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
2
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
3
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.
4
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
5
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.
6
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
7
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
8
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
9
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
10
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.
11
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.
12
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.
13
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.
14
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
15
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.
16
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.
17
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
18
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].
19
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-
20
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
21
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 [email protected] 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 – [email protected] Felix Wehrli – [email protected] Punam Saha – [email protected] Jalal Andre – [email protected] Alex Wright – [email protected] Cheryl Sanchez – [email protected] Mary Leonard – [email protected] 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: [email protected]
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: [email protected] Branimir Vasilić: [email protected] James Pope: [email protected] Catherine Jones: [email protected] Charles Epstein: [email protected] Hee Kwon Song: [email protected] Felix Wehrli: [email protected] 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: [email protected]
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
129
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.
133
References 1. Klaue K, Bresina S, Guelat P, Wallin A, Perren SM, 1997. Morphological 3-
dimensional assessment, pre-operative simulation and rationale of intra-operative navigation in orthopaedic surgery: Practical application for re-orienting osteotomies of the hip joint. Injury, 28(Suppl 2). 12-30.
2. Railhac JJ, Fourcade D, Hobatho MC, Baunin C, Mansat M, 1997. Three-dimensional imaging in orthopaedic surgery: a radiologist's viewpoint. Injury, 28(Suppl 2). 1-11.
3. Olsen RV, Munk PL, Lee MJ, Janzen DL, Mackay AL, Xiang Q-S, Masri B, 2000. Metal Artifact Reduction Sequence: Early Clinical Applications. Radiographics, 20. 699-712.
4. Stulberg DS, Wixson RL, Adams AD, Hendrix RW, Bernfield JB, 2002. Monitoring Pelvic Osteolysis Following Total Hip Replacement Surgery: An Algorithm for Surveillance. J Bone Joint Surg Am, 84-A(Sup 2). 116-118.
5. Hopper TAJ, Crawford RW, Timperely AJ, Slaughter R, Pope JM, 2004. MRI Can Identify High Intensity Bands Around Implants That Correspond to Radiolucent Lines on X-ray: An Ex Vivo Study of Sheep Acetabulae. Clin Orthop Rel Res, (427). 127-131.
6. Ebraheim NA, Savolaine ER, Zeiss J, Jackson WT, 1992. Titanium hip implants for improved magnetic resonance and computed tomography examinations. Clin Orthop Rel Res, 275. 194-198.
7. Link T, Majumbar S, Lin JC, Newitt D, P.Augat, Ouyang X, Mathur A, Genant HK, 1998. A comparative study of trabecular bone properties in the spine and femur using high resolution MRI and CT. J Bone Min Res, 13. 122-132.
8. Majumdar S, Link T, Augat P, Lin JC, Newitt D, Lane NE, Genant HK, 1999. Trabecular bone architecture in the distal radius using MR imaging in subjects with fractures of the proximal femur. Osteoporosis Int, 10. 231-239.
9. Link T, Majumbar S, P.Augat, Lin J, Newitt D, Lu Y, Lane N, Genant H, 1998. In vivo high resolution MRI of the calcaneus: Differences in trabeuclar structure in osteoporosis patients. J Bone Min Res, 13. 1175-1182.
10. Lin JC, Amling M, Newitt DC, Selby K, Srivastav SK, Delling G, Genant HK, Majumdar S, 1998. Heterogeneity of trabecular bone structure calcaneus using magnetic resonance imaging. Osteoporosis Int, 8. 16-24.
11. Majumdar S, Genant HK, Grammp S, Newitt D, Troung V, Lin J, Mathur A, 1997. Correlation of Trabecular Bone Structure with Age, Bone Mineral Density, and Osteoporotic Status: In Vivo Studies in the Distal Radius using High-Resolution Magnetic Resonance Imaging. J Bone Min Res, 12. 111-118.
12. Jones AC, Sheppard AP, Sok RM, Arns CH, Limaye A, Averdunk H, Brandwood A, Sakellariou A, Senden TJ, Milthorpe BK, Knackstedt MA, 2004. Thee-dimensional analysis of cortical bone structure using X-ray micro-computed tomography. Physics A, 339. 125-130.
