array transmission (T) and pulse-echo (PE) mode imaging
will be considered. T-mode is aimed at quantifying internal structure and tissue
properties whereas PE-mode is aimed at high spatial accuracy and resolution image of
bone surface.
1.4 SIGNIFICANCE OF RESEARCH
Destructive mechanical test is the true gold standard for bone strength
assessment, however, it is not feasible to be applied in a living subject and alternative
methods are required. Several non-invasive in-vivo techniques have been developed
and implemented to serve as surrogates for bone strength assessment. Bone mineral
Chapter 1: Introduction 4
density (BMD, g cm-2) describes the amount of calcified mineral per unit area of the
bone, generally estimated using DXA. However, it has been shown that areal BMD
estimation alone is insufficient to accurately determine the increase of osteoporotic
fracture risk with age, which is roughly seven times greater than what can be explained
by BMD alone [36-38]. Quantitative computer tomography (QCT) is a 3D X-ray
imaging modality and provides an estimate of the volumetric BMD (g cm-3); through
image segmentation, it also facilitates separate analysis of cortical and cancellous
components [39, 40]. However, QCT is not used in a routine medical environment as
it exposes the patient to a higher radiation dose (60 µSv) compared to the low dose for
DXA (1 µSv) [41].
QUS has successfully been introduced as an alternative diagnostic technique to
assess osteoporotic fracture risk [16]. It has many advantages over DXA and QCT: it
does not use ionizing radiation, it is easy to use, less expensive, and has been shown
to provide a prediction of osteoporotic fracture risk comparable to DXA, particularly
utilising broadband ultrasound attenuation (BUA) [42-44].
UCT is a promising system, which is capable of providing quantitative
information on the acoustic properties, mainly attenuation and speed of sound, of the
different tissue segments. While most of the UCT studies are applied on soft tissue,
researchers have given little attention to the use of such system for bone imaging and
this is because of the intricacy in ultrasound propagation through bone. Also advanced
reconstruction tools are required for the anisotropic propagation of ultrasound inside
bone due to a high contrast existing between the bone and surrounding soft tissue.
Despite the limitations of applying UCT to bone, it remains an attractive non-
invasive technique that has the same advantages as QUS, being non-ionising and cost-
effective. Further, in addition to 2/3D imaging, UCT may provide quantitative
information of acoustic properties, such as ultrasonic attenuation and speed of sound,
which depends on bone structure.
This study will develop and validate an improved ultrasonic computed
tomography system and investigate the capability of this system to obtain high quality
ultrasonic images and provide more accurate assessment of bone using FEA and
combined transmission UCT (T-UCT) and pulse-echo UCT (PE-UCT) imaging.
Chapter 1: Introduction 5
1.5 THESIS OUTLINE
This is a thesis-by-publication; chapters are therefore based on publications. The
outline of this research can be seen in (Figure 1-1).
Chapter 2 will provide an overview of bone anatomy and osteoporosis health
burden. Moreover, it will demonstrate different approaches that are currently used for
bone strength assessment including gold standard mechanical test, FEA and non-
invasive medical imaging techniques. Ultrasound will be described in more details as
an alternative method, especially the use of UCT. This chapter will be concluded by
the knowledge gap that has been covered by this thesis.
Chapter 3 will present a proof of concept study that shows the feasibility of
ultrasound computed tomography based FEA to estimate the stiffness of plastic rod
phantoms with variable thicknesses that are mimicking bone tissue. This chapter is a
paper that has been submitted to the journal Ultrasonics.
Chapter 4 will demonstrate the feasibility Ultrasound computed tomography
derived finite element analysis (UCT-FEA) for assessment of the mechanical integrity
of cancellous bone replicas. This chapter is a paper that has been published in the
journal Applied Acoustics.
Chapter 5 will show a modified UCT system that has been developed by
combining transmission (T) and pulse-echo (PE) imaging, T-mode is aimed at
quantifying internal structure and tissue properties (e.g. bone strength), whereas PE-
mode is aimed at high spatial accuracy and resolution image of bone surface. This
chapter is a paper that has been published in the journal Frontiers in Materials.
Chapter 6 will provide a general discussion that links the results of the papers,
and highlight the limitations of this research as well as the future work of developing
our UCT system.
Chapter 1: Introduction 6
Chapter 1: Introduction 7
Figure 1-1: Schematic diagram demonstrating the research outline.
Chapter 1: Introduction 8
Chapter 2: Literature Review 9
Chapter 2: Literature Review
This chapter explains the bone anatomy in general and how it is affected by
osteoporosis. Furthermore, it describes the current techniques that are used for bone
assessment, with more focus on quantitative ultrasound imaging including ultrasound
physics, propagation through solid and complex media, and instrumentation.
Ultrasound computed tomography is described with its usefulness in soft tissue
assessment. Finally, the knowledge gap of this study is highlighted.
2.1 BONE ANATOMY
The skeleton of an adult human consists of 206 bones which support the body
with their rigidity and hardness and are unique in their ability for regeneration and
repair. Bone has an important role in protecting the vital organs, provides a
microenvironment for bone marrow, acts as a mineral storage for calcium homeostasis,
and is also an endocrine organ that secretes and stores growth factors and cytokines
[45]. As a living material, bone falls into two main categories (Figure 2-1): (1) compact
cortical bone forms the outermost layer that can be found on all bones and is
considered to be solid and dense tissue. The porosity in this type of bone ranges
between a few percent to 10%. (2) Cancellous (or trabecular) bone, the inner part of
bones, has a highly porous structure with open-celled network made of rods and plates,
termed trabeculae. This interconnected network is filled with bone marrow. Human
cancellous bone has a porosity range between 50% and 90% [46, 47].
Bone is an amalgam of supporting cells and nonliving material. There are four
main bone cells, osteoblasts, osteocytes, osteoclasts and lining cells. Cells play an
important role in maintaining the mechanical properties of bone and mediate calcium
homeostasis of the body. The living cellular component of bone represents only 2–5%
of its volume, whereas the nonliving material makes up the remaining 95-98% [48]. It
is the nonliving material that gives the bone its basic mechanical properties of
hardness, stiffness, and resiliency. This nonliving material consists of a mineral-
encrusted protein matrix (also called osteoid), with the mineral comprising about half
the volume and the organic matrix the other half. The organic component is mainly
collagen I, which comprises 90% of the organic matrix [49].
Chapter 2: Literature Review 10
Figure 2-1: 3D structure of bone shows the two types of bone, cortical and cancellous [48].
Bone undergoes a continuous remodelling throughout life, a process which
involves resorption, when osteoclasts remove old bone, and replacement, during which
osteoblasts lay down a new bone matrix that is subsequently mineralized. The
remodelling process is essential for bone to stay healthy and adapt to mechanical
change by replacing old microdamaged bone; it also regulates plasma calcium
homeostasis to preserve bone strength [50]. In advanced age, the imbalance between
resorption and formation during bone remodelling leads to decreased bone mass and
strength, which eventually causes the bone fragility syndrome known as osteoporosis
[51].
Chapter 2: Literature Review 11
2.2 OSTEOPOROSIS
Osteoporosis is a skeletal disease which is described as a significant decrease in
the bone mass with a decay of the cancellous bone microarchitecture [52]. This
condition leads to bone weakness and increased fracture risk even under low stress
[53]. Osteoporosis is attributed to an alteration in biochemical and hormonal functions
[54] and is a worldwide health issue that mainly affects persons above the age of 60.
After this age, one-in-two women and one-in-three men will experience a fracture as
a result of osteoporosis and the number of hip fractures due to osteoporosis is predicted
to rise four-fold within the next thirty years. Hip, spinal vertebrae and wrists are the
parts of the skeleton most affected by osteoporosis [55]. The cortical shell thickness
of long bones can be used to determine the osteoporotic fracture risk [56-59].
Figure 2-2: Sectional photographs of the human vertebra showing (a) normal and (b) osteoporotic
cancellous bone, the latter exhibiting a reduction in bone density and loss of structural integrity [60].
2.3 DESTRUCTIVE MECHANICAL TEST
Destructive testing is usually applied to understand the material behaviour under
different loads, and determines the mechanical properties of the material such as
strength (a measure of the load that a material can withstand before breaking), stiffness
(a measure of the material deflection under an applied load) and toughness (a measure
of the required energy to fracture a material). Destructive mechanical testing is the
gold standard for assessing the mechanical behaviour and bone properties in-vitro.
This involves the measurement of different parameters including bone stiffness, yield
Chapter 2: Literature Review 12
point and fracture load. The mechanical testing also allows to derive an estimate of the
Young’s modulus of the tested bone based on the measured stiffness and the geometry
[61-64]. The obtained parameters serve as an input for mechanical simulations, such
as finite element analysis, which is described in section 2.5.
Despite being a straightforward method and more realistic than non-invasive
method, mechanical testing is not applicable to assess bone strength in-vivo due to its
destructiveness, and even though a direct mechanical test can be used in-vitro, a
sample can be tested once only. This limits the assessment of bone mechanical
properties that are orientation dependant, hence alternative methods are required.
2.4 CLINICAL ASSESSMENT OF OSTEOPOROTIC FRACTURE RISK
The development of modern evidence-based medicine was greatly enhanced by
devices which enabled visualization of the internal structures of the human body and
which also became an intermediate between patient and doctor [65]. Medical imaging
has become the most important technique with which to provide fine details of human
body anatomy and its physiology. It is, therefore, important for different medical
applications such as disease diagnosis, therapy and clinical research; e.g. prediction of
bone mechanical integrity [1, 4, 6, 66]. There are a number of medical imaging
techniques available for the clinician and the key difference between them is the
energy source that is required to produce the images, which are referred to as
modalities. The most common non- invasive in-vivo methods currently used for bone
assessment are X-rays, nuclear medicine, magnetic resonance imaging (MRI) and
ultrasound. Each imaging modality has its own application niche within the medical
field.
2.4.1 X-ray Imaging
Modern medical imaging traces its history back to November 1895, when the
German physicist William Roentgen discovered the X-rays, and captured the now
famous images of the bones of his and his wife’s hands (Figure 2-3 (left)) [67, 68].
Roentgen did not fully understand the nature of these rays, so he called them X-rays
as “x” usually stands for the unknown [7]. X-ray imaging is based on electromagnetic
waves with high frequency characteristics which enable them to pass through the body
where their degree of absorption varies from tissue to tissue depending upon its density
[65]. X-rays have energies in the range of 1–500 keV and wavelengths ranging from
Chapter 2: Literature Review 13
6×10-3 to 125×10-2 nm [69]. In clinical X-ray imaging, the production of X-rays occurs
inside a vacuum tube when electrons at very high speeds attack a metal. When X-rays
penetrate the human body, parts of the beam’s energy is absorbed, whereas other parts
are attenuated. The rays are detected by a detector or captured on photographic film
on the opposite side of the body thus producing an image. This mode of imaging is
referred to as planar X-ray imaging which results in 2D image of the tissue as in Figure
2-3 (left) [70].
Figure 2-3: (left) 2D X-ray image of Roentgen's wife hand [65] and (right) 3D CT coronal image of the
hip [71].
The conventional planar imaging is insufficient to produce the resolution
necessary to view finer details hidden within tissues, so the slice imaging methods
(tomography) (also known as computed tomography or CT) was developed by
Hounsfield and Cormack in the early 1970s [7]. They combined computer technology
with an X-ray system in which the X-ray source and detectors rotate around the
scanned object (Figure 2-4) to obtain multiple projections of the same tissue from
different angles [72]. The resulting 2D cross-sectional images are then reconstructed
by computer algorithms to produce 3D images (Figure 2-3 (right)).
Chapter 2: Literature Review 14
Figure 2-4: CT acquisition set up; a) third-generation geometry, where the X-ray source and detectors
are rotated around the object, b) fourth-generation geometry, where the source is rotated inside a fixed
detector ring [73].
Bone density and its quality are two major metrics that are assessed for
symptoms of osteoporosis using the various imaging techniques. Bone mineral density
(BMD) refers to the amount of mineral substance per unit area of the bone. The quality
of bone reflects the component properties such as bone architecture, bone remodelling,
mineralization, and microfractures [74]. Dual energy X-ray absorptiometry (DXA) and
quantitative X-ray computed tomography (QCT) are the common clinical X-ray based
methods used for bone mineral density measurement.
DXA is considered the gold standard technique and is most commonly used for
osteoporosis diagnostics by virtue of the sensitivity of X-ray absorption to calcium,
the predominant inorganic component of bone [75]. The X-ray method allows the
measurement of mineral content of all bone in the body, but is especially well suited
for areas such as lumbar spine and the proximal femur. It works on the principle of
measuring the transmission of two beams that pass with different energies (high and
low energies) through the region of interest in the bone. DXA is a 3-component system
for body composition, i.e. soft tissue and bone mineral or fat and lean mass in the
absence of bone. The transmission of radiation through the body is given by:
𝐼𝐿,𝐻 = 𝐼0𝑒−[(
𝜇
𝜌)
𝑆
𝐿,𝐻 𝜎𝑆 + (
𝜇
𝜌)
𝑏
𝐿,𝐻 𝜌𝑏]
(Eq. 2.1)
Where 𝐼0 and I are the X-ray intensity before and after passing through a material
respectively, H and L denote the high and low energy of the two X-ray beams
respectively, σ is the areal density (g cm-2), (µ/ρ) is the mass attenuation coefficient
Chapter 2: Literature Review 15
(cm2 g-1) and subscripts s and b respectively represent soft tissue and bone [76]. DXA
has the advantage of testing a patient with an X-ray dose that is up to 90% less than a
standard chest X-ray. On the down side, when using DXA in the peripheral sites and
proximal femur there is a limitation as to the accuracy of the BMD value which affects
the prediction power of the fracture risk, as well as the treatment decisions [77]. Also,
it only provides 2D images and therefore no volumetric BMD data [75].
Compared with DXA, quantitative computed tomography (QCT) is a 3D
imaging technique, which can be performed using either single or dual X-ray source.
It provides separate measurement of cortical and trabecular bone [78]. Moreover, QCT
is more accurate for measuring the volumetric BMD of bone and more sensitive to
changes in BMD [77]. Despite the accuracy of QCT, it is rarely used in routine tests
since it exposes the patient to a high radiation dose. Furthermore, both DXA and QCT
have drawbacks, such as cost and the necessity of space to house large machines [60].
X-rays imaging is non-invasive and fast but its major disadvantage is the use of
ionizing radiation, which carries with it an increased risk of cancer for patients and
practitioners alike [79, 80].
2.4.2 Magnetic Resonance Imaging
In most atoms, the atomic nucleus has a magnetic moment which arises from the
spin of the protons and neutrons making it behave as a small magnet, 1H with spin of
½ is the best example. MRI is based on imaging the distribution of protons in tissue
[81, 82]. This technique can visualise organs and tissues (Figure 2-5) using radio
waves and the resonance of magnetic fields to produce images. MRI involves the
emission of strong radio waves that can propagate through the body. These waves
cause hydrogen atoms to vibrate which results in a detectable radiation emission that
can be assembled into an image with the use of a computer [65, 83]. The image density
is affected by two factors: the number of protons in the imaged object and the physical
properties of the tissue.
With the recent advances in MR imaging hardware and software, it has become
possible to obtain high resolution (HR) MR images of long bone and trabecular bone
using the signal generated from the surrounding soft tissue and the medullary canal.
Such HR images have been obtained from bone samples in vitro as well as in the distal
radius, the phalanges, and the calcaneus in vivo [84-87].
Chapter 2: Literature Review 16
MRI has many advantages compared to the other medical imaging techniques.
First of all, it uses non-ionizing energies, which eliminates the danger of genetic
mutations implicit with the use of X-rays and radioisotopes. Moreover, the penetration
effects can be ignored since the images show excellent soft tissue contrast [70, 88]. It
can be used for many applications, such as the evaluation of heart, kidney, liver,
bladder and blood vessels [89-93]. There are, however, some disadvantages with MRI,
namely: (i) slow image acquisition compared to CT and ultrasonic modalities; (ii)
significantly more costly than other techniques; (iii) it cannot be used with patients
with metallic implants; (iv) the images can be rendered blurry and distorted by even
the slightest motion such as breathing; (v) and contrast media are known to cause
allergic reactions in some patients [65, 70].
Figure 2-5: MRI image of the from the distal region of the femur [94].
2.4.3 Quantitative Ultrasound Characterisation of Bone
Quantitative ultrasound (QUS) is a non-imaging method that has successfully
been used as a diagnostic technique to assess osteoporotic fracture risk and was first
described by Langton et al in 1984 [95]. In general, QUS is based on a mechanical
wave, hence its behaviour in bone is different to that of X-rays. A number of features
can be measured by QUS, such as absorption, velocity and reflected waves inside the
bone and from its interfaces [96]. QUS has become an alternative method to X-ray
systems for several reasons. First of all, it does not use ionizing radiation; it is easy to
use; less expensive; and provides a prediction of fracture risk comparable to DXA [43,
97]. The two main parameters typically used for bone diagnosis with QUS are: speed
of sound through the bone (SOS, ms-1) and broadband ultrasonic attenuation (BUA,
Chapter 2: Literature Review 17
dB MHz-1) [96, 98, 99]. A number of studies have shown that QUS parameters provide
a prediction of osteoporosis and bone fracture risk comparable to DXA, especially with
the use of BUA [42-44, 100, 101]. In order to use ultrasound imaging quantitatively to
estimate bone mechanical integrity and predict osteoporotic fracture risk, a
development of an ultrasound computed tomography (UCT) system is required. This
will be discussed in more detail in section 2.6.
2.4.4 Overview of Medical Imaging Modalities for Bone Assessment
For bone assessment, a comparison of the various medical imaging techniques
available reveals that each has its advantages and disadvantages. X-ray radiography is
fast, easy to use, able to penetrate the bone, and provides good spatial resolution;
however, it exposes the patient to ionising radiation and can only reveal gross
anatomical structure. X-ray CT has the same advantages as standard X-ray in addition
to providing slice-through images of the bone, but exposes the patient to a higher
radiation dose. Nuclear Medicine provides physiological functional information and
diagnosis of bone metastases; however, besides having a relatively limited range of
applications, it also exposes the patient to ionizing radiation. MRI offers excellent soft
tissue contrast and identifies the bone cortex using the signal of the surrounding tissue;
but it is expensive, and generally only available at major hospitals, hence it is not
routinely used for bone scanning.
Compared to the use of these imaging modalities to estimate the mechanical
integrity of bone, ultrasound imaging has been introduced as an alternative imaging
technique that is non-invasive, low cost, widely available, easy to use, non-ionizing
and yields real time imaging; however, it has poorer spatial resolution than X-ray
radiography and MRI and suffers from a number of artefacts that are described in
section 2.7.1.
