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Optimizations in the assessment of pediatric bone
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Content
OPTIMIZATIONS IN THE ASSESSMENT OF
PEDIATRIC BONE
by
David Choen Lee
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)
May 2009
Copyright 2009 David Choen Lee
ii
Dedication
To my parents and my sister, Amy.
iii
Acknowledgements
First, I would like to thank my advisor and mentor, Tishya Wren. I am most
grateful for the opportunity to learn and grow under such fine supervision. I also thank
Vicente Gilsanz for his guidance, as well as Manbir Singh, Jill McNitt-Gray, and David
D’Argenio for their valuable feedback and timely flexibility.
The members of the lab have made my graduate experience very enjoyable. Bitte,
my second mother, is one I can always count on for personal advice. Sandi is so
thoughtful and an excellent manager. Susan is a joy to talk with especially about culinary
topics. Reiko challenges me with her solid appetite. Greg’s ability to keep a tidy
workstation gives me much peace. Cynthia keeps it real. And who could forget
Cristyna’s giddy laughter and Patrick’s famous fruit salads?
My friends have also been integral in keeping me motivated. I appreciate all the
basketball/football games, runs around the Rose Bowl, meals, coffee, and conversations.
A special thanks to Phil & Jess, Paul & Isabel, Hubert & Jean, Ben & Eunice, Joe &
Linda, Calvin, Edward, Frank, James, Judy, Julia, Kathy, Patrick, Ronald, Sharon, Tina,
Tony, the Epicentre family, the Gemmers, the Kusumotos, and the Tasty Tuesday crew.
Finally and most importantly, I thank my parents and my sister, Amy for their
constant support throughout the years. I deeply value their endless love and
encouragement.
iv
Table of Contents
Dedication ii
Acknowledgements iii
List of Tables vii
List of Figures viii
Abbreviations xi
Abstract xiii
Preface xv
Chapter 1: Introduction 1
1.1 Motivation ..................................................................................................... 1
1.2 Outline........................................................................................................... 4
Chapter 2: Bone background 6
2.1 General bone ................................................................................................. 6
2.2 Measures of bone strength ............................................................................ 7
2.3 Pediatric bone................................................................................................ 10
Chapter 3: Non-invasive assessments of bone 12
3.1 DXA – Dual energy x-ray absorptiometry .................................................... 12
3.2 QCT – Quantitative computed tomography .................................................. 17
3.3 MRI – Magnetic resonance imaging ............................................................. 21
3.4 QUS – Quantitative ultrasound ..................................................................... 22
Chapter 4: Variability of cancellous bone along the metaphysis 23
4.1 Background ................................................................................................... 23
4.2 Considerations............................................................................................... 25
4.2.1 Defining the metaphysis.................................................................... 25
4.2.2 Sampling within a cross-section ....................................................... 26
4.2.3 Tibia curvature .................................................................................. 27
4.2.4 Constructing the core ........................................................................ 28
4.3 Methods......................................................................................................... 28
4.3.1 Subjects ............................................................................................. 28
4.3.2 Data acquisition and processing ........................................................ 29
4.3.3 Data analysis ..................................................................................... 31
4.4 Results ........................................................................................................... 33
4.5 Discussion ..................................................................................................... 38
v
Chapter 5: Evaluating soft-tissue based errors in DXA 43
5.1 Background ................................................................................................... 43
5.2 Methods......................................................................................................... 45
5.2.1 Subjects ............................................................................................. 45
5.2.2 DXA image acquisition ..................................................................... 46
5.2.3 QCT image acquisition ..................................................................... 47
5.2.4 QCT image analysis .......................................................................... 47
5.2.5 Calculation of DXA error ................................................................. 49
5.2.6 Correction using anthropometric relationships ................................. 51
5.2.7 Validation of aBMD correction equation.......................................... 52
5.2.8 Statistical analysis ............................................................................. 52
5.3 Results ........................................................................................................... 52
5.3.1 DXA soft-tissue error ........................................................................ 52
5.3.2 Anthropometric relationships ............................................................ 53
5.4 Discussion ..................................................................................................... 55
Chapter 6: Optimal ROI in DXA AP lumbar spine scans 59
6.1 Background ................................................................................................... 59
6.2 Methods......................................................................................................... 62
6.2.1 Data acquisition................................................................................. 62
6.2.2 QCT image analysis .......................................................................... 63
6.2.3 Patient-specific ROI analysis ............................................................ 64
6.3 Results ........................................................................................................... 65
6.4 Discussion ..................................................................................................... 67
Chapter 7: Impact of the vertebral posterior elements in DXA 71
7.1 Background ................................................................................................... 71
7.2 Methods......................................................................................................... 74
7.2.1 Clinical study .................................................................................... 74
7.2.2 DXA analysis .................................................................................... 75
7.2.3 QCT analysis ..................................................................................... 76
7.2.4 Statistical analysis ............................................................................. 77
7.3 Results ........................................................................................................... 78
7.4 Discussion ..................................................................................................... 81
Chapter 8: Automated bone cross-section extraction with MRI 85
8.1 Background ................................................................................................... 85
8.2 Methods......................................................................................................... 87
8.2.1 Data acquisition................................................................................. 87
8.2.2 Image segmentation .......................................................................... 88
8.2.3 Cross-sectional properties ................................................................. 91
8.2.4 Validation with QCT ......................................................................... 94
8.3 Results ........................................................................................................... 94
8.4 Discussion ..................................................................................................... 96
vi
Chapter 9: Conclusions and future work 99
9.1 pQCT – Peripheral quantitative computed tomography ............................... 99
9.2 DXA – Dual energy x-ray absorptiometry .................................................... 101
9.3 MRI – Magnetic resonance imaging ............................................................. 103
9.4 GUIs – Graphical user interfaces .................................................................. 104
9.5 Concluding remarks ...................................................................................... 105
Bibliography 106
Appendix A: Cross-sectional geometry formulas & calculations 118
Appendix B: Derivation of DXA & soft-tissue error equations 121
Appendix C: GUI documentation 123
vii
List of Tables
Table 3-1: Comparison of bone densitometry modalities. ........................................... 13
Table 4-1: Subject anthropometric data at baseline (n = 35). ...................................... 33
Table 4-2: Change in subject anthropometric data from baseline to follow-up. ......... 34
Table 4-3: Metaphysis properties for baseline study. .................................................. 34
Table 4-4: Change in metaphysis properties from baseline to follow-up. ................... 35
Table 5-1: Mass attenuation coefficients (μ, cm
2
/g), ratio of coefficients (R) and
density (ρ, g/cm
3
) values for adipose tissue, muscle, and bone. Subject-
specific values for soft tissue are calculated as a linear weighting of the
adipose and muscle values based on the adipose percent for each subject. ..... 50
Table 5-2: Difference in adipose tissue content between bone and soft-tissue
regions and resulting influence on aBMD. ...................................................... 53
Table 5-3: Regression of DXA error with subject mass and trunk circumference
(n = 500). .......................................................................................................... 53
Table 5-4: Regression results (R
2
) comparing DXA BMC with QCT BMC. ............. 55
Table 6-1: Averages and ranges of soft-tissue differences in the two regions
(mean ± standard deviation; 5th percentile to 95th percentile). ....................... 66
Table 7-1: Correlations between DXA/QCT BMD (underlined) and BMC
(italicized). ....................................................................................................... 80
Table 8-1: Regression coefficients of area, moments of inertia, and other
geometric parameters comparing QCT and MRI measurements. .................... 95
Table A-1: Integral and summation equations for area and moments of inertia. ........ 119
viii
List of Figures
Figure 1-1: QCT scan of femur mid-shaft in 14 yr boy after injury and two
months casting on left leg (right side). Figure courtesy of the Radiological
Society of North America (Kovanlikaya et al., 1996). .................................... 1
Figure 1-2: Normal bone (left) and osteoporotic bone (right). Figures courtesy of
the National Osteoporosis Foundation. ............................................................ 2
Figure 2-1: Transverse cross-sections of the L3 vertebra (left) and the tibial
metaphysis (right). Cortical bone in bright white and cancellous bone in
spotted white within the cortical shell. ............................................................ 6
Figure 2-2: Different types of stresses that can be applied to bone. Arrows depict
loading direction. ............................................................................................. 8
Figure 2-3: Disproportionate human growth and changes in vertebral cross-
sections. Figure courtesy of Dr. Vicente Gilsanz. .......................................... 10
Figure 3-1: Hologic Delphi W DXA scanner at Childrens Hospital Los Angeles. ..... 14
Figure 3-2: Sample DXA AP projection image of the lumbar spine. .......................... 15
Figure 3-3: Illustration of size bias effect. Two objects with the same volumetric
density, but different areal densities. Adapted from Carter et al., 1992. ........ 16
Figure 3-4: Left: GE Lightspeed Q/Xi CT scanner, The General Electric
Company; right: StraTec XCT 2000 pQCT scanner, StraTec
Medizintechnik GmbH..................................................................................... 18
Figure 3-5: Sample QCT image of a cross-section through L3. .................................. 19
Figure 3-6: Sample MRI image of a cross-section through the femoral mid-shaft. .... 21
Figure 4-1: pQCT data of the proximal tibia represented as a 3-D rendering (top)
and sagittal cross-section (bottom) with volume of interest in dotted lines. ... 30
Figure 4-2: Density gradient of cancellous core. ......................................................... 31
Figure 4-3: Density gradient profiles from three different subjects. ........................... 35
Figure 4-4: Box plots showing percent change from baseline to six month follow-
up using single slice density at 48% length of metaphysis, single slice
density 1.25 mm from growth plate, and mean density of entire
metaphysis........................................................................................................ 37
ix
Figure 4-5: Variability of cancellous bone density changes at different positions
along the length of the metaphysis using A) 1.25 mm slices and B) 2.5 mm
slices. ................................................................................................................ 37
Figure 5-1: Projection image of lumbar spine from DXA scan. Region of interest
width was set to 105 mm, and bone region was separated from soft-tissue
region by vertebral contour lines. A second ROI was defined to represent
the 10 mm thick slice imaged by QCT. ........................................................... 46
Figure 5-2: A) Original QCT image; B) QCT image segmented into bone,
adipose, and lean tissues; C) histograms showing soft-tissue components,
adipose (solid) and lean tissue (dotted); D) histogram showing percentage
of soft tissue consisting of adipose. DXA bone region between vertical
dotted lines and soft-tissue region between vertical dotted and solid lines. .... 48
Figure 5-3: Regression of DXA error with subject mass and trunk circumference
(n = 500). .......................................................................................................... 54
Figure 5-4: Box plots of calculated error before and after application of the
correction equation in the validation group. .................................................... 55
Figure 6-1: The “bone region,” shown in the gray area, contains both soft-tissue
and bone in the AP direction. The “soft-tissue region,” shown in the non-
shaded area, contains only soft-tissue. ............................................................. 60
Figure 6-2: Two DXA scans with the same ROI width of 105 mm (left: 9.3 yr
female; right: 18 yr female). ............................................................................ 61
Figure 6-3: Original QCT image with two dynamic AP lines traversing the trunk
width laterally (vertical dotted lines tangent to vertebra), soft-tissue
density per AP line (dashed line), cumulative soft-tissue density from the
bone region (horizontal solid line), cumulative soft-tissue density from the
soft-tissue region (curved solid line), and point in which soft-tissue
densities in both regions are equal (white circles). Y-axis shows
cumulative soft-tissue density difference......................................................... 64
Figure 6-4: Box plots showing range of difference in soft-tissue density in the
original DXA ROI and in three optimal ROIs (fixed distance, percentage
of trunk width, and multiple of vertebral body width)..................................... 66
Figure 6-5: Difference in soft-tissue along the width of the trunk from 22% to
100% of trunk width (all subjects in black; average in white). ....................... 67
x
Figure 7-1: Sample images from the same subject with QCT (left) and DXA
(right). The QCT scan location and thickness (10 mm) are shown in a
shaded region on the L3 DXA scan. ................................................................ 75
Figure 7-2: Regions of interest for the CT images. Left to right: cancellous bone
region; isolated vertebral body; vertebral body including the posterior
elements. .......................................................................................................... 76
Figure 7-3: Posterior element contribution as a function of age. ................................. 78
Figure 7-4: Comparisons of DXA and QCT measures. ............................................... 79
Figure 8-1: Low bone contrast in MRI image. ............................................................ 86
Figure 8-2: Image histogram showing detected peaks of bone, lean (muscle), and
adipose (fat) tissues from a sampled region of interest. ................................... 89
Figure 8-3: Isolated cortical bone from femur: original contrast (left) and new
contrast (right). ................................................................................................. 89
Figure 8-4: Contours from femoral mid-shaft (left); segmented into adipose and
lean tissues (right). ........................................................................................... 94
Figure C-1: Screen shot of tibiagui.m – image selection. ............................................ 124
Figure C-2: Screen shot of tibiagui.m – data output. ................................................... 124
Figure C-3: Screen shot of fatgui.m – image segmentation......................................... 126
Figure C-4: Screen shot of fatgui.m – data output. ...................................................... 126
Figure C-5: Screen shot of fatgui2.m – image selection. ............................................. 128
Figure C-6: Screen shot of fatgui2.m – data output. .................................................... 128
Figure C-7: Screen shot of spinegui.m – regions of interest........................................ 130
Figure C-8: Screen shot of spinegui.m – image processing......................................... 130
Figure C-9: Screen shot of mriviewer.m – image selection. ........................................ 132
Figure C-10: Screen shot of mriviewer.m – data output. ............................................. 133
xi
Abbreviations
Abbreviation Name Units
AP anterior-posterior –
AUC area under the curve cm·mg/cm
3
aBMD Areal bone mineral density g/cm
2
σ areal density g/cm
2
BMI body mass index kg/m
2
BMC bone mineral content G
BMD bone mineral density (hydroxyapatite equiv.) mg/cm
3
(mgHA/cm
3
)
CSA cross-sectional area mm
2
CSMI cross-sectional moment of inertia mm
4
ρ density mg/cm
3
DXA dual energy x-ray absorptiometry –
HU Hounsfield unit unitless
HA hydroxyapatite Ca
5
(PO
4
)
3
(OH)
α linear attenuation coefficient cm
-1
MRI magnetic resonance imaging –
μ mass attenuation coefficient cm
2
/g
I
max
maximum principal moment of inertia mm
4
I
min
minimum principal moment of inertia mm
4
xii
Abbreviation Name Units
pQCT peripheral quantitative computed tomography –
J polar moment of inertia mm
4
pSSI polar stress-strain index mm
3
QCT quantitative computed tomography –
QUS quantitative ultrasound –
ROI region of interest –
rem Röentgen equivalent in man 10
-3
Sv
Sv sievert kg/J
vBMD volumetric bone mineral density mg/cm
3
xiii
Abstract
Peripheral quantitative computed tomography (pQCT) and dual energy x-ray
absorptiometry (DXA) are fundamental imaging technologies in the assessment of bone
in children and adolescents. However, they may both produce misleading outcomes,
particularly in growing subjects. The goal of this thesis is to quantify and minimize the
shortcomings of pQCT and DXA. We have isolated factors that lead to potential errors in
pQCT and DXA, offered corrections for those errors or alternative measures, and
introduced an automated MRI (magnetic resonance imaging) bone feature extraction
program.