13. Martin-Badosa E, Amblard D, Elmoutaouakkil A, Vico L, Peyrin F, 2003. Excised Bone Structures in Mice: Imaging at Three-dimensional Synchrotron Radiation Micro CT. Radiology, 229. 921-928.
14. Nuzzo S, Lagage-Proust MH, Martin-Badosa E, Boivin G, Thomas T, Alexandre C, Peyrin F, 2002. Synchrotron Radiation Microtomography Allows the Analysis of Three-Dimensional Microarchitecture and Degree of
134
Mineralization of Human Iliac Crest Biopsy Specimens: Effects of Etidronate Treatment. J Bone Min Res, 17(8). 1372 - 1382.
15. Goldstein SA, 1987. The mechanical properties of trabecular bone: dependence on anatomic location and function. J Biomechanics, 20. 1055-1061.
16. Melton LJ, Chao EYS, Lane J, Biomechanical aspects of fractures. In: Riggs B L, Melton LJ (ed) Osteoporosis: Etiology, Diagnosis, and Management. 1995, New York: Lippincott-Raven. 111-131.
17. Chung H, Wehrli FW, Williams J, Kugelmass S, Wehrli S, 1995. Quantitative Analysis of Trabecular Microarchitecture by 400 MHz Nuclear Magnetic Resonance Imaging. J Bone Min Res, 10. 803-811.
18. Parfitt AM, 1984. Age-related structural changes in trabecular and cortical bone: cellular mechanisms and biomechanical consequences. Calcif Tissue Int, 36. S123-128.
19. Hodgskinson R, Currey J, 1990. The effect of variation in structure on the Young's Modulus of cancellous bone: a comparison of human and non human material. Proc Inst Mech Engrs, 204. 115-121.
20. Vieth V, Link T, Lotter A, Persigehl T, Newitt D, Heindal W, Majumdar S, 2001. Does the Trabecular Bone Structure Depicted by High-Resolution MRI of the Calcaneus Reflect the True Bone Structure? Investigative Radiology, 36. 210-217.
21. Kleerekoper M, Villanueva AR, Stanciu J, Rao DS, Parfitt AM, 1985. The role of three-dimensional trabecular microstructure in the pathogenesis of vertebral compression fractures. Calcif Tissue Int, 37. 594.
22. Chung HW, Wehrli F, Williams J, Wehrli S, 1995. Three-dimensional nuclear magnetic resonance microimaging of trabecular bone. J Bone Min Res, 10. 1452-1461.
23. Cho ZH, Kim DJ, Kim YK, 1988. Total inhomogeneity correction including chemical shifts and susceptibility by view angle tilting. Med Phys, 15. 7-11.
24. Seeley RR, Stephens TD, Tate P, Anatomy and physiology. 5th ed ed. 2000, Boston: McGraw-Hill.
25. Parfitt AM, 1982. The contribution of bone histology to understanding pathogenesis and improving the management of osteoporosis. Clin Ivest Med, 5. 163-167.
26. Seeley DG, Browner WS, Nevitt MC, Genant HK, Cummings SR, 1995. Almost all fractures are osteoporotic. J Bone Min Res, 10 suppl. 1. S270-274.
27. Parfitt AM, Drezner MK, Glorieux FH, Kanis JA, Malluche H, Meunier PJ, Ott SM, Recker RR, 1987. Bone Histomorphometry: Standardization of Nomenclature, Symbols, and Units. J Bone Min Res, 2(6). 595 - 610.
28. Leonard MB, Zemel BS, 2004. Assessment of Bone Mineralization in Children and Adolescents. Clin Rev Bone Miner Metab, 2. 3-18.
29. Leonard MB, Shore RM, Radiologic Evaluation of Bone Mineral in Children, in Primer on the Metabolic Bone Diseases and Disorders of Mineral Metabolism., Favus MJ, Editor. 2003: Washington DC. p. 173-188.