2.5 NON-DESTRUCTIVE NUMERICAL METHOD: FINITE ELEMENT
ANALYSIS
Non- destructive and surrogates mechanical simulations can be used to assess
bone stiffness in-vivo. These simulations are significant computational tools to provide
better understanding of the effects of bone microstructures alterations on its
mechanical properties. Finite element analysis (FEA) is a non-destructive numerical
technique which can be used to predict the deformation of a 3D structure under an
Chapter 2: Literature Review 18
applied load; which in turn may provide a measure of mechanical stiffness (N mm-1),
and it was used first in orthopaedic applications in the early 1972s [102, 103].
The FEA method divides the structure into a number of simple parts, called finite
elements that are connected by points termed nodes. Material properties are defined to
each element, for example, density, Young’s modulus and Poisson’s ratio in the case
of static, elastic analysis of an isotropic material structure. Constraints and loads may
then be applied to the structure at defined locations. The displacement of each node is
determined by solving inter-connected simultaneous equations following Newton’s
First Law, that integrate the material properties, loads, constraints and geometry of the
test sample. With regard to bone assessment, finite element analysis is sensitive to both
material and structural properties. FEA requires two inputs, first, in-vivo imaging data
to assess bone structure, and second, mechanical properties of the material such as
density, Young’s modulus and Poisson’s ratio. Proper software packages should be
used to solve the image-based FE models such as Ansys (ANSYS INC, Canonsburg,
Pennsylvania, USA) and Abaqus (Dassault System, France).
The computer time needed (and thus the costs of the analysis) depends
progressively on the number of elements applied, and on the element type. The
solution obtained with this method is approximate in the sense that it converges to the
exact solution for the model when the mesh density approximates infinity. Thus, the
accuracy of an FE model can be checked by refining the mesh and comparing the
results obtained with the refined mesh to the original one, which is called a
convergency test. The medical imaging-based FEA will be described further in chapter
3 and 4.
Several studies demonstrated that FE modelling is a promising technique to
predict the fracture load and monitor the changes in bone strength. Cody et al. reported
that more than 20% of the variance in predicted strength could be explained by QCT
based FE method but not by DXA or QCT alone [32]. Zysset et al. also concluded
that QCT-FEA is more reliable than densitometric variables to predict bone strength
in the most common osteoporotic fracture sites [34].
Chapter 2: Literature Review 19
2.6 ULTRASOUND PHYSICS, INSTRUMENTATION AND
CONVENTIONAL IMAGING
It is well known that ultrasound is a promising technique that has been used as
an alternative method for bone assessment. Being dependent on the structure and
mechanical properties, ultrasound parameters such as ultrasound attenuation and
velocity can provide a prediction of bone fracture risk [44, 104, 105]. Ultrasound
computed tomography (UCT) is a novel technique that is capable of providing 3D
images and quantitative analysis using ultrasound velocity or attenuation
measurements. This brings our attention to investigate the feasibility of the UCT
method to estimate the mechanical integrity of bone with a perspective of osteoporotic
fracture prediction. Before moving forward, the fundamental physics and
instrumentation of ultrasound imaging, along with UCT techniques, will be explained
in more detail in the following sections.
2.6.1 Physics of Ultrasound Propagation
Ultrasound is a mechanical wave with frequencies that exceed 20 kHz, which is
above the threshold of human hearing [106]. The ultrasound is transmitted through a
medium (fluids or solid or gas) by pressure waves, which causes the molecules to
oscillate about their status. The repetition of the movement of these particles is called
a cycle, whereas the number of cycles per second, measured as Hertz (Hz), is the
frequency of the sound wave [106]. The propagation of sound represents the
transmission of pressure changes, caused by oscillating molecules interacting with
adjacent molecules, radiating away from the source of sound. At its most basic, there
are two types of waves: longitudinal and transverse. Longitudinal waves are waves in
which the molecules of a medium vibrate in a parallel direction to the direction of the
wave motion (Figure 2-6a). In transverse waves, the movement of the molecules is
perpendicular to the wave direction (Figure 2-6b) [18]. All sound waves, including
ultrasound, are classified as longitudinal [107].
Chapter 2: Literature Review 20
Figure 2-6: Particle wave motion: (a) shows the longitudinal particle motion; (b) shows the transverse
particle waves. Only longitudinal waves can produce ultrasound waves that provide useful diagnostic
information [108].
Ultrasound has the same properties as audible sound waves such as frequency
(f), acoustic velocity, wavelength (velocity/frequency) [106]. When sound waves
propagate through a medium, the distance between two successive peaks (two
compression areas or two rarefaction areas) is referred to as the wavelength (λ).
Amplitude is the vertical distance (height, +peak to -peak) of a wave which represents
the change in magnitude of acoustic variables (Figure 2-7). The velocity of sound (𝑣)
is the speed of a wave when it is propagating through a medium, in other words it is
the transmission rate of the mechanical vibrations [18, 107].
Chapter 2: Literature Review 21
Figure 2-7: Sound wave properties [109].
2.6.2 Ultrasound Interactions with Tissue
The use of ultrasound for diagnostic or therapeutic reasons requires the
ultrasonic beam to be directed into the body, so the propagation of such waves through
tissues is affected by the interaction between these waves and the tissues. The types of
interactions include reflection, scattering, refraction, absorption and interference.
These interactions are influenced by the characteristics of ultrasound waves and the
physical properties of the propagated tissues. All these interactions, except the
interference, reduce the intensity of ultrasound beam, a phenomenon known as
attenuation [11, 20].
a) Interface Interactions
• Reflection
For diagnostic ultrasound, reflection is the main interaction of interest. When the
incident beam of ultrasound encounters the interface separating different tissues, part
of the beam will be reflected back as an echo and part of the beam will keep being
transmitted (Figure 2-8). The ratio of reflected over transmitted waves depends on the
difference in the acoustic impedance (or resistance) between the two different tissues
[18].
Chapter 2: Literature Review 22
Figure 2-8: Reflection and transmission of ultrasound depending on the acoustic impedance of
materials.
Acoustic impedance (Z, Kg s.m-2) is defined as the product of density (ρ) and the speed
of sound (𝑣).
𝑍 = 𝜌𝑣 (Eq. 2.2)
This physical property of materials describes the behaviour of its particles when
they are subjected to a pressure wave. Dense substances, such as bone, have a high
acoustic impedance due to the fact that movement of densely packed particles at a
specific velocity requires higher excess pressure (or energies) than materials that have
loosely packed molecules. The energy of the ultrasound will be totally transmitted if
two media have the same acoustic impedance. The amount of a sound wave that is
reflected is proportional to the acoustic impedance, such that if the difference in
acoustic impedance between two tissues is little then only a small fraction of the
ultrasound beam will be reflected, whereas most of it will pass straight through the
interface. If the acoustic impedance of the interface is large then a commensurately
larger fraction of the sound wave will be reflected and only a small fraction
transmitted. The amount of reflected and transmitted energies is determined by the
amplitude reflection coefficient (RC) and the amplitude transmission coefficient (TC).
𝑅𝐶 = (𝑍2−𝑍1
𝑍2+𝑍1) (Eq. 2.3)
Chapter 2: Literature Review 23
𝑇𝐶 = 2𝑍2
(𝑍2+𝑍1) (Eq. 2.4)
Where: Z1 and Z2 are the acoustic impedance values of medium 1 and medium 2
respectively [10, 110]. Specular reflection occurs when the interface between two
media is smooth and larger than the wavelength of the ultrasonic beam. Table 2-1
shows the acoustic impedance values for different tissue materials.
Table 2-1: Acoustic impedance values of different tissue materials.
• Refraction
Refraction occurs at a boundary between two tissues through which the
ultrasound travels at different velocities. This results in a change in the direction of
sound waves and if the difference in velocities is large enough it may lead to an
artificial change of the position of the imaged organ from its actual position. The
greater the change in the speed of sound in a medium the more the ultrasound wave is
refracted [111].
b) Propagation Interactions
• Attenuation
Attenuation is referred to as the reduction of wave energy of the ultrasound beam
by any mechanism. It is the sum of all effects of mechanisms, such as absorption and
Chapter 2: Literature Review 24
scattering [55]. The type of tissue that the ultrasonic wave is travelling through has a
considerable impact on the amount of attenuation, being greater in dense tissues, such
as bone, than soft tissues, such as fat depots or breast tissue; each tissue type has its
unique attenuation coefficient. Attenuation also depends on the frequency of the sound
wave (Eq 2.5), in which higher frequency sounds are more prone to attenuation than
lower frequencies [110]. The attenuation can be calculated at each frequency as:
20 log [𝐴𝑟(𝑓)
𝐴𝑠(𝑓)] (Eq 2.5)
where 𝐴𝑟(𝑓) and 𝐴𝑠(𝑓) are the reference and signal amplitude respectively at
frequency 𝑓.
• Scattering
Scattering as an interaction is very important in diagnostics since it provides the
image with much of the information about the internal texture of an organ. Scattering
is called non-specular reflection because the interface is small and equivalent to the
beam dimension [18]. Since the size of the boundary is equivalent or smaller than the
size of wavelength, the incident ultrasonic beam is reflected in many directions (Figure
2-9). Most of the scattered waves are, therefore, not recorded by the transducer and
those that are tend to be reflected echoes [112].
Figure 2-9: Diagram describing the scatter of an ultrasound beam interacting with a small object.
Chapter 2: Literature Review 25
• Absorption
The wave energy is absorbed by the tissue and transformed into heat. The rate
of absorption depends on tissue structure and components as well as the wave
frequency. The absorption coefficient for bone is significantly higher than for soft
tissue [106]. The absorption coefficient is defined as
𝐼𝑥 = 𝐼0 𝑒−𝛼(𝑓)𝑥 (Eq. 2.6)
Where 𝐼0 and 𝐼𝑥 are the intensities of the incident and propagated waves at
distance 𝑥 (m), and 𝛼(𝑓) is the attenuation coefficient that is frequency dependent
(dB m-1).
• Phase Interference
Interference occurs when two or more waves travel from the source through the
same tissue. Each point in the medium is affected by each wave, such that the pressure
at each point equals the sum of the pressure from each individual wave at that particular
point. Interference depends on the waves whether or not they are in phase.
Consequently, there are two types of interference: (1) constructive interference occurs
when the waves have the same frequency and are in phase (i.e. the peaks and the
troughs of the waves are matched). The sum of the amplitude from this kind of
interference is greater than each of the individual wave; (2) destructive interference
happens when the waves have the same frequency but are out of phase. The peaks and
troughs are not matched and the waves cancel each other out, reducing the amplitude
[113].
2.6.3 Ultrasound Instrumentation
The main component of an ultrasound device is the transducer which generates
the ultrasonic waves [114]. The ultrasound transducer (Figure 2-10) transforms an
electrical pulse into the ultrasound beam that is transmitted into the tissue. The
received pulse is subsequently converted back into an electrical signal that is
computationally processed and displayed [18]. Ultrasound transducers are based on
the piezoelectric effect, which refers to a material that is capable of producing an
electrical signal when subjected to an applied pressure. Most piezoelectric sensors are
made from crystalline materials; the most commonly used material in medical
transducers is the ceramic lead zirconate titanate (PZT) and a polymer film,
polyvinylidene difluoride (PVDF) [10, 106]. Quartz crystals are also used as a
Chapter 2: Literature Review 26
piezoelectric material in medical ultrasound transducers due to their superior
transmission features [18].
Figure 2-10: Ultrasound transducer components.
Ultrasound transducers can be categorized into two types: single-element probes
and phased-array probes. Phased-array (PA) transducers are multi-element transducers
which consist of several identical piezoelectric sensors working as a single probe.
These transducers can be used to generate signals that can be pulsed separately from
each element, which is capable of transmitting and receiving signals [115, 116].
Computer programs are used to control ultrasonic beam parameters such as: focal spot,
focal distance and angle of incidence [117]. The ultrasonic beam can be focused and
steered by applying time delays to the various elements (Figure 2-11). When the
elements are pulsed at time delays, a series of concentric waves can be created with
different wavefronts (envelope). This creates constructive interference wavefronts that
enables the energy to be focussed at a site of interest within the anatomical sample
[116, 118].
Chapter 2: Literature Review 27
Figure 2-11: Diagrams show the beam forming and time delay for firing and receiving multiple beams
[117].
Figure 2-12 illustrates how to focus the ultrasonic beam with a phased array for normal
and angled incidences.
Figure 2-12: Beam focusing principle for (a) normal and (b) angled incidences [117].
Chapter 2: Literature Review 28
The implementation of phase-array transducers has several advantages: (1) they
provide computer-controlled excitation of individual elements in a multi-element
probe to produce a focused ultrasound beam and modify the beam parameters; (2)
electronic scanning results in faster inspection; (3) enhanced signal to noise ratio
increases image resolution and detection probabilities; (4) the delay laws feature
contributes to better performance and simplifies the scanning procedure [117].
Simple RF System
• Transmission Mode
The simplest ultrasound system (Figure 2-13), operating in transmission mode,
consists of a Radio-Frequency (RF) transmitter connected to a transducer. In addition,
there is a receive transducer connected directly to an oscilloscope. The transmitter,
which provides either continuous or tone-burst signals, may be a signal generator of
sufficient output voltage (≈ 20 V). Alternatively, an electric spike generator provides
a spike of approximately 200 V with a width of approximately 100 ns. A rate generator,
which controls the pulse repetition frequency–i.e. the number of ultrasound pulses
produced per second–is incorporated within the spike generator, and typically operates
in the region of 500–1000 Hz. The generator should ideally provide a pulse to trigger
the oscilloscope.
Figure 2-13: Simple RF system (transmission mode), kindly provided by Prof. Christian Langton.
Chapter 2: Literature Review 29
• Pulse-Echo A-Scan System
In pulse-echo mode (Figure 2-14), a single transducer is used to both generate
and detect the ultrasound pulses.
In the receiver section the voltage signals produced by the transducer, which represent
the received ultrasonic pulses, are amplified. The amplified radio frequency (RF)
signal is available as an output for display or capture for signal processing. Receiver
circuit serves several purposes.
▪ Voltage ‘clipping’ circuit (a simple one being a pair of crossed diodes)
only allows signals within a small voltage band to pass - ensures
received echo signals (typically millivolts) are not lost due to the
magnitude of the transmission spike (several hundred volts).
Effectively, the amplitude of the ‘detected’ transmission pulse is
significantly cut, enabling the received echo signals to be seen.
▪ Provide amplified output signal.
▪ May also contain signal-processing functions including filtering to
shape and smooth return signals.
Figure 2-14: Simple RF system (pulse-echo mode), kindly provided by Prof. Christian Langton.
2.6.4 Conventional Ultrasound Imaging of Soft Tissue
There are several techniques of ultrasound imaging that can be used to obtain
qualitative images of a specific region within the human body. A-mode (amplitude-
mode) and B-mode (brightness-mode) are the two common scanning techniques used
to collect and display ultrasonic data [119]. A-mode (Figure 2-15 (left)) is a one-
Chapter 2: Literature Review 30
dimensional representation of the amplitude of the signal versus depth. In this scan,
the ultrasonic wave is directed into the region of interest and the echoes produced at
different interfaces along the beam path are received and displayed as vertical
deflections (peaks) along the scan line; the height of the peaks are proportional to the
amplitude. This type of scan is beneficial for simple structures and provides valuable
information for tissue characterization such as determination of the mechanical
properties of a tissue. In addition, it is also useful for detecting the reflectors
(interfaces) that cause the echoes. A-scan is not only used for pulse-echo mode but
also used for transmission [18, 119]. B-scan is a 2D image composed of A-scans
captured during the linear scanning (Figure 2-15 (right)).
Figure 2-15: Diagram depicting the creation of B-scan from A-scan.
Qualitative 2D images (Figure 2-16 (left)) of the human body can be readily
achieved using ultrasound scanning, referred to as the B-mode. In this technique, the
sample is scanned from various directions by moving the ultrasonic transducer across
the field of view, so that the echoes at each position of the transducer are collected.
The amplitude and timing of the collected echoes are calculated to create a composite
2D image. The advantage of this system is the ability to visualise the scanned object.
On this point, the amplitude of the received signals can be displayed using various
shades of grey [18, 119]. Three-dimensional (3D) images can also be created by
combining multiple 2D B-mode images from different positions as in Figure 2-16
(right) [18].
Chapter 2: Literature Review 31
Figure 2-16: (left) 2D B-scan image, and (right) 3D ultrasound image showing my daughter at 19 weeks
of gestation.
2.7 ULTRASOUND COMPUTED TOMOGRAPHY
In spite of the advantages of conventional 2/3D ultrasound imaging, the modality also
exhibits some disadvantages:
1) Poor spatial and temporal resolution due the assumption that ultrasound travels
through different tissues at the same velocity. In reality the velocity varies.
2) Speckle noise and shadowing effects that contribute to a reduction in image
quality.
3) The probe is manually guided, so the image contents and quality depend on
the operator which results in non-reproducible images [24, 25, 27].
4) Failure of providing quantitative information of ultrasound parameters such as
velocity and attenuation [20].
Ultrasound computed tomography was specifically developed to overcome these
disadvantages and since UCT has a fixed setup there is no deformation and post-beam
forming [24, 27]. The use of this technology was borne out of the necessity of being
able to produce 3D images with reproducible high quality and resolution as well as the
possibility of quantitative measurements of ultrasound parameters [28]. UCT is a novel
imaging technique that is capable of producing volume images with high spatial
resolution down to 300 µm [26].
Chapter 2: Literature Review 32
UCT also provides quantitative information of ultrasound properties
(attenuation, speed of sound) [120, 121]. UCT was first described in 1974 when
Greenleaf et al. reported the ability to produce ultrasonic images of the distribution of
the attenuation coefficient of ultrasound waves in tissue [122]. UCT can best be
described as combining X-ray computed tomography (CT) techniques (sans X-rays)
with ultrasound technologies [20]. After acquiring the ultrasound projections of an
object from varied directions, the image is reconstructed using reconstruction
algorithms such as iterative and back-projection algorithms [82, 123].
In UCT systems, two different architectures can be used for arranging the
ultrasonic transducers:
a) Two linear arrays facing each other and rotating around the sample (Figure
2-17a).
b) A ring-shaped transducer arrays surround the object (Figure 2-17b).
In both methods, the ultrasound signals for each slice, a 2D map of ultrasound
attenuation or velocity, of the sample are recorded and 3D images can readily be
assembled by repeating the data acquisition for different slices. Mostly, the opposite
two arrays are implemented using focused transducers where the transmitter sends
ultrasonic signals along a straight path to the receiver which measures the directly
transmitted and reflected signals. The circular setup is capable of recording transmitted
and backscattered signals from all angles [124].
