Quantitative MRI and micro-CT of Bone Architecture: Applications and

Limitations in Orthopaedics

Doctorate of Philosophy

Timothy Andrew John Hopper

Submitted by Timothy Andrew John HOPPER, B.App.Sc (Hons), Medical Physics

Program, School of Physical and Chemical Sciences, Queensland University of

Technology in partial fulfilment of the requirements of the degree of Doctor of

Philosophy

February 2005

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Abstract The aim of this thesis was to investigate some methods for quantitative

analysis of bone structure, particularly techniques which might ultimately be applied

post-operatively following orthopaedic reconstruction operations.

Initially it was decided to explore the efficacy of MRI in quantifying the bone

structure at high resolution by comparing high resolution MRI against ‘gold

standards’ such as Scanning Electron Microscopy (SEM) and optical histology. This

basic study provided a measure of the distortions in the morphological bone

parameters derived from MR images due to susceptibility artefacts and partial volume

effects. The study of bone architecture was then extended to a model of advanced

renal osteodystrophy in a growing rat. For this study, high-resolution micro computed

tomography (microCT) was used and as a result of the high resolution images

obtained, three new bone morphological parameters were introduced to characterise

the bone structure.

The desire to study bone architecture post-operatively in hip replacements led

to a preliminary study on ex-vivo sheep acetabulae following total hip replacement, to

determine the extent that the bone architecture could be investigated around the

acetabulum. The motivation for studying the acetabulum was based on the high

occurrence of debonding at the bone / prosthesis interface. This study demonstrated

the superior nature of 3D MRI over conventional x-ray radiographs in early

quantitation of fibrous membranes located between the host bone and the non-metallic

implant and/or the bone cement. The presence of such fibrous membranes is strongly

indicative of failure of the prosthesis.

When using clinical MRI to image post-operative hip replacement, the image

quality is severely affected by the presence of the metallic implant. The head of the

prosthesis is shaped like a metal sphere and is located in the acetabular cup. This

problem was investigated by performing simulations of MR images in the presence of

the field perturbation induced by the presence of a metal sphere, with the effects of

slice excitation and frequency encoding incorporated into the simulations. The

simulations were compared with experimental data obtained by imaging a phantom

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comprising a stainless steel ball bearing immersed in agarose gel. The simulations

were used to predict the effects of changing imaging parameters that influence artefact

size and also to show how current metal artefact reduction techniques such as view

angle tilting (VAT) work and to identify their limitations. It was shown that 2D SE

and VAT imaging techniques should not be used when metallic prosthesis are present

due to extreme slice distortion, whereas 3D MRI provided a method that has no slice

distortion, although the effects of using a frequency encoding gradient still remain.

Key Words MRI, microCT, orthopaedics, trabecular bone, cortical bone, architecture,

morphological parameters, intra-and inter- trabecular porosity, view angle tilting,

metal artefact, orthopaedic implants, slice distortion, magnetic susceptibilities, field

inhomogeneity.

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Glossary of Terms and Abbreviations

MRI – Magnetic Resonance Imaging

microCT – micro Computed Tomography

VAT – View Angle Tilting

SEM – Scanning Electron Microscopy

DEXA – Dual Energy X-Ray Absorptiometry

BMD – Bone Mineral Density

MARS – Metal Artefact Reduction Sequence

FDT – Fuzzy Distance Transform

DTA – Digital Topological Anaylsis

MIL – Mean Intercept Length

SMI – Structure Model Index

ACF – Autocorrelation Function

BVF – Bone Volume Fraction

SACA – Spatial Autocorrelation Analysis

ROI – Region of Interest

SE – Spin Echo

GE – Gradient Echo

TR – Relaxation time

TE – Echo Time

FID – Free Induction Decay

PVE – Partial Volume Effect

SNR – Signal to Noise Ratio

ROD – Renal Osteodystrophy

CCD – Charged Coupled Device

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List of Publications and Manuscripts Refereed Publications 1) TAJ Hopper, B Vasilić, JM Pope, CL Epstein, HK Song, FW Wehrli, Slice distortion from a metal in an MRI phantom: experimental and computational analysis of the effects of slice distortion in 2D and 3D. (submitting to Journal of Magnetic Resonance Imaging, March 2005) 2) T.A.J. Hopper, P.K. Saha, J.B. Andre, F.W. Wehrli, C.P. Sanchez, M.B. Leonard; Quantitative micro-CT assessment of intra- and inter-trabecular and cortical bone architecture in a model of advanced renal osteodystrophy in a growing rat. (submitted JBMR, July 2004, revised Oct 2004) 3) T.A.J. Hopper, R. Meder, J. Pope, Comparison of High-resolution MRI, Optical Microscopy and SEM in Quantitation of Trabecular Architecture in the Rat Femur. Magnetic Resonance Imaging, Vol 22 (7), 953-961 (2004) 4) T.A.J. Hopper, R.W. Crawford, A.J. Timperley, R Slaughter, and J.M. Pope, MRI Can Identify High Intensity Bands Around Implants That Correspond to Radiolucent Lines on X-ray: An Ex Vivo Study of Sheep Acetabulae, Clinical Orthopaedics and Related Research, 427:127-131, October 2004. Refereed Conference Publications 1) T.A.J. Hopper, F.W. Wehrli, P.K. Saha, J.B. Andre, C.P. Sanchez, M.B. Leonard, 3D morphological analysis of bone architecture in a model of renal osteodystrophy (ROD) in growing rats. 13th Congress for the International Pediatric Nephrology Association, Adelaide, August 2004. 2) T.A.J. Hopper, H. K. Song, J. M. Pope, F. W. Wehrli, Slice distortion due to a metal sphere in a phantom: comparison of 3D and 2D TSE, SPI and 2D View Angle Tilting. 12th Scientific Meeting of International Society for Magnetic Resonance in Medicine, Kyoto, May 2004. 3) T.A.J. Hopper, R. Meder, J. Pope, Comparison of High-resolution MRI, Optical Microscopy and SEM in Quantitation of Trabecular Architecture in the Rat Femur. 11th Scientific Meeting of International Society for Magnetic Resonance in Medicine, Toronto, July 2003. 4) T.A.J. Hopper, R. Meder, J. Pope, Comparison of High-resolution MRI, Optical Microscopy and SEM in Quantitation of Trabecular Architecture in the Rat Femur. 7th ICMRM Conference, Sept 2003. Invited Talks University of Pennsylvania – Oct 2002, Professor Felix Wehrli’s group.

Australian Institute of Physics – Queensland Postgraduate Student Presentation, Oct

2004.

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Table of Contents

Abstract and Key Words 2

List of Abbreviations 4

List of Publications and Manuscripts 5

Table of Contents 6

Statement of Original Authorship 9

Acknowledgements 10

List of Figures 11

List of Tables 16

Chapter 1 Introduction 17

1.1 Description of Scientific Problem Investigated

1.2 Overall Objectives of the Study

1.3 Specific Aims of the Study

1.4 Account of Scientific Progress Linking the Scientific Papers

Chapter 2 Bone Structure and Morphology 25

2.1 Background Biology of Bone and Bone Substitutes

2.1.1 Bone Physiology and Histology

2.1.2 Bone Matrix and Structure

2.2 Morphological Parameters: Standard Stereological Measures of

Trabecular Bone Structure.

2.2.1 Recent Techniques used to Measure Trabecular Morphological

Parameters.

2.3 Advanced Image Processing

2.4 Research into the Role of Trabecular Bone in Osteoporosis

Chapter 3 Magnetic Resonance Imaging 42

3.1 Theory of Magnetic Resonance Imaging

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3.1.1 Principles of Pulsed Nuclear Magnetic Resonance (NMR)

3.1.2 Magnetic Resonance Imaging (MRI)

3.1.3 Imaging Sequences

3.1.4 Magnetic Susceptibilities

3.1.5 Requirements for High Resolution MRI

3.1.6 MRI of Trabecular Bone

3.1.7 An Alternative Method of Measuring Trabecular Bone

Architecture Using MRI

3.1.8 Multinuclear Solid-State MRI of Bone and Synthetic Calcium

Phosphates

3.2 View Angle Tilting - Technique Used to Reduce Susceptibility Artefacts

Chapter 4 Micro Computed Tomography 64

4.1 Monochromatic x-ray Projection

4.2 Polychromatic x-ray Projection

4.3 Synchrotron Radiation

4.4 Artefacts

4.5 Specifications of the μCT System used in PhD Studies

Chapter 5 Comparison of High-resolution MRI, Optical Microscopy

and SEM for Quantitation of Trabecular Architecture in the Rat Femur

71

Chapter 6 Quantitative micro-CT Assessment of intra- and inter-

Trabecular and Cortical Bone Architecture in a Model of Advanced Renal

Osteodystrophy in a Growing Rat. 82

Chapter 7 Orthopaedic Application of MRI in the Presence of Implant

Materials

MRI can Identify High Intensity Bands Around Implants That Correspond to

Radiolucent Lines on X-Ray: an ex vivo Study of Sheep Acetabula 100

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Chapter 8 Experimental and Computational Analysis of the Effects of

Slice Distortion from Metal in an MRI Phantom 107

Chapter 9 General Discussion 126

References 133

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Statement of Original Authorship The work contained in this thesis has not been previously submitted for a

degree or diploma at any other tertiary educational institution. To the best of my

knowledge this report contains no material previously published or written by another

person except where due reference is made.

Signed

Date

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Acknowledgements Thankyou to my principal supervisor Professor Jim Pope for his time, energy

and patience throughout my project. Thankyou to my associate supervisors; Professor

Felix Wehrli, Professor Ross Crawford, and Dr Richard Slaughter for their assistance

and guidance throughout my PhD. A special thanks to Professor Wehrli for letting me

study with his group at the University of Pennsylvania for one year during my PhD.

I would like to acknowledge and thank the American-Australian Fulbright

Council for awarding me a Fulbright Scholarship to the USA and hence providing me

with a remarkable opportunity to study abroad.

Thanks to the people in my lab at Queensland University of Technology; Dr

Roger Meder, Dr Catherine Jones and Dr Markus Rokitta for their assistance

throughout my studies and to members at the University of Pennsylvania; Dr Branimir

Vasilic, Assistant Professor Hee Kwon Song, Mike Wald, Robert Wilson and Dr Jalal

Andre, for their help. Thanks to my good friends who supported me during this time;

Michael Bozhoff, Ryan Kathage, Steven Goodman, Ben Birt, Sean Wallace, and

Corinne Ryan as well as many others I haven’t mentioned. I would also like to

acknowledge my immediate family; my mother Sue Hopper, father Keith Hopper and

his partner Theresa Gallagher, my brother DJ and wife Karrina, my sister Penny and

her partner Mark Deo, for their support during my candidature. And also to my

extended group of friends around the world that have all been a part of this long

journey.

A big thankyou to Associate Professor BJ Thomas and Mrs Elizabeth Stein for

their general support and administrative help and to Dr Dmitri Gramotnev for his

mentoring when I was an undergraduate student at QUT.

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List of Figures Figure 2.0: Picture of a growing long bone showing the three major components: a

diaphysis, an epiphysis, and an epiphyseal plate.

Figure 2.1: Bimodal histogram taken from μCT trabecular bone in the rat femur

showing two distinct peaks for bone and bone marrow. The peak for bone is the large

one on the right.

Figure 3.0: Sequence diagram for a 2D spin echo imaging sequence. The arrow

pointing downward in the gradient table indicates that the phase encoding gradient is

stepped sequentially.

Figure 3.1: A schematic diagram of a 2D gradient echo sequence.

Figure 3.2. Susceptibility spectrum. The upper diagram uses a logarithmic scale to

indicate the full range of observed magnetic susceptibility values: It extends from χ =

-1.0 for superconductors to χ > 100 000 for soft ferromagnetic materials. The bottom

diagram uses a linear scale (in ppm) to indicate the properties of some materials with

|χ| < 20 ppm. The susceptibilities of most human tissues are in the range from –7.0 to

–11.0 ppm.

Figure 3.3: Schematic of pulse sequence used in View Angle Tilting technique. Note

the extra gradients applied in the GSS at the same time as the GR.

Figure 3.4: Displacement of a voxel by susceptibility occurs along an angle θ with

respect to the GR and GSS gradients.

Figure 3.5: Degree of blurring is affected by slice thickness and the angle θ. Smaller

slice thickness and increased angle θ result in less pixel overlap and hence less partial

volume blurring.

Figure 4.0: Diagram of a basic Cone Beam microCT system showing the path of the

beam from the x-ray source through an object onto a detector and then the information

is converted to visible light and piped through fiberoptic cables to a CCD where it is

then converted to electric charges and sent to an ADC and then a computer (Figure

courtesy of Prof. Felix Wehrli, UPenn).

Figure 4.1: Inside of microCT machine showing the x-ray source, filters and timing

fan device on the left. In the centre of the image is the specimen bath (the bath is used

to help filter out low energy photons) and the detector is on the right.

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Figure 4.2: Sample test tubes used to place specimens in. These test tubes are then

inserted into the specimen bath shown in Figure 4.2.

Figures within Submitted Papers

Chapter 5 Figure 1: A typical optical image from light microscopy of a sectioned rat femur

(left) and the corresponding MR image taken from 3D SE data set (right).

Figure 2: A typical SEM image from a sectioned rat femur (left) and the

corresponding MR image taken from the 3D SE data set (right).

Figure 3: Difference between optical and MRI derived values for unfiltered and

filtered data as a percentage of the optical data.

Chapter 6 Figure 1: Presence of small pores in trabecular struts affect measures of trabecular

morphology. These pores can be seen on a subsection of a μCT image of the

trabecular bone (a) within the femur head of a rat (8.2 μm resolution). The pore size

distribution on a number of test slices (b) provided the threshold level for pore size

(20 μm2). Above this level the ‘pore’ was no longer considered as a hole in one

trabeculae, instead it was considered as two distinct trabeculae

Figure 2: Intact-control (a) and NX-control (b) axial images from the distal end of the

epiphyseal growth plate (8.2 μm resolution) illustrate the differences in bone structure

between healthy and nephrectomized rats. The intact-control animals have

significantly smaller Cl.Tb.Th, smaller Ma.Sp and more numerous trabeculae

compared with the NX-control animals.

Figure 3: Surface rendered images of the sub-volumes from the femur neck used in

the analysis for the intact-control (a) and the NX-control (b) show the three

dimensional nature of the bone loss in the NX-control compared to the intact-control.

Figure 4: In sagittal images at 8.2 μm resolution of the intact-control (a) and NX-

control (b) the sclerotic nature of the bone is evident in the femur neck. The pores in

the cortical bone of the NX-control are also readily seen.

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Figure 5: In the NX-GH (a) and NX-VitD (b) axial images the intra-trabecular pores

are clearly visible. These specimens are indistinguishable from the NX-control image

in Figure 2b.

Figure 6: Axial images of cortical bone from the midshaft of a rat femur at 8.2 μm

resolution for intact-control (a), NX-control (b), NX-VitD (c) and NX-GH (d). Note

the significantly increased cortical porosity in the three nephrectomized specimens,

compared with the intact-control.