A major limitation of pQCT measurements arises from scan positioning in
metaphyseal density determinations. Due to a considerable gradient of cancellous bone
in the region, the density reported by a conventional single slice is dependent on the
location of the scan and may not come from the same exact anatomical site in different
individuals or over time. As a result, interpretation of these data may be difficult. We
have presented a method to measure the gradient of cancellous bone with pQCT and
obtain overall measures of cancellous bone such as average density.
DXA’s limitations are a product of its two-dimensional design. To derive bone
measures, it assumes a homogeneous soft-tissue distribution, which leads to errors when
the distribution is actually inhomogeneous. In addition, the inclusion of the vertebral
posterior elements in anterior-posterior projections of the spine may misrepresent actual
spine strength, which is usually associated with the vertebral body. These two factors
impact DXA bone measures and may lead to recommendations that deviate from
xiv
analogous outcomes from QCT (quantitative computed tomography), a three-dimensional
modality. In a series of three studies, we have investigated the extent of the error due to
these limitations, and attempted to reduce those errors.
Lastly, we explore the possibility of extracting bone features with MRI. Since
MRI does not use ionizing radiation, it would be advantageous to use in lieu of QCT or
pQCT. However, since bone suffers poor contrast in MRI, manual tracing or semi-
automatic methods are usually required. To reduce operator error and improve
efficiency, we have designed a fully automatic program and compared its results with
established QCT methods.
xv
Preface
I would like to especially acknowledge Tishya Wren and Vicente Gilsanz for their
contributions to the research presented in this dissertation. This work would not have
been possible without their constructive insights.
This research has been published in Journal of Clinical Endocrinology &
Metabolism (Chapter 4) and in Journal of Bone and Mineral Research (Chapter 7). Parts
of this research have been presented at the American Society for Bone and Mineral
Research (Chapters 4, 5, 7), Biomedical Engineering Society (Chapters 4, 5), and
Orthopaedic Research Society (Chapter 4).
These studies were supported in part by the National Institutes of Health and the
Department of the Army.
1
Chapter 1: Introduction
1.1 Motivation
Bone is a remarkable material from an engineering perspective. As a structural
material, it is designed to support the human body and withstand normal physiological
loads. Yet unlike non-biological structural materials, bone has the capacity to efficiently
adapt itself to changing stimuli (Rubin, Judex, & Hadjiargyrou, 2002). For example,
when subjected to continuous or heavy impact, as in the legs of a marathon runner or the
axial skeleton of gymnasts, bone will respond by adding mass (Agarwal & Stout, 2003;
Stewart & Hannan, 2000; Ward, Roberts, Adams, & Mughal, 2005) to decreases stress,
such that loading forces are distributed over a larger cross-sectional area. Inversely, bone
mass can atrophy in periods of disuse such as bed rest or space flight (Agarwal & Stout,
2003; Kovanlikaya et al., 1996; Lang et al., 2004; LeBlanc, Spector, Evans, & Sibonga,
2007) (Figure 1-1).
Figure 1-1: QCT scan of femur mid-shaft in 14 yr boy after injury and two months casting on left leg (right
side). Figure courtesy of the Radiological Society of North America (Kovanlikaya et al., 1996).
2
Figure 1-2: Normal bone (left) and osteoporotic bone (right). Figures courtesy of the National
Osteoporosis Foundation.
In addition to being a structure, bone is a living tissue that can grow, age, fail,
self-repair, and become diseased. As with any other organ in the body, it is important to
maintain its health. In fact, bone health is a rising concern among post-menopausal
women and geriatric populations, where the inevitable onset of bone loss and
deterioration of bone micro-architecture (Figure 1-2) can lead to osteoporosis and an
increased risk of fracture (Rosen, 2005), usually in the hip, spine, and wrist.
Osteoporosis is a disease that impacts millions of Americans: 10 million already have
osteoporosis and 34 million more are at risk with low bone mass. The National Institutes
of Health estimate that 50% of all women and 25% of men over 50 years of age will
experience an osteoporosis-related fracture in their lifetime, 30% of whom will die within
a year having fractured the hip. Further, osteoporosis and related fractures translate to
$10-15 billion each year in hospital costs and nursing homes ("Osteoporosis prevention,
3
diagnosis, and therapy," 2001). Indeed, the impact of osteoporosis is costly financially
and in quality of life.
Although the risk of osteoporosis increases with age, low bone mass can be
identified as early as childhood (Loro et al., 2000). Children and adolescents with low
bone mass and density are likely to grow into osteopenic adults, which may ultimately
result in osteoporosis and related fractures (Bachrach, 2007). It is therefore important to
maximize at-risk pediatric bone with interventions such as load-bearing exercise,
hormone therapy, or calcium and vitamin D intake, since bone gain is favored during
puberty (Faulkner & Bailey, 2007; Specker & Vukovich, 2007). After puberty, bone
mass peaks and slowly declines with age (Mora & Gilsanz, 2003). Consequently, there is
a critical window of opportunity to boost bone mass before the onset of age-related
declines.
Whether bone mass is increasing, declining, or stable, it is important to monitor
skeletal health and structural integrity with noninvasive imaging techniques (Bouxsein,
2008). Several methods of assessing bone are available, each with their unique
advantages and disadvantages (Wren & Gilsanz, 2006). The limitations in accuracy and
precision of these modalities warrant investigation since subtle changes in bone can be
difficult to detect, and may have significant implications (Bachrach, 2006). This thesis
evaluates the current methods of bone assessment with the intention of optimizing
clinical techniques by quantifying and correcting their inherent errors and by accounting
for the dynamic and disproportionate growth of children and adolescents.
4
1.2 Outline
A background on bone is presented in Chapter 2. Common bone measures and
pediatric bone are also introduced, which are relevant to the following chapters. In
Chapter 3, methods of measuring bone are presented along with their respective strengths
and weaknesses. Imaging modalities are not only subject to their own limitations, but
also potential errors are compounded by the variable nature of growing children.
Therefore pediatric bone measures may be difficult to interpret. The accurate and precise
measurement of bone is integral to evaluating bone health, whether tracking the effects of
osteopenic trends, intervention, or normal growth. The following studies (Chapters 4 – 8)
aim to optimize measurements of bone in children and adolescents.
In Chapter 4, a method of extracting cancellous bone from the tibial metaphysis
with peripheral quantitative computed tomography (pQCT) is presented, leading to a
characterization of the behavior of cancellous bone density along the metaphysis. The
implications of a variable density gradient are discussed. Alternative bone measures
related to the total amount of cancellous bone are proposed to minimize error.
Chapter 5 investigates dual energy x-ray absorptiometry’s (DXA) fundamental
assumption of a homogeneous soft-tissue distribution surrounding the bone with
quantitative computed tomography (QCT) data. Specifically, soft-tissue is segmented
into adipose and lean tissues to determine the homogeneity in the DXA scan regions.
The difference in soft-tissue content is then used to calculate a theoretical error. The
amount of error is related to anthropometric measures to generate a correction equation.
5
Another approach in Chapter 6 explores alternative DXA scan regions by
analyzing the extra-osseous soft-tissue contained in whole trunk. Conventional scan
regions that use a fixed width may not account for a proportional amount of soft-tissue in
subjects of different sizes. To evaluate the soft-tissue attenuations contained in the DXA
regions of interest, QCT is used. Using this data, the possibility of an optimal region of
interest is investigated and related to patient-specific measures such as vertebral body
width and trunk width.
The contribution of the vertebral posterior elements in DXA lumbar spine scans is
quantified in Chapter 7. Since the posterior elements do not play a major role in
compressive fractures, yet contain a significant amount of bone, DXA bone density
measures that include the posterior elements may not appropriately reflect cancellous
bone or estimate fracture risk. This study uses QCT to measure the vertebral body and
posterior elements. The results are related to age, and the implications regarding DXA’s
agreement with QCT are discussed.
In Chapter 8, the potential use of magnetic resonance imaging (MRI) to extract
cross-sectional bone geometry is investigated. Traditional analysis of bone with MRI
requires manual tracing, a tedious and error prone process. In this study an automated
extraction algorithm is designed and implemented in a graphical user interface. The bone
measures collected from MRI are compared to QCT data obtained with established
techniques.
Chapter 9 summarizes the contributions of the work presented in this thesis.
Future studies are suggested for the new techniques requiring thorough investigation.
6
Chapter 2: Bone background
2.1 General bone
The dynamics of bone growth and adaptation is a balanced process of renewing
bone. While osteoclasts remove old bone tissue, osteoblasts generate new bone. This
cellular interplay of resorption and formation changes according to age, hormones, and
external conditions (Agarwal & Stout, 2003; Riggs & Melton III, 1995).
Figure 2-1: Transverse cross-sections of the L3 vertebra (left) and the tibial metaphysis (right). Cortical
bone in bright white and cancellous bone in spotted white within the cortical shell.
On a macroscopic level, there are two main types of bone: cancellous and cortical
(Figure 2-1). Cancellous or trabecular bone is characterized by its porous matrix. Its
spongy micro-architecture supports a metabolic tissue in which high rates of bone
remodeling occur on the tissue surfaces. Bone sites rich in cancellous bone can be found
within the vertebral body, the calcaneus, and the metaphyseal regions of long bones.
Cortical bone, although porous, is much denser and more mineralized than cancellous
7
bone and plays more of a mechanical role (Favus, 2006). It is usually found in the
compact, outer layers of bones. Measurements of both types reveal different, but critical
information regarding the strength of bone.