Figure 2-17: Architectures of ultrasound tomographic systems. a) Two linear opposite transducer arrays
rotating mechanically around the object. b) Ring shaped array enclosing the object [124].
Chapter 2: Literature Review 33
Reflection-UCT is based on the measurements of reflected signals at the various
boundaries within the sample; it therefore yields qualitative mapping of object
interfaces; however, it is not particularly useful for achieving quantitative images of
acoustic parameters. The transmission-UCT technique, on the other hand, is generally
used to reconstruct cross-sectional images and obtain quantitative information of the
distribution of ultrasound parameters, such as time of flight (TOF) and attenuation
[125, 126].
Ultrasound transmission tomography is based on the processing of the received
signals after sending an ultrasound beam. The differences in TOF and the amplitude
or intensity of the signal are the parameters that have to be processed. TOF is the time
it takes for an ultrasonic signal to pass from the transmitter to the receiver [127]. This
parameter is measured to achieve a reconstruction of the speed of sound distribution
within a sample using the following formula [120]:
𝑇𝑂𝐹 = ∑𝑑𝑖
𝑣𝑖𝑖 (Eq 2.7)
Where 𝑑𝑖 and 𝑣𝑖 are the distance and velocity of the 𝑖th component respectively.
For intensity measurements, the loss of ultrasonic signals is determined by
comparing the amplitude or intensity of the received signals while a sample is present
with its value in the absence of a sample. The attenuation coefficient of ultrasound (β),
is a logarithmic scale defined in terms of intensity, or more generally, the measured
signal voltage amplitude, and is calculated using the following equation:
𝛽 = 10 log (𝐼1/𝐼2) For intensity (W m-2) or (Eq 2.8)
𝛽 = 20 log (𝐴1/𝐴2) For amplitude (volts) (Eq 2.9)
Where β is the ultrasound attenuation coefficient in decibels (dB), 𝐼1 and 𝐴1 are
the intensity and amplitude while a sample is present and 𝐼2 and 𝐴2 are the intensity
and amplitude in the absence of the scanned object, respectively [128].
2.7.1 Image Reconstruction and Artefact Reduction
Ultrasonic CT images can be reconstructed using the projected data taken from
various orientations around the imaged sample. The data may be displayed as a 2D
amplitude plot as a function of projection angle, termed a sinogram (Figure 2-18). [82].
Chapter 2: Literature Review 34
Figure 2-18: (right) Projection profiles of point source taken at 8 angles (views): (left) 2D sinogram
represents a set of projection profiles, r (horizontal axis) and φ (vertical axis) are the location in the
projection and rotation angle respectively [129].
For tomographic image creation, several reconstruction algorithms can be
implemented; the most common techniques are iterative algebraic methods and back-
projection algorithms [82]. The back-projection reconstruction algorithm is a widely
applied reconstruction technique that is relatively simple to use. An individual
‘constant value’ projection is smeared back along all the pixels within the ray path
corresponding to the particular projection orientation. The resultant back-projected
image is the sum of the combined data of all the projection orientations (Figure 2-19).
Chapter 2: Literature Review 35
Figure 2-19: Back-projection reconstructs an image by taking each view and smearing it along the path
it was originally acquired. The obtained image is a blurry version of the correct image [130].
The back-projected images are generally blurry, however; this can be remedied
by the use of the ‘filtered back-projection’ technique, where each projection is filtered
before being back-projected (Figure 2-20).
Figure 2-20: Filtered back-projection reconstructs an image by filtering each view before back-
projection which removes the blurring of the simple back-projected image [130].
Chapter 2: Literature Review 36
Although the filtered back projection (FBP) is a common technique for CT
image reconstruction, it is not useable if there is missing data on a particular angular
interval, and iterative methods should be used instead.
Algebraic reconstruction technique (ART) uses three or more projections to
reconstruct the 2-dimensional beam density distribution. ART is an iterative algorithm
that solves a system of linear equations: y = Ax, where y is the measured attenuation
vector, A is the matrix that contains length of each ray intersects each "pixel" of the
image, and x is the attenuation image (in vector form) [131]. Algebraic methods use
Kaczmartz method [132] to solve the linear equation. An advantage of this approach
is that elements of A can be computed easily when they are needed, and the matrix A
is never stored in a full form. It is possible to use regularization when solving the linear
equation, for example Tikhonov regularization or statistical methods. This is required
when A is not invertible or measurements contain noise. Compared to FBP, which
require a complete data set to reconstruct the image correctly, iterative algebraic
methods apply a refinement to their solution at each step, and can process
reconstructions even with lost or missing data. Also, algebraic methods are more
efficient and yield higher quality images [131, 133-135].
The objective for medical imaging is to create an accurate representation of the
object’s anatomy [136]. The quality of the ultrasound images can be affected by a
number of artefacts, which may contribute to misdiagnoses [18]; these artefacts
include speckle, reverberations, shadowing, velocity errors and refraction [137].
• Speckle
Speckles are comprised of image artefacts resulting from scattering centres
within the tissue. The interference of the wavefronts of scattered echoes leads to
fluctuating intensities in the image [137].
• Reverberations
Reverberations refer to multiple reflections from the interfaces of reflectors in
the ultrasound path. They appear as separate and equally-spaced bright lines [137].
Chapter 2: Literature Review 37
• Shadowing
Shadowing is a reduction of echo intensity resulting from the ultrasound passing
through structures with highly reflective interfaces and high absorption [138].
• Velocity Errors
In ultrasound imaging, the speed of the ultrasound wave is assumed to be
constant (1540 m s-1) when creating B-mode images. As a result, scanning tissues with
different SOS may lead to a dimension artefact [18].
• Refraction
The refraction artefact is the result of a change in the direction of ultrasonic
waves when propagating through two tissues with different SOS [138].
Ultrasound image quality can be improved by using pre-processing and post-
processing methods. Pre-processing techniques reduce image artefacts that result from
signal properties such as bandwidth, attenuation and nonlinearity of propagation.
Besides modifying the signal generation, pre-processing techniques may also be
applied to the acquisition steps and involve beam forming and compounding. In the
beam-forming methods, the generation of ultrasound is improved by reducing the
effects of structure heterogeneities on ultrasound propagation. These techniques can
reduce side lobes–that is, multiple sound beams with intensities below the main beam–
and velocity errors.
After generating and digitizing an ultrasound image, post-processing techniques,
such as signal processing algorithms, are used to improve image quality. These
methods can significantly reduce noise and blurry edges and improve contrast, all of
which assist in image interpretation. The other two post-processing methods used after
image creation are filtering and deconvolution [137].
2.7.2 Applications
UCT has been used for a number of medical applications, including soft tissue
imaging such as the analysis of breast cancers in women [28], and bone imaging,
measuring the cortical thickness of children’s long bones [139] and the
characterization of bone in cattle [140].
Chapter 2: Literature Review 38
2.7.2.1 Soft Tissue Assessment
In 1978, Greenleaf et al. [125] first published the study which demonstrated the
feasibility of the transmission UCT. They found that the transmission UCT is capable
of providing images representing quantitative distribution of ultrasound attenuation
coefficients within the sample by measuring amplitude of transmitted signals. They
could also extend their work to reconstruct ultrasonic images from the TOF
distribution of ultrasonic signals [122]. Many studies have later been conducted to
develop tissue and organ specific approaches for UCT, and novel prototypes have been
invented and used for such developments [24, 26, 126, 127, 141]. Nguyen et al. [142]
developed an ultrasonic tomography system using four transducer arrays to scan men’s
testes and women’s breasts. A spiral tomography system has been introduced by
Ashfaq et al. [143], in which they used a standard medical transducer array for breast
scans. Stotzka et al. [124] used UCT direct imaging of a volume and they implemented
cylindrical arrays of many thousand transducers, enclosing the object to acquire the
transmitted and reflected signals. This method provides reproducibly high quality
images.
Ruiter et al. [144] designed the first experiment system for 3D UCT (Figure
2-21) to investigate the feasibility of this system for breast cancer diagnosis and
provides the conclusion for future work. This system consists of a cylindrical tank
filled with water and ultrasonic transducers, which are fixed geometrically onto the
tank wall, of which 384 are emitters and 1536 are receivers. This system was found to
be feasible with modern technology but has some disadvantages such as sparse
aperture and long data acquisition (DAQ) time.
Chapter 2: Literature Review 39
Figure 2-21: Cylindrical aperture for first experimental 3D setup of UCT [144].
2.7.2.2 Bone Assessment
The imaging of bone, which is required to predict mechanical integrity of bone,
is more challenging than soft tissue due to the high difference in acoustical properties
existing at the junction of bone and surrounding soft tissue and the high heterogeneity
of bone. However, some promising trials were achieved by echo-tomography utilising
single element ultrasound transducers and B-mode image processing of long bones
[145-147] and brain [148]. These techniques provided qualitative images of the imaged
object but failed to yield quantitative estimates of the relative ultrasound parameters
such as ultrasound velocity and attenuation. UCT has been proposed to provide
quantitative cross-sectional images; representing ultrasound velocity and attenuation.
Despite several studies that have implemented the UCT technique on soft tissue
with more emphasis on the diagnosis of breast cancer in women, only a few studies
have applied UCT on hard tissue, specifically bone. Sehgal et al. [149] described an
ultrasound system to generate tomographic images based on ultrasound attenuation,
time of flight and backscatter data. They concluded that ultrasound can be used to
create 3D images of bone. However, this study did not show quantitative information
and utilised single element transducers which limited the flexibility of beam forming
and focussing of ultrasound waves. Zheng and Lasaygues [150] successfully
demonstrated the use of transmitted and reflected pulses for determining bone SOS
and cortical shell thickness using single element transducers at a single angle. They
Chapter 2: Literature Review 40
showed that a transmission-echo system is a feasible method to image bones. However,
the use of single element transducer may result in positioning errors if the sample is
larger than the transducer element.
Lasaygues et al. have extended the use of UCT for quantitative imaging of long
bones by developing two main methods. Compound Quantitative Ultrasonic
Tomography (CQUT), which compensates for refraction by adjusting the transmitting
and receiving transducer locations and angles to sample the equivalent straight path
through the bone [31, 151]. Distorted Born Diffraction Tomography (DBDT) uses a
single set of experiments but performs iterative simulations of the sample [152].
Although both CQUT and DBDT have resulted in good quantitative images of the
cortical shell, they require either multiple experiments and heavy data processing
requirements (CQUT) or are very computationally expensive (DBDT).
2.8 SUMMARY AND KNOWLEDGE GAP
For bone assessments, QUS is strongly recommended and many studies have
demonstrated the feasibility of this technique to predict osteoporotic fracture risk.
Ultrasound quantitative imaging is in many ways considered an alternative or even
superior solution compared to other imaging system due to its safety, affordability and
mobility. UCT is a promising technique which is used to provide quantitative
information on the acoustic properties, mainly attenuation and speed of sound, of the
different tissue segments. Most of the earlier UCT studies were related to soft tissue,
and only a few studies have used this technique for bone assessment, mainly because
of the intricate and complex nature of ultrasound propagation through bone. Also,
more advanced reconstruction tools are required for the anisotropic propagation of
ultrasound waves inside bone.
Despite the difficulties that hamper our understanding of quantitative ultrasound
tomography, it is still an attractive non-invasive technique that provides quantitative
information of acoustic properties, such as ultrasonic attenuation and velocity, which
can be translated into 2D or 3D reconstruction, which can be used to estimate the
mechanical integrity of bone.
The aim of this research is to develop and validate an improved ultrasonic
computed tomography system utilizing phased array transducers and investigate the
capability of this system to obtain high quality ultrasonic images of complex structures
Chapter 2: Literature Review 41
and provide more accurate assessment of bone. The motivation of this research is that
none of the previous UCT studies of bone incorporated FEA to assess bone stiffness.
A combination of UCT with FEA could be used as a non-ionising, non-invasive, cost-
effective and portable method to accurately predict osteoporotic fracture risk. Hence
there is a need to investigate the feasibility of the UCT system to scan complex
structures and estimate the mechanical properties of bone replica models by combining
3D UCT images and FEA. There is also a need for a simple technique for quantitative
ultrasound imaging of the cortical shell of long bones.
Chapter 2: Literature Review 42
2.9 DISCRIPTION OF A NOVEL UCT SYSTEM
A novel lab-built system was used to provide cross-sectional images of a sample,
using transmission and pulse-echo data. Compared to other existing UCT systems, the
system is more advanced, fully automated and easy to use. This system consists of
three main components: a robotic arm, Omniscan and TomoView functions. This
system also utilises linear phased-array transducers (described in section 2.6.3.
2.9.1 Robotic Arm
The robotic arm is equipped with an NX100 controller and programming
pendant (Figure 2-22).
Figure 2-22: Robotic arm (left), NX100 controller and programming pendant (right).
The programming pendant is equipped with the keys and buttons that are used
to control robotic arm operations in teaching mode. The pendant has a remote switch
which provides another option to control the robotic arm movement using a computer
instead of the pendant. The robotic arm has 6 degrees of freedom which allows for
Chapter 2: Literature Review 43
ease of data collection by moving the phantom or the transducers in a selected x, y, z
position. The UCT setup can be configured in two different ways:
I. Stationary transducers and rotating phantom between transducers
(using robotic arm).
II. Stationary phantom and rotating transducers around phantom (using
robotic arm).
2.9.2 Omniscan
The Olympus Omniscan apparatus (Figure 2-23) is an advanced ultrasound flaw
detector marketed to the industry for weld and material inspection. It combines a
number of non-destructive technologies, such as conventional ultrasound technology
(UT) using a single element and phased array ultrasonic technology (PA). The
Omniscan is a portable instrument which is controlled by the Olympus TomoView
software and used for firing and receiving the ultrasonic signals.
Figure 2-23: Olympus Omniscan MX
Chapter 2: Literature Review 44
2.9.3 TomoView
TomoView is a PC-based software designed to perform ultrasonic testing data
acquisition with several Olympus phased array or conventional UT units, giving it the
flexibility to choose the configuration for a desired application.
The TomoView software package is a powerful and versatile platform with a
number of advanced functions and features that makes it ideal for data acquisition and
analysis during UT inspections using Omniscan. This package allows real-time
imaging of UT signals, as well as offline analysis of previously acquired data files.
TomoView user-interface (Figure 2-24) combines the setup, inspection and
analysis functions in one software package.
Figure 2-24: TomoView user interface showing menus, toolbars and different representation views of
the data imaging.
Chapter 2: Literature Review 45
TomoView has three operation modes:
▪ Setup
This mode is used to set up hardware and software parameters, including
ultrasonics, inspection sequence and window layout setting. The setup
mode is used to configure the hardware prior to scanning and inspection.
▪ Inspection
Inspection mode is used when performing the data acquisition and it is
available only when TomoView is connected to the Omniscan.
▪ Analysis
This mode is used to analyse and create reports of the recorded data.
There are two options to perform the UCT scan:
1) UCT Scan with One Omniscan
In this setup, a single Omniscan device is used (Figure 2-25). The UCT
system is capable of acquiring or transmitting through 128 individual
channels, which leaves 64 elements available for the transmitter and 64
elements for the receiver as the two linear phased-array transducers
(transmitter and receiver) are connected to one Omniscan. This setup has
the advantage of displaying the ultrasonic signals on the TomoView
window so that any problems with the signal or the phantom position can
be rectified immediately. This setup was used for the first and second
studies, and was useful for testing a range of parameters and investigating
the geometrical issues such as positioning errors that affect the obtained
images.
Chapter 2: Literature Review 46
Figure 2-25: Sketch of the UCT setup utilizing one Omniscan device.
2) UCT Scan with Twin Omniscan
In this type of scan, two Omniscan devices are used (Figure 2-26), each
connected to a 128-element transducer, with one serving as a transmitter
and the other as a receiver. This setup enables maximizing the field of
view. This setup was used for the third study to allow for simultaneous
transmission and PE signal acquisition.
Robotic Arm
NX100 Controller
PC Running UCT Program
Microcontroller
Omniscan
PC1-TomoView PC2-TomoView
Chapter 2: Literature Review 47
Figure 2-26: Sketch of the UCT setup utilizing two Omniscan devices.
Robotic Arm
NX100 Controller
PC Running UCT Program
Microcontroller
Omniscan 1
PC1-TomoView
Omniscan 2
PC2-TomoView
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 51
Chapter 3: Estimation of Mechanical
Stiffness by Finite Element
Analysis of Ultrasound
Computed Tomography (UCT-
FEA); A Comparison with
Conventional FEA in Simple
Structures
3.1 PRELUDE
This chapter is based on a manuscript submitted to the journal Ultrasonics. It
proves the hypothesis that ultrasound computed tomography can be combined with
FEA and be equally efficient to predict stiffness as conventional FEA. This study
reports for the first time the use of attenuation UCT images as an input geometry into
FEA.
3.2 ABSTRACT
Several non-invasive methods are currently used to assess osteoporotic fracture
risk, including X-ray derived bone mineral density, and quantitative ultrasound (speed
of sound and broadband ultrasound attenuation). Finite element analysis (FEA) is a
computerised simulation tool providing an estimate of mechanical stiffness (N m-1),
conventionally utilising single material properties. This paper reports for the first time,
the feasibility of utilising ultrasound computed tomography (UCT) data as a geometric
input into FEA; comparing its ability to estimate mechanical test derived stiffness with
conventional FEA.
Six test samples were designed, all consisting of five parallel rods of constant
length; each sample exhibited constant diameter that varied between samples (0.5 to
5.5 mm). Each sample design was 3D-printed and scanned with the UCT system.
Variable-displacement FEA was performed for both conventional FEA, and that
incorporating UCT data. Each 3D-printed sample was then mechanically tested under
compression.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 52
Coefficients of Determination (R2) to estimate the gold-standard mechanical test
stiffness of 92.6% and 95.2 ± 8.8% were obtained for conventional and UCT derived
FEA respectively.
FEA based on UCT data may have the potential to provide a non-invasive, non-
destructive, measurement of the mechanical integrity of bone with significant potential
to improve clinical assessment and management of osteoporosis.
3.3 INTRODUCTION
The quality of bone reflects the component properties such as bone architecture,
bone remodelling, mineralization, and micro-fractures. The mineral components of the
bone are responsible for its mechanical properties, such as bone strength, stiffness and
elasticity [153]. Osteoporosis is a skeletal disease describing a significant decrease in
bone mass and micro-architectural integrity [52], leading to an increased fracture risk,
and a worldwide health issue in the elderly [154].