Figure 7: Coronal images at 8.2 μm resolution of the cortical bone midshaft (top of

image is towards proximal femur head) emphasize the degree of cortical bone loss

suffered in the NX-control (b), NX-VitD (c) and NX-GH (d) compared to the intact-

control (a).

Chapter 7 Figure 1: Axial MR image slice (a) of a sample that displays a pronounced high

signal intensity band (thickness < 2 mm). The corresponding radiolucent line in the

antereoposterior x-ray (b) is the dark line between the between the bone cement and

the bone. The presence of bone cement in the x-ray has partially obscured the view of

the RLL in the x-ray.

Figure 2: Axial MR image slice (a) of a sample with a very small high signal

intensity band. In the corresponding x-ray (b) the RLL can hardly be seen. The cup

was found to be mechanically stable when physically inspected by a surgeon.

Figure 3: Axial MR image slice (a) of a sample that displays a very large high signal

intensity band (thickness > 2 mm). The corresponding x-ray (b) does not show the

entire RLL due to the bone cement masking its presence. The RLL in the x-ray can

only be seen in zone 2. The cup was mechanically unstable when inspected by a

surgeon.

Chapter 8

Figure 1: 2D images (x-y plane, cropped FOV 125 × 100 mm, 2 mm slice thickness)

of an 8 mm diameter stainless steel ball bearing in an agarose gel phantom. Every

second slice is presented. Slice positions are in mm with the frequency encoding (x)

direction from left to right and B0 into the page.

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Figure 2: Simulated 2D images (x-y plane, FOV 117 × 97 mm) corresponding to the

experimental data of Fig.1. The magnetic susceptibility difference between the

stainless steel ball and the surrounding gel was assumed to be Δχ = 4000 ppm in all

simulations.

Figure 3: Simulated slice profile of the centre slice (a) before application of the

readout gradient and (b) after application of the readout gradient. In both (a) and (b)

the x-axis (frequency encoding direction) is left to right and B0 is up the page. The

simulated image (c) is the projection of the signal in the z-direction from (b) with the

x-axis left to right and B0 into the page.

Figure 4: Experimental images (x-y plane, cropped FOV 125 × 100 mm, 2 mm slice

thickness) from a 3D data set, of an 8 mm diameter stainless steel ball bearing in an

agarose gel phantom. Every second 2 mm slice is shown. The frequency encoding

direction (x-axis) is left to right and B0 is into the page.

Figure 5: Re-sliced image of the 3D experimental data (x-z plane) through the centre

of the ball. FOV 200 mm × 144 mm and slice thickness of 2mm with the readout

direction left to right and B0 up the page.

Figure 6: a) Side view (x-z plane) of the simulated 3D slab that has been excited. b)

excited 3D slab after application of readout gradient (same as (a)) from left to right,

B0 is orientated up the page. The observed 3D images would be obtained by taking

slices from (b) normal to the page with the central slice presented in (c). The observed

slice (c) (x-y plane, B0 into the page) is from the 3D data set obtained by volume

averaging a 2mm slice through the center of the sphere (0 mm location).

Figure 7: 3D simulated images (x-y plane, B0 into page, FOV 117 × 97 mm) using

BWREAD of 300 Hz / pixel, slab thickness of 144 mm, 2 mm slice thicknesses taken

from the slab With every second slice of the 3D data set shown. These images

compare well to the 3D experimental images in Figure 4.

Figure 8: Simulated 2D images with 2mm slice thickness, BWREAD 300 Hz/pixel and

readout gradient from left to right. Figures a-d show the slice profile (x-z plane, B0 up

the page), with slice select gradients of a) 6, b) 18, c) 60 and d) 120 mT/m. Figures e-

h are the corresponding slice profiles after application of the readout gradient and

Figures i-l are the conventional 2D images (x-y plane, B0 into the page).

Figure 9: Simulated 2D images where GR and BWREAD are increased in the same ratio

as GSS. a) GSS = 6 mT/m, BWREAD = 300 Hz/pixel, b) GSS = 18 mT/m, BWREAD = 900

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Hz/pixel c) GSS = 60 mT/m, BWREAD = 3000 Hz/pixel d) GSS = 120 mT/m, BWREAD

= 6000 Hz/pixel. Figures e-h are the corresponding slice profiles after application of

the readout gradient. For figures a-h, B0 is up the page with the frequency encoding

from left to right (x-z plane). Figures i-l are the 2D image slices (x-y plane, B0 into

the page) taken from Figures e-h.

Figure 10: Simulated 3D acquisition slabs in which the slab select gradient is

increased; (a) 24 mT/m, (b) 48 mT/m, and (c) 240 mT/m. The size of the signal void

is decreased as the slab select gradient becomes larger. After the readout gradient is

applied (d-f) for each of the slabs in (a-c), while the signal voids are reduced, the

signal anomalies are increased. For figures a-f, B0 is up the page with the frequency

encoding from left to right (x-z plane). Figures g-i are the central 2D image slices

taken from the 3D data set through the centre slice of figures d-f respectively (x-y

plane, B0 into the page).

Figure 11: Simulated slice profile of the centre slice (a) before application of the

readout and VAT gradients and (b) after application of the readout and VAT gradients

and (c) is the slice profile after tilting the slice by the view angle. In both (a), (b) and

(c) the x-axis (frequency encoding direction) is left to right and B0 is up the page. The

simulated image (d) is the projection of the signal in the z-direction from the rotated

slice profile (c) with the x-axis left to right and B0 into the page.

Figure 12: 2D experimental VAT images (x-y plane, cropped FOV 125 × 100 mm, 2

mm slice thickness) of an 8 mm diameter stainless steel ball bearing in an agarose gel

phantom. Every second slice is presented. Slice positions are in mm with the

frequency encoding (x) direction from left to right and B0 into the page.

Figure 13: Simulated 2D VAT images (x-y plane) corresponding to the experimental

data of Fig. 12. Slice positions are in mm with the frequency encoding (x) direction

from left to right and B0 into the page. Note the compression of the images in the x-

direction caused by the extra VAT gradient.

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List of Tables Table 2.1. Morphological parameters used to quantify trabecular architecture.

Table 2.2: Measures of bone structure calculated from MR and optical images.

Table 4.0: Specifications of GEMS microCT scanner used in project

Tables Within Submitted Papers Chapter 5 Table 1: Measures of bone structure calculated from MR, SEM and optical images.

Table 2: Formulae used to calculate morphological parameters of bone samples.

Table 3: Mean values and standard deviations of morphological parameters derived

from SEM, MRI and optical images.

Table 4: Coefficients of determination (r2) for MRI derived values versus optical or

SEM derived values of trabecular morphology.

Table 5: Correlations between morphological parameters for MRI derived values

(n=27)

Table 6: Correlations between morphological parameters for SEM derived values

(n=20)

Table 7: Correlations between morphological parameters for optical microscopy

derived values (n=7)

Table 8: Comparison of bone morphological parameters obtained by MRI (n=7) for

calcified and de-calcified bone.

Chapter 6 Table 1: Trabecular bone morphologic parameters; Results of comparison with Intact-

controls. a: p < 0.0001; b: p < 0.001; c: p < 0.01; d: p < 0.05

Table 2: Cortical bone morphologic parameters; Results of comparison with intact-

controls. a: p < 0.0001; b: p < 0.001; c: p < 0.01; d: p < 0.05

Chapter 7 Table 1: Correlations between MRI and x-ray measurements of radiolucent line

thickness.

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Chapter 1

Introduction

1.1 Description of Scientific Problems Investigated

In-vivo imaging in orthopaedics began with the discovery of X-rays over one

hundred years ago and has developed significantly since those early years.

Conventional radiography brought with it many pitfalls and misinterpretations due to

the planar projection of three-dimensional structures [1]. The development of 3D

imaging techniques such as CT and MRI have now enabled surgeons to more

accurately assess bone structure and deformations within bone anatomy. Eventually it

is anticipated that 3D imaging will be used as a therapeutic tool where anatomical

contour extraction will enable simulated surgical procedures (CARS – Computer

Aided Reconstruction and Surgery), virtual manipulation of bony parts, anatomical

modelling and customised prosthesis design and manufacture [2].

Imaging of orthopaedic implants has traditionally been achieved by plain x-

rays, CT and bone scintigraphy methods. All of these techniques use ionizing

radiation and although x-ray images are low dosage, prolonged use of them in

longitudinal studies to assess such things as implant component migration is

questionable due to uncertain implications for patient health. Avascular necrosis of

the femoral head is a common complication post traumatic injury or surgery and is

difficult to detect with radiography, CT or bone scintigraphy. In addition, plain

radiograph findings are often unremarkable in detecting blood supply lost after a

femur neck fracture until total collapse of the femur head. Early diagnosis of

avascular necrosis is very desirable as it will result in a reduction of weight bearing

activities by the patient and decreases the likelihood of femoral head collapse and

fragmentation [3].

Osteolysis of the pelvis secondary to polyethylene wear of an uncemented

acetabular implant has emerged as one of the most serious and challenging aseptic

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consequences of total hip replacement surgery [4]. The early detection of osteolysis is

essential in that it allows for the preservation of some bone stock and hence increases

the chance of revision surgery being successful [4]. Since osteolysis occurs and

progresses in the absence of clinical symptoms it has been suggested that follow-up

surveillance must be instituted. One group [4] has recommended that CT be used to

detect clinically silent and radiographically unobservable osteolysis. In the absence of

metal components MRI is ideally suited to this task and in fact could potentially

provide more soft tissue anatomical information than its CT imaging counterpart [1-3,

5-7]. MRI is also ideal for in-vivo imaging due to its non-invasive nature, and its use

of non-ionising radiation.

MRI was initially restricted in its use in orthopaedics partly due to uncertainty

about the magnetic properties and compatibility of metallic prostheses. Metallic

prostheses used for surgical reconstruction purposes are generally non-ferromagnetic

and thus there will be no significant forces on the metal arising from the static

magnetic field B0. However metal prostheses can produce a large artefact in the MR

image caused by the difference in magnetic susceptibility between the prosthesis and

the surrounding tissue and/or bone. This artefact can obscure anatomical information

in the regions of interest and the associated image distortion may result in inaccurate

diagnostic information. Consequently, reduction of the image artefacts associated

with metal prostheses may be important in expanding the scope and range of

applications of orthopaedic MRI in the future.

Metal implants not only affect MR images they also affect CT scans. In MRI

the implants result in significant image distortions and signal irregularities whist in

the CT the effects can be seen as beam hardening artefacts. The beam hardening

artefacts can be reduced by increasing the radiation dosage but this is clinically

unacceptable due to patient radiation exposure risks. Plain radiographs are less

affected by beam hardening artefacts but only provide 2D superimposed images of

bone structure and hence presence of opaque implants such as bone cement can

‘mask’ other bone structures [5].

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Magnetic resonance micro-imaging (μMRI) has been used for the study of

trabecular bone architecture in the diagnosis of osteoporosis in both ex-vivo and in-

vivo studies [7-10]. In-vitro studies using clinical MR scanners have shown the

potential of μMRI to predict the biomechanical strength of bone [7], and in vivo

studies have shown this technique’s capability to discriminate between patients with

and without osteoporotic fractures [9-11]. MRI has been applied to the study of

osteoporosis since it has the potential to obtain information pertaining to both

trabecular bone density and structure. MRI also has the ability not only to distinguish

between cartilage and cortical and trabecular bone, but also has the capacity to

provide high contrast images of trabecular micro-architecture, both in-vitro and in-

vivo, in three dimensions without the use of ionising radiation.

Micro-Computed Tomography (μCT) has been used in ex-vivo studies to

provide 3D anatomical information on cortical and trabecular bone structure at

resolutions around 5-20 μm [12-14]. One of the advantages of this technique is that

the inherent image artefacts are small compared to the other imaging modalities.

Unfortunately, the large radiation dosage used and the restriction in sample size

negate its usefulness for in-vivo clinical applications.

Accurate quantification of bone architecture is central to understanding bone

metabolic diseases such as osteoporosis. Evidence presented over the past two

decades has shown that bone mineral density (BMD), the traditional measure of bone

strength is not the sole determinant of the mechanical properties of cancellous bone.

Various groups around the world have shown that changes in trabecular morphology

play an important role in determining bone strength and trabecular bone mechanics

[15, 16]. It is now known that BMD explains only 70% of the variance in the stiffness

of the human femur and tibia bones [15, 17, 18]. This new understanding of the role

of the micro-architecture in determining bone strength has stimulated a search for

other predictors of cancellous bone strength, including predictors based on measures

of trabecular bone morphology [17-19].

Current in-vivo assessment of osteoporotic status is based on bone

densitometry techniques such as quantitative computed tomography (QCT), dual-

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energy X-ray absorptiometry (DEXA) and more recently magnetic resonance imaging

(MRI). Although BMD values obtained from DEXA are widely used as an indicator

for assessing fracture risk and therapeutic efficacy, BMD does not always predict the

risk of individual fractures, explain the pathophysiology of osteoporotic changes, or

completely assess the impact of a particular therapeutic intervention [11, 20]. This is

because BMD does not provide information on the trabecular bone architecture. Thus,

the quantitative analysis of trabecular bone structure and the elucidation of

relationships between structural parameters and bone strength have been important

topics of research in osteoporosis and related conditions.

Obtaining information on the trabecular micro-architecture has traditionally

involved standard optical microscopy of the iliac crest bone biopsies [7, 20]. This

technique is fundamentally flawed due to the fact that it does not take into account the

heterogeneous nature of the bone, both between individual bones and anatomical

locations [8, 11, 21]. Furthermore, there are important structural parameters, such as

connectivity and structural anisotropy, which are difficult to derive from 2D sections

[7, 8, 11, 17, 20-22]. The major drawbacks of optical microscopy are that it is time

consuming, invasive, destructive, requires considerable preparation of specimens that

may introduce artefacts, and if specimens are embedded, does not permit subsequent

mechanical testing.

The study of bone architecture has resulted in a large international effort that

is concentrated on developing and improving techniques to assess trabecular bone

micro-architecture non-invasively and identifying and overcoming problems

associated with their clinical application. This thesis represents a contribution to this

ongoing effort.

1.2 Overall Objectives of the Study

The aims of this research included understanding and refining techniques for

quantifying the changes in trabecular bone structure that accompany metabolic bone

diseases, result from orthopaedic reconstruction operations, or that are a consequence

of different therapeutic interventions. These techniques may then be used to improve

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our understanding of the mechanisms underlying these changes and assess the

efficacy of various remedial treatments such as hormone treatment, bone growth

inducers or physiotherapy.

A further aim was to apply these quantitative techniques to regions of interest

to orthopaedic surgeons with a view to providing information on bone structure and

debonding at the interface between bone and prosthesis. This would enable physicians

to prescribe the most effective treatment program based on exercise, medication, and

dietary treatment for the patient. Further to this objective, an additional aim of the

thesis was to clarify the origin and magnitude of problems associated with MR

imaging in the vicinity of a metallic prosthesis, and identify improvements in imaging

technique to enable the assessment of bone structure in the presence of the associated

image artefacts.

1.3 Specific Aims of the Study

Specifically, the aims of the thesis were to:

1) Provide an accurate statistical comparison of bone structure as measured by

high-resolution MRI against ‘gold standards’ such as scanning electron microscopy

and optical histology.