30. Kibe LW, Zemel BS, Leonard MB, 2004. Assessment of cortical bone mineral density by peripheral quantitative computed tomography in children: impact of partial volume effects. American Society of Bone and Mineral Research, Abstract.
135
31. Oden ZM, Selvitelli DM, Hayes WC, Myers ER, 1998. The effect of trabecular structure on DXA-based predictions of bovine bone failure. Calcif Tissue Int, 63. 67-73.
32. Mosekilde L, 1990. Consequences of the remodelling process for vertebral trabecular bone structure: a scanning electron microscopy study. Bone Miner, 10. 13-35.
33. Parfitt AM, 1983. Stereologic basis of bone histomorphometry: Theory of quantitative microscopy and reconstruction of the third dimension. CRC Press, Boca Raton. 53-87.
34. Keller TS, Moeijanto E, Main JA, Spengler DM, 1992. Distribution and orientation of bone in the human lumbar vertebral centrum. J Spinal Disorders, 5. 60-74.
35. Saltykov SA, 1958. Stereometric Metalography. Metallurgizdat, Moscow, Russia.
36. Odgaard A, 1997. Three-Dimensional methods for quantification of cancellous bone architecture. Bone, 20. 315-328.
37. Harrigan TP, Mann RW, 1984. Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J Mater Sci, 19. 761-767.
38. Synder BD, Cheal EJ, Hipp JA, Hayes WC, 1989. Anisotropic structure-property relations for trabecular bone. Transactions of the Orthopaedic Research Society, 14. 265.
39. Odgaard A, Jensen EB, Gundersen HJG, 1990. Estimation of structural anisotropy based on volume orientation. A new concept. J Microscopy, 157. 149-162.
40. Synder B, Hayes W, Multiaxial structure-property relations in trabecular bone. In : Mow V, Ratcliffe A, Woo S (eds) Biomechanics of Diarthrodial Joints, 2nd Ed, Springer-Verlag, New York. 31-59.
41. Majumdar S, Newitt D, Jergas M, 1995. Evaluation of technical factors affecting the quantification of trabecular bone structure using magnetic resonance imaging. Bone, 17. 417-430.
42. Majumdar S, Gies A, Jergas M, Grampp S, Genant H, 1993. Quantitative measurement of trabecular bone structure using high resolution gradient echo imaging of the distal radius. Proc. Soc. Mag. Res. Med.. 455.
43. Hipp JA, Jansujwicz A, Simmons C, Synder B, 1996. Trabecular bone morphology from micro-magnetic resonance imaging. J Bone Min Res, 11. 286-291.
44. Simmons C, Hipp J, 1997. Method-Based Differences in the Automated Analysis of the Three-Dimensional Morphology of Trabecular Bone. J Bone Min Res, 12. 942-947.
45. Hildebrand T, Laib A, Muller R, Dequeker J, Ruegsegger P, 1999. Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from sine, femur, iliac crest, and calcaneus. JBMR, 14. 1167-1174.
46. Hildebrand T, Ruegsegger P, 1997. Quantification of bone microarchitecture with the structure model index. Comput Methods Biomech Biomed Eng, 1. 15-23.
47. Rotter M, Berg A, Langenberger H, Grampp S, Imhof H, Moser E, 2001. Autocorrelation analysis of bone structure. J Mag Res Imag, 14. 87-93.
136
48. Saha PK, Wehrli FW, 2004. Measurement of trabecular bone thickness in the limited resolution regime of in vivo MRI by fuzzy distance transform. IEEE Transactions on Medical Imaging, 23. 53-63.
49. Wachter NJ, Krischak GD, Mentzel M, Sarkar MR, Ebinger T, Kinzl L, Claes L, Augat P, 2002. Correlation of Bone Mineral Density With Strength
and Microstructural Parameters of Cortical Bone In Vitro. Bone, 31(1). 90-95. 50. Fernandez-Seara M, Song HK, Wehrli FW, 2001. Trabecular Bone Volume
Fraction Mapping by Low-Resolution MRI. Magn Reson Med, 46. 103-113. 51. Goulet RW, Goldstein SA, Ciarelli MJ, Kuhn JL, 1994. The relationship
between the structural and orthogonal compressive properties of trabecular bone. J Biomechanics, 27. 375-389.