The true gold standard for assessing bone strength is a destructive mechanical
test, however destructive testing in a living subject is not feasible and alternative
methods are required. FEA is a non-destructive computer simulation method, which
estimates the stiffness (N m-1) of a structure, dividing it into a number of simple parts,
termed finite elements that are connected by points termed nodes. Material properties
are defined to each element, for example, density, Young’s modulus and Poisson’s
ratio in the case of static-elastic analysis of an isotropic material structure. Constraints
and loads may then be applied to the structure at defined locations. Under simulated
loading, compressive or tensile, the displacement of each node is determined by
solving inter-connected simultaneous equations following Newton’s First Law, that
integrate the material properties, loads, constraints and geometry of the test sample.
With regard to bone assessment, finite element analysis is sensitive to both material
and structural properties.
Several non-invasive in-vivo techniques have been developed and implemented
to serve as surrogates for bone strength assessment. Bone mineral density (BMD, g
cm-2) describes the amount of calcified mineral per unit area of the bone, generally
estimated using dual X-Ray absorptiometry (DXA). However, it has been shown that
areal BMD estimation is insufficient to accurately determine a subject’s osteoporotic
fracture risk [36, 37]. Quantitative computer tomography (QCT) is a 3D X-ray imaging
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 53
modality and provides an estimate of the volumetric BMD (g cm-3); through image
segmentation, it also facilitates separate analysis of cortical and cancellous
components [39, 40]. QCT is not however used in a routine medical environment as
it exposes the patient to a higher radiation dose (60 µSv) compared to the low dose for
DXA (1 µSv) [41]. Infrared imaging has recently been described as a non-contact,
safe, remote and fast technique which can be used for detecting and evaluating bone
density. However, this technique is still in its early stage and has not been compared
with other medical imaging techniques for bone assessment [155, 156]. Quantitative
ultrasound (QUS) has successfully been introduced as an alternative diagnostic
technique to assess osteoporotic fracture risk [16]. It has many advantages over DXA
and QCT: it does not use ionizing radiation, it is easy to use, less expensive, and has
been shown to provide a prediction of osteoporotic fracture risk comparable to DXA,
particularly utilising broadband ultrasound attenuation (BUA) [42-44].
UCT is a novel technique which allows for the creation of 3D images and
quantitative analysis based upon velocity or attenuation measurements. The fixed and
automated setup of UCT makes it operator independent and provides images with high
resolution [25-28]; this is especially useful for soft tissue diagnostics, such as breast
cancers in women [21, 29, 30] but has also used for imaging the skeleton [20, 31].
Ultrasound attenuation computed tomography has previously been reported for bone
imaging of human cadaver heads [157], legs of lambs [158], turkey and dog limbs
[149].
Combinations of imaging data and FEA have previously been reported to
estimate the mechanical integrity of bone. Langton described a novel technique of
converting a single 2D DXA image, first into a 3D spatial model, and then incorporated
into FEA, providing a coefficient of determination (R2%) to predict the failure load of
excised human femurs of 80.4% compared to 54.5% for BMD [159]. Several studies
have incorporated QCT image data into FEA to predict the bone stiffness of the
proximal femur [32, 33, 160, 161], reporting significantly improved estimation
compared to areal DXA-BMD or volumetric QCT-BMD estimation [32].
We hypothesised that ultrasound CT may be combined with FEA and be equally
efficient to predict stiffness as conventional FEA; the authors are not aware that this
has previously been reported. The objective of this study was to incorporate
quantitative ultrasound attenuation CT measurements of plastic rod phantoms into
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 54
finite element analysis to estimate mechanical-test derived stiffness, and to compare
with conventional FEA. UCT-FEA is a new technique that has potential to provide a
non-invasive, non-destructive, measurement of the mechanical integrity of long bones
such as the tibia and femur with significant potential to improve clinical assessment
and management of osteoporosis and post-amputation prosthetics utilising non-
ionising ultrasound.
3.4 MATERIAL AND METHODS
3.4.1 3D Phantom Samples
This is a proof of concept study consisting of a range of simplistic bone tissue
mimicking samples, which were designed in 3D using SolidWorks (version 2014,
Dassault Systems, Waltham, MA, USA). For simplicity and constancy, the samples
have the same design but with variable thicknesses. The six samples consisted of a 50
mm diameter planar disc, which served as a sample holder, and five rods of 40 mm
length that were orientated perpendicular to the disc. The rod diameter varied for each
sample and ranged from 0.5 to 5.5 mm, while keeping the centre to centre distances
constant at 10 mm; hence the diameter of the scan area was 25.5 mm as shown in
Figure 3-1b. The samples were 3D printed by a n Alaris30 (Statasys, Eden Prairie,
MN, USA) using a photopolymer (Object VeroWhitePlus FullCure835) with density
of 1190 kg m-3, ultrasound attenuation coefficient of 2000 dB m-1 at 5 MHz and
ultrasound velocity of 2503.2 m s-1. The acoustic properties of the sample materials
were measured experimentally using a transmission technique which required two
transducers, one as a transmitter and the other as a receiver. Both transducers had the
same properties, viz: single-element, unfocused, broadband 1 MHz frequency, and ¾”
diameter. The transducers were placed co-axially in a cylindrical holder, the internal
diameter of which matched the external diameters of the transducers. The transmitter
was energized by a 400-V spike from a pulser-receiver (Panametrics 5800PR,
Waltham, MA, USA). The receiver was connected directly to a 14-bit digitizer card
(National Instruments PCI5122, Austin, TX, USA) operating at 50-MHz digitization
rate (digitization period = 2 × 10-8 s). Figure 3-1a shows a photograph of the printed
samples.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 55
Figure 3-1: (a) Photograph of the rod samples with varying rod diameter (from left to right) of 0.5, 1.5,
2.5, 3.5, 4.5, and 5.5 mm. (b) Sketch of the 5.5 mm rod sample design showing the rod diameter, distance
from centre to centre and total scan area, measurements are in mm.
3.4.2 Ultrasound Computer Tomography System
Figure 3-2 shows the experimental set-up of the ultrasound computer
tomography system. Two 5 MHz 128-element linear phased-array transducers with an
element size of 12 mm by 0.75 mm (5L128-I3, Olympus, Corporation, Shinjuku,
Tokyo, Japan), one acting as a transmitter, the other as a receiver, were coaxially
aligned in a fixture 100 mm apart and immersed in a water tank with the sample placed
in between. In order to obtain a 360° ultrasound scan, the phased-array transducers
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 56
remained stationary, but the sample was rotated using a user-programmed Motoman
HP6 robotic arm (YASKAWA Electric Corporation, Japan) with six degrees of
freedom. The phased-array transducers were connected to an Omniscan MX device
(Olympus, Corporation, Shinjuku, Tokyo, Japan), and controlled by the Olympus
TomoView software (version 2.7, Olympus, Corporation, Shinjuku, Tokyo, Japan), to
emit and receive the ultrasound signals as described in the next section.
Figure 3-2: a): Sketch of the UCT system set-up. b): Photograph of the experimental set-up showing the
sample attached to the robotic arm and positioned between the two transducers.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 57
3.4.3 Ultrasound Data Acquisition and Image Reconstruction
TomoView was used to set all signal acquisition parameters as well as the beam
profile. The scan was performed by individually firing 64 elements of the transmit
transducer, and detecting the propagated ultrasound wave with 64 correspondingly-
aligned elements of the receive transducer. The sample was rotated 360° in 1° steps,
thereby obtaining a total of 23,040 signals (360 projections, which is the maximum
number that can be obtained, by 64 element-pairs). Each signal consisted of 1,344 data
points, recorded at a digitization frequency of 100 MHz. A ‘system gain’ of zero was
utilised; the ‘true depth’ option set at 50 mm, the distance from each transducer to the
centre of a sample.
The 2D ultrasound image reconstructions were computed using the
Simultaneous Iterative Reconstruction Technique (SIRT) [162]. This method belongs
to the family of Algebraic Reconstructing Methods, based on the Kaczmarz method
[132]. Numerical properties of the algebraic methods have been widely studied and
applied to tomographic image problems such as X-ray CT and ultrasound tomography
[163-166].
An attenuation value βi,θ for each measured ultrasound signal was computed.
The logarithmic dB-scale was used and hence
𝛽𝑖,𝜃 = 20 ln𝐴𝑟𝑒𝑓
𝑖
𝐴𝑚𝑒𝑎𝑠𝑖,𝜃 (Eq. 3.1)
where i is the number of the emitting and receiving transducers (1 to 64), 𝜃 is the
rotation angle of the sample, 𝐴𝑟𝑒𝑓𝑖 is the maximum peak value of the reference
measurement (through water only) of transducer i, and 𝐴𝑚𝑒𝑎𝑠𝑖,𝜃
is the maximum peak
value of the measured signal. The values of βi,θ are called sinogram, as shown in Figure
3a.
In theory, if the sample rotation axis is perfectly centred, then
𝛽𝑖,𝜃 = 𝛽𝑁−𝑖+1,𝜃+𝜋 (Eq. 3.2)
where N is the total number of transducers (64 elements in this study). However, in
practice, the position of the sample rotation axis relative to transducers is hardly
known, resulting that the measured sinogram is asymmetric, as demonstrated in Figure
3-3a. Since the wave-rays of a projection are parallel, only the position in y-direction
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 58
affects the signal if parallel rays are assumed. The sinogram can be corrected
numerically by moving the measurement signals so that cross-correlation with the
symmetric signals is maximized and the sinogram is centred. The final step of SIRT
computes the attenuation field using the corrected sinogram (Figure 3-3b) as the input
data. Figure 3-3c and Figure 3-3d show the image before and after the correction
respectively.
Figure 3-3: a) uncorrected sinogram is asymmetric with the rotation axis (y-axis) being off-centred by
three times of the transducer element width, b) corrected and symmetric sinogram. The red solid line
indicates the symmetric centre line, c) 2D UCT image before correction, and d) 2D UCT image after
correction. For subfigure (a) and (b), x-axis is measurement index (angle) and y-axis is sensor pair
index. For c and d, the colourmaps display the attenuation map in dB m-1, x- and y-axes are in pixels
unit.
Another factor that had to be considered before scanning all the samples was the
effect of the projection number upon the image quality. Therefore, the 1.5 mm sample
was scanned and cross-sectional UCT images were reconstructed using different
numbers of projections. These tests showed that image quality was affected by the
number of projections and that the best images were obtained from 360 projections as
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 59
shown in Figure 3-4. All subsequent UCT images of the samples were, therefore,
reconstructed from 360 projections.
Figure 3-4: The reconstructed 2D UCT images of 1.5 mm rod sample from different number of
projections; a) 360 projections, b) 180 projections, c) 91 projections, d) 46 projections, e) 23
projections and f) 11 projections.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 60
3.4.4 Creation of a 3D Model from a Single 2D UCT Image
The reconstructed 2D UCT image (attenuation maps, Figure 3-5a) for each
sample was first analysed using Matlab (The MathWorks Inc., Natick, MA, USA),
applying a constant threshold value of 2000 dB m-1, which is the attenuation coefficient
of the material, on a range from 0 to 9000 dB m-1 to eliminate noise and image artefacts
(Figure 3-5b). The resulting 2D binary data was extruded (Figure 3-5c), converted into
triangular faces and vertices, and the 3D data set saved in STL (Stereolithography) file
format.
Figure 3-5: a) Raw 2D UCT image (attenuation map in dB m-1), b) binary 2D UCT image, c) 3D STL
file, axes are in mm unit. The STL files were imported into SolidWorks v2014 (Dassault Systems,
Waltham, MA, USA) as mesh files in order to save them into solid part format (SLDPRT), which was
then used as the input geometry for the finite element analysis simulation in Ansys.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 61
A number of threshold values, ranging between 1800 and 2000 dB m-1, were
tested. There was no discernible differences in the binary images attributable to the
threshold values, as shown in Figure 3-6 below.
Figure 3-6: The binary images of 1.5 mm rod sample using different threshold values, a) 1800 dB m-1,
b) 1900 dB m-1 and c) 2000 dB m-1.
3.4.5 Estimation of Young’s Modulus
For FEA simulation, the Young’s Modulus of the bulk material (VeroWhitePlus)
is required. This was measured using the standard three-point bending test, following
the ASTM D790-02 standard for measuring the elastic modulus of plastic materials.
Six strips were designed and 3D-printed, each 3.75 mm thick, 12 mm wide, and 100
mm long (Figure 3-7). A three-point bend rig with a span of 60 mm was used, with
each strip tested five times, using an Instron 5848 MicroTester (Instron, Norwood,
MA, USA) testing machine and a 500 N load cell. The recorded load and deformation
were used to calculate the elastic modulus as:
𝐸 =𝐹𝐿3
4𝑤ℎ3𝑧 (Eq. 3.3)
where E is the modulus of elasticity in bending (MPa), F is the applied force (N), L is
the support span (mm), w is the beam’s width (mm), h is the beam’s depth (mm) and
z is the displacement (mm). The resulting Young’s modulus value obtained for the
photopolymer was 2000 ± 200 MPa, being within the range of the manufacturer’s
material property data sheet (2000-2700 MPa).
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 62
Figure 3-7: Photograph of the six strips that have been used in the three-point bending test to measure
Young’s Modulus of the bulk material, each 3.75 mm thick, 12 mm wide, and 100 mm long.
3.4.6 Finite Element Analysis
1) Conventional FEA
The input geometry and parameters for the conventional finite element analysis
were derived from the 3D design of the samples and the experimentally
measured Young’s Modulus. The sample material was assumed to be isotropic,
with a constant Poisson’s ratio of 0.35. The simulations were performed with
Ansys Workbench v15 (ANSYS INC, Canonsburg, Pennsylvania, USA) in order
to determine the structure-stiffness (N mm-1), using following steps.
i) The 3D sample designs were exported using SolidWorks in SLDPRT format,
and then imported to Ansys.
ii) The 3D sample designs were orientated with the rods parallel to the z-direction
and meshed before conducting the FEA (Figure 3-8).
iii) The boundary conditions were applied by defining the fixed support, which
was the base of the sample, and the displacement direction (z-direction).
iv) After the FEA was solved, the stiffness (N mm-1) was measured by dividing
the reaction force by the displacement.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 63
Figure 3-8: a) FE model of the rod sample with 5.5 mm diameter rod, b) shows the applied displacement
(in z-direction).
2) Ultrasound Computed Tomography Finite Element Analysis (UCT-
FEA)
The UCT-FEA utilised the 3D model obtained from the UCT system, as
described in Section 3.4.4, along with the experimentally-derived Young’s
Modulus. Finite element analysis was again performed, as described above for
the conventional approach, thereby deriving the sample stiffness (N mm-1). UCT
scans were repeated three times for each sample, at different z-plane positions;
the sample being removed and replaced between scans.
To improve the accuracy of the analysis, different Poisson’s ratios were
implemented, including 0.3, 0.35 and 0.45, but this had no effect on the FEA
results. The dependence on the number of mesh elements for FEA results was
analysed, which also showed the results were independent of mesh size. Figure
3-9 shows that a mesh size convergence in the 2.5 rod sample, with element sizes
of 2 mm, 1 mm and 0.5 mm, only resulted in a 0.09% change in stiffness values
versus a 435% increase in the number of elements between mesh sizes of 1 mm
and 0.5 mm.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 64
Figure 3-9: Mesh size convergence in the 2.5 rod sample with element sizes of 2 mm, 1 mm and 0.5
mm.
3.4.7 Experimental Mechanical Testing
The six rod samples were mechanically tested using an Instron testing machine
(Figure 3-10), with a 500 N load cell, providing a measure of (gold standard) stiffness.
The compression mechanical testing was performed with the same boundary
conditions as defined in the FEA simulations; specifically, the base of the sample was
fixed, and the compression force was applied from the top with displacement control.
The maximum displacement was set to be 0.25 mm for all the samples at a rate of 1
mm min-1, corresponding to a strain of 0.625%. The stiffness (N mm-1) of the six
samples was calculated by dividing the recorded load by the applied maximum
displacement.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 65
Figure 3-10: Set-up of the mechanical test of a rod sample using an Instron 5848 MicroTester testing
machine with a 500 N load cell.
3.5 RESULTS
3.5.1 Ultrasound Computed Tomography Images
The reconstructed 2D ultrasound images are shown in Figure 3-11. The
ultrasound images are 256x256 pixels in size which correspond to the width of the
sensor array used, i.e. 1 pixel corresponds to 187.5 µm. While an ultrasound image
was obtained for the 0.5 mm rod sample, it was excluded from the stiffness analysis;
the mechanical test data being considered inaccurate since the rods bent under loading.
Table 3-1 shows the UCT diameter for the samples compared to the actual measured
diameter from the test pieces. From these measurements, the resolution of the UCT
system was estimated to be approximately 2 mm.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 66
Table 3-1: The UCT diameter for the samples compared to the actual measured diameter from the test
pieces.
Figure 3-11: The reconstructed 2D UCT images. (a) 0.5 mm rods thickness, (b) 1.5 mm rods thickness,
(c) 2.5 mm rods thickness, (d) 3.5 mm rods thickness, (e) 4.5 mm rods thickness and (f) 5.5 mm rods
thickness. The colour bars in the images display the attenuation map in dB m-1. Axes are in pixel units.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 67
3.5.2 Stiffness Estimation
Following the ASTM D790-02 standard, the three-point test obtained an
estimate of elastic modulus for the photopolymer material that was within the range
reported by the manufacturer, being 2000 ± 200 MPa. The repeatability (coefficient of
variation) for the UCT-FEA derived stiffness was calculated to be 5.9 × 10-4.
The dynamic range of stiffness values, obtained from the mechanical tests and
both FEA approaches, were first normalised to unity. Regression analysis for a)
conventional FEA stiffness vs mechanical test stiffness and b) UCT-FEA stiffness vs
mechanical test stiffness are shown in Figure 3-12. The coefficient of determination
(R2) to estimate mechanical test derived stiffness was 92.6% for conventional FEA and
95.2 ± 8.8% for UCT-FEA.
Figure 3-12: Estimation of the experimental mechanical test stiffness by (a) conventional FEA (left)
and (b) UCT-FEA (right). The range of all data sets were normalised to unity. 1.5 mm (○), 2.5 mm (□),
3.5 mm (∆), 4.5 mm (ⅹ), 5.5 mm (◊).
3.6 DISCUSSION
It has been shown that the ultrasound computed tomography system described
in this paper is able to facilitate reconstructed 2D images with a pixel size of 0.1875
mm. The experimental set-up is similar to X-ray microCT devices, where the source
and detector are stationary, while the sample is rotated. By utilising a robotic arm, the
system is operator-independent and therefore offers high reproducibility. It has also
been shown that the UCT system is able to scan small objects with a diameter of 0.5
mm. However, structures with small dimeters in the UCT images widened due to the
limited resolution of the UCT system, which is estimated to be about 2 mm.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 68
Ultrasound reflection and refraction effects are more dominant for the thicker
rod phantoms (4.5 and 5.5 mm), as evidenced by the circular rods appearing elliptical
(Figure 3-11). The results further suggest that maximum spatial accuracy is obtained
for diameters of 2.5-3.00 mm. Interestingly, Figure 3-11 also shows that ultrasound
attenuation of the 3.5 mm rod sample was significantly higher than the thicker samples
(4.5 and 5.5 mm), being in agreement with mechanical test stiffness data. These
findings were consistently observed during repeat measurements, one potential
explanation is that the 3.5 mm diameter sample may have an alternate structure caused
by the 3D printing process, that changed mechanical, and hence ultrasound
propagation, properties.