2) Determine the extent to which partial volume artefacts, filtering, and magnetic

susceptibility differences (between bone and bone marrow) affect calculation of

trabecular bone morphological parameters from MR images.

2) Use high resolution micro-CT to analyse changes in bone architecture in

situations of high turnover bone disease and determine the effects of treatment with

growth hormone and Calcitriol.

3) Determine the efficacy of MRI in imaging around the acetabulum following

hip replacement surgery in an ex-vivo situation where the effects of the metallic

prosthesis in creating artefacts in the MR image had been removed.

22

4) Theoretically examine the effect of magnetic susceptibility differences arising

from a stainless steel ball (designed to mimic the head of femur in a metal prosthesis

as it sits in the acetabulum cup) and compare these theoretical simulations with

experimental data.

5) Investigate current MR imaging techniques used to image around a metal

implant and determine their effectiveness.

6) Provide recommendations on imaging techniques and protocols that are

appropriate for imaging in the presence of metallic prosthesis.

1.4 Account of Scientific Progress Linking the

Scientific Papers

This thesis begins with a literature review of orthopaedics and imaging

techniques that are used in current assessment of bone structure. Chapter 2 is an

overview of bone structure and morphology and research conducted into analysing

bone structure. In Chapter 3 the principles of MRI are outlined, with particular

reference to the effects of magnetic susceptibility artefacts and techniques that have

been developed to minimize them. Chapter 4 contains a brief theoretical outline of

μCT and the current state of the art. Chapters 5-8 are papers that have been written by

the thesis author on research into bone structure and artefact correction.

Chapter 5 is the first paper presented for examination and is an initial study

that compared high resolution MR images (22 microns in plane and 37 microns slice

thickness) with ‘gold standards’ such as scanning electron microscopy (SEM) and

optical histology. The study was conducted in order to determine the effects of

magnetic susceptibility differences between bone and bone marrow on the ability of

NMR micro-imaging to quantify trabecular structure and morphology.

Chapter 6 is a more advanced study that extends from that in chapter 5 and

which used advanced image processing techniques to quantify bone structure in a

23

model of advanced renal osteodystrophy in a growing rat model. The study used a

high resolution μCT scanner to generate very high resolution 3D images (8.2 microns

isotropic resolution) that were analysed using an image processing technique known

as Fuzzy Distance Transform (FDT). This study provided new insight into quantifying

bone structure in situations of high turnover bone disease.

After using rat models to determine the feasibility of quantifying bone

structure we decided to investigate a region of orthopaedic interest, the acetabulum, in

a sheep model of total hip replacement, using a clinical MRI scanner. The aim of the

study was to determine if MRI was able to show debonding at the interface between

host bone and bone cement and if it had the potential to achieve a higher efficacy than

standard x-ray radiographs. This paper forms chapter 7 of the thesis.

If a metal prosthesis was still present in the acetabulum in the context of the

study described in chapter 7 then the magnetic susceptibilities from the prosthesis

head would have created massive image artefacts preventing visualisation and

measurement of the fibrous membrane between host bone and bone cement. To

investigate this artefact a phantom was made using a stainless steel ball bearing

centred in a container of agarose gel (to mimic soft tissue). The experimental data

from this study were compared with computer simulations to determine the accuracy

of the theoretical model we had used, and forms Chapter 8 of the thesis. The

simulations were then used to investigate methods for reducing the artefact around the

ball bearing. This paper also includes simulations of a metal artefact reduction

sequence that has been employed for reducing artefacts from metallic implants [3,

23].

The thesis concludes with a general discussion of the outcomes and a

summary of the four papers presented for examination. 3D imaging and image

processing techniques should be used to quantify bone structure to avoid the problems

inherent in previous ‘gold standards’ such as histomorphometry. It is shown that

additional morpholological parameters are needed to quantify bone architecture in

situations of high turnover bone disease where there are very complex bone

remodelling mechanisms. The thesis also demonstrates that in some instances it may

24

be feasible to use MRI to image in the vicinity of metal implants by utilising 3D

imaging techniques in combination with larger readout bandwidths (BWREAD),

provided that susceptibility differences are not too large. However other situations

may still require the use of single- and multi-point imaging techniques, although

clinical application of these methods is currently restricted by excessive imaging

times. MRI is already used to quantify bone structure in regions where there are no

metallic prostheses present, but with further developments in hardware and artefact

reduction techniques, MRI has the potential to become the standard bone imaging

modality for post-operative orthopaedic reconstruction operations.

25

Chapter 2 Bone Structure and Morphology

2.1 Background Biology of the Bone and Bone

Substitutes

2.1.1 Bone Physiology and Histology

Each growing long bone has three major components: a diaphysis, an

epiphysis, and an epiphyseal plate, as shown in Figure 2.0. The diaphysis or shaft, is

composed primarily of compact bone, which is mostly bone matrix surrounding a few

small spaces. The epiphysis, or end of the bone, consists primarily of cancellous, or

spongy, bone, which has many small spaces or cavities surrounded by bone matrix.

The outer surface of the epiphysis is a layer of compact bone, and within joints the

epiphyses are covered by articular cartilage. The epiphyseal, or growth plate, is

hyaline cartilage located between the epiphysis and diaphysis. Growth in bone length

occurs at the epiphyseal plate. When bone stops growing in length, the epiphyseal

plate becomes ossified and is called the epiphyseal line.

Bone consists of extracellular bone matrix and bone cells. The composition of

the bone matrix is largely responsible for the characteristics of bone. Optimum

skeletal function is maintained by a continuous process of removal and replacement of

bony tissue. This is a very complex process that involves many different cell types

and processes, however in simplified terms, the bone remodelling ‘units’ consist of

osteoclasts, which are cells that remove old bone, and osteoblasts which deposit new

bone in place of that removed [16].

26

Figure 2.0: Picture of a growing long bone showing the three major components: a diaphysis, an

epiphysis, and an epiphyseal plate [24].

2.1.2 Bone Matrix and Structure

By weight, mature bone matrix normally is approximately 35% organic and

65% inorganic material. The organic material primarily consists of collagen and

proteoglycans. The inorganic material primarily consists of a calcium phosphate

crystal called hydroxyapatite, which has the molecular formula Ca10(PO4)6(OH)2.

27

Bone tissue can be classified as woven or lamellar bone according to the

organisation of collagen fibres within the bone matrix. In woven bone the collagen

fibres are randomly oriented. Woven bone is first formed during fetal development or

during the repair of a fracture. Woven bone is remodelled to form lamellar bone.

Lamellar bone is mature bone that is organised into thin sheets or layers

approximately 3-7 μm thick called lamellae. In general, the collagen fibres of one

lamella lie parallel to one another but at an angle to the collagen fibres in the adjacent

lamellae.

Woven or lamellar bone can be further classified according to the amount of

bone matrix relative to the amount of space within the bone. Cancellous bone is

characterised by less bone matrix and more space than compact bone, which

conversely has more bone matrix and less space than cancellous bone.

Cancellous bone consists of interconnecting rods or plates of bone called

trabeculae. Between the trabeculae are spaces that in living tissue are filled with bone

marrow and blood vessels. Cancellous bone is sometimes called spongy bone because

of its porous appearance and is also known as trabecular bone.

Most human trabeculae are thin (50-400 μm), consisting of several lamellae

with osteocytes located between the lamellae (rat trabeculae are typically of the order

of 40 μm). Each osteocyte is associated with other osteocytes through canaliculi.

These canaliculi are extensions of the cell processes between the cells that enable

movement of nutrients and waste products. Usually no blood vessels penetrate the

trabeculae, so osteocytes must obtain nutrients through their canaliculi. The surfaces

of trabeculae are covered with a single layer of cells mostly osteoblasts with a few

osteoclasts. Trabeculae are orientated along the lines of stress within a bone. If the

direction of weight-bearing stress is changed slightly the trabecular pattern realigns

with the new lines of stress via the bone modelling process described earlier.

28

2.2 Morphological parameters: Standard

stereological measures of trabecular bone structure

Microstructural organisation plays an important role in defining the

mechanical properties of trabecular bone [10, 19, 21, 25]. Moreover, trabecular

morphology adapts to changes in mechanical environment and to aging and disease

[11, 15, 21, 26]. Understanding this adaptive behaviour as well as the influences of

aging and disease on trabecular properties requires characterisation of the three-

dimensional (3D) architecture of trabecular bone. The standard 2D bone

morphological parameters used to quantify bone structure (Table 2.1) can be

calculated using a variety of methods that will be outlined further on in this chapter.

The basic parameters used in a large majority of bone studies are; Bone Volume

Fraction (BV/TV) – ratio of bone pixels in a volume of interest (VOI) to the total

volume; Trabecular number (Tb.N) – this is typically the number of trabeculae per

unit length passing through a test line drawn across a 2D image (not usually used in

3D processing techniques); Trabecular thickness (Tb.Th) – average thickness of the

trabeculae; and Trabecular spacing (Tb.Sp) – average spacing between adjacent

trabeculae. When calculating these parameters the VOI must be selected to remain

within the trabecular bone boundaries so as to ensure reproducibility and accuracy.

.

Table 2.1: Standard bone morphological parameters used to quantify bone architecture [27].

In addition to the parameters in Table 2.1 there are other parameters used to

describe the strength and architecture of bone. Young’s Modulus (YM) of elasticity

has long been used as a measure of mechanical stiffness of bone and is calculated as

the ratio of tensile stress to tensile strain. Bone Mineral Density (BMD) is a parameter

used to quantify bone strength. BMD measurements are usually derived from Dual

29

Energy X-ray Absorptiometry and whilst they are used clinically to determine

osteoporotic status there is increasing evidence that the results have significant errors,

particularly when used in paediatric studies [28-30]. When BMD measurements are

combined with the measures of bone architecture they can provide an accurate

predictor of failure stress [31]. Quantitative Computed Tomography has been used to

provide volumetric measurements on bone and is able to selectively identify and

measure the trabecular bone. It is generally only used for measurements of the spine

and has the significant disadvantage over DEXA in that it uses a much higher

radiation dosage.

The traditional methods employed for ex vivo imaging of trabecular bone are

two-dimensional (2D) optical microscopy [15, 18, 25] or scanning electron

microscopy [32, 33]. In these cases the structural parameters are either inspected

visually or measured from sections and the third dimension reconstructed on the basis

of stereology [18, 32]. The extrapolation from 2D quantities to a third dimension is

inevitably fraught with error and uncertainty [22, 32, 33]. This is particularly so in the

case of trabecular bone which is highly anisotropic. There are also several structural

parameters that are difficult to derive from 2D histologic sections such as structural

anisotropy and connectivity [22, 34].

From the 2D images, morphologic parameters can be determined using a

technique such as the secant method [35]. This method is equivalent to scanning a 2D

matrix of bone and marrow with an array of parallel test lines with a uniform spacing.

The average number of intersections of the test lines with the bone-marrow interface

are counted for several different test line orientations. Based on the area fraction of

bone, the number of intersections, and stereological principles and models, 3D

structural parameters can be estimated from the planar sections [33]. These techniques

are well established and allow estimation of basic morphometric measures such as

BV/TV, Tb.N, Tb.Th, and Tb.Sp. The biggest problem associated with determining

morphological parameters from a 2D reconstruction of optical slices is the substantial

preparation of the specimen required to obtain the results. This preparation includes

embedding in resin, followed by sectioning into thin slices as well as surface

treatment for contrast enhancement. This method is totally destructive and hence does

not allow further testing of the mechanical properties of the sample. To calculate the

30

standard morphological parameters using the secant method there are structural

parameters that need to be measured directly from the image. These are presented in

Table 2.2.

.

.

.

Table 2.2: Measured parameters of bone structure taken directly from bone images [17].

The standard morphological parameters such as Tb.Th, Tb.Sp and Tb.N can

also be calculated using the mean intercept length method (MIL) [36]. In the MIL

method, after choosing a threshold (usually set to be the halfway point between the

bone and bone marrow peaks on the histogram, see Figure 2.1) and binarising a 2D

image of bone to distinguish between bone and marrow spaces, the total number of

black and white pixel edges that cross a set of parallel rays at a given angle θ through

the image are counted as PL(θ), then a measure of the mean intercept length is

computed as the ratio between the total width of the bright pixels and half the number

of edges. This can be expressed as:

)(/2)( θθ LP PPMIL = (1)

where PP is the total width of the pixels contributing to the bone phase (or marrow

phase if you want to calculate Tb.Th).

31

Figure 2.1: Bimodal histogram taken from μCT trabecular bone in the rat femur showing two distinct peaks for bone and bone marrow. The peak for bone is the large one on the right.

Depending on the imaging technique used the bright pixels may represent

bone or the bone marrow, i.e. in optical and MR images the bright pixels are the

marrow spaces and SEM and μCT images the bright pixels are the bone). It has been

shown that when the data is calculated in a 3D polar plot, the data approximates an

ellipsoid which can then be expressed by the quadratic form of a second-rank tensor,

known as the MIL fabric tensor [36, 37]. The mean value of the intercept length for

all angles provides the width of the bright pixels and is defined as apparent trabecular

thickness (Tb.Th) and from this the other measures of Tb.Th, and Tb.N can be

determined [38-40] and are described in Table 2.3. The BV/TV is calculated in the

same way as the previous methods (bone volume divided by the volume of interest).

The use of the term apparent has come about because of the uncertainty associated in

measuring the true morphological parameters due to artefacts in each of the respective

imaging techniques and errors in the quantitative methods. It is typically used when

the image voxel size is comparable to or greater than the trabecular thickness [11].

The differences between the MIL method and the secant method are compared

in the following table.

32

Parameter Abbr.1 Formulae1 (Secant) Formulae2 (MIL)

Bone Volume

Fraction (%)

BV/TV (Tb.Ar ÷ T.Ar) ×100% No. of bone pixels/total

No. of pixels

Trabecular plate

number (mm-1)

Tb.N (1.199/2) × (Tb.Pm ÷

T.Ar)

BV/TV ÷ Tb.Th

Trabecular plate

thickness (μm)

Tb.Th (2000 ÷ 1.199) × (Tb.Ar ÷

Tb.Pm)

Mean value of MIL(θ),

)(/2)( θθ LP PPMIL =

Trabecular plate

spacing (μm)

Tb.Sp (2000 ÷ 1.199) × (T.Ar. –

Tb.Ar) ÷ Tb.Pm

1/Tb.N – Tb.Th

1 from Parfitt et al [25] 2 from Majumdar et al [41, 42]

Table 2.3. Difference between Secant and MIL methods used to calculate morphological parameters.

More recent imaging techniques, such as X-ray computed tomography (CT),

magnetic resonance microscopy and optical serial reconstruction produce 3D images

of trabecular bone. These images allow 3D morphologic measurements using a

variety of methods, one of which is a 3D version of the directed secant method. Very

few of these methods have been applied routinely to describe the microstructure of

trabecular bone [43]. Also, there are no standardised implementations of an

automated 3D directed secant method. A study by Simmons et al. [44] looked at the

effect of varying the user defined parameters such as the test grid spacing, the number

of test grid rotations, and how the bone-marrow interface is defined. They concluded

that the differences in automated morphologic analysis techniques could result in

sizeable and statistically significant differences in basic parameters such as Tb.N,

Tb.Th, and Tb.Sp. This implies that there could be a large variation in morphological

parameters calculated between laboratories around the world.