2.2 Measures of bone strength
The strength of a material is fully appreciated in mechanical tests of its ability to
resist an applied force. In these experiments, axial, bending, or shear stress are applied
directly to the object until the point of failure (Figure 2-2). The material is loaded
beyond its elastic region, defined by Young’s Modulus (the line of proportional stress and
strain), into a plastic region in which the material suffers permanent deformation and
ultimately, failure. This method can be applied to bones from cadavers, animals, and
models, but it is impractical and unethical to perform these tests in live human subjects.
Measurements describing the material and structural properties of living bone can
be obtained from noninvasive imaging techniques. By borrowing principles from beam
theory, bone can be analyzed for parameters related to stress. Although the exact amount
of force required to fracture bone cannot be predicted, given the combinations of loading
patterns and the asymmetry of bone, these measurements can at least provide an
insightful estimate.
The cross-sectional geometry of cortical bone and the distribution of its mass
about its centroid can reveal information about bone’s resistance to stress (Favus, 2006)
(Figure 2-2). These structural measures include cross-sectional area (cm
2
) and moments
of inertia (cm
4
). Cortical bone area describes the total amount of bone, which is inversely
proportional to axial stress; a greater cross-sectional area lowers the overall compressive
8
Figure 2-2: Different types of stresses that can be applied to bone. Arrows depict loading direction.
9
or tensile stress throughout the material. Area moment of inertia is used to predict the
cross-section’s resistance to bending forces; a greater area moment decreases bending
stress. Polar moment of inertia is the torsional analog to area moment and characterizes
an object’s ability to resist shear stress. It should be noted that cross-sections of long
bones are not symmetrical, and their respective moments of inertia cannot be used in
simple stress equations. Bending stress should be calculated with the classic bending
equation, and the solution for shear stresses due to torsional forces does not exist in a
closed form for asymmetrical cross-sections (Bartel, Davy, & Keaveny, 2006).
Nonetheless, moments of inertia of asymmetrical cross-sections of cortical bone can
provide an understanding of the bone’s resistance to stress. The equations used to
calculate cortical bone area and moments of inertia can be found in Appendix A, and are
discussed in further detail in Chapter 8.
Bone mineral content (BMC, g) and bone mineral density (BMD, mg/cm
3
) are
also essential measures that are directly related to bone strength. They describe the
quantity of bone and its porosity, and are measured from common osteoporotic fracture
sites such as the hip and spine. Bone density values are often transformed into T- or
Z-scores based on normative data. A T-score is the number of standard deviations away
from the BMD of the average adult. A Z-score is like the T-score, but is age dependent.
For both types, there can be subsets of scores for males, females, and ethnic groups. A
T-score between -1 and -2.5 is considered osteopenic and at risk for developing
osteoporosis, and a T-score below -2.5 results in a diagnosis of osteoporosis. A Z-score
less than -1.5 suggests non-osteoporotic or non-age related factors that are contributing to
10
low bone density. Scores greater than -1 indicate normal bone (Kanis, Melton,
Christiansen, Johnston, & Khaltaev, 1994; Watts, Lewiecki, Miller, & Baim, 2008).
These parameters describing bone are the conventional measures used in a clinical
setting. There are other methods of assessing bone strength and its resistance to fracture,
but they are not described here.
2.3 Pediatric bone
During childhood and adolescence, the shape and structure of bone undergoes
significant changes. Bone is reshaped and altered in such a way as to optimize its
morphology to withstand the loads imposed upon it (Kontulainen, Hughes, Macdonald, &
Johnston, 2007). The total behavior of pediatric bone is dynamic and disproportional.
The rate of growth is unique for each child, even within the different segments of the
same body, at the two epiphyses of long bones and in all three dimensions of morphology
(Figure 2-3).
Figure 2-3: Disproportionate human growth and changes in vertebral cross-sections. Figure courtesy of
Dr. Vicente Gilsanz.
11
Longitudinal bone growth occurs throughout childhood, but is markedly observed
during the growth spurt, a process characterized by a proliferation of cartilage cells in the
physis, also known as endochondral ossification (Netter, 1987). Eventually, the cartilage
in the metaphyseal growing zone between the epiphyses and diaphysis is replaced with
bone. The two regions merge as the epiphyseal plate closes (Sinclair, 1998; Tachdjian,
1972). The end of this process marks skeletal maturity. Similarly, but not necessarily
occurring at the same time, the amount of bone will also peak. The highest level of bone
mass accrual, which occurs after puberty (sexual and skeletal maturity), is defined as
peak bone mass (Riggs & Melton III, 1995; Wren, Kim, Janicka, Sanchez, & Gilsanz,
2007).
The study of pediatric bone is complex, but extremely valuable. Children with
low bone mass will most likely grow into adults with low bone mass, and may have
osteoporosis and a high risk of fracture at an early age. However, before skeletal
maturity, bone has the most potential for growth and response to intervention.
12
Chapter 3: Non-invasive assessments of bone
Common techniques of imaging and measuring bone are described in this chapter.
Their respective measurement regions, outcomes, radiation exposure, scan time,
advantages, and disadvantages are discussed and outlined in Table 3-1.
3.1 DXA – Dual energy x-ray absorptiometry
DXA is a widely used bone densitometer (Figure 3-1). Its low radiation (1/10
th
of
a chest x-ray), rapid scan time (5 – 10 min), and precision (CV < 2%) make it ideal for
patients requiring periodic examinations (Bachrach, 2000; Margulies et al., 2005;
"Position statement: introduction, methods, and participants. The Writing Group for the
International Society for Clinical Densitometry (ISCD) Position Development
Conference," 2004). DXA is a projection technique which applies two x-rays of different
energy levels to derive bone measures (the governing equations can be found in
Appendix B) (Figure 3-2). Bone density is calculated with the assumptions that the body
is comprised of two components: soft-tissue and bone, and that the soft-tissue anterior-
posterior (AP) to the bone is the same as the soft-tissue directly lateral to the bone. With
two equations from the two x-rays and the soft-tissue attenuation known, it is possible to
solve for areal bone mineral density (aBMD, g/cm
2
) and bone mineral content (BMC, g),
which is calculated by multiplying aBMD by the projected area. It is important to note
that areal density lacks a dimension of depth, which differentiates it from true volumetric
density, a three-dimensional measurement.
13
Table 3-1: Comparison of bone de nsitometry moda lities.
14
Figure 3-1: Hologic Delphi W DXA scanner at Childrens Hospital Los Angeles.
15
Figure 3-2: Sample DXA AP projection image of the lumbar spine.
While DXA has been reported to have a high precision, there are several
limitations that confound DXA measures. Since it is a two-dimensional projection
technique, DXA cannot discern the length along the path of the beam. As a result, there
may be errors due to size bias; aBMD will be different for bones of different sizes, even
though their volumetric densities are the same (Figure 3-3). Corrections for this
shortcoming have used cubic, cylindrical or other geometric approximations to correct for
the missing dimension and shape of the vertebrae (Carter, Bouxsein, & Marcus, 1992).
However, these corrections may be less effective and further confound aBMD measures
in children due to growth-related changes in the vertebral dimensions. These corrections
have primarily been applied in research studies.
16
Figure 3-3: Illustration of size bias effect. Two objects with the same volumetric density, but different
areal densities. Adapted from Carter et al., 1992.
In addition to bone morphology, the body composition of children and
adolescents changes rapidly and disproportionately. It has been shown that weight
change can affect DXA measurements, and it is likely that errors from body composition
arise from the assumption of homogeneous soft-tissue surrounding the bone (Hangartner
& Johnston, 1990). The effects of soft-tissue errors are most pronounced in subjects with
anorexia nervosa or obesity, or those experiencing adolescent growth spurt (Formica,
Loro, Gilsanz, & Seeman, 1995; Glickman, Marn, Supiano, & Dengel, 2004; Tothill,
Laskey, Orphanidou, & van Wijk, 1999).
17
Lastly, DXA is limited by the inclusion of the vertebral posterior elements, such
as the spinous processes and pedicles, which are rich in cortical bone. Measurements
from the isolated vertebral body are preferred since it is a site rich in cancellous bone and
directly loaded in compressive fractures. The inclusion of large amounts of cortical bone
from the posterior elements may skew aBMD and BMC dramatically and may not
provide accurate measures of skeletal status or predict fracture risk.
Despite these limitations, DXA remains the clinical standard in bone
densitometry, especially since its low radiation and wide availability allows for frequent
exams. While potential errors may be minimal and acceptable in mature adults, DXA’s
fundamental assumptions may cause measurement errors in growing populations.
Disproportionate changes in body composition and growth in bone shape and size in
three-dimensions may result in a considerable loss in accuracy (Bachrach, 2006).
3.2 QCT – Quantitative computed tomography
In contrast to DXA, QCT is a three-dimensional modality that provides true
volumetric measurements. QCT can visualize the morphology of bone and discriminate
between cortical and cancellous tissues, as well as different types of soft-tissue. It is able
to achieve this by reconstructing transverse cross-sections of data collected from an array
of x-rays encircling a subject via filtered back projection (Curry III, Dowdey, & Murry
Jr, 1990) (Figure 3-4). Raw data from QCT is saved as a Digital Imaging and
Communications in Medicine (DICOM) image file, which records voxels in Hounsfield
Units (HU) (Equation 3-1) and defines air as -1000 HU and water as 0 HU, using their
respective mass attenuation coefficients (μ) (Curry III et al., 1990).
18
Figure 3-4: Left: GE Lightspeed Q/Xi CT scanner, The General Electric Company; right: StraTec XCT
2000 pQCT scanner, StraTec Medizintechnik GmbH.
1000 ×
−
=
water
water tissue
HU
μ
μ μ
Equation 3-1
Subjects scanned for bone density measures are simultaneously scanned with a
mineral reference phantom made from calcium hydroxyapatite (Ca
10
(PO
4
)
6
(OH)
2
) or an
equivalent material such as dipotassium phosphate (K
2
HPO
4
). The phantom serves two
purposes: to calibrate the image to account for drift in the instrument, and to convert HU
into hydroxyapatite equivalent density (mgHA/cm
3
).
Measures of volumetric density (vBMD, mg/cm
3
) are obtained from transverse
cross-sections of the vertebral bodies in the lumbar spine (L1-L4) (Figure 3-5). BMC is
calculated by multiplying vBMD by bone volume or the product of cross-sectional area
and bone height. It is common to measure the entire vertebral body or sample a region
containing cancellous bone within the vertebral body. These measures are extracted
manually or semi-automatically by a technologist. Since cancellous bone is relatively
uniform throughout the vertebra, a single transverse cross-section through the mid-
section is representative of the whole vertebra.
19
Figure 3-5: Sample QCT image of a cross-section through L3.
pQCT or peripheral QCT images the appendicular skeleton and is often preferred
over QCT since radiation exposure is lower and localized (Figure 3-4). Assessment of
cancellous bone with pQCT is usually measured at metaphyseal sites which are rich in
cancellous bone. Slices at the metaphysis are positioned using a fixed percent of the long
bone length or a fixed distance from the epiphysis (Rauch, Tutlewski, Fricke et al., 2001;
20
Wang et al., 2005; Ward et al., 2005). Cortical bone measures can also be obtained for
structural analyses usually at the mid-shaft of long bones.
The precision of QCT and pQCT is very good. Studies have reported a low
coefficient of variation in short-term precision (CV < 1%) (Sievanen et al., 1998; Takada,
Engelke, Hagiwara, Grampp, & Genant, 1996; Wapniarz et al., 1994). However,
precision is limited by the technologist’s ability to position the scan at the exact location
(Rauch, Tutlewski, Fricke et al., 2001). This is problematic in growing subjects, where
the same location in growing long bones, whether by a fixed percentage or a fixed
distance, may no longer be the same anatomical location over time (Kuhn, Slovis, Haller,
& Caffey, 2003).
Disadvantages of QCT include its high cost and high doses of radiation. The
relatively high cost of QCT limits its usage and makes it less accessible than DXA.