This study demonstrates that FEA based on 3D ultrasound attenuation computed
tomography images provides a comparable estimation of mechanical-test stiffness of
95.2% compared to conventional FEA (R2 = 92.7%).
There were a number of limitations associated with this study. The regular rod
design did not accurately represent the complex structure of bone, and noting the axial
symmetry of the test samples, only one 2D ultrasound CT slice was acquired. Future
work will consider 3D images (2D-stack) of complex structures. A polymer was used
to replicate bone tissue, having lower ultrasound velocity and attenuation values;
although this approach has been reported in several previous papers [167-173]. The
UCT system effectively provided the structural design of the samples, into which an
experimentally-derived value for Young’s modulus for the 3D print material was
incorporated within the UCT-FEA analysis; it should be noted however that QCT-FEA
applies an assumed relationship between estimated bone density and Young’s
modulus. In the future, the potential for ultrasound CT data to estimate Young’s
modulus and variability of material elasticity within a sample, for example, related to
varying degrees of bone mineralisation, will be investigated.
3.7 CONCLUSION
In conclusion, it has been shown that an UCT image can be used as an input
geometry for FEA that can estimate the mechanical stiffness of a sample. It is
anticipated that a combination of UCT and FEA has the potential to provide superior
accuracy for osteoporotic fracture risk than current QUS techniques.
Chapter 3: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with Conventional FEA in Simple Structures 69
3.8 WHAT IS NOVEL?
This chapter demonstrates for the first time a novel UCT technique for imaging
simplistic samples that replicates bone tissue, which produces 2D-UCT images that
can be combined with FEA to estimate the mechanical stiffness of a sample.
Figure 3-13: Summery of the UCT-FEA study in Chapter 3.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 73
Chapter 4: Estimation of Mechanical
Stiffness by Finite Element
Analysis of Ultrasound
Computed Tomography (UCT-
FEA); A Comparison with µCT-
FEA in Cancellous Bone Replica
Models
4.1 PRELUDE
So far, we have demonstrated a new concept for stiffness estimation using UCT-
FEA. However, this technique has been applied to simple structures that do not
replicate bone tissue (chapter 3). Consequently, the next step of the research was to
investigate the UCT-FEA application in trabecular bone replica models. This chapter
reports for the first time the use of attenuation UCT images as an input data into FEA
to predict the stiffness of complex bone replica models. This chapter is based on a
manuscript published in the journal Applied Acoustics.
4.2 ABSTRACT
The mechanical integrity of a bone is determined by its quantity and quality.
Conventional mechanical testing is the ‘gold standard’ for assessing bone strength,
although not applicable in-vivo since it is inherently invasive and destructive. A
mechanical test measurement of stiffness (N mm-1) provides an accurate estimate of
strength, although again inappropriate in-vivo. Several non-destructive, non-invasive,
in-vivo techniques have been developed and clinically implemented to serve as
surrogates for bone strength assessment including dual-energy X-ray absorptiometry
along with axial and peripheral quantitative computed tomography, and quantitative
ultrasound. Finite element analysis (FEA) is a computer simulation method that
predicts the behaviour of a structure such as a bone under mechanical loading; being
previously been combined with in-vivo bone imaging, reporting higher predictions of
mechanical integrity than imaging alone.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 74
We hypothesised that ultrasound computed tomography (UCT) may be
combined with FEA, thereby predicting the stiffness of bone. The objective of this
study was to apply finite element analysis to UCT derived attenuation images of
trabecular bone replica samples, thereby providing an estimate of mechanical stiffness
that could be compared with both, a gold standard mechanical test and surrogate X-
ray CT-FEA.
Replica bone samples were 3D-printed from four anatomical sites (femoral head,
lumbar spine, calcaneus and iliac crest) with two cylindrical volumes of interest
extracted from each sample. Each replica sample was scanned by micro CT and a
bespoke UCT system, from which finite element analysis was performed to estimate
mechanical stiffness. The samples were then mechanically tested, yielding the gold
standard stiffness value.
The coefficient of determination (R2) to estimate mechanical test derived
stiffness was 99% for µCT-FEA and 84% for UCT-FEA. In conclusion, UCT-FEA is
a promising tool for estimating the mechanical integrity of a bone. This study
demonstrated that UCT-FEA based upon quantitative attenuation images provided a
comparable estimation of gold standard mechanical-test stiffness and therefore has
significant potential clinical utility for osteoporotic fracture risk assessment and
quantitative assessment of musculoskeletal tissues.
4.3 INTRODUCTION
The mechanical integrity of bone is determined by two factors; bone quantity
and bone quality. Bone quantity is generally expressed as bone density (g cm-3), and
may be defined as tissue density (bone mass divided by tissue volume) or apparent
density (bone mass divided by sample volume). Bone quality reflects the properties
such as bone shape, cortical thickness, trabecular architecture, mineralization, and
presence of micro-fractures [153].
Conventional mechanical testing is the ‘gold standard’ for assessing bone
strength, although not applicable in-vivo since it is inherently invasive and destructive.
A mechanical test measurement of stiffness (N mm-1) provides an accurate estimate of
strength, although again inappropriate in-vivo. Several non-destructive, non-invasive,
in-vivo techniques have been developed and clinically implemented to serve as
surrogates for bone strength assessment. Dual energy X-ray absorptiometry (DXA)
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 75
provides a measure of areal bone mineral density (BMD, g cm-2; bone mineral content
divided by scan area), and is widely used to diagnose osteoporosis [74, 174, 175].
However, it is only a moderate predictor of fracture risk [36, 176], being a non-
volumetric measure of bone quantity but not bone quality [174]. X-ray quantitative
computed tomography (QCT) allows volumetric bone density assessment, with the
provision of separate analysis for cortical and trabecular components [39, 40] with a
voxel size typically of 500 µm. It is however relatively expensive, and delivers a
significantly higher radiation dose to the subject that DXA [41]. For in-vitro bone
samples, micro-computed tomography (µCT) is considered the gold standard for bone
microstructure imaging, with voxel sizes ranging from a few µm to 100 µm [177].
The clinical utility of Quantitative Ultrasound (QUS) to assess the mechanical
properties of bone was first described by Langton et al [95]. Being non-ionizing, it is
ideal for triage assessment of the general population. QUS parameters of velocity and
attenuation are dependent upon both bone quantity and bone quality, providing a
prediction of fracture risk comparable to DXA [43, 44, 104, 178].
Finite element analysis is a computer simulation method that predicts the
behaviour of a structure such as a bone under mechanical loading [102, 103]. The
structure is divided into a number of regular-shaped parts, termed finite elements that
are interconnected at nodes, as shown in Figure 4-1a. Density, Young’s modulus and
Poisson’s ratio values are prescribed to each finite-element, with constraints and loads
(compressive or tensile) applied to the structure at defined locations, as indicated in
Figure 4-1b. The displacement of each node is then determined by solving inter-
connected simultaneous equations following Newton’s First Law, that integrate the
material properties, loads, constraints and geometry of the test sample. Finite element
analysis is again sensitive to both bone quantity and bone quality, the output parameter
generally being a prediction of mechanical stiffness (N mm-1).
FEA has previously been combined with in-vivo bone imaging, reporting higher
predictions of mechanical integrity than imaging alone [35, 159, 179-181].
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 76
Figure 4-1: The FEA simulation process consists of dividing the structure into regular-shaped finite-
elements (a), onto which constraints and loads (indicated with the yellow arrow on the top) are applied
(b).
Ultrasound computed tomography has the capability to create 3D quantitative
analysis images, being operator independent and providing high resolution images
with a voxel size down to 200 μm [25-28]. Clinical applications to date have
predominantly considered breast tissues [21, 29, 30], although it has also been used to
assess bone [31]. Ultrasound attenuation computed tomography has previously been
reported for bone imaging of human cadaver heads [157], legs of lambs [158], turkey
and dog limbs [149].
We hypothesised that UCT may be combined with FEA, thereby predicting the
stiffness of bone; to the authors’ knowledge, this has not previously been reported. The
objective of this study was to apply finite element analysis to UCT derived attenuation
images of trabecular bone replica samples, thereby providing an estimate of
mechanical stiffness that could be compared with both a gold standard mechanical test
and X-ray CT-FEA.
4.4 MATERIAL AND METHODS
4.4.1 Cancellous Bone Replica Samples
The study utilised externally-sourced µCT-derived binary data sets (bone/void)
of 4 mm cuboid human cancellous bone samples from four anatomical sites (femoral
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 77
head, lumbar spine, calcaneus and iliac crest); the isotropic voxel dimension being 14
microns (28 microns for calcaneus). Two cylindrical volumes of interest were
extracted from each sample, equivalent to a natural tissue diameter of 2.6 mm; the
voxel dimensions were then uni-axially magnified by a factor of 11 to facilitate 3D
printing, the resulting cylinders measuring 30 mm in diameter and 44 mm in length. To
facilitate consistent mechanical test loading, a 2 mm thickness flat-parallel end-plate
of 30 mm diameter was attached to the top of each sample design, and a second end-
plate of 4 mm thickness attached to the bottom of each sample design, additionally
serving as a sample holder for subsequent UCT imaging. Noting that the two end-plate
were attached to the cylindrical volumes before the 3D printing. The samples were 3D
printed by a ProJet 3510 SD (3D Systems, Rock Hill, USA) using a plastic material
(VisiJet M3 Crystal). Figure 4-2 shows a photograph of the printed samples.
Figure 4-2: Photograph of the cancellous bone replicas: iliac crest (IC1 and IC2), calcaneus (CAB1 and
CAB2), femoral head (FR1 and FR2) and lumbar spine (LS1 and LS2).
The aim of this study was to show that UCT was suitable for imaging of complex
structures, which is a significant advance on the initial study (chapter 3) in which
simple rod models were used. The magnification was necessary to accommodate the
spatial resolution of our 3D printer resolution. The current set-up will probably not be
suitable for imaging of real cancellous bone specimens. However, with ongoing
technological advances, one can expect to see improved signal to noise ratios and set-
up modifications, such as incorporating additional high-frequency ultrasound
transducers, is bound to increase bone surface resolution. Imaging of whole bones and
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 78
other complex structures is therefore likely within in the near future. An investigation
of imaging of long bones will be considered in subsequent studies.
4.4.2 Micro CT Scanning
The 3D-printed cancellous bone replica models were micro CT (µCT) scanned
(μCT 40, Scanco Medical, Brütisellen, Switzerland) in air at 45 kVp and 177 μA, with
an isotropic voxel size of 36x36x36 μm3 and a sample time of 750 ms. Each scan
contained 1400 slices which were exported to DICOM format for further processing.
Each DICOM stack was imported using the image processing package Fiji [182], a
distribution of ImageJ [183]. A region of interest (ROI) was manually selected,
corresponding to the diameter of the sample. The outer region was removed and the
ROI converted into a binary image stack which was downscaled by a factor of 0.25,
thereby reducing the stack size from 1.2 GB to 14 MB with a corresponding voxel size
of 57x57x57 μm3. The binary image stack was displayed as a surface with the 3D
Viewer plugin [184], and finally exported as a 3D structure in STL (Stereolithography)
file format for further analysis in the FE modelling software.
4.4.3 UCT Scanning
The samples were scanned using a custom-built ultrasound computed
tomography (UCT) system (Figure 4-3), incorporating two 5 MHz 128-element linear
phased-array transducers with an element size of 12 mm (vertical axis) by 0.75 mm
(5L128-I3, Olympus Corporation, Shinjuku, Tokyo, Japan). One transducer served as
transmitter, the other as receiver, being coaxially aligned in a fixture at a separation of
100 mm; this was immersed in a water tank with the test sample placed in between.
The phased-array transducers were connected to an Omniscan MX device (Olympus,
Corporation, Shinjuku, Tokyo, Japan), and controlled by the Olympus TomoView
software (version 2.7, Olympus Corporation, Shinjuku, Tokyo, Japan), to emit and
receive the ultrasound signals as described in the next section. In order to obtain a 360°
ultrasound scan, the phased-array transducers remained stationary and the sample
rotated using a user-programmed Motoman HP6 robotic arm (YASKAWA Electric
Corporation, Japan) with six degrees of freedom. Further 2D slices were obtained by
vertically-translating the test sample using the robotic arm.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 79
Figure 4-3: Left: Sketch of the UCT system set-up. Right: Photograph of the experimental set-up
showing the sample attached to the robotic arm and positioned between the two phased-array
transducers.
TomoView was used to set all signal acquisition parameters as well as the beam
profile. The scan was performed by individually firing 64 elements of the transmit
transducer, and detecting the propagated ultrasound wave with 64 correspondingly-
aligned elements of the receive transducer. The sample was rotated in 1° steps, thereby
obtaining a total of 23,040 signals (360 projections by 64 element-pairs). Each signal
consisted of 626 data points, recorded at a digitization frequency of 25 MHz, and a
‘system gain’ of zero was utilised to avoid signal saturation. The effect of digitization
frequency on the image quality was investigated and 25 MHz was found to be
sufficient. For each sample, multiple 2D UCT images were automatically obtained at
2 mm increments after each 360° rotation.
Ultrasound attenuation (βi,θ, dB) was calculated by measuring the insertion loss,
given by
𝛽𝑖,𝜃 = 20 ln𝐴𝑟𝑒𝑓
𝑖
𝐴𝑚𝑒𝑎𝑠𝑖,𝜃 (Eq. 4.1)
where i is the number of the emitting and receiving transducer (1 to 64), 𝜃 is the
rotation angle of the sample, 𝐴𝑟𝑒𝑓𝑖 is the maximum peak value of the reference
measurement (through water only) of transducer i, and 𝐴𝑚𝑒𝑎𝑠𝑖,𝜃
is the maximum peak
value of the measured signal. The values of βi,θ are termed a sinogram, and in theory,
if the sample rotation axis is perfectly centred, then
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 80
𝛽𝑖,𝜃 = 𝛽𝑁−𝑖+1,𝜃+𝜋 (Eq. 4.2)
where N is the total number of transducers (64 elements in this study).
The 2D UCT images were computed using the Simultaneous Iterative
Reconstruction Technique (SIRT) [162], which is an Algebraic Reconstructing
Method based on the Kaczmarz method [132]. The 2D UCT images of all the samples
were reconstructed producing an image of 256x256 pixels, which corresponds to the
width of the sensor array used, i.e. 1 pixel corresponds to 187.5 µm. This results in a
UCT voxel size of 0.18x0.18x0.18 mm3. However, from our previous study (see
chapter 3), we estimated the resolution of our UCT system to be approximately 2 mm.
Matlab (The MathWorks Inc., Natick, MA, USA) was used to convert the 2D UCT
images into 3D models. First, dynamic thresholding was applied to each image to
create 2D binary images which were then stacked to build the 3D ultrasound models,
seen in Figure 4-4. These were then converted into triangular faces and vertices, and
the 3D data set saved in STL file format for subsequent FEA simulations.
Figure 4-4: a) a typical 2D attenuation map obtained by the UCT, the x and y axis represent the pixel
number, the colour bar denotes the attenuation values in [dB m-1]. b) 2D binary image after applying
the threshold. c) reconstructed 3D ultrasound model after stacking all 2D images. The axes are in [mm].
4.4.4 Finite Element Analysis
The FEA simulation was performed using Ansys Workbench (version15,
ANSYS INC, Canonsburg, Pennsylvania, USA). Since STL format files provide only
the surface of the structure, they were converted into the solid body format required
for FEA in Ansys. Noting that a direct conversion from STL to SLDPRT format could
not be identified, Geomagic Wrap (version 2014, 3D Systems, Rock Hill, USA) was
used to convert the STL files into Initial Graphics Exchange Specification (IGES)
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 81
format. The IGES files were then imported into SolidWorks software and saved as
SLDPRT (Solid Part) format after manually fixing any faulty faces. The file
conversion flow-chart is shown in Figure 4-5. The 3D µCT and UCT models in
SLDPRT format were used as input geometry to the FEA. The material and mechanical
properties for the VisiJet M3 Crystal 3D-print material were obtained from the
manufacturer’s data sheet, being a Young’s modulus of 1463 MPa and Poisson’s ratio
of 0.35. Boundary conditions were applied by defining the fixed support, being the
bottom endplate of a sample, with a vertical displacement applied to the top end-plate.
The FEA was solved for a maximum displacement of 1 mm, corresponding to a strain
of 20%; the stiffness (N mm-1) calculated by dividing the applied reaction force by
the observed displacement.
Figure 4-5: File conversion flow-chart diagram from STL to SLDPRT, required for input into Ansys
software.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 82
The dependence of the results on the number of mesh elements was studied and
showed that the results of FEA were not affected by changing the mesh size. Figure
4-6 shows mesh size convergence in the CAB1 sample with element sizes of 5 mm, 3
mm and 1 mm, and that a 145% increase in number of elements between mesh sizes
of 5 mm and 1 mm only resulted in a 0.07% change in stiffness values.
Figure 4-6: Mesh size convergence in the CAB1 sample with element sizes of 5 mm, 3 mm and 1 mm.
Both the derived 3D-UCT and microCT models were rendered from tetrahedron
elements whereby a smooth triangular bone surface is generated from voxel gray-scale
images by interpolating the nodes of the triangles. Compared to hexahedron elements,
the tetrahedron meshing can model trabecular connections that are smaller than the
voxel size of the images, this prevents loss of connectivity and better representation of
the original geometry than with hexahedron elements. Also, the smooth surface that is
generated from tetrahedron meshing provides more accurate calculation of the bone
tissue loading at the trabecular surface [185]. The hexahedron elements are not
generally used in medical simulation because this meshing requires a significant
amount of user interaction compared to tetrahedral meshing, which can be automated.
The reason is that hexahedral meshes are more rigid structures and cannot always be
automatically constructed for complex geometries [186].
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 83
4.4.5 Experimental Mechanical Test
The eight 3D-printed cancellous bone replica models were mechanically tested
using an Instron testing machine (Figure 4-7) with a 500 N load cell, providing a (gold
standard) measure of stiffness. Mechanical testing was performed using the same
boundary conditions as defined in the FEA simulations; specifically, the base of the
sample was fixed, and the compression force was applied from the top with
displacement control. The maximum displacement was set to be 1 mm for all the
samples, corresponding to a strain of 20%. The stiffness (N mm-1) of the eight samples
was again calculated by dividing the recorded load by the applied maximum
displacement.