Despite these concerns several studies have found significant differences in

the morphological parameters as presented in the above table between fracture/non-

fracture, osteoporotic/non-osteoporotic and pre- and post-menopausal patients, thus

affirming the important contribution these parameters play in explaining adverse

changes in bone mass and strength.

33

More advanced 3D morphological parameters used to quantify bone structure

have been developed to address the inadequacy of two-dimensional approaches to

characterise trabecular bone lattices. A measure of the connectivity known as the

Euler number, N(3), is a 3D measure computed from the number of nodes n and the

number of branches b as,

N(3) = n – b + 1 (2)

A well connected network will have a large negative Euler number that becomes less

negative as connections are broken. The ‘1’ in the equation can be replaced by the

number of components, however if the trabecular structure is assumed to be a singly

connected object then the ‘1’ is removed from the equation. The Structure Model

Index (SMI) is a recently developed quantitative measurement providing information

on a bone’s plate or rod character [45, 46]. This idea stems from the fact that the

volume change upon radial expansion (consider the partial derivative δV/δr, where V

is volume and r is ‘radius’ of structural element) is largest for an element of circular

cross section (i.e. a ‘rod’) and smallest for a plate. There are other more advanced

image processing techniques used in bone analysis that will be discussed in the next

section on advanced image processing.

2.3 Advanced 3D Image Processing

Quantification of bone structure using MRI is significantly limited by the

signal to noise (SNR) ratio, susceptibility artefacts and achievable resolution. Thus

image processing techniques have to be robust as well as fast for their use in clinical

diagnosis of bone diseases and as a result there has been significant research

conducted to improve on the old 2D stereological approaches [44, 47-50] .

Image processing remains one of the key elements in obtaining clinically

useful information from MR and μCT images of bone. The recognition of the

implications of trabecular morphology on the bone’s mechanical strength [21, 51]

provides a strong impetus for the development of non-destructive imaging techniques

capable of directly acquiring a 3D volume data set from which trabecular lattice

parameters can be derived without resorting to planar sections. Correct and accurate

34

determination of bone morphological parameters in a reproducible manner has been

one of the biggest problems facing trabecular bone image analysis.

Wehrli et al. [48, 52, 53] have developed a method for extracting quantitative

information in the limited spatial resolution regime. Resolving individual trabeculae

can be difficult and failure to do so can result in partial volume blurring. This limited

resolution results in a mixing or ‘contamination’, of the voxels at the bone and bone

marrow interface. The bone voxels can contain signal from the marrow resulting in a

histogram that instead of being bimodal (two distinct peaks for bone and marrow),

becomes monomodal. In the absence of partial volume blurring, delineation between

bone and bone marrow pixels is achieved by setting the threshold near the midpoint of

the two peaks in the histogram, to yield a binary image. When partial volume errors

are present this becomes very problematic [53].

Majumdar et al. have proposed to select a threshold on the leading edge of the

grey scale-inverted image at half the peak height [11], whereas, Hwang and Wehrli

have proposed to use a region based grey scale bone volume fraction (BVF) rather

than setting a threshold to binarise the image. The regional BVF must also take into

account the regional intensity variations from RF inhomogeneity, but in principle all

the information in the image is retained [53]. The basis of the method involves

iteratively deconvolving the original histogram by resorting to a model histogram

consisting of two δ-functions (bone and bone marrow). The model histogram is first

convolved with Rician noise (the type of noise inherent in modulus MR images) and

then compared with the experimental histogram. The error between the two

histograms is then subtracted from the initial estimate and the process repeated until

the error has fallen below a predetermined threshold [53]. This method can provide

grey scale images suitable for use in structure analysis programs such as Spatial

Autocorrelation Analysis [47, 53, 54].

Using the BVF images a technique called Spatial Autocorrelation Analysis can

be calculated to effectively represent a probability map that provides information on

bone and bone marrow interfaces. A BVF = 0.5 can be interpreted as a 50

% probability that a randomly chosen point in the voxel is bone. If two neighbouring

35

voxels are considered then a two-point probability can be calculated as the product of

the BVFs from the two voxels. If both voxels have significant BVF the two-point

probability has a large value, whereas if one voxel falls into a marrow cavity, the

product vanishes [53]. Averaging over all voxel locations results in the three-

dimensional spatial autocorrelation function (ACF) given by:

ZYXZYXZYX nznynxPnnnACF,,1 ),,((),,( +++= (3)

where P1 represents a single-point probability and the angle brackets symbolize

averaging [53, 54]. Due to the irregular nature of the trabecular lattice, the ACF

decays rapidly with increasing n resulting in an initial maximum following the parent

peak (in a plot of BVF(0)×BVF(n) vs n) that corresponds to the mean distance

between trabeculae [54].

Rotter et al. [47] developed a Spatial Autocorrelation Analysis (SACA)

program to determine the spatial anisotropy of the trabecular bone in order to

investigate osteoporosis. This method was used to measure osteoporotic status by

using the ratio of the autocorrelation functions in the lateral (x) and proximal (y)

directions. The autocorrelation function was defined as:

∑ +

+=

1)(*(

)(*)()(

1ddxIxI

dxIxIda

r

rrr

rrrr

(4)

where )(dar

is calculated for distance vectors ),( YX ddd =r

by integrating over every

image pixel ),( yxx =r in the region of interest (ROI) [47]. By integrating over the

polar angle φ the autocorrelation )(dar

is calculated as an average over several

directions dr

. By summing up the Cartesian components of d the partial

autocorrelation functions for )( XX da and )( YY da can be derived [47]. All

autocorrelation functions are defined to be normalised to 1 and the ratio )(dr of

partial autocorrelation functions is given by

)(/)()( YYXX dadadr = (5)

The ratio )(dr is a parameter for quantifying anisotropy and in the Rotter

study [47] these were calculated using regions of interest (ROIs) from gradient-

corrected, contrast-maximized, inverted MR-microimages on images of human female

36

calcaneus. The method makes use of the assumption that bone is more anisotropic

when osteoporotic. One of the advantages of the SACA method is that it is operator

independent but unfortunately it is not very useful for characterisation of general bone

morphological parameters and its use so far has been limited to the diagnosis of

osteoporosis.

Using autocorrelation analysis another morphological parameter can be

calculated that describes the “tubularity” of bone. This expresses the relative

likelihood for two points with identical x and y coordinates in adjacent slices to be

both in bone [53, 54]. Tubularity is calculated as:

)0(

)1,,()0,,(,11

LONG

YX

ACF

yxPyxPTub = (6)

where ACFLONG is the autocorrelation function from equation (3) calculated in the

longitudinal direction (z). Tubularity is essentially a measure for the bone’s

directedness perpendicular to the plane of the section (e.g. along the long axis of the

forearm) [53, 54].

The noise-deconvolved grey scale BVF images described at the start of the

section still suffer from some partial volume blurring and thus cannot be accurately

segmented into bone and bone marrow (necessary for analysis of network topology).

Subvoxel processing [55] can be used to provide a more accurate grey scale map of

the BVF. Grey scale subvoxel processing assigns partial bone fractions to each

subvoxel. The method has two simple hypotheses: (1) smaller voxels are more likely

to have high BVF; and (2) bone is generally in close proximity to more bone. The

algorithm starts by partitioning each voxel into eight subvoxels. The bone is then

redistributed among the subvoxels, whilst ensuring that the total BVF in the original

voxel is maintained and that bone is sequestered in subvoxels that are closer to other

bone. The precise amount allotted to a subvoxel is determined by the amount and

location of bone outside the voxel but adjacent to the subvoxel [53, 55]. As a result of

this, bone tends to be sequestered in subvoxels that is close to other bone. Subvoxel-

processed BVF maps derived from in vivo images have exhibited the same

characteristic structures in trabecular bone only previously seen in resolutions

obtained using ex vivo images [53].

37

The subvoxel-processed BVF maps can be used to delineate between rods and

plates (the Euler number cannot do this) by evaluating the topological class of each

voxel in a skeleton representation of the trabecular network [48, 53]. This method is

known as Digital Topological Analysis (DTA) [56] and is based on a branch of

mathematics known as Topology. Topology is concerned with the geometric

properties of deformable objects (that are invariant in scale, rotation and translation)

[53, 57, 58]. The difference between scale and topology is important in the study of

bone architecture. An increase in the thickness of the trabeculae will result in changes

to the scale but, topologically the network is the same. This increase in scale will

affect its mechanical properties. In contrast to this, if two networks have identical

BVF but one has rod-like trabecular bone and the other has strut-like trabecular bone

then the network topology will be different despite having the same BVF (scale) [53,

56].

DTA classifies each voxel in the three-dimensional structure based on the

connectivity of the neighbouring voxels [56]. The DTA process starts by converting

the 3D network to a skeletonised surface representation consisting of only one- and

two- dimensional structures (i.e. surfaces and curves). The BVF maps must first be

binarised by selecting an appropriate threshold point. Wehrli et al determined that a

threshold of BVF = 0.25 was the ideal point based on an observation that in the range

of BVFs from 0.25 to 0.4 the change in skeleton voxel counts as a function of BVF

threshold was minimal [53]. The local topology must be determined in a 3 × 3

neighbourhood of a bone voxel (26 voxels) in terms of the number of objects, tunnels,

and cavities. The topological class of the central bone voxel can be established by

determining the number of objects, tunnels, and cavities in the bone structure when

this central voxel is replaced by marrow [53]. The classes are: isolated voxels (I-type),

curve interiors (C-type), curve edges (CE-type), curve-curve junctions (CC-type),

surface interiors (S-type), surface edges (SE-type), surface-surface junctions (SS-

type), and surface-curve junctions (SC-type) [53]. There is also a profile class (P-

type) defined as a thin two-voxel segment having no neighbouring S-type, SC-type, or

SS-type voxels. In addition to this there are also profile interior (PI-type) and profile-

edge (PE-type) voxel classes [53]. It is possible to also define composite parameters

38

useful in discriminating different structural arrangements such as the surface-to-curve

ratio (S/C). This is the ratio of the sum of all surface-type voxels (S,SE, SS, SC)

divided by the sum of curve-type voxels (C, CE, CC). This ratio is sensitive to the

conversion of plates to rods. Finally, an erosion index (EI) can be defined as the ratio

of the sum of parameters that increase upon osteoclastic resorption (e.g. CE- and SE-

types) divided by the sum of parameters that decrease secondary to such processes

(e.g., S-type). One of the reasons that the DTA method has been successful is that it is

able to delineate between rod and plate-like structures. The method has been

successfully employed in analysing clinical images [57] and more importantly,

morphological parameters derived using it have been compared with Young’s

Modulus of elasticity with excellent correlations[57]. The significance of a technique

which has the ability to predict the mechanical strength of bone through topological

analysis cannot be overestimated.

To avoid thresholding the images and hence increase reproducibility, a method

known as the Fuzzy Distance Transform (FDT) was developed by Saha et al. [48, 52]

and has been used to study trabecular bone. In the limited spatial resolution regime of

in vivo MRI, partial volume blurring causes the trabecular bone edges to become

fuzzy [53]. The FDT method uses 3D noise-deconvolved subvoxel-processed grey-

scale images that have not been thresholded as a starting point in its calculations. The

method is employed in the study of trabecular bone due to its ability to calculate the

distance between objects in fuzzy subsets (denoted S). In the case of fuzzy objects the

shortest path between two points is no longer assumed to be a straight line [52]. The

fuzzy distance [52] between any two points in a space with non-uniform material

density is defined by first defining the (fuzzy) length of a path as an integral of

membership values (material density) along the path and then fuzzy distance is

defined as the length of the shortest path between the two points. Mathematically the

length of the path π, in S, denoted by ∏S)(π , is the value given by the following

integration [52];

∫∏ =1

0

)()]([)( dtdt

tdtSS

ππμπ (7)

where the membership value )]([ tS πμ acts as a weighting factor on the value of the

pixels in the BVF map (i.e. pixels representing reduced BVF should be assigned

39

reduced weight) and dttd /)(π represents the instantaneous velocity of the ‘walk’

along the path. The fuzzy distance transform (FDT) [52] at any point inside the object

(region with nonzero membership) is defined as the minimum distance between that

point and a point on the boundary of the support of the object (i.e. trabecular bone).

The FDT measure at a point represents its depth in the presence of material

heterogeneity and partial voluming. The thickness value (i.e. Tb.Th) of an object is

estimated by sampling FDT along a skeleton representation of the trabecular structure

(obtained by tracing the ridge on its FDT map) [52] and is determined as twice its

FDT value.

The FDT-based method has been used to compute Tb.Th due its high

precision and accuracy [52, 53, 59]. Average Tb.Sp can be then measured by

computing FDT-based thickness of the marrow space. Further detail on this

complicated image processing technique can be found in references [48, 52, 57].

2.4 Research into the role of trabecular and cortical

bone structure

The first imaging technique to be applied to 3D structural analysis of

trabecular bone was X-ray micro-computed tomography (μCT) [14, 60-62]. CT

appears to be an ideal imaging technique for bone due to the large difference in

attenuation coefficients between bone and the surrounding soft tissue and bone

marrow. In previous studies by Bonse et al. and Nuzzo et al the highest resolution

achievable was of the order of 5-15 μm using synchrotron radiation [14, 62, 63].

Other groups have achieved resolutions of around 15-36 μm by using conventional

micro-focus X-ray tubes (‘table top’ μCT systems) as the source [12, 60, 61, 64].

Studies have characterized the cortical porosity, Tb.Th, Tb.Sp, Tb.N, and effects of

different treatment regimes in rodent, primate and human models [12-14, 64-66].

This technology typically uses rotation of the specimen rather than the X-ray

source/detector to obtain projections at various angles [60] and is confined to the

study of small samples. Extensions of the technology to in vivo micro-morphometry

40

are difficult and limited because of the substantial radiation dose required to achieve

the necessary signal-to-noise ratio (SNR).

Magnetic resonance microscopy (μMR) has evolved during recent years into a

powerful method for the non-destructive visualisation of microstructure in biology

and the material sciences. Because of its ability to produce 3D images, μMRI is

particularly useful for analysing highly anisotropic porous structures like trabecular

bone. Unfortunately quantification of bone structure using MRI is significantly

limited by the signal to noise (SNR) ratio and the resolution. The theoretical

considerations of MRI will be discussed in detail in Chapter 3.

Traditionally, research into the role of trabecular structure has concentrated on

the differences in the micro-architecture between osteoporotic and non-osteoporotic

fractures. These studies normally match the patients based on bone volume or density.

Studies by various groups to date have shown qualitatively that a common pattern of

bone loss in osteoporosis is characterised by a reduction in bone volume, trabecular

thickness and number, and an increase in trabecular spacing [11, 67, 68]. Similar

changes in trabecular bone structure have also been reported to occur with ageing [11,

68]. It has also been suggested that the mechanism responsible for the loss of bone

volume involves, primarily, a loss, rather than a generalised thinning, of trabeculae [7-

11, 68].