Efforts can be taken to minimize exposure to the subject while maintaining an acceptable
spatial resolution, but there are still risks associated with radiation. A standard
abdominal QCT exposes the stomach to 10 mSv in adults and 20 mSv in children (single
slice). In comparison, a standard chest x-ray exposes 0.01 mSv to the lungs. Radiation
dosage is especially important in children since they are more radiosensitive and have
more potential to develop radiation-induced cancer later in life (Brenner & Hall, 2007;
McNitt-Gray, 2002). Due to these reasons, QCT measurements are not as common as
DXA for bone measures, even though QCT is superior in many ways.
Recent advances in QCT technology can provide high resolution images on a
micron level with conventional radiation exposure on human subjects. Previously micro-
21
QCT was exclusively used in vitro or in small animal studies due to extraordinarily high
radiation doses. Nonetheless, these scanners are still quite expensive and require further
research as an emerging technology (Genant & Jiang, 2006).
3.3 MRI – Magnetic resonance imaging
Traditionally, MRI pulse sequences are optimal for contrasting soft-tissues. Bone
image intensity in MRI is suppressed due to lack of H ions and thereby detection of spin,
which is the basis of how MRI reconstructs images (Curry III et al., 1990). However, it
is possible to apply a bone enhancing pulse sequence to achieve a reasonable contrast of
bone against soft-tissue and manually trace the contours to find cross-sectional geometry
(Hogler, Blimkie, Cowell, Kemp, Briody, Wiebe, Farpour-Lambert, Duncan, Woodhead
et al., 2003; Hong, Hipp, Mulkern, Jaramillo, & Snyder, 2000) (Figure 3-6). To be able
to use MRI instead of QCT would be advantageous due to the lack of ionizing radiation.
Figure 3-6: Sample MRI image of a cross-section through the femoral mid-shaft.
22
High resolution MRI (HR-MRI) has recently been developed and has the capacity
to analyze cancellous bone on a trabecular level. These measures include bone volume
fracture, trabecular thickness, trabecular number, and trabecular spacing (Modlesky,
Subramanian, & Miller, 2008). While promising, these measures are relatively new and
have not been thoroughly researched for use in clinical settings.
Limitations of MRI include long scan times, high cost, small field of view, and
low signal to noise ratio in scanners with smaller magnets.
3.4 QUS – Quantitative ultrasound
QUS is another modality used to measure bone density. It is used primarily to
screen for low bone density, and may require other sources for confirmation. QUS uses
sound waves to measure BMD usually in the calcaneus. The main advantages of QUS
are the lack of ionizing radiation, low cost, and portability. However, it is limited to
measurements sites at which fractures do not usually occur.
Though QUS has gained popularity and is increasingly available, it only
correlates moderately with DXA, which has a higher predictive power (Blake &
Fogelman, 2007). The use of QUS has not been established for children and standalone
clinical settings, and may be better suited in combination with DXA (Gilsanz, 1998).
QUS was not used in the research presented here.
23
Chapter 4: Variability of cancellous bone along the metaphysis
This chapter investigates peripheral quantitative computed tomography (pQCT) as
a bone densitometer for the appendicular skeleton. The density of bone is a strong
indicator of skeletal health and is used in the diagnosis of low bone mass or osteoporosis.
Traditionally, measures of cancellous bone are taken in the spine (L1-L4), since those
sites are prone to compressive fractures. However, due to the location of the vertebrae, a
significant amount of the central body is irradiated.
In contrast, pQCT enables localized scans of cancellous bone from the peripheral
body, which minimizes radiation exposure. However, it is unclear that measures of
cancellous bone in the appendicular skeleton are more reliable than those from the spine.
Transverse cross-sections through the vertebral are relatively uniform, and therefore
provide consistent measures. Cancellous bone in long bones is not uniform. There is no
cancellous bone in the shaft, and there is a substantial amount near the growth plate. In
between and in the metaphysis region, there is a gradient of bone that has not been fully
described. This chapter explores the reproducibility of measuring the density of
cancellous bone from a single slice from the metaphysis by sampling the entire volume of
cancellous bone in the metaphysis, and proposes alternative measures that describe the
overall and total density.
4.1 Background
The development of precise noninvasive methods for measuring bone has
significantly improved our ability to study the influence of genetic and environmental
factors influencing the attainment of bone in children (Nelson & Koo, 1999). Currently,
24
the most commonly used quantitative radiologic method to assess bone mass is dual-
energy x-ray absorptiometry (DXA) ("Position statement: introduction, methods, and
participants. The Writing Group for the International Society for Clinical Densitometry
(ISCD) Position Development Conference," 2004). However, DXA is limited by a two-
dimensional interpretation of a three-dimensional structure. In contrast, peripheral
quantitative computed tomography (pQCT) provides three-dimensional images, allowing
for volumetric density measures, an evaluation of bone morphology, and an independent
assessment of trabecular and cortical bone in the appendicular skeleton (Leonard, Shults,
Elliott, Stallings, & Zemel, 2004).
Because of its porosity and large surface area, trabecular bone has greater
turnover, and is a better indicator of bone remodeling than cortical bone. Trabecular
bone density determinations by pQCT are commonly obtained by a single scan at a
relative location, such as 4 or 8% length of the radius or tibia (Macdonald, Kontulainen,
Petit, Janssen, & McKay, 2006; Macdonald, Kontulainen, Khan, & McKay, 2007; Neu,
Manz, Rauch, Merkel, & Schoenau, 2001; Rauch, Tutlewski, & Schoenau, 2001; Wang
et al., 2005), or a fixed location, such as 10 mm from the end of the growth plate (Ward
et al., 2005).
While available data indicate that the short-term reproducibility of these
measurements is excellent (Takada et al., 1996; Wapniarz et al., 1994), positioning is
critical, and due to the variability of trabecular bone density throughout the metaphysis,
any offset in the location to be scanned would significantly influence the values obtained
(Rauch, Tutlewski, Fricke et al., 2001). Additionally, the large range of metaphyseal
25
morphology among subjects, diseases and ages limits comparative cross-sectional studies
and interpretation of the same scan location in longitudinal examinations (Kuhn et al.,
2003).
In this study, we characterized the variability in trabecular bone density values
along the length of the proximal tibial metaphysis and the change in cancellous bone
density over a 6 month period in a cohort of children with cerebral palsy who were
participants in an ongoing study requiring longitudinal pQCT determinations.
4.2 Considerations
4.2.1 Defining the metaphysis
The metaphysis is a region in long bones with no clear boundaries. It can be
described as a combination of where the cortical shell of the long bone begins to thin and
flare, and/or where there is presence of cancellous bone. To analyze the behavior of
cancellous bone density within the metaphysis, we need to first define the end points of
the metaphysis.
In other studies, the proximal end of the proximal metaphysis was located by the
point at which the fibula connects with the tibia or the tibio-fibular junction (Ward et al.,
2004). In our initial analyses, we found that the fibula did not connect with the tibia in
the same location in all our subjects. In instances in which the fibula connected higher
than the growth plate or physis, the volume of cancellous bone included the dense
developing bone tissue of the physis. We found that the most efficient way to define the
proximal end of the proximal metaphysis was to manually mark the slice just below the
physis, a cartilaginous region where longitudinal growth occurs.
26
The distal end of the proximal tibial metaphysis can be defined as where the
cortical shell is thick and its circumference becomes narrow, while cancellous bone
disappears. We first used a method based on cortical thickness. The cortical thickness
from the mid-shaft decreased by approximately 20% at the typical flare of the metaphysis
in a sample set of test subjects. However, when applied to more subjects, it became
apparent that a technique based on cortical thickness was flawed; either cancellous bone
was cut off and unaccounted for, or there was a cavity in which there was no cancellous
bone. Instead we used a method based solely on cancellous bone. The mineral reference
phantom used to calibrate pQCT was designed for bone measures, with 0 mgHA/cm
3
(hydroxyapatite equivalent density) as water. As such, density values below
0 mgHA/cm
3
in cancellous bone are considered mostly from non-bone elements or fat.
Therefore it was appropriate to define the distal end of the proximal tibial metaphysis by
the presence of cancellous bone, or the slice at which density values are greater than
0 mgHA/cm
3
.
4.2.2 Sampling within a cross-section
Ideally, data from the entire volume of cancellous bone should be collected.
However, there are factors that limit its practicality. In the metaphysis and away from the
shaft, the cortical shell thins and converges with cancellous bone. As a result, cortical
bone becomes progressively undistinguishable from cancellous bone. This is similar to
the difficulties in histopathologic studies of the subcortical region along the endosteum,
where there is a gradual transition from cortical to trabecular bone. Although this
concern can be resolved with higher resolution imaging such as micro-CT, it is
27
impractical in human subjects due to the high radiation exposure. In this study, we found
it appropriate and representative to sample cancellous bone uniformly with a fixed region
of interest from each cross-section.
A circular cross-section of each slice from the metaphysis was centered about the
centroid of the periosteum, and the radius was determined by the maximum fit within the
cavity of the tibia, without contacting the cortex. Since the tibia is not uniform along its
length, this method would result in a contiguous series of circular cross-sections with
varying area. To resolve this, our solution was to confine all circular cross-sections to the
cross-section with the smallest area (i.e., the cross-section closest to the diaphysis).
Using this method, a cylindrical core can be generated within the tibial cavity without
contacting the cortical shell and thus avoiding any cortical/cancellous ambiguity near the
growth plate since the circular cross-section sampled is centered and away from the
cortical shell.
Regression analysis was performed to determine if the circular cross-sections
represent the entire cancellous bone area within each slice. Manual contours were traced
in the cross-sections with blurred cortical/cancellous separation of three randomly
selected subjects. It was found that the sampled density was not significantly different
from the density of the total amount of cancellous bone (R
2
= 0.97).
4.2.3 Tibia curvature
We also took into account the tibia’s natural curvature. Most tibiae are not
aligned in the superior-inferior orientation. Most have a natural curve, and some are
imaged at a slight angle. It is possible that the cylindrical core might sample a piece of
28
the cortex, which could drastically and artificially increase the measurement of
cancellous bone density. However this would not occur in most cases, since data is
extracted towards the growth plate (increasingly larger cross-sectional area) using a circle
fitted to the narrowest cavity. There is a high likelihood that the core will remain within
the cancellous region. However, even if a pure cancellous core is extracted, the core may
not follow the natural axis of the metaphysis. While this may be a limitation, a
comparison using two cancellous cores, one following the natural centroid of each cross-
section and one fixed to the centroid axis from the first slice showed a strong relationship.
Regression analysis of data from three randomly selected subjects gave an R
2
of 0.98
(p < 0.001). Therefore, we elected to use the straight core for simplicity.
4.2.4 Constructing the core
Density data within each circular cross-section is extracted and averaged starting
at the most distal slice, closest to the tibial shaft. The location where density becomes
greater than 0 mgHA/cm
3
is defined as the distal end of the metaphysis, and the radius of
the circle is saved. The same circle is then used to extract cancellous bone from the
remaining slices in the metaphysis region towards the slice below the growth plate. The
accumulation of the contiguous circular sampling of cancellous bone in the metaphysis is
a cylindrical core.
4.3 Methods
4.3.1 Subjects
This study examined existing pQCT data from 37 children with cerebral palsy.
Two were excluded for motion artifacts, leaving 35 for analysis (5 hemiplegic,
29
22 diplegic, 2 triplegic, 6 quadraplegic). The subjects were originally recruited for
ongoing studies at Childrens Hospital Los Angeles, and informed consent was obtained
for all subjects. All subjects were ambulatory either with or without assistive devices and
were excluded if they had recently undergone any procedure or medication which could
alter bone or muscle function. Of the 35 children, 19 returned for a 6 month follow-up
measurement. Tanner stage was not evaluated at the time of the exams.
4.3.2 Data acquisition and processing
pQCT was performed on the proximal tibia of each subject using the same
scanner (General Electric Hilite Advantage, Milwaukee, WI) and with the same K
2
HPO
4
mineral reference phantom for simultaneous calibration (CT-T bone densitometry
package; General Electric). The thickness of each cross-section was 1.25 mm, and the
field of view was 345 mm. Data sets of at least 70 contiguous slices per subject were
obtained to ensure coverage of the metaphysis region (Figure 4-1). The same
technologist analyzed all images. Scans were evaluated and excluded if motion artifacts
were found.
To isolate cancellous bone from within the metaphysis, a cylindrical core was
built from the contiguous slices (Figure 4-1). The circular cross-section of the core was
determined by fitting the largest circle possible into the narrowest region of the proximal
tibia, without coming into contact with the cortex.
