TOWARDS ULTRASOUND COMPUTED TOMOGRAPHY ASSESSMENT OF BONE Ahmad M... · 2018. 6. 12. · Towards...

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

Towards Ultrasound Computed Tomography Assessment of Bone i

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

Towards Ultrasound Computed Tomography Assessment of Bone ii

Towards Ultrasound Computed Tomography Assessment of Bone iii

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

Towards Ultrasound Computed Tomography Assessment of Bone iv

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

Towards Ultrasound Computed Tomography Assessment of Bone v

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.

Towards Ultrasound Computed Tomography Assessment of Bone vi

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

Towards Ultrasound Computed Tomography Assessment of Bone ix

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

Towards Ultrasound Computed Tomography Assessment of Bone x

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

Towards Ultrasound Computed Tomography Assessment of Bone xi

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

Towards Ultrasound Computed Tomography Assessment of Bone xii

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

Towards Ultrasound Computed Tomography Assessment of Bone xiii

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

Towards Ultrasound Computed Tomography Assessment of Bone xiv

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

Towards Ultrasound Computed Tomography Assessment of Bone xv

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.

https://doi-org.ezp01.library.qut.edu.au/10.1016/j.apacoust.2017.12.002

https://doi.org/10.3389/fmats.2017.00040

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].


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


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


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.


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.


Figure 1-1: Schematic diagram demonstrating the research outline.

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].


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].


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


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


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)).


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


(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].


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,


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


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].


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].


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].


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].


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)


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


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.


• 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


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].


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].


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.


• 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-


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].


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].


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].


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].


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).


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].


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].


• 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].


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.


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


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


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.


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


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


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.


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.


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


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.



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



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



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.



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



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.



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



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



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.



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.



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).



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.



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.



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.



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.



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.



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.



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.



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.


(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.



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)



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].



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.


4.4.1 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



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



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.



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.


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



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)



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.



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].



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



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.



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.



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



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.



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.



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).



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.



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.



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 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

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



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.



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)



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)


5.5.1 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



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.



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.


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.



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



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-



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



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].



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.



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



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



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.



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


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 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


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.

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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

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