Quantitative studies for example by Kleerekoper, Recker, Majumdar, Wehrli

and Vieth [7-9, 11, 20-22, 68, 69], have compared trabecular structure in osteoporotic

and non-osteoporotic specimens / patients that were matched for trabecular bone

volume. Recker et al. found that osteoporotics (matched for bone volume) have an

11% decrease in trabecular number (Tb.N) and a 9% increase in trabecular spacing

(Tb.Sp). The surprise amongst the results was that the trabecular thickness (Tb.Th)

was 9% greater in the subjects with osteoporosis [68]. Recker et al. also found a 37%

decrease in trabecular connectivity in the patients [68]. Similarly, star volume data, a

surrogate measure of connectivity [70], revealed a significant difference of 36%

between subject groups [68]. Thus, it appears that in osteoporotic patients, trabeculae

41

are less numerous, thicker, more widely separated and less connected than in normal

subjects.

Kleerekoper et al. have suggested that the same amount of trabecular bone is

biomechanically less competent when distributed as thicker plates that are fewer,

more widely separated, and less connected, than when distributed as thinner plates

that are more numerous, less widely separated, and more connected [21]. These

finding have been supported in numerous studies [7-9, 11, 20, 21, 68]. Overall, these

studies suggest that trabecular architecture makes a contribution to the mechanical

integrity of trabecular bone that is independent of bone density.

42

Chapter 3 Magnetic Resonance Imaging

3.1 Theory of Magnetic Resonance Imaging

Nuclear Magnetic Resonance (NMR) as a spectroscopic tool is an established

technique with widespread research applications in the fields of physics, chemistry,

biochemistry and molecular biology. Since the 1970's, NMR has also been developed

as an imaging method to map the spatial distribution of substances within an object

[71]. Currently MRI is the pre-eminent clinical imaging modality for the human body

since it is non-invasive, provides excellent soft tissue contrast, and does not use

ionising radiation. Clinical MRI utilises the NMR signals generated by 1H nuclei

(protons). A high natural abundance in the body of 1H (in the forms of water and

lipid) as well as a high NMR sensitivity make the 1H nucleus the ideal candidate for

use in diagnostic imaging [71]. MRI has the ability to generate exquisitely detailed

images of internal anatomy and can also be used to study biochemical processes in

vivo. NMR can also provide ‘functional’ information concerning factors such as

blood flow and perfusion, tissue water diffusion and changes in blood oxygen levels

that reflect brain (neuronal) activation [72]. This ability of MRI to emphasise different

properties of the tissue in the acquired image by the proper choice of experimental

parameters also makes it a powerful tool for biomedical research.

3.1.1 Principles of Pulsed Nuclear Magnetic Resonance (NMR)

In the presence of an external magnetic field, B0, a proton of magnetic dipole

moment μ experiences a torque that tends to align it with the magnetic field. Because

the proton also possesses spin angular momentum, its motion is to precess about the

field direction with angular frequency:

00 Bγω = (8)

where γ is a constant (the gyromagnetic ratio) which in the case of the proton has a

value of approximately 2.68 × 108 rad/s/Tesla.

43

Only nuclei with non-zero spin exhibit magnetic resonance. In the case of the

proton the z-component of the spin angular momentum can only take on values of

±1/2h . If we place the 1H nucleus into a static magnetic field B0 (which is

conventionally assumed to be aligned along the +z axis) then the corresponding

values of z-component of the magnetic moment are given by:

21

hγμ ±=Z (9)

Whereh is Planck’s constant divided by 2π and has the value of approximately 1.055

× 10-34 Js.

In the absence of the static magnetic field the two states of the spin are

indistinguishable (degenerate states), but in the presence of a static magnetic field B0,

these two different orientations are no longer equivalent. The nucleus acquires an

energy:

21

00 BBE Z hγμ ±=−= (10)

Thus we can see that the allowed energies of the nucleus are discrete or ‘quantised’.

NMR involves the excitation of transitions between these quantised Zeeman energy

levels by application of a suitable perturbation to the sample containing the nuclear

spins in the form of a time dependent magnetic field oscillating or rotating in a plane

perpendicular to the static magnetic field B0.

Equation (8) can also be called the resonance condition and is one of the

conditions that must be satisfied to cause a transition between two spin states. This

resonance condition tells us that the frequency of the oscillating magnetic field ω

(used to excite the spins) must match the resonance frequency 0ω (Larmor frequency)

of the 1H nucleus. This oscillating field will induce transitions between the two states,

provided that the field applied to perturb the spins, B1(t), is applied both at the

resonance frequency and perpendicular to B0. This excitation, B1(t), is typically in the

radiofrequency (RF) range and is applied in the form of a pulse of duration τp. By

adjusting the amplitude of the RF and/or the duration of the pulse, the equilibrium

nuclear magnetisation of the sample can be tipped through any chosen angle

θ = γB1τp (11)

44

with respect to B0.

Detection of an NMR signal is achieved through the use of a receiver coil

surrounding the sample. This receiver coil may double as the transmit coil that is used

to apply the RF pulses, B1(t). As the sample magnetization rotates in the x-y plane

following the pulse, there is a weak, oscillating, decaying e.m.f. signal induced in the

receiver coil called the Free Induction Decay (FID). The intensity of the FID signal

induced in the probe coil depends on the concentration of protons in the sample and

their relaxation times (see below) and this signal is amplified by a receiver and

converted to a digital signal using an analog-to-digital (ADC) converter. The

amplification of the signal is adjusted for each sample such that the signal is spread

out in the range of integer values available to the ADC.

In the case of complex molecules, different groups of protons in the molecule

experience slightly different static magnetic fields due to chemical shielding effects

(see section 3.1.5 below) so that each proton has its own resonant frequency and

hence the FID consists of a superposition of a number of frequencies, corresponding

to a number of peaks in the spectrum, each with a finite width due to line broadening

effects. A single proton signal would give a simple sine wave with a particular

frequency corresponding to the chemical shift of that proton. This signal dies out

gradually as the protons recover from the pulse and relax.

There are two main contributions to relaxation: spin-lattice relaxation

(characterised by time constant T1) and spin-spin relaxation (denoted by T2). The

spin-lattice relaxation time T1 is also known as the longitudinal relaxation time as it

involves the recovery of the z component of the magnetisation (the magnetisation

parallel to the applied static field B0) through energy exchange between the spins and

the thermal energy reservoir of the sample. T2, which is also called the transverse

relaxation time, is the relaxation of the magnetisation in the transverse (x,y) plane and

arises from interactions between neighbouring spins.

45

3.1.2 Magnetic Resonance Imaging

The key to magnetic resonance imaging is the application of magnetic field

gradients. In the presence of a magnetic field gradient, G, the Larmor frequency

becomes a function of position since the frequency is proportional to the magnetic

field strength (Equation 8). Thus the precession frequency of a particular spin, in the

presence of a magnetic field gradient, labels its spatial coordinate in the direction of

the gradient and we see that in the presence of a gradient, planes of constant field

strength also become planes of constant resonance frequency. This fundamental

relationship between the spatial domain and the frequency domain in the presence of a

gradient forms the basis for MRI.

In MRI we are often interested in visualising a slice through the patient. To

achieve this we must select the particular slice to be imaged by applying a specially

shaped RF pulse, of well defined (narrow) bandwidth, in the presence of a slice

selection gradient GS. This pulse excites only those spins whose Larmor precession

frequencies lie within the range spanned by the bandwidth of the RF pulse. These are

only in a slice that is perpendicular to GS. The thickness of this slice is determined by

the bandwidth of the pulse and the magnitude of the slice selection gradient.

SRFSI GBWd γπ /2= (12)

The bandwidth of the slice selection pulse BWRF depends on the details of its shape.

Typically sinc shaped pulses are employed for slice selection because they can excite

a well defined rectangular slice (remember that the Fourier Transform of a rectangle

is a sinc function), whereas a Gaussian pulse is not able to excite a well defined

rectangular slice.

To create a 2D image in MRI the frequency of the signal can be used to

encode in-plane spatial position in one direction in the plane of the selected slice,

whilst a second (orthogonal) direction can be encoded by applying stepped magnetic

field gradient at right angles to both readout (GR) and slice select (GS) gradients. The

effect of this ‘phase encoding’ gradient (GP) on the nuclear spins is to impart to the

transverse magnetisation a phase modulation whose frequency is a function of

46

position in the direction of the phase encoding gradient. In principle either the

magnitude or duration of the phase encoding gradient may be varied.

A FID is acquired for each ‘step’ or strength of the phase encoding gradient

(GP) and the set of FIDs constitute the raw time-domain data that is used to generate

an image of the sample. To convert this time-domain data into a frequency spectrum a

mathematical operation called a Fourier Transform (FT) is used. When there are many

different types of protons with different chemical shifts, the FID will be a complex

sum of a number of decaying sine waves with different frequencies. The FT extracts

the information about each of the frequencies, their intensities, and the rate at which

they decay. Likewise a 2-dimensional Fourier Transform can be used to convert the

raw time-domain data acquired via the processes of frequency and phase encoding

outlined above to create a 2D image. This method is known as Fourier or ‘spin-warp’

imaging and will be discussed in detail in the next section.

A more detailed discussion of basic MRI theory can be found in a number of

books – see e.g. Refs [72-74]. Consequently the discussion will not be extended

beyond the above overview in this thesis.

3.1.3 Imaging Sequences

Contrast in MR images is a complex function of spin density (the number of 1H nuclei per unit volume in the tissue of interest) and NMR signal relaxation times,

which determine the recovery of the signal following a perturbation and are

themselves functions of the tissue type and pathology. Different imaging sequences

are used to emphasise the effects of different relaxation times (e.g. T1 or T2) and are

capable of providing information pertaining to such things as; anatomy, perfusion,

rheology and diffusion.

The spin-echo (SE) sequence uses a 90° RF pulse to initially perturb the

nuclear spins and then after a certain time (denoted as TE/2) a 180° pulse is applied to

refocus the decaying FID into a spin echo at a time TE (echo time). An advantage of

using a spin-echo sequence is that it introduces T2 dependence to the signal. Since

47

some tissues and pathologies have similar T1 values but different T2 values it is

advantageous to have an imaging sequence, which produces images with T2

dependence. In practice, following a 90 degree pulse, instead of decaying with time

constant T2, the transverse magnetisation actually decays with a time constant denoted

by T2*. This relaxation time takes into account loss of transverse magnetisation via

dephasing of the spins due to local magnetic field inhomogeneities as well as that

arising from spin-spin interactions, i.e. the true T2 processes. Thus in practice T2*<

T2.

The spin echo sequence removes some of the effects of signal de-phasing due

to static field inhomogeneity. In the absence of molecular diffusion, the effect of the

180° pulse is to refocus the dephasing due to B0 inhomogeneity, so that the echo peak

decays with time constant T2.

An example of a spin-echo sequence is presented below. TR is the time of

recovery, that is the time between one 90° pulse and the next 90° pulse.

Figure 3.0: Sequence diagram for a 2D spin echo imaging sequence. The arrow pointing downward in the gradient table indicates that the phase encoding gradient is stepped sequentially.

rf

GSS

ADC

GR

GPE

TA

π π/2

48

A gradient echo (GE) sequence uses a reversal of the magnetic field gradient

to generate a gradient echo. By utilising a small flip angle excitation pulse, the

gradient echo sequence is capable of more rapid imaging than the spin echo sequence

but also suffers from some disadvantages such as a reduction in image quality due to

enhanced sensitivity to magnetic susceptibility effects compared with the SE sequence

(see below). To reduce the effects of magnetic susceptibility in GE imaging a

reduction in echo time (<10ms) has been applied in a few studies [8, 11, 42, 75-77].

These drawbacks will be discussed further below. Figure 3.1 is an example of a

typical GE sequence used in imaging.

Figure 3.1: A schematic diagram of a 2D gradient echo sequence [72]. GSS is the slice select gradient, GPE is the phase encoding gradient and GR is the frequency encoded readout gradient. ADC is the analogue to digital converter and represents the duration that it is switched on to record the FID.

Spin-echo (SE) and gradient-echo (GE) sequences have been used

successfully to image trabecular bone and both have their particular advantages and

disadvantages. SE based images tend to be used for quantitative analysis of trabecular

architecture and in vitro imaging, whilst GE based images may be better suited to in

49

vivo imaging because of the considerably shorter imaging times compared with SE

based imaging.

3.1.4 Magnetic Susceptibilities

Magnetic properties of materials can generally be classified according to three

main categories. These are diamagnetic, paramagnetic and ferromagnetic. In general

the relationship between the equilibrium sample magnetization and the applied

magnetic field can be expressed as:

M = χH (13)

Where M is the magnetisation vector, χ is the magnetic susceptibility and H is

the magnetic field strength. The susceptibility is negative (χ < 0) for diamagnetic,

positive (χ > 0) for paramagnetic materials. In the case of ferromagnetic materials the

relationship is non-linear, with χ >> 1 [72].

Large susceptibility differences such as those between tissue and orthopaedic

implants incorporating metals such as stainless steel or titanium cause major problems

with the static magnetic field homogeneity in an MRI scanner. Figure 4.2 is a

diagram of the susceptibility spectrum [78] and shows the three main classes of

materials.

50

Figure 3.2. Susceptibility spectrum. The upper diagram uses a logarithmic scale to indicate the full range of observed magnetic susceptibility values: It extends from χ = -1.0 for superconductors to χ > 100 000 for soft ferromagnetic materials. The bottom diagram uses a linear scale (in ppm) to indicate the properties of some materials with |χ| < 20 ppm. The susceptibilities of most human tissues are in the range from –7.0 to –11.0 ppm [78]. Diamagnetic Materials

A substance that has no permanent magnetic dipole moment is called a

diamagnetic substance. When an external magnetic field is applied to a diamagnetic

substance it follows from Faraday’s and Lenz’s laws that the electrons will be

perturbed in such a way as to induce a magnetic field that is anti-parallel to the

external field. The associated macroscopic field opposes (weakly) the external field,

leading to a small negative magnetic susceptibility (-1 << χ < 0). Effects arising from

diamagnetism are typically weak compared to those arising from paramagnetism and

ferromagnetism.

Paramagnetic Materials

Paramagnetic substances contain atoms (or molecules) with permanent

magnetic dipole moments arising from the presence of unpaired electrons, but the

interactions between them are insufficiently strong to cause spontaneous alignment.

51

In the presence of an external magnetic field the bulk magnetic moment is aligned

parallel to the external field leading to a small positive magnetic susceptibility (0 < χ

<< 1) [79].

Ferromagnetic Materials

Certain materials, whose atomic constituents contain unpaired electrons and

consequently have permanent magnetic dipole moments, exhibit strong magnetic

effects even in the absence of an external magnetic field. These arise from the

spontaneous alignment of the (electronic) magnetic moments over regions called

domains, (which can span distances of millimeters). The size of the domains is limited

by the size of the spin-spin interactions. Ferromagnetic materials should not be taken

near an MRI scanner as the material will be attracted strongly to the MRI magnet.

In MRI, differences in magnetic susceptibility between different regions of a

sample (or patient) give rise to non-uniform perturbations of the magnetic field in

localised regions near the interface between them and thus cause the static magnetic

field B0 to be inhomogeneous. This degradation in B0 homogeneity results in reduced

image quality due to increased spin de-phasing, irregular voxel sizes, and incorrect

slice excitation.