52. Saha PK, Wehrli FW, Gomberg BR, 2002. Fuzzy distance transform - theory, algorithms, and applications. Computer Vision and Image Understanding, 86. 171-190.
53. Wehrli FW, Saha PK, Gomberg BR, Song HK, Synder PJ, Benito M, Wright A, Weening R, 2002. Role of Magnetic Resonance for Assessing Structure and Function of Trabecular Bone. Topics in Magnetic Resonance Imaging, 13(5). 335-356.
54. Hwang SN, Wehrli FW, Williams JL, 1997. Probability-based structural parameters from 3D NMR images as predictors of trabecular bone strength. Med Phys, 24. 1255-1261.
55. Hwang SN, Wehlri FW, 2002. Subvoxel processing: A method for reducing partial volume blurring with application to in vivo MR images of trabecular bone. Magn Reson Med, 47. 948-957.
56. Saha PK, Chaudhuri BB, 1996. 3D digital topology under binary transformation with applications. Comput Vision Image Understand, 63. 418-429.
57. Gomberg BR, Saha PK, Song HK, Hwang SN, Wehrli FW, 2000. Topological Analysis of Trabecular Bone MR Images. IEEE Transactions on Medical Imaging, 19(3). 166-174.
58. Maunder CRF, Algebraic Topology. 1980, Cambridge, U.K: Cambridge Univ. Press.
59. Saha PK, Wehrli FW, 2004. Measurement of trabecular bone thickness in the limited resolution regime of in vivo MRI by fuzzy distance transform. IEEE Transactions on Medical Imaging, 23. 53-62.
60. Feldkamp LA, Goldstein SA, Parfitt AM, G.Jension, Kleerekoper M, 1989. The direct examination of three-dimensional bone architecture in vitro by computed tomography. J Bone Min Res, 4. 3-11.
61. Kuhn JL, Goldstein SA, Feldkamp LA, Goulet RW, Jension G, 1990. Evaluation of a microcomputed tomography system to study trabecular bone structure. J Orthop Res, 8. 833-842.
62. Bonse U, Busch F, Gunnewig O, Beckmann F, Pahl R, Delling G, Graeff W, 1994. 3D computed X-ray tomography of human cancellous bone at 8 microns spatial and 10(-4)
energy resolution. Bone Miner, 25. 25-38. 63. Salome' M, Peyrin F, 1999. A synchroton radiation microtomography system
for the analysis of trabecular bone samples. Med Phys, 26. 2194-2204. 64. Sato M, Westmore M, Ma YL, Schmidt A, Zeng QQ, Glass EV, Vahle J,
Brommage R, Jerome CP, Turner CH, 2004. Teriparatide [PTH(1-34)] Strengthens the Proximal Femur of Ovariectomized Nonhuman Primates Despite Increasing Porosity. J Bone Min Res, 19(4). 623 - 629.
137
65. Abe S, Watanabe H, Hirayama A, E.Shibuya, Hashimoto M, Ide Y, 2000. Morphological study of the femur in osteopetrotic (op/op) mice using microcomputed tomography. The British Journal of Radiology, 73. 1078-1082.
66. Bousson V, Peyrin F, Bergot C, Hausard M, Sautet A, Laredo J-D, 2004. Cortical Bone in the Human Femoral Neck: Three Dimensional Appearance and Porosity Using Synchrotron Radiation. J Bone Min Res, 19(5). 794 - 801.
67. Croucher PI, Garrahan NJ, Compston JE, 1994. Structural mechanisms of trabecular bone loss in primary osteoporosis: Specific disease mechanism of early aging. Bone Min, 25. 111-121.
68. Recker RR, 1993. Architecture and vertebral fracture. Calcif Tissue Int, 53 (Suppl. 1). S139-142.
69. Kanis J, Melton L, Christiansen C, Johnston C, Khaltaev N, 1994. The diagnosis of osteoporosis. J Bone Min Res, 9. 1137-1140.