The length of the core from the metaphysis was defined as the region containing
cancellous bone, specifically, between the growth plate and where density values drop
below 0 mgHA/cm
3
. Density values below zero, as calibrated by the phantom, were
30
considered mainly fat or non-bone elements, as found in the intermedullary canal. Care
was taken to ensure that the cylindrical core was placed in the same position relative to
the growth plate in all subjects.
All image processing was performed with custom algorithms using MATLAB
R2006b (MathWorks Inc., Natick, MA).
Figure 4-1: pQCT data of the proximal tibia represented as a 3-D rendering (top) and sagittal cross-section
(bottom) with volume of interest in dotted lines.
31
4.3.3 Data analysis
The density data from the cylindrical core containing the metaphyseal cancellous
bone can be depicted graphically (Figure 4-2). For each cross-section along the length of
the core, mean density and density variation are represented. Several parameters of
interest can be extracted from the core data.
Figure 4-2: Density gradient of cancellous core.
First, the mean rate of change in density or slope of the curve was calculated by
averaging the difference of mean density from one transverse slice to the next, and then
dividing by the slice thickness. Similar calculations were performed to express the rate
of change as a percentage. The resultant values describe the variation and potential error
32
associated with a 1 mm offset in the location of a single cross-sectional density
measurement.
Also, the length of the metaphysis can be found by observing the occurrence of
cancellous bone, previously defined as between the growth plate and zero density values.
The overall mean density of the metaphysis is the average of the mean densities from
each cross-section. The area under the curve (AUC), which represents the total amount
of cancellous bone in the metaphyseal core, is the product of the overall mean density and
length of the metaphysis.
Additionally, the overall mean density was compared to density values along the
length of the metaphysis by both relative and fixed distances. The percent length or fixed
distance with the strongest correlation was then used to measure percent change in a
period of six months, and compared with the percent change using overall mean density.
Since the slice thickness used in this study (1.25 mm) differed from other pQCT
studies (2.0 – 2.5 mm) (Kontulainen, Macdonald, Khan, & McKay, 2005; Macdonald et
al., 2006; Macdonald et al., 2007; Macdonald et al., 2005; Neu et al., 2001; Rauch,
Tutlewski, & Schoenau, 2001; Wang et al., 2005), we also approximated a thicker slice
(2.5 mm) by averaging two adjacent slices (2 × 1.25 mm) in an example subject. We
compared the measurements using 1.25 mm and 2.5 mm slices.
Regression analysis was used to relate the metaphyseal bone measurements to the
subject anthropometric measures. Regression was also used to compare the overall mean
density and density from a single slice. Paired t-tests were used to compare baseline and
follow-up measurements. Wilcoxon sign rank tests were used to compare variables with
33
skewness coefficients greater than one. All statistical analysis was performed with
Statistics Toolbox Version 5.2 (MathWorks Inc., Natick, MA).
4.4 Results
A total of 35 subjects were included in this study. Seventeen of the subjects were
independently ambulatory, and 18 used assistive devices. There were 18 females and
17 males at baseline (Table 4-1). Follow-up data were available for 19 of the subjects
(8 females and 11 males) (Table 4-2).
n = 35 Mean ± Std Dev Range
Age
9.5 ± 1.5 6.0 to 12.4
(yr)
Weight
30.5 ± 10.5 14.6 to 59.7
(kg)
Weight
37.5 ± 33.9 0.0 to 99.8
(percentile)
Height
127.8 ± 12.2 101.5 to 150.3
(cm)
Height
12.7 ± 17.0 0.0 to 88.8
(percentile)
Body Mass Index
18.3 ± 4.3 13.0 to 31.0
(kg/m
2
)
Body Mass Index
56.6 ± 34.9 0.2 to 99.9
(percentile)
Table 4-1: Subject anthropometric data at baseline (n = 35).
34
Change from Baseline to Follow-up
n = 19 Mean ± Std Dev Range p value
Age
0.6 ± 0.05 0.47 ± 0.67 p < 0.001
(yr)
Weight
1.7 ± 2.9 -5.4 to 6.8 p = 0.019
(kg)
Weight
0.0 ± 12.3 -21.9 to 31.8 p = 0.999
(percentile)
Height
3.8 ± 2.6 0 to 9 p < 0.001
(cm)
Height
2.5 ± 6.3 -5.3 to 18.2 p = 0.106
(percentile)
Body Mass Index
-0.2 ± 1.6 -3.7 to 2.2 p = 0.673
(kg/m
2
)
Body Mass Index
-3.7 ± 22.1 -62.0 to 43.0 p = 0.476
(percentile)
Table 4-2: Change in subject anthropometric data from baseline to follow-up.
n = 35 Mean ± Std Dev Range
Length
25.6 ± 10.4 2.50 to 46.3
(mm)
Mean Density
59.1 ± 25.8 9.0 to 118.6
(mg/cm
3
)
Area Under the Curve
1360.6 ± 893.0 26.9 to 3202.5
(mg/cm
3
-mm)
Mean Density Slope
6.9 ± 2.7 4.2 to 14.7
(mg/cm
3
/mm)
Mean Density Slope
16.8 ± 8.2 8.6 to 37.9
(% change/mm)
Table 4-3: Metaphysis properties for baseline study.
35
Figure 4-3: Density gradient profiles from three different subjects.
Change from Baseline to Follow-up
n = 19 Mean ± Std Dev Range p value
Length
-2.1 ± 6.5 -16.3 to 12.5 p = 0.175
(mm)
Mean Density
-5.1 ± 6.1 -16.0 to 7.3 p = 0.002
(mg/cm
3
)
Area Under the Curve
-282.2 ± 381.1 -1112.4 to 335.3 p = 0.005
(mg/cm
3
-mm)
Mean Density Slope
-0.3 ± 2.4 -3.3 to 4.6 p = 0.613
(mg/cm
3
/mm)
Mean Density Slope
2.0 ± 9.1 -18.9 to 20.9 p = 0.348
(% change/mm)
Table 4-4: Change in metaphysis properties from baseline to follow-up.
The profiles or patterns of decay in metaphyseal trabecular bone density appeared
to be unique in all subjects (Figure 4-3). The length of the metaphysis, overall mean
density of the entire metaphysis, and AUC all had wide ranges (Table 4-3). None of
these measures from the metaphysis correlated strongly with anthropometric measures.
The highest correlation was between metaphysis length and subject height (R
2
< 0.14).
The mean change in density also varied greatly between subjects. Among all subjects the
mean change in density was 6.9 ± 2.7 mg/cm
3
/mm, ranging from 4.2 to 14.7 mg/cm
3
/mm.
36
As a percentage, the mean change in density per millimeter was 16.8 ± 8.2%, ranging
from 8.6 to 37.9% (Table 4-3). These results indicate that a 1 mm offset in positioning of
a slice would result in errors averaging 6.9 mg/cm
3
or 16.8%.
Significant differences between baseline and follow-up were found in age, weight,
height, AUC, and overall mean density. Age, height, and weight increased (Table 4-2),
and AUC and overall mean density decreased (Table 4-4).
The percent length of metaphysis that best reflected the mean metaphysis density
was found to be at approximately 48% of metaphysis length from the proximal growth
plate. Regression analysis showed high correlation (R
2
= 0.89, p < 0.001) between
density measures at 48% length of the metaphysis and the overall mean density of the
entire metaphysis. The fixed location that best reflected mean metaphysis density was
the second slice from the growth plate (1.25 to 2.5 mm), which also had a strong
correlation with mean density of the entire metaphysis (R
2
= 0.88, p < 0.001).
When the percent change over a six-month period was examined, regression
strength between density from the 48% slice and overall mean density was weak
(R
2
= 0.36, p = 0.013). The range of percent change using a single slice at 48% length of
metaphysis was wide, ranging from -50.2 to 31.3%, compared with a range of -32.8 to
11.9% for percent change using overall mean density (both ranges are without outliers,
defined as points outside the 5
th
or 95
th
percentiles) (Figure 4-4). The regression strength
between the change in density over six months from the slice 1.25 mm away from the
growth plate and overall mean density was stronger (R
2
= 0.58, p < 0.001), but the range
was even wider at -45.1 to 50.9% (Figure 4-4).
37
Figure 4-4: Box plots showing percent change from baseline to six month follow-up using single slice
density at 48% length of metaphysis, single slice density 1.25 mm from growth plate, and mean density of
entire metaphysis.
Figure 4-5: Variability of cancellous bone density changes at different positions along the length of the
metaphysis using A) 1.25 mm slices and B) 2.5 mm slices.
A case example demonstrating the difficulty of using density measurements from
a single slice is illustrated in Figure 4-5A. The shape of the cancellous bone density
curve has changed in a six month period during which the subject grew 4.3 cm. At the
38
cross-section where the curves intersect, there is no change in density. At the same time,
it is possible to select a slice in which the change is a 25.3% decrease in density. For
comparison, the percent change using the overall mean density of the entire metaphysis
was -25.4%. When using a thicker slice of 2.5 mm, approximated by combining two
1.25 mm slices, the density curve was smoother although the general shape of the curve
did not change (Figure 4-5B). There was a 24.0% decrease in the same location where a
25.3% decrease was found using the 1.25 mm thickness data. The mean density slope
and AUC remained the same using the two thicknesses.
4.5 Discussion
To our knowledge, this is the first study to examine trabecular density along the
entire length of the metaphysis using pQCT. While informative, the data obtained in this
study reflect a pediatric population with cerebral palsy and cannot be directly
extrapolated to healthy subjects or other bones. Studies have shown that subjects with
cerebral palsy have inhibited growth compared with healthy children (Henderson,
Kairalla, Barrington, Abbas, & Stevenson, 2005; Stevenson et al., 2006). Decreases in
bone density are not uncommon due to the disease process which leads to osteopenia and
prevents normal weight bearing activities. Future studies examining healthy subjects and
other metaphyseal sites are needed to provide a more complete understanding of the
variability in metaphyseal trabecular bone density.
Another significant limitation of this study is that tibia length was not measured,
and so assessments involving percentage of tibia length could not be done. We attempted
to use percentage of metaphysis length as a surrogate for bone length. While metaphysis
39
length is theoretically useful, it would not be known by clinicians before a scan, and the
relationship between metaphysis length and bone length is complex. Longitudinal
growth of long bones occurs at the growth plate and is associated with extension of the
metaphysis (Sinclair, 1998; Tachdjian, 1972). At the same time, the metaphysis
gradually shortens as a proportion of bone length. This dynamic process is specific to
each extremity of the long bone. The distal and proximal growth plates grow at
disproportionate and varying rates (Pritchett, 1992), making exact locations difficult to
track longitudinally. It is therefore likely that cross-sections based on a percentage of
long bone length will not be measuring the same site over time.
In contrast, our results suggest that a scan location near the growth plate (1.25 to
2.5 mm) may be a promising measurement site. There was a strong correlation between
trabecular density at this location and mean density of the entire metaphysis.
Nevertheless, we observed tremendous variability in the percent change after six months
at this location. At this site, some children showed a decrease of up to 45.1% in
trabecular bone density, while others showed an increase of up to 50.9%. The
unexpectedly large range suggests that even if we were able to choose the site that best
reflects overall trabecular density in cross-sectional studies, longitudinal measures would
still yield conflicting results. Additional studies are needed to determine if mean density
or a slice reflecting mean density is indeed superior to single slice measurements at other
locations. Additional studies are also needed to discern which slice, if any, is the best
choice and whether a single slice can provide sufficient information to infer any relation
to bone strength or fracture risk.
40
Previous studies using pQCT in children have investigated the effects of age or
maturity related growth, gender differences, physical activity, disease, geometry and
strength (Binkley T. et al., 2005; Kontulainen et al., 2005; Macdonald et al., 2006;
Macdonald et al., 2007; Macdonald et al., 2005; Neu et al., 2001; Schlenker &
VonSeggen, 1976; Wang et al., 2005; Ward, Adams, Freemont, & Mughal, 2007). These
studies employed a variety of methods, such as measurements at 4% or 10% length of the
radius or tibia, or at a fixed length 10 mm distal to the growth plate. More recent studies
employing high resolution pQCT (HR-pQCT) have scanned 9 mm thick sections of long
bones to assess trabecular microarchitecture (Boutroy S, Bouxsein ML, Munoz F, &
Delmas PD, 2005; Macneil & Boyd, 2007a, 2007b; Sornay-Rendu, Boutroy, Munoz, &
Delmas, 2007). Although this relatively new technique is promising, further evaluation is
necessary to determine how measures from a 9 mm thick section should be interpreted,
especially across a growing population.