Inhomogeneities in the field B0 cause inherent problems in both SE and GE

sequences, but it is a much larger problem in the GE sequence due to the fact that the

signal intensity in a GE sequence is dependent on T2* (rather than T2). This time

constant can be very short in the presence of susceptibility artefacts arising from the

inhomogeneous nature of trabecular bone.

There are important differences in the size of the susceptibility artefacts

arising from the trabeculae and pore spaces in bone and those arising from metal

prostheses. In the former case the length scale over which the magnetic field

variations occur is smaller than the voxel dimensions, leading to intra-voxel de-

phasing of the signal, which cannot be corrected for by techniques such as View

Angle Tilting (VAT – to be discussed in detail in section 3.2.1). While this may also

be the case close to a metal implant, in this case the susceptibility effects are much

52

larger and longer range, so that at some distance from the implant the effects of intra-

voxel dephasing become relatively minor and the inter-voxel (pixel to pixel)

frequency shifts can be corrected by VAT.

3.1.5 Requirements for High Resolution MRI

There are very stringent operating conditions that must be placed on the

system in order to be able to produce high-resolution images. These include:

1) Homogeneity. It is imperative that the magnetic field across the sample be as

uniform as possible. An accepted static B0 homogeneity level for a 1.5 T clinical

scanner over a spherical volume of diameter 50cm is 5ppm [72]. For state of the art

clinical systems the maximum imaging gradients are around 40 mT/m and are

generally accurate to about 5% of their ideal values over the imaging region. The

image distortion resulting from this varies from application to application and the

requirements of homogeneity should be determined based on the imaging method

used. A higher degree of homogeneity can be achieved using superconducting

magnets rather than electromagnets or permanent magnets.

2) Susceptibility. The magnetic susceptibility differences between tissues in a

sample create field perturbations that affect the static magnetic field B0 and result in

local dephasing of spins.

3) Stability. A highly homogeneous field is of little practical value if there

are significant fluctuations or drift of field or frequency during the period of

observation. This is not a major consideration for superconducting magnets, which are

inherently stable, when they are in the persistent mode.

4) Diffusion. Diffusion of spins during a scan results in a loss of signal in the

image. This arises because of the effect of the imaging gradients (especially the

frequency encoding gradient) which acts in a similar way to the diffusion gradients

used in Diffusion Tensor Imaging (DTI), producing additional de-phasing of the water

proton signal and attenuation of the echo peak, leading to signal voids in regions of

high (unrestricted) diffusion. Fortunately for most biological samples, the diffusion of

water is restricted by tissue boundaries and thus is not a severe problem in clinical

MRI, although it can cause problems in NMR micro-imaging, where imaging

gradients can exceed 1 T.m-1 [73]. The average distance that a free proton can diffuse

53

during the time interval between the excitation pulse and the echo peak is given by

ΔxD = √(2DTE), where D is the (effective) self diffusion coefficient.

5) Chemical Shift. Nuclear spins are partially shielded from the effects of

the applied static magnetic field by the electron cloud of the atom or molecule

surrounding them, so that the effective magnetic field experienced by the nucleus is

given by )1(0 σ−= BB , where σ is the chemical shielding constant. Differences in

chemical shielding cause nuclei in different chemical environments to precess at

slightly different frequencies. The chemical shift is defined with respect to a reference

subject, usually tetramethylsilane (TMS) in the case of proton spectra, and is given by

(δ=(Δω/ωREF)×106 ppm), Chemical Shift Anisotropy (CSA) can give rise to

heterogeneous line broadening and hence can limit resolution in MRI.

The inherent resolution achievable for a given sample is determined not only

by the pixel size. It is primarily determined by the T2 time of the sample as well as the

strength of the magnetic field gradient and also the signal to noise ratio (SNR). The

natural linewidth of the signal from each pixel at half-width maximum is given by

2

1Tπ

. Thus for a short T2 time the signals from neighbouring pixels in the frequency

encoding direction may overlap and give a mixed signal. However if the magnetic

field gradient is strong enough such that the frequency difference between adjacent

pixels is greater than the natural linewidth, the signals from these pixels will be

effectively separated. This leads to a limit on resolution imposed by the natural

linewidth of the sample given by:

ΔxL ≥ 1/(γGT2) (14)

Hence we can see that the resolution of the sample is inherently determined by

the T2 time of the sample and the magnetic field gradient G.

3.1.6 MRI of trabecular bone

MR micro-images that resolve trabecular bone structure can be obtained in

vitro at high magnetic field strengths [7-9, 21] and in vivo using clinical scanners at

1.5T or above [11]. The in-plane spatial resolution achievable in vivo is similar to the

dimensions of trabeculae (78-200 μm – for humans), while it may be lower in the

54

slice direction (400 μm - 1000 μm) [11, 42]. Despite this and the fact that bone itself

gives no observable signal, MR imaging appears to be well suited for analysing

trabecular bone. MR imaging is multi-planar and thus it is capable of imaging at any

arbitrary angle without sample repositioning. It requires a minimum of sample

preparation and can provide high-resolution 3D images in vivo.

Bone is devoid of protons with sufficiently long T2 relaxation times to allow

detection under normal scanning conditions. By contrast, the protons in bone marrow

(primarily water and lipids) provide a strong signal of sufficient duration (T2~100 ms)

to permit spatial encoding [17]. Consequently it would appear that there should be a

clear delineation between bone and marrow components at the interface.

Unfortunately, with limited spatial resolution and a finite slice thickness, the MR

image is prone to signal mixing. This reduces trabecular bone edge acuity and is

known as partial volume averaging. This leads to partial volume effects (PVE), which

increase with magnetic field strength and echo time [80].

As a result of these partial volume effects the depiction of trabeculae in MR

images may represent an integrated projection of a trabecular plate or an average over

several trabeculae. While extensions of standard stereological techniques [41] may

provide a means of quantifying trabecular bone structure depicted in MR images, the

MR-derived measures differ from those obtained at ~20 μm resolution. Despite

limitations in resolution, it has been demonstrated in vitro, using cubes from human

distal radii [76] and vertebral bodies [77] that structural indices derived from these

images correlate with biomechanical properties such as the elastic modulus [11]. As

discussed in Chapter 2 (section 2.3) there are advanced image processing algorithms

that have recently demonstrated that clinical images can be processed to provide

‘images’ at resolutions sufficient to characterise trabecular architecture [47, 48, 57].

Susceptibility of the image to PVEs depends upon the orientation of the image

plane with respect to trabecular orientation, the size of the trabeculae, spatial

resolution, and slice thickness [17, 81, 82]. It is essential to minimise PVEs for

accurate depiction and quantification of trabecular architecture. Highly anisotropic

bone (e.g. tibia), when imaged in a plane orthogonal to the primary trabecular

55

orientation, is less susceptible to PVEs than isotropic bone (e.g. vertebrae), which has

a more random orientation. It has been suggested [17, 81] that to minimise the effect

of PVE’s (and also maximise contrast to noise ratio (CNR)) the slice thickness should

be comparable to the thickness of the trabeculae.

The effect of having the slice thickness larger than the size of the trabeculae

has a greater impact on the parameters Tb.Th, Tb.Sp and Tb.N than a reduction in in-

plane resolution does. The magnitude of the impact of having larger slice thicknesses

is also affected by the trabecular orientation and the imaging plane from which the

slice is taken [11]. Other studies [9, 20, 21] have shown that the Tb.Th is the most

affected out of Tb.N, Tb.Sp and Tb.Th by PVE’s.

When imaging trabecular bone, design of the RF-coil used to detect the signal

is of utmost importance [7, 21, 42, 75, 76]. There is a need to use specially designed

coils, which maximise the SNR by minimising the space between the site and the coil

and hence maximise the ‘filling factor’. There have been some coils developed for the

wrist [42], calcaneus [7, 9] and finger [83]. As the object to be imaged and coil size

increase, signal amplitude achievable for a given voxel volume decreases.

Consequently the resolution achievable for example in the wrist, using a wrist-sized

coil, is considerably less than the SNR obtainable in the phalanx using a finger-sized

coil [83]. This becomes a major problem when trying to image the most important

sites in terms of fracture risk (hip and vertebrae). The design of such a coil is vital in

obtaining high resolution in vivo images of these sites.

Previous in vivo studies that have used GE sequences in combination with

surface coils have applied an automated intensity correction algorithm to adjust the

images due to the surface coils having an inhomogeneous sensitivity over the imaging

region [84]. In addition to this the static magnetic field creates an induced magnetic

field in the hydroxyapatite molecules that form an integral part of the trabecular

structure causing local field inhomogeneities. In a SE sequence these effects are

minimised by the refocusing effect of the 180° pulse, whereas a GE sequence is

highly susceptible to these induced fields. This can actually be used in an

advantageous way in GE imaging by acquiring the free induction decay signal (FID)

56

just before the refocusing of the gradient echo signal. In this case the image is highly

susceptible to the artefacts and the information from this can be used to map the

trabecular structure using the T2* times [81, 85]. This technique will be discussed in

full in the next section.

3.1.7 An alternative method of measuring trabecular bone architecture using MRI

In vivo MR images of sufficient resolution for direct analysis can only be

obtained at a peripheral site, such as the radius or calcaneus [86]. MRI offers another

means by which trabecular structure can be quantified at any anatomic location

without the need to resolve individual trabeculae [81, 85, 86]. This second method is

based on measuring the field inhomogeneities, which result from the different

magnetic susceptibilities of bone and marrow [75, 82, 86]. The discontinuity in the

magnetic properties induces magnetic field perturbations, which increase the rate of

NMR relaxation. Since the degree of field inhomogeneity depends upon the geometry

of the bone/marrow surface, the relaxation rate provides an indirect measure of

trabecular architecture, compressive elastic modulus and fracture risk [75, 82].

This work has mostly been carried out by Chung and Wehrli [81, 82, 85, 86].

Using a 9.4T μMR system they investigated the magnetic-field perturbations induced

by the trabecular network. Their results demonstrated that T2* is sensitive only to the

arrangement of trabeculae orientated perpendicular to the external polarising field B0.

This selective sensitivity of T2* to trabeculae perpendicular to B0 explains its

directional property in cancellous bone [82]. Thus when the orientation of cancellous

bone is altered with respect to B0, proton T2* also changes according to the number

density of field-perturbing trabeculae [81, 82, 85, 86].

The study also showed that T2* is critically dependent on image voxel size.

When the incremental line broadening was compared with the voxel size it was shown

that on increasing the image voxel size the line broadening increases, but at a non-

linear rate [81]. The implication from this observation is that the susceptibility-

induced magnetic field distortions arising from the bone-marrow interface are of short

57

range compared to the spatial resolution commonly used in clinical MR imaging [81].

As the image-voxel size increases above that corresponding to the average distance

between adjacent trabeculae, larger voxels do not correspondingly cover a wider field

distribution. Hence the line broadening at this spatial scale is expected to remain

invariant and independent of voxel size.

The volume susceptibility of mineralised trabeculae has been estimated to be

between 0.3-0.5 ppm relative to bone marrow [81, 82]. This was determined by

summing atomic susceptibilities for the constituent atoms of calcium hydroxyapatite,

as well as by measuring the incremental NMR linewidth of suspended bone

specimens in diamagnetic solution [85], and by using a vibrating sample

magnetometer [81]. The conclusions reached by this latter group were that if T2* is to

be used in the diagnosis of osteoporosis, the effect of bone-marrow composition

should also be taken into consideration [81].

3.1.8 Multinuclear Solid-State imaging of bone and synthetic calcium phosphates

As discussed above, one of the major disadvantages of using proton imaging

for evaluation of bone architecture is the presence of magnetic susceptibility artefacts

at the bone and bone marrow interface. These susceptibility artefacts result in a slight

blurring of the image due to the dephasing of the spins induced by variations in the

local magnetic field. Another disadvantage is that proton imaging only offers

information about the bone marrow. It does not provide direct information about the

bone content. Instead this information is inferred from the absence of signal from the

bone. Solid state imaging using 31P nuclei provides a means of directly imaging bone

content [87].

Bone mineral is a non-stoichiometric calcium-deficient apatite, whose crystal

structure is basically similar to that of synthetic or geological mineral hydroxyapatite,

Ca10(OH)2(PO4)6. There are however significant compositional and functional

differences between bone apatite and hydroxyapatite. These differences include

smaller crystal size, reduced short-range crystalline order, the absence of OH- groups,

58

and the presence of CO and HPO groups in bone apatite [87]. Also the HPO24- in

bone apatite is distinctly different in its environment from HPO24- in synthetic

hydroxyapatites and other calcium phosphate phases containing HPO24- groups [88].

These differences markedly affect the reactivity of bone apatite crystals with ions and

organic constituents present both in extracellular fluids and in bone cells. They

therefore also affect the ability and effectiveness of bone apatite crystals in

participating in the various biological and structural functions of the crystals in vivo

[89]. The most important point to note is that these compositional and structural

differences change significantly with the time that the crystals remain in the tissue

(crystal maturation), thus reflecting the local and / or systemic rates of bone formation

and resorption [87].

Using this knowledge a new approach has been developed by Wu et al. that

characterises bone by a method sensitive to the chemical composition and structure of

bone apatite crystals. This method can in principle also provide the true volumetric

mass densities of bone mineral and matrix independently. The method is based on 31P

solid state projection reconstruction MRI and has been shown to be safe for use on

human patients [87]. The back-projection MRI pulse sequence as employed by Wu et

al. [87] consists of a single fixed-amplitude magnetic field gradient pulse, during

which a short (hard) RF pulse is applied after a suitable delay following the start of

the gradient pulse to allow eddy currents (induced in the electrically conductive

structures of the probe and magnet) to decay. The spatial resolution and sensitivity of

the method are inherently low but may be improved by significantly increasing

imaging time. Typically a total of 256 samples of the FID are then obtained while the

gradient is held constant. The sequence is then repeated for a total of 998 gradient

directions distributed in a uniform pattern about the unit sphere [87]. This method is

promising because it provides a means for quantification of bone mineral and bone

matrix separately due to different T1 relaxation times of the synthetic and natural

calcium phosphates. Despite these having similar chemical composition the native

bone 31P has a T1 an order of magnitude longer than the synthetic 31P. Thus this

technique can show the degree of mineralisation of bone and will enable

characterisation of the remodelling process [87]. The unfortunate drawback with such

a technique is the extremely long imaging times required to obtain images with

sufficient resolution to be clinically useful.

59

Single point imaging (SPI) can also be used to image the solid structure of

bone. This technique is advantageous because of the very short effective echo times

achievable and because each data point is sampled at equal time during signal

evolution, thus acquired images are free of susceptibility and chemical shifts and B0

inhomogeneities. The imaging time for SPI is large and in addition to this the SNR is

typically quite low. It is possible to reduce the time by encoding four points at each

acquisition instead of one (called multiple point imaging (MPI) [90]). Recently SPI

was used to image polymeric acetabulum sockets and metal prosthesis [91]. There are

still problems with the clinical in-vivo use of this SPI technique due to the large

gradient strengths needed for high spectral resolution, stimulated echos, and acoustic

noise considerations for the patient [91].