Figure 4-7: Set-up of the mechanical test of a cancellous bone replica sample using an Instron 5848
Micro Tester testing machine with a 500 N load cell.
4.5 RESULTS
Noting that each sample UCT data set contained over 20 slices at 360 projection
angles and over 64 elements, significant memory issues within the TomoView
software were encountered. To minimize the memory required, the effect of ultrasound
signal digitizing frequency on the image quality of the reconstructed UCT attenuation
maps was investigated. Three different values of digitization frequency (25, 50 and
100 MHz) were used to reconstruct a 2D UCT image from a high bone volume fraction
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 84
sample (FR1) as shown in Figure 4-8. The effect of changing the digitization frequency
was unnoticeable; hence a digitizing frequency of 25 MHz was applied to reconstruct
the 2D UCT slices for all 3D-printed samples.
Figure 4-8: 2D UCT images of the same slice but with different digitizing frequency: 25 MHz, 50 MHz
and 100 MHz (from top to bottom). The image size is 256x256 pixels (48x48 mm2). The colour bar
represents the attenuation values in [dB m-1].
Reconstructed 3D-UCT STL files of the 3D-printed samples are shown in Figure
4-9. In general, the UCT system was able to identify the majority of the features of the
samples. However, most structures within the samples have increased in width and
some of the finer structures have been lost during the thresholding process.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 85
Figure 4-9: 3D UCT models of the 3D-printed samples; a) CAB1, b) CAB2, c) LS1, d) LS2, e) IC1, f)
IC2, g) FR1 and h) FR2.
The stiffness values obtained from the mechanical tests and both FEA
approaches were first normalized to unity. Regression analysis results for a) µCT-FEA
stiffness vs mechanical test stiffness and b) UCT-FEA stiffness vs mechanical test
stiffness are shown in Figure 4-10. The coefficient of determination (R2) to estimate
mechanical test derived stiffness was 99% for µCT-FEA and 84% for UCT-FEA. The
CAB1 and CAB2 samples show a discernible deviation in their UCT-FEA derived
stiffness compared to the other samples. To investigate this further, the samples
apparent density was measured for each sample and normalised to unity. The
correlations between the sample density and a) mechanical test stiffness, b) µCT-FEA
stiffness and c) UCT-FEA stiffness are shown in Figure 4-11.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 86
Figure 4-10: Estimation of the experimental mechanical test stiffness by µCT-FEA (a) and UCT-FEA
(b). LS1 and LS2 (x), CAB1 and CAB2 (□), IC1 and IC2 (○), FR1 and FR2 (Δ).
Figure 4-11: Correlation between bone replicas density and (a) mechanical test stiffness, (b) µCT-FEA
stiffness, (c) UCT-FEA stiffness. LS1 and LS2 (x), CAB1 and CAB2 (□), IC1 and IC2 (○), FR1 and
FR2 (Δ).
The samples show a high correlation (r = 0.97) between sample apparent density
and measured mechanical stiffness. The µCT-FEA derived stiffness also displays this
correlation (r = 0.98) despite the overestimated stiffness values. The UCT-FEA
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 87
derived stiffness also correlated with sample density with r = 0.90; however, there are
clear outliers in the CAB1 and CAB2 samples.
An estimation of the solid volume fraction (SVF, solid component volume
divided by total sample volume) was made of all the 3D models. The models were
derived from the µCT-FEA and UCT-FEA measurements as shown in Figure 4-12.
The SVF was consistently overestimated in every sample; however, CAB1 and CAB2
samples have a noticeably higher overestimation of the SVF compared to the other
samples.
Figure 4-12: SVF measurement for all the bone replicas samples obtained from µCT-FEA and UCT-
FEA, showing that the UCT-FEA overestimates the SVF for all the samples but CAB1 and CAB2 have
a noticeably higher overestimation of the SVF compared to the other samples.
The cross-sectional area of CAB1 was scrutinised and revealed a complex
structure with thin trabeculae and a lower SVF compared with, for example, FR1
which had thicker trabeculae and a higher SVF. This is illustrated in Figure 4-13,
which shows the cross-sectional area images of the two samples.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 88
Figure 4-13: Cross-section area images for CAB1 (top) and FR1 (bottom), black = microCT and UCT
overlap, dark grey = UCT only, light grey = microCT only and white = no microCT or UCT.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 89
4.6 DISCUSSION
The ultimate aim is to use UCT-FEA to estimate the mechanical stiffness of the
trabecular bone samples. To do this, the effectiveness of FEA without the
complications of imaging artefacts that can occur in UCT reconstructions should first
be determined. Since the resolution of the µCT system is very high compared to the
feature size of the samples studied here, µCT-FEA effectively demonstrates the
effectiveness of FEA alone. The correlation between the actual mechanical stiffness
and µCT-FEA derived mechanical stiffness was very high (R2 = 99%); there was also
a very high correlation between mechanical stiffness (µCT and actual) and actual
sample apparent density.
Structures in the UCT images generally widened and the attenuation values
decreased, partly due to voxel averaging, but also due to refraction artefacts,
potentially leading to larger than actual structures being incorporated into the UCT-
FEA analysis; however, some of the smaller structures could be lost during the
thresholding process. Despite these issues, the correlation between the actual
mechanical stiffness and UCT-FEA derived mechanical stiffness was still high (R2 =
84%), as was the correlation between actual sample apparent density and UCT-FEA
derived mechanical stiffness (r = 0.90).
The higher than expected mechanical stiffness of the CAB1 and CAB2 models
obtained with UCT-FEA was investigated further by measuring SVF of the samples,
which is considered to be the best histomorphometric predictor of bone strength [187,
188]. CAB1 and CAB2 have SVF values that are higher compared to the measured
SVF by µCT-FEA as shown in Figure 4-12; an indication that these two samples
appeared to be stiffer compared to their stiffness measured by other methods. This
issue may be attributed to the complexity and porosity of these two samples, i.e. many
thin trabeculae with sharp ends, which affected the propagation of ultrasound through
the samples, leading to a higher reflection that could dilate the apparent trabecular
thickness. Further investigations were conducted by measuring the cross-sectional area
along the sample height (z axis) for UCT-CAB1 and UCT-FR1 models (Figure 4-14).
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 90
Figure 4-14: Cross-sectional area measurement along the z axis for two UCT-FEA models, CAB1 (top)
and FR1 (bottom).
In both samples, the cross-sectional area was consistently overestimated. In the
FR1 sample which has a larger average cross-sectional area (large trabeculae), the
overestimation is smaller and the same features can be seen in both the UCT and µCT
plots. However, in the CAB1 sample, which has a much lower average cross-sectional
area (small trabeculae), the overestimation is more significant and the features in the
µCT plot are not replicated in the UCT plot.
Despite the issues with the CAB samples, the correlation between UCT-FEA
and the actual mechanical stiffness was considered to be sufficiently high for potential
future clinical applications to be considered. Furthermore, the very high µCT-FEA
correlation observed would be lower for a clinical X-ray CT system, which would have
a significantly lower spatial resolution. Hence, UCT-FEA may perform comparably
against clinical X-ray CT in human subjects.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 91
4.7 CONCLUSION
Ultrasound computed tomography based finite element analysis (UCT-FEA) is
a promising tool for estimating the mechanical integrity of a bone. This study
demonstrated that UCT-FEA based upon quantitative attenuation images provided a
comparable estimation of gold standard mechanical-test stiffness of 84% compared to
µCT-FEA (R2 = 99%). This opens the door for further research as it shows that UCT-
FEA is a promising technique to provide a non-invasive, non-destructive estimation of
the mechanical integrity of bone that may have significant potential clinical utility for
osteoporotic fracture risk assessment and quantitative assessment of musculoskeletal
tissues.
This study was limited by using 3D-printed replica bone samples that do not
represent real human bones. Furthermore, a single material was used to create the
samples and the Young’s modulus of the material was assumed. Since this was a proof
of concept study, we decided to use phantoms instead of real specimens to have more
control over sample properties (attenuation, velocity of sound, homogeneous material)
since our aim was to verify our technique. Future work should consider using real bone
tissue samples along with the potential for UCT to estimate the Young’s modulus of
bone tissue. Another limitation was the resolution of the UCT system which currently
is approximately 2 mm. Any improvements of the resolution is an important challenge
for future UCT-FEA assessment of cancellous bone samples. However, it is our view
that short-term clinical applications for the UCT system will be material/mechanical
assessment of (a) fracture risk in long bones and (b) hard/soft-tissue changes associated
with influencing factors such as amputation-prosthetics.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 92
4.8 WHAT IS NOVEL?
This chapter provides a validation of the use of the UCT-FEA technique to image
complex samples using cancellous bone replicas. It shows that this is a promising
technique for bone imaging and to estimate bone mechanical properties.
Figure 4-15: Summery of the UCT-FEA study in Chapter 4.
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 93
Chapter 4: Estimation of Mechanical Stiffness by Finite Element Analysis of Ultrasound Computed Tomography
(UCT-FEA); A Comparison with µCT-FEA in Cancellous Bone Replica Models 94
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 96
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 97
Chapter 5: Combining Ultrasound
Computed Tomography Using
Transmission and Pulse-Echo
for Quantitative Imaging the
Cortical Shell of Long Bone
Replicas
5.1 PRELUDE
This chapter demonstrates a simple and fast UCT technique combining
ultrasound Pulse-Echo and Transmission computed tomography (PE-T-UCT) for
measuring the cortical shell thickness and the speed of sound in the cortical shell of
long bone replicas. It is based on a paper published in the journal Frontiers in
Materials.
5.2 ABSTRACT
We demonstrate a simple technique for quantitative ultrasound imaging of the
cortical shell of long bone replicas. Traditional ultrasound computed tomography
instruments use the transmitted or reflected waves for separate reconstructions but
suffer from strong refraction artefacts in highly heterogeneous samples such as bones
in soft tissue. The technique described here simplifies the long bone to a two-
component composite and uses both the transmitted and reflected waves for
reconstructions, allowing the speed of sound and thickness of the cortical shell to be
calculated accurately. The technique is simple to implement, computationally
inexpensive and sample positioning errors are minimal.
5.3 INTRODUCTION
X-ray based modalities are currently used as the primary method to determine
bone health [189, 190]. Unfortunately, they are far from perfect at predicting the
mechanical properties and regular testing of patients can’t be performed due to limits
on x-ray exposure levels. Over the past 3 decades, quantitative ultrasound methods
have been heavily investigated for quantifying bone health due to the inherent
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 98
relationship between ultrasound waves and mechanical properties of materials [95,
190, 191].
One of the earliest demonstrations of a portable clinical quantitative ultrasound
system to determine bone ultrasound properties was the CUBA system [192] which
measured the broadband ultrasound attenuation (BUA) and speed of sound (SOS)
through ultrasound transmission measurements. However, for long bones, most recent
efforts have focussed on single sided pulse echo techniques to determine the cortical
shell thickness and SOS [193-195]. These instruments require a highly trained operator
to make decisions on how and where to place the transducers on the skin, making them
inherently operator dependent. A computed tomography (CT) based quantitative
ultrasound approach for long bones would not require a highly trained operator, would
be highly repeatable and provide 3D detailed spatial information to the clinician as
well.
There has been a plethora of research into quantitative ultrasound computed
tomography (UCT) for soft tissues for applications such as detecting cancer risk in
breast tissue [196]. In these soft tissues, refraction artefacts have a small but significant
effect on reconstructed images. Several image reconstruction methods have been
developed to overcome this small perturbation from the straight ray approximation.
Unfortunately, using these techniques in highly heterogeneous media such as bone is
not possible [197].
Typically, there are two types of UCT techniques, transmission UCT (T-UCT)
and pulse-echo UCT (PE-UCT). T-UCT use a similar principle to traditional x-ray CT
by measuring the ultrasound pulse transmitted through the sample at different rotation
angles and translational positions. In soft tissue, this can produce accurate high
resolution quantitative maps of BUA and SOS in the tissue. In samples containing
bone, the images are not quantitative and produce a blurry image of the bone, the
cortical thickness cannot be accurately measured.
PE-UCT methods are usually defined as non-quantitative, they usually can’t
provide a SOS map of the bone. They can produce high resolution image of the outer
bone surface. To acquire details of the inner cortical shell surface requires assuming a
value for the bone SOS based on previous ex-vivo ultrasound transmission
measurements of a population. Since bone SOS is an indicator of bone health as well
as cortical shell thickness, the reconstruction of the shell inner surface is unreliable.
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 99
The Lasaygues group has led the way in extending UCT to allow quantitative
imaging of the long bone cortical shell with two main methods developed. Compound
Quantitative Ultrasonic Tomography (CQUT) is an iterative experimental method that
compensates for refraction by adjusting the transmitting and receiving transducer
locations and angles to sample the equivalent straight path through the bone [31].
Distorted Born Diffraction Tomography (DBDT) uses a single set of experiments but
performs iterative simulations of the sample [152]. Although both CQUT and DBDT
have resulted in good quantitative images of the cortical shell, they require either
multiple experiments and heavy data processing requirements (CQUT) or are very
computationally time expensive (DBDT). A fast and simple technique for quantitative
UCT of long bones to output the key clinically relevant metrics has not been developed
yet.
Here, we demonstrate a simple and fast UCT technique (PE-T-UCT) to extract
an average bone SOS and a mean cortical shell thickness. The useful data in T-UCT is
combined with the reconstructed PE image using a two component model of the
cortical shell. We then used this averaged SOS to accurately reconstruct each PE
image, avoiding the use of a population averaged SOS.
5.4 THEORY
Using transmitted and reflected pulses for determining bone SOS and cortical
shell thickness has been proposed by Zheng and Lasaygues [150] using single element
transducers at a single angle. It is extended here using reconstructed pulse-echo UCT
images (PE-UCT) and transmission-UCT (T-UCT) data instead of the raw echo data.
We also use multi-element transducers so that positioning errors are minimal and a
better sample average is obtained. For a simple two component model of cortical bone,
the SOS in the bone cortical shell (𝑣𝑏) is assumed to be a constant and all other volumes
are assumed to have the SOS in water (𝑣𝑤 = 1483 m s-1). The apparent delay time ( t
) of an ultrasound wave travelling through the bone is measured directly in T-UCT. It
is calculated as the time taken for the ultrasound wave to pass through the sample
minus the time through a reference measurement (water only). It is related to 𝑣𝑏 by:
∆𝑡 = 𝑑 (1
𝑣𝑏−
1
𝑣𝑤) (Eq. 5.1)
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 100
Here 𝑑 is not the bone diameter, but rather the total length of bone that the ultrasound
wave propagates through to be detected at the receiving transducer. If we only consider
propagation through the middle of the bone then 𝑑 is given by the addition of the bone
shell thickness on both sides (𝑇1, 𝑇2) that the wave propagates through:
𝑑 = 𝑇1 + 𝑇2 = (𝑡1 + 𝑡2)𝑣𝑏 (Eq. 5.2)
where 𝑡1 and 𝑡2 are the time taken for the wave to propagate through the first and
second side of the bone shell respectively. These equations can be solved to find the
speed of sound in bone as:
𝑣𝑏 = 𝑣𝑤𝑡1+𝑡2−∆𝑡
𝑡1+𝑡2 (Eq. 5.3)
Although 𝑡1 and 𝑡2 can be measured directly in a PE sonogram, it is more
intuitive to use the reconstructed PE-UCT image. This is particularly important in
complex samples where different transducer positions are required to resolve the inner
and outer interfaces. In the PE-UCT reconstruction, the speed of sound is assumed to
be a 𝑣𝑤 everywhere, causing the shell thickness to appear thinner in a PE-UCT image.
This reduced thickness (𝑇′1 or 𝑇′
2) can be converted back into a shell propagation
time using:
𝑡 =𝑇′
𝑣𝑤 (Eq. 5.4)
Combining (5.3) and (5.4) allows the calculation of 𝑣𝑏 for various angles of sample
rotation. The true cortical shell thickness uses the calculated 𝑣𝑏 values along with the
measured apparent thickness values to calculate the corrected thickness values:
𝑇 = 𝑇′ 𝑣𝑏
𝑣𝑤 (Eq. 5.5)
5.5 MATERIAL AND METHODS
5.5.1 Phantom Samples
A simple hollow cylinder structure was studied first to demonstrate the PE-T-
UCT concept. Two hollow Perspex cylinders were used with outer diameters of 25 and
35 mm and labelled as P25 and P35 respectively. The holes were drilled as close as
possible to the centre and the thickness of the shell was approximately 7.5 mm.
Although these don’t represent real bones, they are simple test cases for demonstrating
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 101
the PE-T-UCT concept and they have no variation in the z-direction so there are
minimal slice averaging effects.
To demonstrate the concept with long bone like shapes, a plastic femur bone
from 3B Scientific was used. Three plastic bone segments each approximately 30 mm
long were cut. Holes were drilled through the centre of each segment and allowed to
fill with water in UCT experiments to mimic the medullary cavity. One sample (PB1)
was taken from the Metaphysis and two (PB2 and PB3) were taken from the Diaphysis.
Figure 5-1 shows a photograph of the samples.
Figure 5-1: Photograph of the Perspex cylinder samples; P25 and P35 with 25 and 35 mm diameters
respectively, and the plastic bone samples; PB1, PB2 and PB3.
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 102
5.5.2 Data Acquisition
The samples were scanned using a lab-built ultrasound computed tomography
(UCT) system (described in chapter 3 and 4). Two 2.25 MHz 128-element linear
phased-array transducers (Olympus, Corporation, Shinjuku, Tokyo, Japan) with an
element width of 0.75 mm (xy plane) and height of 12 mm (z-axis). The total
transducer width was therefore 128×0.75 = 96 mm. One transducer acted as a
transmitter and receiver (for PE-UCT), and the other as a receiver only (for T-UCT).
They were coaxially aligned in a fixture 137 mm apart and immersed in a water tank
with the sample placed roughly in the centre between the two transducers. To obtain a
360° ultrasound scan (in 1° steps), the phased-array transducers were rotated around
the z-axis using a user-programmed Motoman HP6 robotic arm (YASKAWA Electric
Corporation, Japan). Each transducer was connected to an Omniscan MX device
(Olympus, Corporation, Shinjuku, Tokyo, Japan), and controlled by the Olympus
TomoView software (version 2.7, Olympus, Corporation, Shinjuku, Tokyo, Japan), to
emit and receive the ultrasound signals. Figure 5-2 shows a schematic representation
of the UCT system.