The results of this study highlight the limitations of current pQCT methodology
using single scans as outcome measures in cross-sectional and longitudinal studies
assessing trabecular bone density. We found a large variability in metaphyseal
morphology among subjects; the length of the metaphysis, overall trabecular mean
density, and slope of the density curve all had wide ranges. In addition, longitudinal
assessments showed that the slopes of the density curve drastically changed in some
children, even over a short period of six months. These results emphasize the need for
developing pQCT acquisition techniques that provide more accurate bone density
determinations in the appendicular skeleton of children.
41
The findings of this study corroborate the presence of a considerable gradient in
trabecular bone density from the physeal plate, where values are higher, to the shaft of
the bone, where no trabecular bone is present. The large intra- and inter-subject
variability in the bone density measures along the metaphysis highlights the limitations of
assessments with a single scan. Subjects in this study showed a substantial range of
variability from a 1 mm offset slice positioning with an average of 6.9 mg/cm
3
or 16.8%.
Single slice studies are also prone to error from the metaphysis’ changing
morphology. In the case example (Figure 4-5), the density slope or gradient changed
over six months. Thus, any cross-section selected would yield a unique percent change.
Several issues regarding the design of this study need to be considered for the
appropriate interpretation of the current results. First, because the image resolution of
pQCT does not allow clear delineation between the inner margin of cortical bone and the
outer margin of trabecular bone especially near the growth plate, we chose to measure a
defined cylindrical core of trabecular bone rather than sample all the trabecular bone in
the metaphysis. Secondly, the slice thickness (1.25 mm) used in this study differs from
that typically used in other studies (2.3 – 2.5 mm) (Macdonald et al., 2006; Macdonald et
al., 2007; Rauch, Tutlewski, & Schoenau, 2001). The thinner slices enabled greater
resolution in examining density variation, the main objective of this study. However, to
better compare with other studies, we also simulated a 2.5 mm slice by averaging
adjacent 1.25 mm slices. The thicker slice made the density curves slightly smoother but
did not greatly reduce the effect of positioning errors. The slope of the density curve
remained the same whether using 1.25 mm or 2.5 mm slices.
42
In summary, this study which quantified the variability of trabecular bone density
along the length of the metaphysis, underscores the difficulties in obtaining reproducible
pQCT measures from a single scan in the appendicular skeleton of children. Future
studies are needed to determine whether different acquisition methods could provide
more representative measures of bone density.
43
Chapter 5: Evaluating soft-tissue based errors in DXA
Chapters 5, 6, and 7 examine the limitations of dual energy x-ray absorptiometry
(DXA) and use quantitative computed tomography (QCT) to quantify the associated
errors. Chapters 5 and 6 analyze the composition of soft-tissue in the DXA scan region
using QCT cross-sections of the vertebra. In Chapter 7, the effect of the vertebral
posterior elements in DXA anterior-posterior (AP) spine scans is accounted for in
children and adolescents.
DXA is traditionally used in adults to assess bone mass and to diagnose
osteoporosis. Adult populations are skeletally mature and generally do not dramatically
fluctuate in body mass and body content. DXA’s technical principles and assumptions
which were designed for these subjects may not be ideal in pediatric populations.
This chapter analyzes the amount of soft-tissue surrounding the vertebra in
children by segmenting soft-tissue into adipose and lean tissues. Generally, larger
subjects have underestimated areal bone mineral density (aBMD) which appears to arise
from a greater concentration of adipose tissue overlying and underlying the vertebra, than
directly lateral to it.
5.1 Background
Dual energy x-ray absorptiometry (DXA) is currently the most common method
of bone mineral density (BMD) assessment in children and adults. DXA has gained
popularity due to its short scan time, low radiation exposure, and excellent short-term
precision (Laskey, 1996; Njeh, Samat, Nightingale, McNeil, & Boivin, 1997). Although
its growth-related limitations are known, they have generally been accepted, in part due
44
to the predominately adult population that uses DXA. The machine and software have
been standardized for adults whose growth has peaked. In contrast, children undergo
constant and dynamic changes associated with growth. The resulting changes in bone
size and body composition may significantly bias DXA bone measures (Gilsanz, 1998;
Wren & Gilsanz, 2006).
The focus of this study is DXA’s fundamental assumption that the soft-tissue
overlying and underlying the bone is the same as the soft-tissue directly lateral to it
(Blake & Fogelman, 1997; Laskey, 1996). This assumption is integral to how DXA
calculates areal bone mineral density (aBMD, g/cm
2
). However, if the soft-tissue
surrounding the bone is not homogeneous, inaccurate aBMD measures will result (Tothill
& Avenell, 1994; Tothill & Pye, 1992). This is especially significant for growing
children and individuals undergoing extreme changes in body composition. Swings in
body mass index (BMI) from obesity, anorexia nervosa, or adolescent growth spurt may
alter aBMD measures. This concern has been acknowledged in several studies, but
approaches to minimize soft-tissue related errors have not been fully explored (Bolotin,
2007; Formica et al., 1995; Hangartner & Johnston, 1990; Laskey, 1996; Svendsen,
Hendel, Gotfredsen, Pedersen, & Andersen, 2002; Tothill & Avenell, 1994; Tothill et al.,
1999; Tothill & Pye, 1992). Studies have examined body-fat distribution in various
regions of the body (Ley, Lees, & Stevenson, 1992), but not specifically in the DXA
region of interest.
Our goal was to investigate the effect of an inhomogeneous soft-tissue
distribution in anterior-posterior (AP) scans of the lumbar spine, a common site for DXA
45
measurements. We hypothesized that inhomogeniety in soft-tissue content dramatically
alters aBMD determinations. Using quantitative computed tomography (QCT) to
separate soft-tissue into adipose and lean tissues, we quantified the error in aBMD in a
large sample of healthy children, adolescents, and young adults. The calculated error was
related to easily obtainable anthropometric measures, and a correction equation was
generated and validated in a separate group of subjects. Finally, we examined whether
this correction for soft-tissue inhomogeneity improved the agreement of DXA with QCT,
a standard in bone densitometry.
5.2 Methods
5.2.1 Subjects
Our subjects included 500 children, adolescents, and young adults (250 female,
250 male), age 6.1 – 24.9 yr (15.5 ± 3.7). A second group (n = 74; 44 female, 30 male),
age 6.3 – 20.8 yr (15.5 ± 3.3), was used to validate the correction equation derived from
the first group. All subjects were healthy, without any known illnesses or conditions that
would affect bone or muscle. The Institutional Review Board for clinical investigations
at Childrens Hospital Los Angeles approved the protocols for this study, and written
informed consent was obtained from
all parents and/or participants (for minors, parents
provided consent and participants provided assent). The quantitative CT protocol
was
designed to keep radiation exposure to a level roughly equivalent
to the exposure during a
round-trip airplane flight across North
America (Cann, 1991; Kalender, 1992), making its
use in healthy subjects possible.
46
5.2.2 DXA image acquisition
AP scans of the lumbar spine were performed using the fast array scan protocol
on a Hologic Delphi W DXA scanner and analyzed using Hologic QDR software v11.2.
A projection image of the spine was generated in the frontal plane, and a region of
interest (ROI) with the default width of 105 mm was centered about each vertebral body
(Figure 5-1). The DXA software automatically detected the bone and soft-tissue regions,
and used attenuation values from the soft-tissue regions to estimate the contribution of
soft-tissue in the bone region. The software reported the standard measures of aBMD,
bone mineral content (BMC, g), and projected area (cm
2
).
Figure 5-1: Projection image of lumbar spine from DXA scan. Region of interest width was set to 105 mm,
and bone region was separated from soft-tissue region by vertebral contour lines. A second ROI was
defined to represent the 10 mm thick slice imaged by QCT.
47
The DXA data were then reanalyzed using the same Hologic QDR software to
obtain a second set of DXA measures representing the region imaged by QCT. The
height of the ROI was set to match the QCT slice thickness (10 mm), and the ROI was
placed at the center of the L3 vertebra (Figure 5-1). The ROI width remained fixed at
105 mm. The software calculated the aBMD, BMC, and projected area for this region.
DXA data from the 10 mm region will be referred to as “10 mm L3,” whereas DXA data
from the whole vertebra will be referred to as “total L3.”
5.2.3 QCT image acquisition
The same 574 subjects scanned with DXA were also scanned with a GE
LightSpeed QX/i QCT machine (General Electric, Milwaukee, WI) on the same day by
the same technologist. The scan site was identified with a lateral scout view, and a
10 mm thick transverse cross-section at the midsection of the L3 vertebra was imaged in
each subject using 80 kVp, 70 mA, and 2 s (Figure 5-2A). A hydroxyapatite equivalent
(HA) mineral reference phantom was included in the scans for simultaneous calibration.
5.2.4 QCT image analysis
QCT images were segmented into three tissues: adipose, lean, and bone (Figure
5-2B). First, the image was calibrated according to the mineral reference phantom and
converted to hydroxyapatite (HA) equivalent density values from Hounsfield Units (HU).
Predefined density ranges were used to separate the three tissues ([-125,0), [0,75),
[75,1200] mgHA/cm
3
for adipose, lean, and bone tissue, respectively). These values
were determined by manually sampling data from several subjects. The upper bound of
bone density was set arbitrarily high under the assumption that there were no tissues
48
denser than bone. Values below -125 mgHA/cm
3
were assumed to be air. The calibrated
density measures do not represent actual physical density, but rather values based on the
mineral reference phantom, which scale linearly using three compartments with 0, 75,
and 150 mgHA/cm
3
. This results in negative density values for adipose which is less
dense than water (0 HU) and does not contain hydroxyapatite.
Figure 5-2: A) Original QCT image; B) QCT image segmented into bone, adipose, and lean tissues; C)
histograms showing soft-tissue components, adipose (solid) and lean tissue (dotted); D) histogram showing
percentage of soft tissue consisting of adipose. DXA bone region between vertical dotted lines and soft-
tissue region between vertical dotted and solid lines.
49
The cross-section was rotated to align the spine in the AP direction. The DXA
region of interest was defined on the QCT cross-section using the same DXA 105 mm
window (solid vertical lines in Figure 5-2), centered about the centroid of the vertebral
body. The DXA bone region was determined by an algorithm designed to find the lateral
edges of the vertebral body. Two AP lines drawn through these points separate the bone
and soft-tissue regions (dotted vertical lines in Figure 5-2). The contents of the adjacent
soft-tissue regions were assumed to be either adipose or lean tissue, unless excluded as
air or parts of the transverse processes protruding into the soft-tissue region.
From the segmented image, the number of pixels of adipose and lean tissue in the
AP direction were summed and visualized in a histogram (Figure 5-2C). From these
values, we calculated the proportion of soft-tissue composed of adipose in the bone and
soft-tissue DXA scan regions (Figure 5-2D).
For the validation study, BMC was determined for the 10 mm mid-section of L3
using QCT. First, volumetric bone mineral density (vBMD, mg/cm
3
) was calculated
containing the vertebral body and vertebral elements directly posterior. This was done
because DXA includes all bone in the path of the x-ray beam. QCT BMC was then
calculated by multiplying the vBMD values by the corresponding cross-sectional area
and height (10 mm). All image analysis and processing of QCT data was performed in
MATLAB 2006b (MathWorks Inc., Natick, MA).
5.2.5 Calculation of DXA error
A theoretical error equation based on soft-tissue inhomogenity was originally
derived by Hangartner (Hangartner & Johnston, 1990):
50
R R
b b
s s b
μ μ
σ μ σ
′ −
′ −
=
∂
∂
,
s
s
R
μ
μ
′
= Equation 5-1
where σ is areal density, μ is mass attenuation coefficient, b is bone, s is soft-tissue, and
R is the ratio of soft-tissue attenuation coefficients of two energies. The primed symbols
denote values of higher x-ray energy. This error equation was derived by taking the
partial derivative of areal bone mineral density (from the original DXA equation) with
respect to R. The calculations can be found in Appendix B.