3.2 View Angle Tilting - Technique Used To Reduce

Susceptibility Artefact

A number of researchers have attempted to devise methods for eliminating or

reducing susceptibility artefacts in MRI [3, 6, 23, 92-96]. Most of these methods are

in fact just simple scan parameter modifications that can be utilised to reduce the

observed artefact. However, a method described by Cho et al. [23] provides a means

to correct for susceptibility artefact and is known as View Angle Tilting. This

technique has shown promise and further development of it is currently underway in a

number of labs around the world.

View Angle Tilting (VAT) involves the application of an extra set of imaging

gradients applied in the slice direction at the same time as the readout gradients and

with the same amplitude as the slice select gradients, see Figure 3.3.

60

VAT was first proposed by Cho et al [23] in 1988 as a way to correct for both

susceptibility differences and chemical shift artefacts simultaneously. The basic

concept is that because artefacts created by both of these sources are proportional to

the strength of the applied static magnetic field B0 they involve a displacement of the

image signal along a well defined direction with respect to the frequency encoding

(readout) and slice selection gradient directions. The signal from a given voxel will be

displaced in both the slice selection and frequency encoding gradient directions by an

amount proportional to the magnetic offset ΔB. This can be seen in Figure 3.4.

rf

GSS

GPE

GR

rf

GSS

GPE

GR Figure 3.3: Schematic of pulse sequence used in View Angle Tilting technique. Note the extra gradients applied in the GSS at the same time as the GR.

61

Figure 3.4: Displacement of a voxel by susceptibility artefacts occurs along a direction making an angle θ with respect to the readout (GR) and slice selection (GSS) gradients.

The angle θ of this displacement with respect to the slice selection gradient

(normal to the image plane) is independent of the magnitude and sign of the field

offset / anomaly ΔB. Consequently if we tilt the view angle by the same amount, the

anomaly will be removed, except for some blurring arising from the finite slice

thickness that gives rise to signal overlap at the edges of the pixels. An important

point to note is that the VAT method assumes that each voxel corresponds to a unique

Larmor frequency and that there is no significant frequency variation within each

voxel (i.e. no intra-voxel de-phasing - as discussed above in section 3.1.4).

Consequently if this is not the case and the magnetic susceptibility artefacts are large

enough to produce significant variations in magnetic field across a voxel, the VAT

method will not be as effective.

The degree of blurring is governed by the angle θ that the readout gradient

direction makes with respect to the normal to the slice plane; bl = T.tan θ, where T =

slice thickness, bl = degree of blurring and:

θ = tan-1(GSS/GR) (15)

Slice Select (z) ΔB/GX

ΔB/GZ

θθ=tan-1(GZ/GX)

Frequency Encoding (x)

62

The VAT technique has been shown to reduce the artefact from metallic

prosthesis in in-vivo clinical situations [3] including interventional MRI where

inserted needles distort the local magnetic field [97].

A recent study by Kolind et al [92] used the sum of squares of the pixel

values of an MR image as the energy, E, of the MR image. This total energy was

defined as containing a noise field, N, superimposed on a noise-free signal field, S.

NS EEE += (16)

where

∑ +=Pixel

NSE 2)( (17)

In this study they used wax replica phantoms made from moulds of stainless steel and

titanium prostheses. These replicas were non-metallic and were used to determine the

difference between the images of each metallic phantom and its replica. By

subtracting the energy value of the stainless steel image from the wax phantom the

energy difference ED, should provide a measure of the artefact. If we assume that

there is an additional artefact energy term, A, that is uncorrelated with the signal field

and has a zero-mean then the energy difference between the images from the wax and

steel phantoms is;

ANND EEEE ++=21

(18)

where N1 and N2 are the noise contributions from the wax and steel phantoms

respectively. For regions that contain no artefact, the sum of squares of the pixel

values in the difference image will be equal to 21 NN EE + and hence the artefact

T T

bl

bl

θθ

Figure 3.5: Degree of blurring is affected by slice thickness and the angle θ. Smaller slice thickness and increased angle θ result in less pixel overlap and hence less partial volume blurring.

63

energy can be calculated by subtracting the normalised energy of 21 NN EE + from the

normalised total energy of the entire image. This is a quantitative way to calculate the

artefact energy EA. In a similar method to this the blur energy (EB) can be calculated

by replacing the artefact field with a blur field, B.

Using these energy calculations Kolind et al. [92] investigated the effects of

increasing readout bandwidth (BWREAD – this is the bandwidth of the gradient pulse

used to encode the frequency axis) and applying the VAT gradients. They combined

an increased BWREAD (±62.5 kHz), an increased GSS (increased by 20%) and VAT

into one sequence which they named the Metal Artefact Reduction Sequence (MARS)

[3, 92]. The conclusions drawn from this study was that the MARS sequence resulted

in the least amount of image distortion, reducing the artefact by an average of 79%

compared to a standard 2D spin echo sequence with BWREAD of ±15.63 kHz [92].

64

Chapter 4 Micro Computed Tomography

Generally speaking, tomography refers to the cross sectional imaging of an

object from either transmission or reflection data collected by illuminating the object

from many different directions [98]. MicroCT has developed significantly since the

principles of X-ray computed tomography (CT) were first demonstrated by

Hounsfield in the 1960’s.

In x-ray tomography, image contrast is determined by the fact that attenuation

of the x-ray photons is a function of position in a heterogeneous sample. Over the

range of most commonly encountered photon energies, (20 to 150 keV), there are two

contributions to attenuation of the photon energies; the photoelectric effect, and the

Compton effect. Photoelectric absorption consists of an x-ray photon imparting all its

energy to a tightly bound inner electron in an atom and hence being absorbed. In this

process the electron uses some of this acquired energy to overcome the binding

energy within its shell, the rest appearing as the kinetic energy of the freed electron

[98]. Compton scattering consists of the interaction of the x-ray photon with either a

free electron, or one that is only loosely bound in one of the outer shells of an atom.

As a result of this interaction, the x-ray photon is deflected from its original direction

of travel with some loss of energy, which is gained by the electron [98]. Both the

photoelectric and Compton effects are energy dependent. As a result, the probability

of a given photon being lost from the original beam due to either absorption or scatter

is a function of the energy of that photon.

There are two main types of micro computed tomography systems in use. One

is based on the use of a synchrotron x-ray source(SRμCT) and the other uses a table

top x-ray (μCT) source that produces polychromatic radiation but which can be

filtered to produce approximately monochromatic radiation. When this

monochromatic approximation is used a further correction (from an experimental

calibration curve) for beam hardening artefact is often utilised, but in some cases the

65

mathematical algorithms developed for use with a polychromatic source are still used

in the processing without the consideration of filtering and beam hardening. The use

of a filter often depends on the sample used and the dynamic range of the exit

spectrum of the x-rays.

The general working principles of both types of systems are the same. First an

x-ray beam is generated and passed through the object of interest to a detector that

converts the x-ray to visible light. This light is then ‘piped’ to a CCD (usually using

fibre optic cables) that converts the light to an electrical signal that is then sent to a

computer. This data is processed using back projection reconstruction techniques to

create a 3D image of the data. The type of reconstruction algorithm used depends on

the type of x-ray source employed, i.e monochromatic or polychromatic. A schematic

diagram of a basic microCT setup using a conebeam source is shown in Figure 4.0

Figure 4.0: Diagram of a basic Cone Beam microCT system showing the path of the beam from the x-ray source through an object onto a detector and then the information is converted to visible light and piped through fiberoptic cables to a CCD where it is then converted to electric charges and sent to an ADC and then a computer (Figure courtesy of Prof. Felix Wehrli, UPenn).

4.1 Monochromatic X-ray Projections

If all photons possess the same energy then we can analyse the absorption and

scatter of electrons using a simple mathematical model. Consider an incremental

thickness of a slab, Δx, with N monochromatic photons incident on the front boundary

66

of the material. If N + ΔN electrons pass through (ΔN is negative) then the following

condition holds:

μ−=Δ⋅

ΔxN

N 1 (19)

where the attenuation coefficient μ represents the combined losses due to

photoelectric and Compton effects.

Solving this equation by integrating across the thickness of the slab, X, where

N0 is the number of photons that enter the object; XeNxN μ−= 0)( (20)

This equation holds true when μ is linearly dependent through the material and only

varies in one dimension. If we consider μ to be a function of two space coordinates, x

and y, then for incident photons, NIN, entering the object from side A and Nd the

number of photons exciting via side B, we can obtain the following relationship:

d

INRAY N

Ndsyx ln),( =∫ μ (21)

where ds is an element of length and the integration is carried out along the

path from A to B [98].

4.2 Polychromatic x-ray sources

A polychromatic source can be filtered to produce photons of approximately a

single energy but in clinical situations this approach is not used as the number of

photons available is greatly reduced and hence the degradation in SNR is too severe

for practical applications (one cannot just increase dosage due to patient safety

concerns). Table top microCT systems using cone beam sources also produce a

spectrum of energies. When the source is not filtered we must take into consideration

the spectrum of energies emitted. Equation (20) must be replaced with:

∫=− dsEyx

INEXIT ESES),,(

exp)()(μ

(22)

where SIN(E) represents the incident photon number density (also called energy

spectral density of the incident photons) [98]. SIN(E)dE is the total number of incident

67

photons in the energy range of E to E + dE. Equation (22) takes into account that the

linear attenuation coefficient is also a function of energy [98].

From equation (22) we can derive a formula for the measured attenuation

coefficient, μmeasured, at a point in a cross section that is related to the actual

attenuation coefficient μ(E) at that point by [98];

∫

∫=dEES

dEESE

EXIT

EXITmeasured )(

)()(μμ (23)

It must be noted that this expression is true only when the output of the detector is

proportional to the total number of photons incident on it [98, 99].

4.3 Synchrotron radiation

Synchrotron radiation is a highly coherent, brilliant source of x-rays that are

emitted when high energy electrons are accelerated in the magnetic field of a particle

accelerator. The magnetic field exerts a force on the electrons perpendicular to the

direction in which they are travelling causing them to be accelerated and to radiate

electromagnetic energy. This is called magnetic bremsstrahlung (literally 'braking

radiation') or synchrotron radiation. If the electrons have enough energy, the emitted

radiation can be in the form of X-rays.

Synchrotron radiation is effectively monochromatic and is collimated such

that the beam has a very small thickness. It is also highly polarized and can be emitted

in very short pulses, typically less than a nano-second. Synchrotron radiation is of

current research interest for x-ray micro-CT not only because of the very high

resolutions possible when using it, but also because it can extend the classical

absorption tomography concepts towards edge-enhanced and phase sensitive

investigations [100]. MicroCT systems using synchrotron radiation can produce

images with resolutions around 1 μm [100] although typical resolutions may be

around 3-7 microns [13, 14].

68

4.4 Artefacts

One of the most common sources of artefacts in CT imaging is beam

hardening. When the mean energy of the exiting photon spectrum is higher than that

of the incident spectrum (due to preferential attenuation of lower energy photons) we

see an artefact known as beam hardening. This artefact results in streaks in the image

between regions of the sample with high attenuation coefficients.

Another artefact is caused by x-ray scatter as a result of the Compton

interactions. In these interactions the x-ray beam is deflected from its original course

with a random scatter angle, although generally more x-rays are scattered in the

forward direction. Correcting for scatter is easier than correcting for beam hardening

and good results have been obtained by assuming a constant scatter intensity over the

entire projection [98].

4.5 Specifications of the μCT system used in the

current studies

The μCT system used during this PhD project was a GEMS microCT scanner

located at the University of Pennsylvania in Philadelphia, USA. The GEMS eXplore

MS Micro CT scanner is designed to non-destructively image intact tissue specimens

at high-resolution. It is capable of imaging samples up to 40mm in diameter and can

achieve resolutions of less than 10 microns. The μCT system uses Volumetric

Conebeam CT (vCT) technology which, unlike conventional CT, allows the entire

volume of a sample to be imaged in one rotation, rather than slice by slice. vCT also

produces data sets with isotropic resolutions (slice thickness is equal to the axial

resolution).

This method is significantly faster than conventional single slice or multi-slice

CT. Volumetric Conebeam CT provides exceptional image quality with short scan

times with a greater signal to noise ratio. The specifications of the system are listed

below in Table 4.0.

69

. .

.

.

Table 4.0: Specifications of GEMS microCT scanner used in project [101].

The typical scan time for a rat femur was around 3:30 hrs for a resolution of 8.2

microns followed by approximately 3-5 hrs of processing. Once the sample was

prepared it is placed into the specimen bath (housing) shown in Figure 4.1. The

samples were normally immersed in phosphate buffered saline (PBS) to both preserve

the specimen and to reduce beam hardening artefacts caused by differences in

attenuation coefficients of the material and air. The resolution is dependent on the size

of the object to be imaged and examples of sample test tubes are shown in Figure 4.2.

It was possible to fit a small rat (minus limbs) into the largest test tube.

70

Figure 4.1: Inside of microCT machine showing the x-ray source, filters and timing fan device on the left. In the centre of the image is the specimen bath (the bath is used to help filter out low energy photons) and the detector is on the right. Figure 4.2: Sample test tubes used to place specimens in. These test tubes are then inserted into the specimen bath shown in Figure 4.1.

The microCT systems are relatively compact and don’t require any shielding

other than what is already in the casing. Thus the system can be placed almost

anywhere and requires very little room space (Fig. 4.3). Providing more specific

details as to the processing algorithms, filtering and other aspects of the GEMS

microCT system is not possible due to intellectual property reasons and as such this

chapter is only to serve as a basic guide to the operation of a microCT system.

Detector

Specimen bath (housing)

X-ray source, timing fan and filters

71

Chapter 5

Comparison of High-resolution MRI, Optical Microscopy and SEM for

Quantitation of Trabecular Architecture in the Rat Femur

Tim A.J. Hopper, BSc(Hons), Roger Meder, PhD and James M. Pope, PhD

School of Physical and Chemical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane 4001, Australia.

Published in: Magnetic Resonance Imaging 22 (2004), 953-961

Corresponding author: Professor James Pope, School of Physical and Chemical Sciences, Queensland University of Technology, 2 George St, Brisbane, Australia. Fax: +61 7 3864 1804, Email j.pope@qut.edu.au Keywords: Trabecular bone, MRI, SEM, optical microscopy, morphological

parameters.