70. Vesterby A, 1993. Star volume in bone research. A histomorphometric analysis of trabecular structure using vertical sections. Anatomical Record, 235. 325-334.
71. Talagala S, Lowe I, 1991. Introduction to Magnetic Resonance Imaging. Concepts in Mag Res, 3. 145-159.
72. Haacke EM, Brown RW, Thompson MR, Venkatesan R, Magnetic Resonance Imaging: Physical Principles and Sequence Design. 1999: John Wiley and Sons.
73. Callaghan PT, Principles of Nuclear Magnetic Resonance Microscopy. 1991, New York: Oxford.
74. Abragam A, The Principles of Nuclear Magnetism. 1961: Oxford. 75. Majumdar S, Genant H, 1992. In vivo relationship between marrow T2* and
trabecular bone density determined with a chemical shift-selective asymmetric spin-echo sequence. J Mag Res Imag, 2. 209-219.
76. Majumdar S, Newitt D, Mathur A, Osman D, Gies A, Chiu E, Lotz J, Kinney J, Genant H, 1996. Magnetic resonance imaging of trabecular bone structure in the distal radius: relationship with X-ray tomographic microscopy and biomechanics. Osteoporosis Int, 6. 376 - 385.
77. Newitt DC, Majumdar S, Jergas M, al e, 1995. Relaxation and high resolution MRI of vertebral body specimens: T2*, structural and strength correlations. 11th Int. Bone Densitometry Workshop, Gleneden Beach, Oregon. 61.
78. Schenck JF, 1996. The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds. Med Phys, 23. 815-850.
79. Serway RA, Physics for Scientists and Engineers, Fourth edition. 1996: Saunders College Publishing. 887.
80. Bradely WG, Bydder GM, Worthington BS, Magnetic Resonance Imaging: Basic principles. In Grainger RG, Allison D(Eds) Grainger & Allison's Diagnostic Radiology: A textbook of medical imaging. 1997: Churchill Livingston, New York. 63-81.
81. Chung H-W, Hwang S, Yeung H, Wehrli F, 1996. Mapping of the magnetic-field distribution in cancellous bone. J Mag Res, 113. 172-176.
82. Wehrli F, Ford J, Attie M, Kressel H, Kaplan F, 1991. Trabecular structure: Preliminary application of MR interferometry. Radiology, 179. 615-621.
138
83. Jara H, Wehrli FW, Chung H, Ford JC, 1993. High-resolution variable flip angle 3D MR imaging of trabecular microstructure in vivo. Magn Reson Med, 29. 528-539.
84. Wald L, Caravajal L, Moyher S, al e, 1995. Phased array detectors and an automated intensity-correction algorithm for high-resolution MR imaging of the human brain. Magn Reson Med, 34. 433-439.
85. Hwang S, Wehrli F, 1995. Calculation of the susceptibility-induced magnetic field from 3D NMR images with applications to trabecular bone. J Mag Res, 109. 126-145.
86. Hwang S, Wehrli F, 1999. Experimental evaluation of a surface charge method for computing the induced magnetic field in trabecular bone. J Mag Res, 139. 35-45.
87. Wu Y, Chesler DA, Glimcher MJ, Garrido L, Wang J, Jiang HJ, Ackerman JL, 1999. Multinuclear solid-state three-dimensional MRI of bone and synthetic calcium phosphates. Proc. Natl. Acad. Sci. USA, 96. 1574-1578.
88. Wu Y, Glimcher MJ, C R, Ackerman JL, 1994. A unique phosphate group in bone mineral not present in synthetic calcium phosphates: identification by phosphorus-31 solid state NMR spectroscopy. J. Mol. Biol., 244. 423-435.
89. Glimcher MJ, 1997. Metabolic Bone Disease. eds Avioli L.V, Krane S.M., (Academic, San Diego). 23-50.
90. Fernandez-Seara MA, Wehrli SL, Wehrli FW, 2003. Multipoint mapping for imaging of semi-solid materials. J Mag Res, 160. 144-150.