TomoView was used to set all signal acquisition parameters as well as the beam
profile. The transmitting transducer was set to fire 5 neighbouring elements at a time
(equivalent emitter size of 3.75 mm). These set of 5 elements were incremented by 1
for successive scans to give a total of 124 measurements per rotation angle per
transducer. The transmitting transducer received data only on the central firing
element. The receive only transducer was set to receive on the same element number
directly opposite. Ideally, this results in both transducers only sampling 124 straight
paths perpendicular to the transducers. The electronic gain on each transducer was set
dynamically depending on the sample to minimize saturation but still resolve all the
sample features. The digitization frequency was 25 MHz and the pulse length was 300
ns.
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 103
Figure 5-2: Schematic representation of the UCT system. The robotic arm is used to position the
transducers such that the sample is approximately centered between the transducers in the xy plane and
positioned at the correct z position for imaging. The robotic arm also rotates the transducers during
acquisition.
5.5.3 PE-UCT Reconstructions and Reduced Thickness Calculation
PE-UCT reconstructions were performed using the fully rectified data collected
from the transmitting transducer. Time since transducer firing (𝜏) was converted into
a distance perpendicular to the emitting transducer (𝑦′) using:
𝑦′ = 𝑣𝑤 𝜏 2⁄ (Eq. 5.6)
Using the element position on the transducer (𝑥′) and the rotation angle, the location
that the signal originated from can be calculated in the stationary frame (𝑥, 𝑦). Each
signal from a total of 124×360 = 44,640 scans were then binned onto a common x y
grid (square pixel size of 0.375 mm) and summed.
ImageJ was used to remove reconstructed interfaces originating from reflections
from the sample interfaces on the far side of the sample. These reflections appear much
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 104
closer to the centre of the samples due to the higher velocity experienced through the
first side of the sample. They are easily identified by reconstructing only the first half
of the data to give a one-sided view of the sample. For the Perspex samples, the inner
and outer interfaces were identified using the ‘findpeaks’ function in MATLAB
(release 2016b, The MathWorks, Inc., Natick, Massachusetts, United States) in a fully
automated fashion. For the plastic bone samples, identification of the interfaces was
required by manually drawing a polygon of the inner and outer interfaces over the
reconstructed images and thresholding. The apparent shell thickness (𝑇′1or 𝑇′
2) as a
function of rotation angle (𝜃) was found by rotating the image 𝜃, finding the centre of
the bone on the 𝑥′-axis and taking the average thickness along the 𝑦′-direction over a
width of 1.875 mm. Samples were taken over 360° in 1° steps to compare with the
transmission data.
5.5.4 Calculating Apparent Delay Time from Transmission Data
The apparent delay time for each element at each 𝜃 is found as the difference in
time of arrival (using the maximum of the fully rectified data) of the ultrasound pulse
at the receiver compared to when there is no sample present (water only). For samples
with a SOS higher than water, this results in a negative Δ𝑡 if the path length of the
received sample is equal to the path length in water. For each 𝜃, only t that satisfy
−20 < ∆𝑡 < −0.5 μs are used. These bounds were chosen to remove physically
unrealistic data that can occur when the signal strength is below the noise level. If there
are no elements for an angle that satisfy this criteria, the angle is not used for further
calculations and the corresponding 𝑇1′and 𝑇2
′ calculated earlier are also removed from
further calculations. From the allowed Δ𝑡 values, the middle (spatially along the
transducer) third elements are used to calculate a mean value of Δ𝑡 for each allowable
angle.
5.5.5 SOS and Thickness Calculations
The set of calculated Δ𝑡, 𝑇1′ and 𝑇2
′ values are then used to calculate a set of 𝑣𝑏
values using Eq. (5.3) and (5.4). If any of the 𝑣𝑏 values are outside the bounds of
1500 < 𝑣𝑏 < 5000 m s-1 then they are excluded along with the corresponding 𝑇1′ and
𝑇2′ values. From these allowed 𝑣𝑏, 𝑇1
′ and 𝑇2′ values, the corrected thickness values are
then calculated from Eq. (5.5). Average values of the bone SOS (�̅�𝑏) and shell
thickness (�̅�) are then calculated. For visualization of the cortical shell in the PE-T-
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 105
UCT image, �̅�𝑏 is used to reconstruct the inner interface of the cortical shell along with
the existing outer shell from the PE-UCT reconstruction.
5.5.6 Reference Measurements
Speed of sound measurements of the bulk material were taken with the same
experimental apparatus except the transducers remained stationary. For Perspex SOS
measurements, a large rectangular Perspex prism was positioned with its largest faces
parallel to the transducers, the path length was 24 mm. For plastic bone, an 8 mm thick
slice of the femur was cut and positioned with the cut sides parallel to the transducers.
In both materials, an average Δ𝑡 was taken over the middle half of the samples and the
�̅�𝑏 was calculated using Eq. (5.1).
To determine the actual shell thickness of the samples, optical images of the
samples in the xy plane from one side were taken using a desktop optical scanner.
Thresholding in ImageJ was used to produce binary images of the sample cross-
sections for comparison with UCT images and to calculate the average cortical shell
thickness. For plastic bone 1, the side closest to the middle of the shaft was used. For
the plastic bone samples, there are slight changes in morphology across the length of
the cut samples so the images and derived shell thickness are not as accurate as the
Perspex samples.
5.5.7 T-UCT Bulk Attenuation Map Reconstruction
Bulk attenuation (𝛽) maps were reconstructed from the fully rectified
transmission data using MATLAB. The ultrasound pulse amplitude through the
sample for each element and angle (𝐴𝑆) is compared to the amplitude through water
alone (𝐴0) to calculate 𝛽 using:
𝛽 = −20 log (𝐴𝑆
𝐴0⁄ ) (Eq. 5.7)
This produces a 124 × 360 element matrix representing the 124 transducer
element locations in the rotating frame and 360 rotations. A 5 point image median filter
was then applied to reduce the noise level using the ‘med2filt’ function. Image
reconstruction was then performed using the inverse radon transformation (‘iradon’
function) with linear interpolation and Ram-Lak filter. Finally, a 33% threshold of the
maximum attenuation in each image was applied to the reconstructed image for clarity.
Reconstructions using the metrics of Broadband Ultrasound Attenuation (BUA) and
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 106
SOS were also attempted. Unfortunately, the data was too noisy for BUA calculations
and the SOS reconstruction was nonsensical in most samples.
5.6 RESULTS AND DISCUSSION
Strong refraction and reflection in the transition of ultrasound waves between
soft tissue and bone has a detrimental effect in Transmission based UCT. Figure 5-3
shows the received ultrasound signal across the elements after propagating through the
35 mm hollow Perspex cylinder. Since the SOS in Perspex is higher than water, there
should be a negative time delay seen at the receiving transducers in the absence of
refraction. Through the centre of the cylinder where the curvature is at a minimum this
does occur and the delay time would be correctly calculated for image reconstruction.
As we look further from the centre, the delay time increases towards zero even though
the bone projection should appear thicker away from the centre. This is due to
refraction, the path length is increasing and offsetting the higher SOS in the Perspex.
Far from the centre there is a positive delay time due to the very high reflection of
most the incident plane wave. The only part of the wave that is detected by the
receiving transducer element has gone through such large refraction angles that the
path length has increased greatly. This phenomenon makes it impossible to reconstruct
high resolution qualitative (let alone quantitative) reconstructions of bone in T-UCT
without using more complicated methods [197].
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 107
Figure 5-3: Ultrasound signal detected (right) through a hollow 35 mm diameter Perspex cylinder (left).
Ultrasound waves are emitted from the left transducer and detected on the right transducer. As each
wave propagates from the transmitting transducer it experiences different propagation speeds. Each
wave can also experience different path lengths if there is significant refraction occurring. The
combination of both effects result in a time delay registered at the receiving transducer compared to
propagation through water alone. Each transducer element signal is normalized to the maximum value
separately for clarity.
Figure 5-4 shows cross-sections of the samples studied and reconstructed UCT
images. The PE-UCT images generally represent the outside of the samples quite well
except for PB1 where the overall size looks the same but the surface shape looks
different. This could be because we probed the middle of the sample in US but used
the end of the sample for reference images. For the other samples this is not as much
a problem since their morphology does not change drastically over the sample height
like PB1. The T-UCT images give a blurred image of the sample cross-sections. In
general, the size appears contracted but also broadened resulting in smaller and denser
images. The PE-T-UCT reconstructions improved the inner surface of the PE-UCT
images greatly. This is most noticeable in PB2 and PB3 samples where the hole has
almost returned to being perfectly circular.
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 108
Figure 5-4: From left to right: The sample dimensions from optical micrographs, PE-UCT
reconstructions, PE-T-CT reconstruction, T-UCT reconstruction. From top to bottom: P25, P35, PB1,
PB2, PB3. The scale is the same for all images which are 60 mm by 60 mm in size and the tick marks
are 15 mm apart.
To gain a quantitative understanding of how well the UCT system performed,
Table 5-1 shows the calculated bone outer diameter, SOS, and bone thickness, as well
as the reference measurements values. First, we calculate the sample outer diameter
(𝐷) to see how well the PE-UCT system is working. The PE-UCT system performed
quite well considering it is a lab-built system. The diameters measured for P25 and
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 109
P35 suggest there may be a slight centre of rotation offset error in the system as they
both have a positive error value. These values suggest the best accuracy of the PE-
UCT system is approximately 0.5 mm for measuring the bone diameter. Although this
is a large value compared to the thickness of the samples, this error will have little
effect on the bone thickness measurement and SOS since the same offset will apply to
the inner diameter of the bone. In the P25 and P35 samples, the samples have a
perfectly circular cross-section so the standard deviation (𝜎) in the actual diameters is
near zero. Therefore, the PE-UCT standard deviation in P25 and P35 samples (~ 0.2
mm) indicates the precision of the PE-UCT system.
The results for PB1-3 are, as expected, not as good as the ideal Perspex samples.
This is in part due to the inaccuracy of the reference measurements, but also due to the
increased noise in the rougher plastic bone samples. Given the larger distribution of
diameter sizes in the plastic bones, the largest error of less than 4% is still quite
reasonable for a lab-built system.
The SOS measurements for the bulk materials compared to the mean SOS from
PE-T-UCT reconstructions are shown next. The SOS is consistently slightly
underestimated with a maximum error of less than 5%. The standard deviations are not
sufficiently high to suggest it is a noise issue in the measurement technique. It is likely
that the underestimation of the sample velocity is due to refraction in the samples
causing, on average, a slightly longer path length and hence a slightly lower delay time
in the transmission measurements.
Since both the Perspex and plastic bone samples are made of a single
homogeneous material, the SOS standard deviation represents the precision of the
method. For the simple Perspex samples the precision is very high at 30 m s-1 whilst
for the more complex bone samples it is closer to 100 m s-1.
The average measured shell thickness is shown in Table 5-1 with their standard
deviations for both optical micrograph and PE-T-UCT measurements. Despite the
slight underestimation in SOS values from PE-T-UCT, there is no clear overestimation
in the thickness values although the sample size is limited. All the Perspex and plastic
bone samples are within 3% and 7% of the optical micrograph measurements
respectively. The Perspex samples have holes that are well centred, so the standard
deviation in the optical micrograph shell thickness is very small. The standard
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 110
deviation in the PE-T-UCT results suggest the best possible precision for bone
thickness is near 0.1 mm for the PE-T-UCT technique with the UCT setup used. The
bone thickness varies considerably in the plastic bone samples which is adequately
represented in the PE-T-UCT results.
In the traditional ultrasound computed tomography instruments, the transmitted
or reflected waves are used for separate reconstructions. This leads to strong refraction
artefacts in highly heterogeneous tissue such as bones surrounded by soft tissue.
Therefore, the real advantage of our PE-T-UCT technique is simplifying the long bone
to a two-component composite and both the transmitted and reflected waves are used
for reconstructions, allowing the speed of sound and thickness of the cortical shell to
be calculated accurately.
Table 5-1: Tabulated results of the PE-UCT measured bone diameter and PE-T-UCT measured SOS
and shell thickness. Actual values refer to measurements from either optical micrographs or SOS
measurements of bulk material. Bottom numbers in each cell are the measured values minus the
reference values (if applicable). Standard deviations (𝜎) are also shown when appropriate. Blue =
measured value overestimated cf. actual value and red = measured value underestimated cf. actual value.
Chapter 5: Combining Ultrasound Computed Tomography Using Transmission and Pulse-Echo for Quantitative
Imaging the Cortical Shell of Long Bone Replicas 111
5.7 CONCLUSION
We have demonstrated a simple UCT method (PE-T-UCT) to measure the
cortical shell thickness and the speed of sound in the cortical shell of long bone
replicas. Since it uses standard phased array transducers, it can easily be implemented
from standard B-scan ultrasound systems or from commercial UCT breast imaging
systems using rotating phased array transducers. The technique is computationally
inexpensive and sample positioning errors are minimal since a trained operator is not
required to position transducers.
This technique has several avenues for extension and improved accuracy. A
more accurate estimate of the path length through the bone would help obtain more
accurate SOS measurements. Given the simple two component model considered, this
could potentially be done through ray tracing simulations to keep the post processing
time short. This would need to be an iterative procedure since the SOS in bone would
be unknown. The number of iterations would be minimal given the start points are
within 5% of the actual SOS and within 10% of the cortical shell thickness.
5.8 WHAT IS NOVEL?
We have developed a novel UCT system for quantitative imaging of cortical
shell thickness of long bones, by combining transmission and pulse-echo mode.
Compared to existing systems, this technique is fast, simple and non-ionizing, and is,
therefore, a promising alternative technique to monitor cortical shell thickness and
predict the fracture risk of osteoporotic bones.
Chapter 6: Conclusion 113
Chapter 6: Conclusion
This was a proof of concept research project with the principal aim of developing
a novel ultrasound computed tomography (UCT) system to image bone replica models
and estimate the mechanical integrity of these models from the perspective of
osteoporotic fracture prediction.
Osteoporosis is a worldwide health issue that mainly affects older people over
the age of 50 and which leads to bone fragility that results in serious clinical
consequences and economic burden for the health care system. Hence, it has become
imperative to evaluate and predict fracture risk factors associated with osteoporosis
and prevent the morbidity and mortality caused by this condition. Bone mineral density
(BMD) is the current gold standard used to diagnose osteoporosis and predict a
patient’s bone fracture risk. Dual-energy X-ray absorptiometry (DXA) and
quantitative computed tomography (QCT) are the common clinical X-ray based
methods used for BMD measurement. Combining finite element analysis with DXA
and QCT data is found to be more efficient and better to predict bone fracture risk than
DXA or QCT alone. However, both DXA and QCT rely on ionizing radiation and have
other drawbacks such as cost and large and bulky equipment. Quantitative ultrasound
(QUS) is an attractive alternative to X-ray based methods for reasons such as, non-
ionizing beam, cost efficiency, ease of use, and relevant information about bone
density and mechanical properties. However, QUS does not yield an image of bone,
as opposed to DXA and QCT. Conventional ultrasound imaging provides 2/3D
qualitative images of soft tissue; however, it fails produce quantitative images and,
therefore, cannot be used for bone imaging.
These issues have been overcome by the development of quantitative UCT,
which is operator independent and produce 2/3D quantitative images. A number of
UCT studies have been applied on soft tissue whereas a few studies have demonstrated
the use of UCT for bone imaging and assessment, principally because the high
heterogeneity of bone. Hence, the motivation and the aim of this research was to
develop a novel UCT system and investigate its feasibility for imaging and assessing
bone mechanical integrity by, (a) incorporating FEA and (b) combining pulse-echo
Chapter 6: Conclusion 114
UCT (PE-UCT) and transmission UCT (T-UCT) for quantitative imaging of the
cortical shells of long bones.
6.1 HYPOTHESIS 1: DEVELOPMENT OF A NOVEL UCT SYSTEM AND
THE CAPACITY TO IMAGE SOILD OBJECTS
The performance of the UCT system was developed by exploring the functions
of different components of the system, such as Omniscan, the robotic arm, and the
TomoView software. Each component has its own parameters, which were checked
and optimised to arrive at the most appropriate setup prior to conducting the research
experiments. The setup of the system was further improved by designing holders that
provided better alignment of the two transducers. Cross-sectional 2D-UCT images of
the test samples were reconstructed from different projections of the received data,
collected at different angles. For UCT image reconstruction, a developed iterative
algebraic method, i.e. Simultaneous Iterative Reconstruction Technique SIRT, were
used instead of the filtered backprojection (FBP), which is the common technique for
CT image reconstruction. This was chosen because of the high efficiency and better
image quality of SIRT compared to FBP. After trying different number of projections
for image reconstruction, the 360 projections were found to be the optimum number
to provide images with high quality; therefore, all subsequent UCT images in chapters
3, 4 and 5 were reconstructed using 360 projections. The UCT system was capable of
producing quantitative images of solid bodies, such as the bone replica samples shown
in chapters 3, 4 and 5.
6.2 HYPOTHESIS 2: UCT QUANTITATIVE ASSESSMENT
INCORPORATING FEA TO ESTIMATE MECHANICAL
PROPERTIES
Chapter 3 aimed to investigate the feasibility of utilising ultrasound computed
tomography data as a geometric input into FEA, and to compare its ability to estimate
mechanical test-derived stiffness with conventional FEA in simplistic structures. This
study demonstrated, for the first time, that FEA based on 3D ultrasound attenuation
computed tomography images provides a comparable estimation of mechanical-test
stiffness of 95.2% compared to conventional FEA (R2 = 92.7%). However, this study
was limited by the use of regular-shaped simple rod designs, which was not a realistic
representation of the complex structures of bone. Furthermore, only one 2D-UCT slice
was obtained due to instrumentation and data processing limitations.
Chapter 6: Conclusion 115
Chapter 4 demonstrated the application of the UCT-FEA method on more
complex structures, i.e. cancellous bone replica models. 3D-UCT structures of the test
samples were reconstructed from multiple 2D-UCT images of the ultrasound
attenuation. The coefficient of determination (R2) to estimate mechanical test derived
stiffness was 99% for µCT-FEA and 84% for UCT-FEA. This study showed that the
UCT-FEA based upon quantitative attenuation images can provide a comparable
estimation of gold standard mechanical-test stiffness and, therefore, has potential
clinical utility for osteoporotic fracture risk assessment and quantitative assessment of
musculoskeletal tissues.
6.3 HYPOTHESIS 3: COMBINED ULTRASOUND COMPUTED
TOMOGRAPHY USING TRANSMISSION AND PULSE-ECHO
Chapter 5 considered the combination of transmission-UCT and pulse-echo
UCT. The T-mode was aimed at quantifying internal structures and tissue properties
(e.g. quantitative imaging the cortical shell of long bones), whereas the PE-mode was
aimed at producing images of bone surfaces with high spatial accuracy and resolution.