82

Chapter 6

Quantitative micro-CT assessment of intra- and inter-trabecular and cortical

bone architecture in a model of advanced renal osteodystrophy in a

growing rat

1,2TAJ Hopper, 2FW Wehrli, 3PK Saha, 2JB Andre, 2AC Wright, 4CP Sanchez, 5MB Leonard

1School of Physical and Chemical Sciences, Queensland University of Technology,

Brisbane, Australia; 2Laboratory for Structural NMR Imaging, Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA; 3Medical Image

Processing Group, Department of Radiology, University of Pennsylvania, PA, USA; 4Department of Pediatrics, University of Wisconsin Medical School, Madison, WI,

USA; 5Department of Pediatrics, Children’s Hospital of Philadelphia, and Department of Biostatistics and Epidemiology, University of Pennsylvania, Philadelphia, PA,

USA. Funding: Australian-American Fulbright Council, NIH KO8-DK02503 The authors have no conflict of interest. Submitted To: Journal of Bone and Mineral Research (July 2004) Author email addresses; Tim Hopper – ta.hopper@qut.edu.au Felix Wehrli – wehrlif@uphs.upenn.edu Punam Saha – saha@mipg.upenn.edu Jalal Andre – jalala@rocketmail.com Alex Wright – wrighta@uphs.upenn.edu Cheryl Sanchez – cpsanchez@wisc.edu Mary Leonard – leonard@email.chop.edu Correspondence to: Tim Hopper School of Physical and Chemical Sciences Queensland University of Technology, PO BOX 2434 Brisbane, QLD, 4001 Phone: + 61 7 3864 2924 Fax: + 61 7 3864 9079

Key Words: renal osteodystrophy, hyperparathyroidism, cortical bone, trabecular bone, micro-CT

100

Chapter 7 Orthopaedic application of MRI in the

presence of implant materials

MRI Can Identify High Intensity Bands Around Implants That Correspond to

Radiolucent Lines on X-ray: An Ex Vivo Study of Sheep Acetabulae

Tim A.J. Hopper, BSc (Hons); Ross W. Crawford, DPhil, MBBS+; A.J. Timperley, MB, ChB*; Richard Slaughter, MBBS#; and James M. Pope, DPhil.

From the Schools of Physical & Chemical Sciences and +Manufacturing, Material and

Medical Engineering, Queensland University of Technology, Brisbane, Australia; #Division of Medical Imaging, The Prince Charles Hospital, Chermside, Australia;

and *Princess Elizabeth Orthopaedic Centre, Royal Devon and Exeter Hospital, UK Each author certifies that his or her institution has approved the animal protocol for this investigation and that all investigations were conducted in conformity with ethical principles of research. Funding: One or more of the authors have received funding from the Stryker Corporation. Published in: Clinical Orthopaedics and Related Research 427:127-131, October 2004 Correspondence to: Tim Hopper, BSc (Hons) School of Physical and Chemical Sciences, Queensland University of Technology, GPO Box 2434 Brisbane, Australia 4001 Phone: 61 7 3864 2924 Fax: 61 7 3864 1804 Email: ta.hopper@qut.edu.au

107

Chapter 8

Experimental and computational analysis of the effects of slice distortion

from metal in an MRI phantom

1,2TAJ Hopper, 2B Vasilić, 1JM Pope, 2CE Jones, 3CL Epstein, 2HK Song, 2FW Wehrli

1School of Physical and Chemical Sciences, Queensland University of Technology, Brisbane, Australia, 2Department of Radiology, University of Pennsylvania,

Philadelphia, USA. 3Department of Mathematics, University of Pennsylvania, Philadelphia, USA,

Funding: Australian-American Fulbright Association. To Be Submitted To: Magnetic Resonance in Medicine The authors have no conflict of interest. Author email addresses: Tim Hopper: ta.hopper@qut.edu.au Branimir Vasilić: vasilic@rad.upenn.edu James Pope: j.pope@qut.edu.au Catherine Jones: catherine.jones@uphs.upenn.edu Charles Epstein: cle@math.upenn.edu Hee Kwon Song: hsong@uphs.upenn.edu Felix Wehrli: wehrlif@uphs.upenn.edu Correspondence to: Tim Hopper, School of Physical and Chemical Sciences, Queensland University of Technology, GPO Box 2434 Brisbane, Australia 4001 Phone: + 61 7 3864 2924 Fax: + 61 7 3864 9079 Email: ta.hopper@qut.edu.au

Key Words: Metal Artifact, MRI, Slice Distortion

126

Chapter 9

General Discussion

The work presented for examination in this thesis started with an experiment

(Chapter 5) to determine the validity of measuring morphological parameters using

high resolution in-vitro MRI (23 μm in plane and 38 μm slice thickness) as compared

to the current ‘gold standards’. In a rat model it was shown that the ‘gold standards’

such as scanning electron microscopy (backscattered image from polished surface)

and conventional optical microscopy (5 μm thick slices imaged) can become flawed

in the preparation stage and as a result produce errors in the calculated morphological

parameters. There was relatively good agreement between the values of bone

morphological parameters obtained by MRI compared with those derived from SEM

and optical microscopy, with maximum differences typically in the range 20-30% for

the finer measures of trabecular architecture. Correlation between the MRI and SEM

morphological parameters was very high, ranging from r2 = 0.52 (BV/TV) to r2 = 0.83

(Tb.N). Whilst the correlations between the MRI and optical microscopy were

significantly lower, ranging from r2 = 0.26 (BV/TV) to r2 = 0.59 (BV/TbV). MR

images of de-calcified bone displayed much lower correlations between

morphological parameters than un-decalcified images, showing that the de-

calcification necessary for creating thin slices for optical microscopy can affect the

bone structure. Filtering of the images was shown to have a large effect on the

calculation of morphological parameters as filtering decreases the degree of

overestimation or underestimation of parameters calculated by MRI by reducing the

noise associated with the finer measures of trabecular architecture. The paper on this

work also brings to light the dilemma in choosing regions of interest (ROIs) and the

subsequent influence on the morphological parameter calculations. For studies

assessing osteoporotic status the selection of a ROI may result in an inaccurate

comparison in a longitudinal study as bone loss may be localised and bone turnover

may vary from site to site. The non-invasive nature and use of non-ionising radiation

make MRI ideal for assessing trabecular bone structure.

127

In situations of high turnover bone disease such as renal osteodystrophy

(ROD), the pattern of bone loss is inhomgeneous and a large ROI encompassing the

trabecular bone in the femur neck had to be used. This paper (chapter 6) used micro

computed tomography (μCT) to acquire very high resolution (8.2 μm) 3D images of

the rat femur in a model of advanced renal osteodystrophy. In this study it became

apparent that at high resolution there were pores within the trabecular bone that had

not previously been observed (denoted intra-trabecular porosity as opposed to the

standard inter-trabecular porosity). Using advanced image processing algorithms

based on a mathematical theorem known as the Fuzzy Distance Transform [52] some

new morphological parameters were defined with a view to better characterising and

quantifying the observed changes viz.: Open Trabecular Thickness (Op.Tb.Th),

Closed Trabecular Thickness (Cl.Tb.Th), intra-trabecular porosity, Open Cortical

Thickness (Op.Ct.Th) and Closed Cortical Thickness (Cl.Ct.Th). Op.Tb.Th is

calculated with the intra-trabecular pores left open whilst Cl.Tb.Th is calculated with

the pores filled in using a morphological closing algorithm. Op.Ct.Th and Cl.Ct.Th

are calculated similarly for the cortical thickness.

In this study some of the rats received treatment regimes such as calcitrol

(active vitamin D) and growth hormone to combat the effect of the 5/6 nephrectomy

they received to induce secondary hyperparathyroidism. Each of these treatment

groups had a different effect on the bone structure of the rats and was able to be

quantified using the above mentioned morphological parameters. Cortical and

trabecular bone volume/total volume were significantly decreased in all the

nephrectomised (NX) groups compared to intact controls. Op.Tb.Th did not differ

across the intact-control and NX groups. However, after filling of the intra-trabecular

pores Cl.Tb.Th was significantly increased in all NX groups. It was also shown that

Marrow Spacing (Ma.Sp) significantly increased in all NX groups. Ma.Sp and

Cl.Tb.Th were positively correlated (R = 0.59, p < 0.0001) consistent with decreased

trabecular number despite increased trabecular thickness. The correlation between the

thickness with pores open (Op.Tb.Th) and the Ma.Sp, decreased (R = 0.43, p < 0.01)

compared to the Ma.Sp and Cl.Tb.Th correlation. Cortical thickness was significantly

decreased in all NX groups compared with intact-controls; however, after filling in

the cortical pores, thickness did not differ between groups.

128

The conclusion from this study was that severe hyperparathyroidism in the

setting of renal disease resulted in decreased cortical and trabecular bone volume

despite increased trabecular thickness. This data provides new insights into the

complex structural effects of ROD that may contribute to increased fracture risk. The

results demonstrated that deficits in trabecular bone volume were due to intra-

trabecular porosity. The techniques developed in this paper will be invaluable in

assessing therapeutic regimes designed to improve bone structure in this complex

disease with the new morphological parameters providing a quantitative basis for

further studies into the mechanisms of high turnover bone disease.

The ability to monitor bone structure and bone osteointegration around a

prosthesis is important for surgeons when assessing the effectiveness of any

reconstruction operation. To date, magnetic susceptibility differences have prevented

the use of MR images in the visualisation of bone structure up to the interface with a

metallic prosthesis. The observation of 'radiolucent lines' (an indication of de-

bonding), using x-rays is also restricted by the 2D planar superimposition of the

anatomical information on a plain x-ray. A paper presented in this thesis (Chapter 7)

has shown, that in the absence of a metal prosthesis, MRI has the potential to provide

3D images with high resolution (current scanners can image ~180 μm in-plane and 1

mm slice thickness) that enable early accurate detection of de-bonding around the

plastic acetabulum component [5]. Using an ex-vivo sheep model, correlations

between high signal intensity lines on MRI and radiolucent lines on x-ray were

calculated. Correlations obtained for the three main Gruen Zones were in the range

between r2 = 0.58 (superior zones) and r2 =0.86 (inferior zone). In two specimens

MRI was able to detect the presence of high signal intensity bands that were not

present on the x-ray counterparts. The average thickness of these bands measured on

MRI ranged from 14.6% (Zone 2) to 39.9% (Zone 3) larger than the radiolucent lines

on the plain radiographs. Using the techniques developed and utilised previously, the

bone architecture up to the interface of the plastic acetabulum cup can be assessed

quantitatively rather than qualitatively. Thus enabling surgeons to assess

quantitatively the state of the bone around an implant. The presence of a metal

prosthesis nearby will affect this but the region of interest may be far enough away to

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not be too greatly affected. Consequently, in the case of titanium hip implants,

diagnosis around the acetabulum may be achievable using the correct imaging

sequence (Chapter 8).

To visualise the bone osteointegration with the metallic prosthesis in place, a

study (Chapter 8) was undertaken to understand the complex nature of the

susceptibility induced fields around a metal object and effects of imaging gradients on

the final image. Following on from the previous study, the acetabulum was chosen as

the region of interest around the hip prosthesis. The ‘ball head’ of the metal prosthesis

fits into the acetabulum and the artefact from the metal extends into the region of the

acetabulum. To investigate the extent of this artefact, simulations of standard 2D and

3D spin echo sequences were developed as well as a sequence based on View Angle

Tilting. The computer simulations were verified using experimental data obtained

from a phantom containing a non-ferromagnetic stainless steel ball bearing immersed

in agarose gel. The simulations provided a unique way of visualising the extent of the

artefact and the effects that parameters such as the gradient strengths, receiver

bandwidth and slice thickness have on reducing the artefact. It was seen that slice

distortion in a 2D slice is extreme around stainless steel and results in a highly warped

slice. Consequently the use of conventional 2D sequences for imaging around metal

prostheses will provide incorrect information. A 3D sequence that uses phase

encoding in the slice direction removes the slice distortion, although the in-plane

signal distortions are still present due to the effects of the frequency encoding

(readout) gradient.

The technique of View Angle Tilting (VAT) was first described in 1988 but

has not been widely used in clinical practice. Simulations presented in this thesis have

provided a novel way to understand and view the reported correction of the artefact

using VAT. In the presence of a large susceptibility artefact, the selected slice is

highly distorted. The VAT sequence, while removing overlap of signal in the

frequency encoding direction, does NOT remove the slice distortion. When the data is

then projected back along the view angle, the appearance is of an improved image

compared to the standard SE image. This really is just a false impression of removing

the artefact as there is still signal from out of the desired slice location (due to slice

distortion) and the observed image will contain this distorted information. In practice

130

the feasibility of clinical use of VAT is very much dependent of the metal present. For

large susceptibility differences such as that arising from stainless steel, the slice

distortion becomes extreme and VAT will not work. In 3D imaging there is no slice

distortion although the in-plane distortions remain. Phase encoding in all directions

using large gradient strengths is one potential method for further reducing the artefact,

but this approach is severely limited by the very large imaging times required.

Future Directions:

Routine clinical diagnosis of bone disease is important for assessing,

characterising and determining the efficacy of treatment regimes for debilitating bone

diseases such as osteoporosis. Major steps needed to achieve routine clinical

diagnosis of bone structure involve the development of improved imaging gradients

and surface coils to improve the SNR and resolution of the images so as to reduce

partial volume effects. These limitations are not only due to hardware but also are

based on safety considerations. There is a need to limit the switching of strong

gradients to prevent nerve stimulation by the electrical currents induced in the body

when the gradients are pulsed. Also, the commercialisation of image processing

software such as Fuzzy Distance Transform (used to calculate trabecular thickness in

the limited spatial regime) will be an important milestone. Some of these steps are

already under way in various labs around the world including that at the University of

Pennsylvania where part of the work for this thesis was carried out. The group at the

University of Pennsylvania is in the process of designing an in vivo virtual bone

biopsy (VBB) to provide detailed quantitative insight into the architectural

implications of bone loss. It also aims at being able to quantitatively discriminate

patients with vertebral fractures from their gender and bone mineral density matched

peers.

Another consideration for clinical analysis will be the determination of what

VOIs and ROIs to use in the bone analysis. This needs to be systematically

investigated and the effect on the accuracy of the bone morphological parameters

calculated. This is especially important for longitudinal studies involving the

assessment of therapeutic drugs or high turnover bone diseases. There will need to be

131

some significant clinical studies undertaken to validate the use of the morphological

parameters obtained from MRI before these techniques will be widely used by the

medical community.

The discovery of the intra-trabecular pores has some interesting implications

for bone remodelling and there needs to be further development of models to explain

the changes in bone growth and remodelling of diseased bone. A longitudinal study of

the treatment regimes utilised for high turnover bone disease may provide valuable

data that could then be used in theoretical models (through finite element analysis) of

bone turnover. The use of microCT systems designed for small animals is limited in

longitudinal studies by the effects of prolonged radiation exposure and the

consequential degradation of the bone structure. In vivo high resolution MRI on small

animals is ideal as there is no ionising radiation exposure and it is completely non-

invasive. A longitudinal study looking at bone turnover in rats as a consequence of

therapeutic regime using an MRI system would constitute an excellent project.

Unfortunately even in vitro, high resolution MRI doesn’t have the resolution required

to observe the intra-trabecular pores and the study would be limited to the standard

morphological parameters used previously. The benefit of the study is that

longitudinal data may provide important information in terms of rates of bone

formation and locations of increased bone turnover that a single time course study

may not be able to provide.

Education of orthopaedic surgeons and radiographers about the use of MRI on

regions containing non-ferromagnetic prosthesis needs to be conducted with some

time devoted to establish the best MRI parameters to use for each prosthesis and

anatomical location. The use of the VAT technique to clinically diagnose tissue

around a prosthesis or other magnetic susceptibility anomaly should be carefully

considered as the problem of slice distortion still remains and the results can be

erroneous and leading to the possibility of a false diagnosis.

Overall it has been shown in this thesis that, while high resolution MRI has a

number of advantages over existing methodologies for assessing bone structure and

considerable advances in technology have occurred over the last 10 years, there are

132

still significant problems to be overcome before it can be used routinely in many

potential applications.

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