91. Ramos-Cabrer P, Duynhoven JPM, Toorn AVd, Nicolay K, 2004. MRI if hip prosthesis using single-point methods: in vitro studies towards the artifact-free imaging of individuals with metal implants. Mag Res Imag, 22. 1097-1103.
92. Kolind SH, Mackay A, Munk PL, Xiang QS, 2004. Quantitative evaluation of Metal Artifact Reduction Techniques. J Mag Res Imag, 20. 487-495.
93. Shellock FG, Crues JV, 1988. High-field strength MR imaging and metallic biomedical implants: an ex vivo evaluations of deflection forces. AJR, 151. 389-392.
94. Suh J-S, Jeong E-K, Shin K-H, Cho JH, Na J-B, Kim D-H, Han C-D, 1998. Minimizing Artifacts Caused by Metallic Implants at MR Imaging: Experimental and Clinical Studies. AJR, 171. 1207-1213.
95. Bennett LH, Wang PS, Donahue MJ, 1996. Artifacts in magnetic resonance imaging from metals. J. Appl. Phys., 79(8). 4712-4714.
96. Ganapathi M, Joseph G, Savage R, Jones AR, Timms B, Lyons K, 2002. MRI susceptibility artefacts related to scaphoid screws: the effect of screw type, screw orientation and imaging parameters. Journal of Hand Surgery (British and European Volume), 27B(2). 165-170.
97. Butts K, Pauly JM, Daniel BL, Kee S, Norbash AM, 1999. Management of biopsy needle artifacts: techniques for RF-refocused MRI. J Mag Res Imag, 9. 586-595.
98. Kak AC, Slaney M, Principles of Computerized Tomographic Imaging, ed. Cotellessa RF. 1999, New York, NY: Institute of Electrical and Electronics Engineers.
99. McCullough EC, 1975. Photon attenuation in computed tomography. Med. Phys., 2. 307-320.
100. Stampanoni M, Borchert G, Wyss P, Abela R, Patterson B, Hunt S, Vermeulen D, Rüegsegger P, 2002. High resolution X-ray detector of synchrotron-based
139
microtomography. Nuclear Instruments and Methods in Physics Research A, 491. 291-301.
101. GEMS, 2004. http://www.gehealthcare.com/usen/fun_img/pcimaging/products/msmicroct.html.
102. Alem AM, Sherrard DJ, Gillen DL, Weiss NS, Beresford SA, Heckbert SR, Wong C, Stehman-Breen C, 2000. Increased risk of hip fracture among patients with end-stage renal disease. Kidney Int, 58(1). 396 - 399.
103. Parfitt AM, 1998. A structural approach to renal bone disease. J Bone Min Res, 13(8). 1213-1220.
104. Rauch F, Schoenau E, 2001. Changes in bone density during childhood and adolescence: an approach based on bone's biological organization. J Bone Min Res, 16. 597-604.
105. Sanchez CP, 2000. Modulation of endochondral bone formation: roles of growth hormone, 1,25-dihydroxyvitamin D and hyperparathyroidism. Pediatr Nephrol, 14. 646-649.
106. Langman CB, Mazur AT, Baron R, Norman ME, 1982. 25-hydroxyvitamin D3 (calcifediol) therapy of juvenile renal osteodystrophy: benefical effect on linear growth velocity. J Pediatr Endocrinol Metab, 100(5). 815-820.
107. Fine RN, 1997. Growth hormone treatment of children with chronic renal insufficiency, end-stage renal disease and following renal transplantation -- update 1997. J Pediatr Endocrinol Metab, 10(4). 361-370.
108. Watkins SL, 1996. Is severe renal osteodystrophy a contraindication for recombinant human growth hormone treatment? Pediatr Nephrol, 10. 351-354.
109. Laib A, Barou O, Vico L, Lafage-Proust MH, Alexandre C, Rüegsegger P, 2000. 3D micro-computed tomography of trabecular and cortical bone architecture with application to a rat model of immobilisation osteoporosis. Med Biol Eng Comput, 38. 326-332.