μ
50KeV
μ
85KeV
R ρ
Adipose Tissue 0.2117 0.1761 1.202 0.916
Skeletal Muscle 0.2262 0.1782 1.269 1.04
Cortical Bone 0.3526 0.1999 – –
Table 5-1: Mass attenuation coefficients (μ, cm
2
/g), ratio of coefficients (R) and density (ρ, g/cm
3
) values
for adipose tissue, muscle, and bone. Subject-specific values for soft tissue are calculated as a linear
weighting of the adipose and muscle values based on the adipose percent for each subject.
The variables on the right hand side of the equation are constants that can be
determined for each subject. Standard bone attenuation coefficients were fixed (i.e., the
same for all subjects), but the soft-tissue values depend on the distribution of adipose and
lean tissue for each subject. The subject-specific soft-tissue attenuation coefficients and
area density were determined through a linear weighting of values for adipose and lean
tissue (Table 5-1) based on the adipose percent measured in the bone region of the QCT
images. The two beams used by our DXA scanner are rated at 100 kVp and 140 kVp
which can be estimated to effective energies of 50 and 85 keV, respectively (Cullum, Ell,
& Ryder, 1989; Sartoris & Resnick, 1989). Mass attenuation coefficients of adipose
tissue, skeletal muscle, and cortical bone at these energy levels were extrapolated from
data from the International Commission of Radiation Units and Measurements (ICRU,
51
1989), and volumetric densities were taken from the National Institute of Standards and
Technology (Berger, Coursey, Zucker, & Chang, 2005) (Table 5-1). Areal density (σ)
was estimated as the product of volumetric density (ρ) and path length in the AP
direction. It should be noted that different mass attenuation coefficients and densities
values will apply to different DXA scanner models, which may use other energy levels.
Given these parameters, the discretized soft-tissue error equation can be solved.
The absolute error (Δσ
b
) is calculated by multiplying both sides of the error equation
(Equation 5-1) by the difference in R between the soft-tissue and bone regions:
) (
_ _ region bone region tissue soft
b b
s s
b
R R
R
−
′ −
′ −
= Δ
−
μ μ
σ μ
σ Equation 5-2
The percent error is then calculated by dividing the absolute error (Equation 5-2) by the
aBMD reported by the DXA software:
aBMD
Error
b
σ Δ
= % Equation 5-3
5.2.6 Correction using anthropometric relationships
The error associated with soft-tissue inhomogenity (Δσ
b
) was measured against
easily obtained anthropometric parameters using linear regression. The anthropometric
parameters examined included age, mass, height, body mass index (BMI), and their
respective percentiles, and the medial-lateral width and circumference of the trunk at the
L3 cross-section as obtained by QCT. A correction equation for aBMD was generated
using the parameters with the strongest relationship with the soft-tissue inhomogeneity
related error. The “corrected” aBMD values were then multiplied by the DXA projected
area to calculate “corrected” BMC values.
52
5.2.7 Validation of aBMD correction equation
To validate the derived correction equation, a separate group of 74 subjects was
used. DXA and QCT measures were obtained using the same protocols as the original
group. DXA aBMD and QCT vBMD were both converted to BMC, since areal density
lacks the dimension of depth found in volumetric density. The calculated errors in BMC
were compared before and after application of the correction equation. In addition, the
original and corrected DXA BMC values were compared with the QCT BMC to examine
the effectiveness of the correction.
5.2.8 Statistical analysis
Linear regression analysis was used to assess the correlation between adipose
tissue in the bone and soft-tissue regions, and between QCT and DXA measures. Step-
wise regression analysis was used to isolate the anthropometric parameter that most
influenced soft-tissue related errors.
5.3 Results
5.3.1 DXA soft-tissue error
The percentage of adipose tissue in the bone and soft-tissue regions showed a
strong relationship (R
2
= 0.88, p < 0.001), but differed by an average of 7.1% (Table 5-2).
This translated to an absolute error in aBMD of -0.08 g/cm
2
, which corresponds to a
percent error of -11.4% in total L3 aBMD and -10.7% in aBMD of the 10 mm midsection
of L3 (adjusted to match QCT slice thickness). When compared to the original aBMD,
the corrected values were higher in 449 of the 500 subjects (90%).
53
Mean ± SD Range
Difference in adipose tissue (%) 7.1 ± 5.6 -10.5 to 22.0
Absolute error in aBMD (g/cm
2
) -0.11 ± 0.09 -0.42 to 0.10
Percent error in aBMD, total L3 (%) -11.4 ± 9.9 -42.9 to 17.7
Percent error in aBMD, 10 mm L3 (%) -10.7 ± 9.3 -48.0 to 15.9
Table 5-2: Difference in adipose tissue content between bone and soft-tissue regions and resulting influence
on aBMD.
5.3.2 Anthropometric relationships
The calculated error based on the derived DXA equation was related to all
anthropometric parameters except height percentile for both absolute and percent error in
the total L3 and 10 mm L3 analyses (Table 5-3).
R
2
DXA error
(g/cm
2
)
DXA error
(%) total L3
DXA error
(%) 10 mm L3
Age (yr) 0.10* 0.03* 0.04*
Mass (kg) 0.32* 0.16* 0.19*
Mass (%) 0.17* 0.13* 0.14*
Height (m) 0.08* 0.03* 0.03*
Height (%) 0.00 0.00 0.00
BMI 0.34* 0.21* 0.23*
BMI (%) 0.21* 0.18* 0.18*
Trunk thickness (cm) 0.36* 0.21* 0.24*
Trunk circumference (cm) 0.38* 0.24* 0.26*
* significant, p < 0.001, % indicates percentile for age
Table 5-3: Regression of DXA error with subject mass and trunk circumference (n = 500).
54
Figure 5-3: Regression of DXA error with subject mass and trunk circumference (n = 500).
Trunk circumference was the variable with the strongest relationship to absolute
error as determined by step-wise regression analysis (Figure 5-3). Other anthropometric
measures relating to the size of the subject also correlated strongly. Trunk circumference
was slightly stronger than trunk width and subject mass, which were related to each other.
We therefore generated a correction equation using trunk circumference:
] [ _ * 043 . 0 238 . 0 ] / [ ] / [ _
2 2
cm circum Trunk cm g aBMD cm g aBMD Adjusted + − =
The error in aBMD was compared before and after the application of the
correction equation in the validation group. The range of error (excluding outliers less
than 5
th
percentile and greater than 95
th
percentile) was reduced by an average of
0.08 g/cm
2
or 7.1% (33.7% to 26.6%) in total L3 aBMD and 8.1% (31.7% to 23.6%) in
10 mm L3 aBMD. The mean error was also shifted from -0.09 mg/cm
2
to approximately
zero (-0.10 mg/cm
2
), and as a percentage from -9.71% to 0.95% (total L3) and -9.01% to
0.90% (10 mm L3) (Figure 5-4).
55
Figure 5-4: Box plots of calculated error before and after application of the correction equation in the
validation group.
DXA BMC
QCT BMC
Total BMC
Total L3 10 mm L3
Original DXA
0.84 0.87
Corrected DXA
0.84 0.89
Table 5-4: Regression results (R
2
) comparing DXA BMC with QCT BMC.
When compared to QCT as a standard, adjusted DXA BMC measures showed an
improved agreement for the 10 mm region (Table 5-4).
5.4 Discussion
Since DXA measures rely on the assumption that soft-tissue content overlying
and underlying the bone is the same as soft-tissue adjacent to it, an error is introduced if
the soft-tissue is actually inhomogeneous. In our study, we found that the proportion of
adipose was greater anterior-posterior to the vertebra than directly lateral in the majority
56
of our subjects (90%). This deviates from DXA’s fundamental assumption and results in
underestimation of aBMD measures by as much as 42%. In other subjects, DXA aBMD
was overestimated by as much as 17%. Our data shows that larger subjects generally had
a greater underestimation of aBMD (Figure 5-3), as a result of a greater adipose tissue
concentration medially (in the DXA bone region).
The distribution of soft-tissue in the trunk plays an important role in DXA
measures of bone. This is problematic since the body composition of children changes
dramatically and rapidly. Apparent changes in DXA aBMD in these subjects may be due
to changes in soft-tissue rather than bone, or apparent changes in bone may be offset by
changes in soft-tissue distribution. An effective solution may be to adjust soft-tissue
related errors with an equation based on an easily obtainable anthropometric measure.
We found that trunk circumference showed the strongest relationship to the
calculated error, and so a correction equation based on trunk circumference was applied
to the validation cohort. Subject mass and trunk width could also be used to generate a
correction equation, since they had a similar relationship to the DXA error. Applying our
correction resulted in a reduction of the range of error by 8.1% and shifted the mean error
to approximately zero. Although we were able to account for a theoretical error, a
measurement of the same bone, at the same time, with a different technique such as QCT
can assess the usefulness of the correction equation.
QCT was used as a standard in evaluating the effectiveness of the DXA correction
equation derived in this study, since it collects data in three dimensions instead of two.
We found that the correlation between DXA BMC from the 10 mm region corresponding
57
to the QCT region and QCT BMC improved slightly (R
2
= 0.87 to 0.88). The analysis of
BMC between the two modalities used the same unit of measure (grams instead of areal
and volumetric density), and accounted for the same amount of bone in QCT (vertebral
body and posterior elements) as acquired in DXA. Although the improvement in
agreement between DXA and QCT was subtle, this was probably due to the strong
relationship that already exists between DXA BMC and QCT BMC, which other
investigators have also found (Wren, Liu, Pitukcheewanont, & Gilsanz, 2005a).
There were a few limitations in our study. We excluded parts of the vertebral
transverse processes that protrude into the soft-tissue scan region. This bone is normally
included in DXA AP spine scans and would increase the attenuation in the soft-tissue
region. Since soft-tissue attenuation in the bone region is already overestimated it in
most subjects, this effect would widen the disparity between the two regions, thereby
increasing the soft-tissue based error. Therefore, by excluding the transverse processes in
the soft-tissue region in our QCT analysis, we have presented a conservative estimate of
soft-tissue inhomogeneity errors.
This study is also limited by the evaluation of soft-tissue content in a 10 mm thick
cross-section in QCT. This restriction was necessary to minimize radiation exposure to
the study participants. Although we measured the corresponding 10 mm section with
DXA, differences in soft-tissue composition might be minimized by averaging over a
larger area, such as the entire region of soft-tissue lateral to the vertebra. Further study of
the soft-tissue content along the entire vertebra and spine is required to fully evaluate the
effect of soft-tissue differences in the DXA scan region. With complete soft-tissue data
58
from the entire DXA scan volume, there may be similar correction equations that
improve the accuracy of DXA measures. It would also be worthwhile to perform further
analyses on specific patient groups, as they may require different or unique adjustments.
In conclusion, we have shown that soft-tissue in the trunk at the level of the L3 is
not homogeneous, resulting in potential inaccuracies in DXA aBMD measures, and can
be corrected. aBMD was underestimated in larger subjects with greater mass and trunk
dimensions. A correction equation based on trunk circumference successfully reduced
the theoretical range of error. When compared to QCT, DXA BMC was improved after
applying the correction.
59
Chapter 6: Optimal ROI in DXA AP lumbar spine scans
Chapter 5 segmented the soft-tissue in the dual energy x-ray absorptiometry
(DXA) scan region into adipose and lean and quantified the associated error due to
inhomogeneous proportions of soft-tissue surrounding the bone. Chapter 6 addresses the
same issue of soft-tissue distribution, but explores the possibility of minimizing
inhomogeneity by using an optimal or patient-specific DXA scan region or region of
interest (ROI). Traditional DXA measurements may be limited by a fixed ROI width.
Changes in vertebral morphology and body size impact DXA’s measurement of
bone by altering the contents within the scan region. This chapter accounts for these
factors by measuring the cumulative soft-tissue densities along the width of the trunk,
including the original DXA scan region, and finding the most optimal ROIs as a
proportion of trunk width and multiple of vertebral body width. These new methods may
be especially beneficial to pediatric populations who undergo dramatic and
disproportionate changes in bone morphology, truck dimensions, and soft-tissue content.