This study resulted in a simple and computationally inexpensive technique for
quantitative ultrasound imaging the cortical shell of long bone replicas. The technique
simplifies the long bone to a two-component composite and uses both the transmitted
and reflected waves for reconstructions, allowing the speed of sound and thickness of
the cortical shell to be calculated with great accuracy.
6.4 LIMITATIONS
The main limitation of this research relates to the use of replica bone samples
and the fact that real bones were not used in any of the studies. However, this approach
has been reported in several previous papers where a polymer was used to replicate
bones. Moreover, this is the first reporting of the UCT-FEA technique, and as with
other imaging modalities (note early X-ray CT, Nuclear Medicine and MRI images),
it is envisaged that further development will improve performance and the real bone
will be considered in the future. Being a proof of concept research, the findings from
these studies should be validated using tissue phantoms that consist of different
materials first and then investigate the feasibility of the concepts in both in-vitro and
in-vivo experiments before they can be applied in a clinical setting. Further, an
experimentally-derived value for the Young’s modulus of the 3D print material was
Chapter 6: Conclusion 116
incorporated within the UCT-FEA analysis. In the future, the potential for ultrasound
CT data to estimate Young’s modulus should be investigated. Another limitation was
the resolution of the UCT system which currently is approximately 2 mm. Any
improvement of the resolution is an important challenge for future UCT-FEA
assessment of complex bone samples.
6.5 FUTURE WORK
Future development of the UCT system, as well as scientific and clinical
validation, should include:
▪ Improving the system’s performance by increasing the rotation speed of
the robotic arm. This should be considered to reduce the scanning time
and data collection process.
▪ Improving the resolution of the system by using spherical phased array
transducers to collect the lost signals due to refraction/reflection from the
scanned objects. This will reduce the refraction and reflection artefacts,
which are associated with T-UCT.
▪ Variability of material elasticity within a sample should be considered
and the potential for UCT to estimate the Young’s modulus of a sample
material should be investigated.
▪ Extending the UCT-FEA method for the estimation of the mechanical
integrity of long bones, such as tibia and femur, and also consider the
soft tissue surrounding the bone.
▪ Conduct clinical validation of the compound PE and T-UCT system, by
implementing the previous methods of plastic bones on real bones and
estimate their mechanical properties and the fracture risk.
▪ The use of UCT system can be extended for quantifying and monitoring
the mechanical properties and tissue viability of the residuum of
amputees. This will provide early detection, prevention and management
of residuum degeneration, breakdown and ulceration.
Chapter 6: Conclusion 117
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Appendices 130
Appendix 1
%%Reconstruction of the Attenuation Map%%
function [ output_args ] = QUT_work( measfile, reffile) %Summary of this function goes here %Detailed explanation goes here
clear; tic measfile='0.5mm_rod.txt' reffile='water_reference_rodsamples.txt' Mr=62; %number of sensors Ma=360; %number of projections gaussianfilt=true; %apply Gaussian filter filt=[0.05 0.2 0.65 1 0.65 0.2 0.05]; %filter kernel [meas, Nmeas]=QUT_loadmeas(measfile, Mr, Ma); if gaussianfilt %gaussian filter meas=conv2(meas, (1/sum(filt))*filt, 'same'); end if strcmp(reffile, '') Nref=Nmeas; ref=repmat(meas(1, :), [size(meas, 1) 1]); else [ref, Nref]=QUT_loadmeas(reffile, Mr, Ma); if gaussianfilt %gaussian filter ref=conv2(ref, (1/sum(filt))*filt, 'same'); end end
%compute element positions s_w=0.00075; %element width s_x=zeros([size(Mr, 1) 2]); for ms=1:Mr s_x(ms, 1)=(ms-1-(Mr-1)/2)*s_w; s_x(ms, 2)=0.05; end r_w=s_w; r_x=zeros([size(Mr, 1) 2]); for mr=1:Mr r_x(mr, 1)=(mr-1-(Mr-1)/2)*r_w; r_x(mr, 2)=-0.05; end f=100000000; dt=1/f; L=0.1; %distance between sender and
receiver c0=1480; T_ref=size(ref,2); T_meas=size(meas,2); rowsPerMeas=Mr*Ma; Nimage=256; reco_att=zeros(Nmeas, Nimage, Nimage); for measnum=1:Nmeas meas_att=QUT_computeatt(meas((rowsPerMeas*(measnum-
1)+1):(rowsPerMeas*measnum), :), ref); nuf=1; meas_att_corr=meas_att; while nuf>0
Appendices 131
[meas_att_corr nuf]=QUT_fillsinogram(meas_att_corr, Mr); end meas_att_corr=QUT_medianfilt(meas_att_corr, Mr, Ma); [meas_att_corr, shiftN]=QUT_recenter(meas_att_corr, Mr); disp(sprintf('data shifted %d steps', shiftN));
%Utilize packed measurement array meas_att_corr_packed=QUT_packmeas(meas_att_corr, Mr, Ma); reco_att(measnum, :, :)=art_linear_arrayx(r_x, s_x,
((360/Ma)*pi/180)*[0:(Ma/2-1)], meas_att_corr_packed, 0, Nimage,
64);
%Use limited number of projections a_step=1; %NOTE 360/a_step must be integer meas_att_corr_packed=zeros([(Ma/a_step)*Mr 1]); for a=1:(Ma/a_step) for r=1:Mr idx_0=(a-1)*Mr+r; idx_1=r+(a-1)*a_step*Mr; meas_att_corr_packed(idx_0)=meas_att_corr(idx_1); end end reco_att(measnum, :, :)=art_linear_arrayx(r_x, s_x,
((360/Ma)*pi/180)*[0:a_step:(Ma-1)], meas_att_corr_packed, 0,
Nimage, 64); end
imrows=floor(sqrt(Nmeas)); imcols=ceil(Nmeas/imrows); for j=1:Nmeas subplot(imrows, imcols, j); imagesc(reshape(reco_att(j, :, :), [Nimage Nimage]));
colorbar; title(sprintf('%d/%d', j, Nmeas)); end
function [meas N] = QUT_loadmeas( filename, Mr, Ma ) %QUT_LOADMEAS Loads a measurement in QUT format and converts it into %internal format. Returns also number of crossections = N. z=load(filename); lines=size(z, 1); N=floor(size(z,1)/(Mr*Ma)); %number of cross sections separatorlines=mod(lines/Mr, Ma); %T_meas=size(z, 2); idx=ones([size(z, 1) 1]); if separatorlines==1 for j=1:Mr idx((Ma*N+1)*(j-1)+1)=0; end elseif separatorlines==2 for j=1:Mr idx((Ma*N+2)*(j-1)+1)=0; idx((Ma*N+2)*(j-1)+2+(Ma*N))=0; end elseif separatorlines==3 for j=1:Mr idx((Ma*N+3)*(j-1)+1)=0; idx((Ma*N+3)*(j-1)+2+(Ma*N))=0;
Appendices 132
idx((Ma*N+3)*(j-1)+3+(Ma*N))=0; end elseif separatorlines==6 for j=1:Mr*2 idx((Ma+3)*(j-1)+1)=0; idx((Ma+3)*(j-1)+2+Ma)=0; idx((Ma+3)*(j-1)+3+Ma)=0; end end meas_tmp=z(idx==1,:); meas=zeros(size(meas_tmp));
for j=1:Mr for k=1:Ma for l=1:N %meas((l-1)*Mr*Ma+Mr*(k-1)+(j-1)+1,
:)=meas_tmp(Ma*Mr*(j-1)+Ma*(l-1)+(k-1)+1, :); meas((l-1)*Mr*Ma+Mr*(k-1)+(j-1)+1, :)=meas_tmp((l-
1)*Ma+(j-1)*N*Ma+(k-1)+1, :); end end end end
function [ att] = QUT_computeatt( meas, ref ) %QUT_COMPUTEATT Computes attenuation data from two time domain
measurements % Detailed explanation goes here
dummymethod=true;
unknown_attenuation=-1; max_attenuation=500; min_attenuation=0;
if dummymethod att=zeros([size(meas, 1) 1]); for j=1:size(meas, 1) meas_level=max(abs(meas(j, :))); ref_level=max(abs(ref(j, :)));
if ref_level<meas_level att(j)=min_attenuation; else %att(j)=10*log(ref_level/meas_level); %variance is
already on "power domain" att(j)=20*log(ref_level/meas_level); if att(j)>max_attenuation att(j)=max_attenuation;%unknown_attenuation; end end end else pulse_N=50; noise_N=300; att=zeros([size(meas, 1) 1]); for j=1:size(meas, 1)
Appendices 133
s_meas=meas(j, :); s_ref=ref(j, :);
if mod(j, 128)==0 continue; end
s_noise_ref=(s_ref(1:noise_N)); var_noise_ref=var(s_noise_ref); [foo idx_ref]=max(s_ref); ref_level=var(s_ref((idx_ref-pulse_N):(idx_ref+pulse_N)))-
var_noise_ref;
s_noise_meas=(s_meas(1:noise_N)); var_noise_meas=var(s_noise_meas); meas_level=var(s_meas((idx_ref-pulse_N):(idx_ref+pulse_N)))-
var_noise_meas;
if ref_level<meas_level att(j)=min_attenuation; elseif meas_level<=0 att(j)=unknown_attenuation; else att(j)=10*log(ref_level/meas_level); %variance is
already on "power domain" %att(j)=20*log(ref_level/meas_level); if att(j)>max_attenuation att(j)=max_attenuation;%unknown_attenuation; end end end end
end
function [ att_fixed N_unfixed] = QUT_fillsinogram( att, Me) %QUT_FILLSINOGRAM Compute missing points (=-1) from sinogram % Detailed explanation goes here
unknown_attenuation=-1;
att_fixed=att;
N_unfixed=0; Ma=size(att, 1)/Me; for a=1:Ma for e=1:Me att_ae=att(e+Me*(a-1)); if att_ae~=unknown_attenuation att_fixed(e+Me*(a-1))=att_ae; %elseif att(Me-e+1+Me*(mod(a-1+180,
Ma)))~=unknown_attenuation % att_fixed(e+Me*(a-1))=att(Me-e+1+Me*(mod(a-1+180,
360))); else N=0; sum_att=0;
Appendices 134
for aa=(a-1):(a+1) aaa=mod(aa-1+Ma, Ma)+1; for ee=(e-1):(e+1) if ee>=1 && ee<=Me if att(ee+Me*(aaa-1))~=unknown_attenuation sum_att=sum_att+att(ee+Me*(aaa-1)); N=N+1; end end end end if N>0 att_fixed(e+Me*(a-1))=sum_att/N; else N_unfixed=N_unfixed+1; end end end end
end
function [ s ] = art_linear_arrayx( r_x, s_x, angle, meas_tof,
ref_s, N, n_iter) %art_linear_array Compute a reconstruction with linear array
equipment like QUT %system. Center of rotation is assumed in origin (0,0) % r_x = receiver positions (x, y) % s_x = sender positions (x, y) % angle = measurement angles % meas_tof = measured tof % ref_s = slowness in water (reference measurement) % N = size of reconstruction % n_iter = number of iterations
s=ref_s*ones([N N]); Me=size(s_x, 1); Mr=size(r_x, 1); Ma=size(angle, 2); if Me~=Mr error('Me~=Mr'); end
if size(meas_tof, 1)~=Me*Ma error('size(meas_tof, 1)~=Me*Ma'); end
clear Mr; %to make sure we won't accidentaly use this
%tof=zeros([Me Ma]); %for a=1:Ma % for e=1:Me % tof(e,a)=meas_tof(); % end %end
fig=figure;
Appendices 135
L=-1; for j=1:Me L=max([L norm(s_x(j,:)) norm(r_x(j,:))]); end %L=2.05*L; %L=sqrt(2)*L; L=1.05*L; dx=L/(N-1);
disp('CEM'); %Lnu=5e+5*speye([Me*Ma Me*Ma]); Lnu=speye([Me*Ma Me*Ma]); %alpha=0.1; alpha=min(0.25*(N/256), 0.5); lambda=(N/256)*2000/(180000); nu_star=zeros([Me*Ma 1]); L_x=smoothnessCovMatrix(N, 16, 1); %L_x=smoothnessCovMatrix(N, 64, 1); s_star=zeros([N*N 1]); G=L_x'*L_x; %W2=zeros([N*N N*N]); %W2=sparse(N, N); W2_diag=(1./(sum(G'.*G').^2))';
%for j=1:N*N % n2=W2_diag(j);%sum(G(j, :).^2); % W2(j,j)=1./n2; %end
%path=zeros([N N]);
%A=zeros([length(meas_tof) N*N]);
%A=sparse([], [], [], length(meas_tof), N*N);
Ar=zeros([Ma*Ma*N*2 1]); Ac=zeros([Ma*Ma*N*2 1]); Al=zeros([Ma*Ma*N*2 1]); Aptr=0;
for iter=1:n_iter if iter==1 %with linear rays all matrixes are constant over
iterations filename=sprintf('save/art_linear_arrayx_N%d_Ma%d_Me%d.mat',
N, Ma, Me); filelist=dir(filename); if size(filelist, 1)==0 for a=1:Ma phi=angle(a); rotmatrix=[cos(phi) sin(phi); -sin(phi) cos(phi)]; Rx=(rotmatrix*r_x')'; Sx=(rotmatrix*s_x')'; for e=1:Me rowind=sub2ind([Me Ma], e, a); ps_x=1+(Sx(e,1)+L/2)/dx; ps_y=1+(Sx(e,2)+L/2)/dx; pr_x=1+(Rx(e,1)+L/2)/dx; pr_y=1+(Rx(e,2)+L/2)/dx;
Appendices 136
[~, X, Y, l]=bresenham_flighttime(s, ps_x, ps_y,
pr_x, pr_y, dx); if length(X)>1 && (max(X)>N || max(Y)>N ||
min(X)<1 || min(Y)<1) error('Path out of computing area'); end
colind=sub2ind([N N], X, Y); Alen=length(X); if Alen>=1 rowind=rowind*ones(size(rowind)); Ar((Aptr+1):(Aptr+Alen))=rowind; Ac((Aptr+1):(Aptr+Alen))=colind; Al((Aptr+1):(Aptr+Alen))=l; Aptr=Aptr+Alen; end %A(rowind, colind)=l; end end
Ar=Ar(1:Aptr); Ac=Ac(1:Aptr); Al=Al(1:Aptr); A=sparse(Ar, Ac, Al, length(meas_tof), N*N); W1_diag=zeros([Me*Ma 1]); LA=Lnu*A; LA2=LA.*LA; n2=sum(LA2')';
for j=1:Me*Ma if n2(j)>0.0000001 W1_diag(j)=1./n2(j); else W1_diag(j)=0; end end W1=sparse(1:Me*Ma, 1:Me*Ma, W1_diag, Me*Ma, Me*Ma); W1LALnu=(W1*LA)'*Lnu;
clear LA n2 LA2 W1_diag Ar Ac Al rotmatrix W1 Lnu G; save(filename, 'W1LALnu', 'A'); else disp(sprintf('Loading precomputed parameters from %s',
filename)); load(filename); end end S=reshape(s, [N*N 1]); ds=lambda*(W1LALnu*(meas_tof-nu_star-A*S));
ds=reshape(imfilter(reshape(ds, [N N]), fspecial('gaussian',
[ceil(15*N/768) ceil(15*N/768)], (11*N/768)^2), 'same'), [N*N 1]);
S=S+ds;
ds_prior=alpha*(L_x'*(W2_diag.*(L_x*(s_star-S)))); S=S+ds_prior;
tit=sprintf('%d/%d', iter, n_iter);
Appendices 137
%imagesc(reshape(S, [N N])); colorbar, title('S1'); %drawnow; % for j=1:(N*N) % S(j)=max(S(j), 0); % end
%Force positive values S=max(S, 0.0);
s=reshape(S, [N N]); clear S;
%figure(fig); %imagesc(reshape(ds, [N N])); colorbar subplot(2,2,1); imagesc(s); colorbar title(tit); subplot(2,2,2); imagesc(reshape(ds, [N N])); colorbar subplot(2,2,3); imagesc(reshape(ds_prior, [N N])); colorbar %cptcmap('sst.cpt', 'ncol', 256); colormap('gray'); %colormap('hot'); drawnow
end
close(fig);
end
Appendices 138
Appendix 2
%%Binarizing and Converting UCT Attenuation Matrix into STL File%%
clear all close all load('reco_att.mat');
%% Constants and parameters
threshold = 2000; % This is used to remove zero-values. You may
need to change this if the intensity of the original image changes. rod_diameter_mm = 1.5; % For calibration, rod diameter is 1.5mm.
Change this if needed. extrusion_distance_mm = 40; % Required extrusion distance.
%% Read in data and convert to 3d using delaunay method
reco=squeeze(reco_att); %remove 1-d entries and get it into matrix
format
A=size(reco); % get size of matrix
[xi,yi] = meshgrid(1:A(1),1:A(2)); % create mesh tri_i=delaunay(xi,yi); %apply triangularisation
%% Do some image processing to find the width of the rods % THIS IS FOR CALIBRATION ONLY WITH KNOWN ROD DIAMETER % FOR UNKNOWN SAMPLES, USE THE RATIO VALUE CALCULATED BEFORE % NB: ASSUMES ALL RODS ARE THE SAME DIAMETER
% Step 1 - binarise the image to black and white bw = reco > threshold; figure, imshow(bw); title('Black and White image of 3.5 rod');
% Step 2 - get the region properties of the rods stats = regionprops(bw, 'all');
rod_diameter_px = 0; for n = 1:length(stats) rod_diameter_px = rod_diameter_px + (stats(n).MajorAxisLength +
stats(n).MinorAxisLength) / (2 * length(stats)); end
ratio_of_pixels_to_mm = rod_diameter_px / rod_diameter_mm;
%% Prepare for extrusion to 40mm
% Calculate extrusion distance extrusion_distance_px = round(extrusion_distance_mm *
ratio_of_pixels_to_mm);
% Set the extrusion length to the required distance
Appendices 139
reco_clean = bw * extrusion_distance_px;
figure, mesh(reco_clean) %plot mesh figure, imagesc(reco_clean) %plot 2D image
%% Save Output file into STL or Txt format
% figure, % patchesHclean = trisurf(tri_i,xi,yi,reco_clean); %plot
triangularised mesh tr = TriRep(tri_i, xi(:), yi(:), reco_clean(:)); % FVclean.faces = patchesHclean.Faces; %define faces % FVclean.vertices = patchesHclean.Vertices; %define vertices
stlwrite('slice_3D_View_5.5.stl',tr.Triangulation,tr.X)% wrtie file
into STL format % stlwrite('US_reconstruction_clean.stl', tr.Faces, tr.Vertices);
%save as STL file, the stlwrite function was taken from https://www.mathworks.com/matlabcentral/fileexchange/20922-stlwrite-
write-ascii-or-binary-stl-files