110. Jiang Y, Zhao JJ, Mitlak BH, Wang O, Genant HK, Eriksen EF, 2003. Recombinant human parathyroid hormone(1-34) [teriparatide] improves both cortical and cancellous bone structure. J Bone Min Res, 18(11). 1932-1941.
111. Sanchez C, Salusky I, Kuizon B, Abdella P, Juppner H, Gales B, Goodman W, 1998. Growth of long bones in renal failure: roles of hyperparathyroidism, growth hormone and calcitriol. Kidney Int, 54. 1879 - 1887.
112. Saha PK, Chaudhuri BB, 1994. Detection of 3D simple points for topology preserving transformation with application to thinning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16. 1028-1032.
113. Kong TY, Rosenfeld A, 1989. Digital topology: introduction and survey. Computer Vision, Graphics, and Image Processing, 48. 357-393.
114. Schober HC, Han ZH, Foldes AJ, Shih MS, Rao DS, Balena R, Parfitt AM, 1998. Mineralized bone loss at different sites in dialysis patients: implications for prevention. J Am Soc Nephrol, 9. 1225-1233.
115. (K/DOQI) NKFKDQOI, 2000. Clinical practice guidelines for nutrition in chronic renal failure. Am J Kidney Dis, 35(Suppl 2). S1-S140.
116. Eknoyan G, Levin A, Levin NW, 2003. National Kidney Foundation. Bone metabolism and disease in chronic kidney disease. Am J Kidney Dis, 42(4 Suppl 3). 1-201.
117. Suda T, Ueno Y, Fujii K, Shinki T, 2003. Vitamin D and bone. J Cell Biochem, 88. 259-266.
140
118. Altundag O, Altundag K, Silay YS, Gunduz M, Demircan K, Gullu I, 2004. Calcium and vitamin D supplementation during bisphosphonate administration may increase osteoclastic activity in patients with bone metastasis. Med Hypotheses, 63(6). 1010-1013.
119. White LM, Kim JK, Mehta M, Merchant N, Schweitzer ME, Morrison WB, Hutchison CR, Gross AE, 2000. Complications of Total Hip Arthroplasty: MR Imaging - Initial Experience. Radiology, 215. 254-262.
120. Ludeke KM, Roschmann P, Tischler R, 1985. Susceptibility artifacts in NMR imaging. Magn Reson Imag, 3. 329-343.
121. Czerny C, Krestan C, Imhof H, Trattnig S, 1999. Magnetic Resonance Imaging of the Postoperative Hip. Topics in Magnetic Resonance Imaging, 10(4). 214-220.
122. Balcom B, MacGregor R, Beyea S, Green P, Armstrong R, Bremner W, 1996. Single-point ramped imaging with T1 enhancement (SPRITE). Journal of Magnetic Resonance Imaging, 123. 131-134.
123. Daniel BL, Butts K, 2000. The use of view angle tilting to reduce distrotions in magnetic resonance imaging of cryosurgery. Mag Res Imag, 18. 281-286.
124. Callaghan PT, 1990. Susceptibility-limited resolution in nuclear magnetic resonance microscopy. J. Magn. Reson., 87. 304-318.
125. White LM, Buckwalter KA, 2002. Technical considerations: CT and MR imaging in the postoperative orthopedic patient. Semin Musculoskelet Radiol, 6(1). 5-17.
126. Bakker CJG, Bhagwandien R, Moerland MA, Ramos LMP, 1994. Simulation of susceptibility artifacts in 2D and 3D fourier transform spin-echo and gradient-echo magnetic resonance imaging. Magn Reson Imag, 12(5). 767-774.
127. Shellock FG, Morisoli S, Kanal E, 1993. MR procedures and biomedical implants, materials, and devices: 1993 updates. Radiology, 189. 587-599.
128. Beuf O, Briguet A, Lissac M, Davis R, 1996. Magnetic Resonance Imaging for the determination of magnetic susceptibility of materials. J Magn Reson B, 112. 111-118.