6.1 Background
Osteoporosis is a metabolic bone disease characterized by low bone density and
deterioration of bone tissue microarchitecture. Together, these effects increase the
fragility of bone and risk of fracture ("Osteoporosis prevention, diagnosis, and therapy,"
2001). To monitor osteoporosis and skeletal status, scans of the lumbar spine and hip are
often performed with dual energy x-ray absorptiometry (DXA), an established bone
densitometer ("Position statement: introduction, methods, and participants. The Writing
Group for the International Society for Clinical Densitometry (ISCD) Position
60
Development Conference," 2004). DXA has been widely accepted as a clinical standard
in the noninvasive assessment of bone due to its fast scan time, low cost, low radiation,
and high precision (Gilsanz, 1998; Wapniarz et al., 1994).
DXA uses a projection technique to derive bone density. This is possible by
assuming that the body is composed of two general components, soft-tissue and bone,
and that the attenuation of soft-tissue anterior and posterior to the bone (bone region) is
the same directly lateral to it (soft-tissue region) (Laskey, 1996; Sorenson, 1990) (Figure
6-1). In anterior-posterior (AP) scans of the lumbar spine, the lateral edges of the soft-
tissue region are fixed in a standardized region of interest (ROI). The medial boundaries
of the soft-tissue region, which also contain the bone region, are defined by the detected
edges of the vertebral body.
Figure 6-1: The “bone region,” shown in the gray area, contains both soft-tissue and bone in the AP
direction. The “soft-tissue region,” shown in the non-shaded area, contains only soft-tissue.
61
Figure 6-2: Two DXA scans with the same ROI width of 105 mm (left: 9.3 yr female; right: 18 yr female).
A fixed ROI window width would produce consistent results in subjects with little
or no change in soft-tissue composition or body size. However, this width may not be as
effective when applied to growing subjects, since a fixed width would account for
different proportions of soft-tissue in different body sizes (Figure 6-2). If the soft-tissue
content or attenuation from the two scan regions is not consistent, errors in DXA areal
bone mineral density (aBMD) measures will result (Formica et al., 1995; Hangartner &
Johnston, 1990; Sorenson, 1990; Tothill & Pye, 1992). The magnitude of this error is
directly related to the difference in soft-tissue densities or linear attenuation coefficients
between the bone and soft-tissue regions (Hangartner & Johnston, 1990) and is more
apparent in subjects with dramatic changes in body composition, such as in obesity,
anorexia nervosa, or during normal growth or adolescent growth spurt (Tothill &
Avenell, 1994). Although this confounding factor has been studied, little has been done
62
to improve the measurement of bone by DXA regarding soft-tissue differences in the
scan region.
One aspect of soft-tissue inhomogeneity which we have explored in this study is
the region of soft-tissue that is accounted for. Since conventional DXA machines apply a
fixed distance for all subjects, the proportions of soft-tissue in the scan regions depends
on trunk width and vertebral body width. For example, a fixed ROI width of 105 mm
would account for only 50% the trunk width in a subject with a trunk width of 210 mm
and 100% in a subject with a trunk width 105 mm. Moreover, even if the same
proportion of the total trunk were measured in two subjects, the proportions of soft-tissue
contained in the two scan regions will vary if the vertebrae are not the same size. The
contents of the soft-tissue region are dependent on the width of the scan region and the
width of the vertebral body. Perhaps a patient-specific soft-tissue region can reduce
differences in cumulative soft-tissue density between the bone and soft-tissue regions.
This report examines the soft-tissue surrounding the bone in a pediatric
population. We hypothesize that a dynamic DXA AP lumbar spine ROI that adjusts its
width according to each subject, in order to match the composition of soft-tissue in the
soft-tissue region to that of the bone region, will improve DXA bone measures by
minimizing the difference in soft-tissue density between the two regions.
6.2 Methods
6.2.1 Data acquisition
We examined 574 subjects (294 female, 280 male), age 6 – 25 yr (15.5 ± 3.6).
Scans of the L3 vertebra were obtained using the same mineral reference phantom, by the
63
same technologist with QCT. QCT scans were obtained with General Electric
LightSpeed QX/i and analyzed with custom software developed in MATLAB 2006b
(MathWorks Inc., Natick, MA). The recruited subjects were healthy and were not taking
any medication that could affect bone or soft-tissue. Written informed consent was
obtained for all subjects.
6.2.2 QCT image analysis
The QCT images were read into custom software, which automatically calibrated
and converted the images from Hounsfield Units (HU) to hydroxyapatite equivalent
density units (mgHA/cm
3
) using the mineral reference phantom. Nonessential image data
such as the phantom, gantry, and image artifacts were automatically removed. The
images were then rotated to align the spine in the AP direction. An algorithm detected
each vertebra and drew two AP lines through the lateral edges of the vertebral body
(Figure 6-3). These two lines contained the vertebra (less the transverse processes) and
separated the DXA bone region from the soft-tissue region.
The lateral edges of the soft-tissue regions traversed the width of the trunk equally
and simultaneously on both sides of the vertebra, beginning at the edge of the vertebral
body and ending at the lateral edges of the trunk (Figure 6-3). The cumulative averages
of soft-tissue density in the soft-tissue regions (between each dynamic AP data line and
vertebral edge) were saved to a database, along with the cumulative average of soft-tissue
density in the bone region, which was a constant for each subject.
64
Figure 6-3: Original QCT image with two dynamic AP lines traversing the trunk width laterally (vertical
dotted lines tangent to vertebra), soft-tissue density per AP line (dashed line), cumulative soft-tissue density
from the bone region (horizontal solid line), cumulative soft-tissue density from the soft-tissue region
(curved solid line), and point in which soft-tissue densities in both regions are equal (white circles). Y-axis
shows cumulative soft-tissue density difference.
6.2.3 Patient-specific ROI analysis
The data were analyzed using three methods to find the most optimal ROI based
on a fixed distance, percent of trunk width, and multiple of vertebral body width. Each
algorithm imposed boundary conditions for the possible ROIs. For example, the width of
the fixed ROI must be greater than the width of the largest vertebral body among the
subjects, and the width must be no wider than the narrowest trunk width.
The difference between cumulative soft-tissue densities from the two regions
were averaged across all subjects for each method: fixed width, percent of trunk width,
and multiple of vertebral body width. Then the most optimal ROI was determined by the
65
point at which the difference was zero, a requirement for accurate DXA measures. We
performed these analyses on all subjects and in gender subgroups.
6.3 Results
For each of the three optimal methods, average, standard deviation, and range of
the difference in cumulative soft-tissue density between the soft-tissue and bone regions
are reported (difference = soft-tissue region – bone region) (Table 6-1).
In the fixed distance method, the cumulative soft-tissue density in the soft-tissue
region approached the cumulative soft-tissue density in the bone region at 169.3 mm.
The average difference in density using this ROI width was 0.49 ± 5.13 mg/cm
3
(range:
-16.95 to 16.60 mg/cm
3
). This distance was also the maximum width applicable to all
our subjects. In comparison, a standardized window width of 105 mm yielded an average
difference in soft-tissue density of 7.50 ± 4.93 mg/cm
3
(range: -9.39 to 22.20 mg/cm
3
)
(Figure 6-4).
The method based on percentage of trunk width located a point in which soft-
tissue density in the two regions were equivalent. Using a ROI width of 63% of the trunk
width and centering the ROI about the spine, the average difference in soft-tissue density
was -0.01 ± 4.63 mg/cm
3
(range: -16.18 to 17.02 mg/cm
3
) (Figure 6-4, Figure 6-5).
Using a ROI based on the width of the vertebral body, the most optimal size was
four times the width of the subject’s vertebral body. At this location, the average
difference in soft-tissue density was 0.75 ± 4.99 mg/cm
3
(range: -14.83 to 15.32 mg/cm
3
)
(Figure 6-4). This multiple of vertebral body width translated to the maximum trunk
width for some subjects.
66
All Females Males
Original fixed distance
7.43 ± 4.96 6.91 ± 5.10 8.02 ± 4.75
-0.76 to 15.22 -1.63 to 14.78 -0.35 to 15.60
Optimal fixed distance
0.49 ± 5.13 0.06 ± 5.33 1.29 ± 4.95
-7.67 to 9.10 -8.42 to 8.60 -6.78 to 9.83
Optimal percent of
trunk width
-0.01 ± 4.64 -0.04 ± 4.78 0.06 ± 4.47
-7.74 to 7.42 -7.87 to 7.68 -6.21 to 7.82
Optimal multiple of
vertebral body width
0.76 ± 4.99 0.32 ± 5.16 1.21 ± 4.77
-7.48 to 9.07 -8.17 to 8.29 -6.03 to 9.29
Table 6-1: Averages and ranges of soft-tissue differences in the two regions (mean ± standard deviation;
5th percentile to 95th percentile).
Figure 6-4: Box plots showing range of difference in soft-tissue density in the original DXA ROI and in
three optimal ROIs (fixed distance, percentage of trunk width, and multiple of vertebral body width).
67
Figure 6-5: Difference in soft-tissue along the width of the trunk from 22% to 100% of trunk width (all
subjects in black; average in white).
Females and males showed similar results (Table 6-1). The fixed optimal ROI
was 167.6 mm in females and 169.3 mm in males. A trunk width percentage of 64% was
found for females and 62% for males. For multiple of vertebral body width, both females
and males had optimal ROIs of four times the vertebral body width.
6.4 Discussion
In this study, we have calculated the difference in soft-tissue density between the
two sub-regions in the DXA ROI using data from the entire trunk in QCT L3 scans, and
determined optimal window widths for DXA’s AP lumbar spine scan using three
68
methods: fixed distance, percentage based on trunk width, and multiple of vertebral body
width. We chose these methods since their measures can be easily obtained by DXA.
By analyzing all possible ROI window widths, we can observe the trends of soft-
tissue distribution, including the distribution from the ROI currently employed by the
Hologic DXA scanner software. The standard width of 105 mm yielded a difference in
soft-tissue density of 7.5 mg/cm
3
(higher in the bone region), which violates DXA’s
fundamental assumption of a homogeneous soft-tissue region surrounding the bone and
causes a general underestimation in DXA bone measures. In contrast, we found the
smallest difference (0.5 mg/cm
3
) between soft-tissue regions using an ROI width of
169.3 mm. The difference approached zero as the trunk width increased, but the width
was limited by the subject with the narrowest trunk width.
The patient-specific methods were both able to find an optimal ROI in which the
soft-tissue densities in the two regions were equal or approximately equal (63% of trunk
width and 4x the width of the vertebral body). It is likely that the central region
contained within 63% of the trunk width represents the same anatomical regions across
subjects and longitudinally in the same subject more consistently than with fixed width
methods, since a fixed width does not account for growth or different subject sizes.
Using a multiple of the vertebral body width, we found an optimal ROI that ensures the
same proportion of soft-tissue is measured in both scan regions in all subjects.
Despite these optimal ROI widths, these patient-specific methods may still be
subject to growth-related limitations. The anatomy of soft-tissue contained within 63%
of the trunk width can change if adipose and lean tissues are not distributed evenly
69
throughout the trunk. Similarly, using a multiple of vertebral body width for an optimal
window may not yield the same soft-tissue region over time if the spine does not grow
proportionally with changes in soft-tissues.
In a comparison of all three optimal ROIs with the original DXA ROI, the optimal
methods shifted the average difference in soft-tissue density to approximately zero, but
did not reduce the range of differences. The method using a percentage of trunk width
had the smallest range of difference in soft-tissue density (without outliers) and was
centered about zero (Figure 6-4). However, the standard deviations of soft-tissue density
differences using percentages from 22% to 100% of trunk width are all approximately the
same (Figure 6-5). In the other optimal ROIs, the ranges were similar as were the
standard deviations of soft-tissue density difference (4.6 – 5.1 mg/cm
3
) (Figure 6-4).
These results were comparable in the female and male subgroups and suggest that
cumulative soft-tissue distribution in optimal ROIs is not gender-specific. Overall, bone
measures derived from patient-specific ROIs did not reduce the range of error, even
though the average error was shifted to zero. The range of error may be an effect of
inherent variability among subjects.
Nonetheless, it is important to note, particularly regarding pediatric DXA bone
measures, that using a conventional fixed window width of 105 mm underestimates bone
density and accounts for different amounts and proportions of soft-tissue during growth.
This may complicate interpretations of DXA measures among different subjects or even
within the same subject during growth, since errors in aBMD would be inconsistent. A
patient-specific ROI may reduce these errors and shift the overall aBMD error to zero.
70
This study was limited by using a 10 mm cross-section of the trunk through L3
with QCT. Soft-tissue surrounding the bone at this slice may not represent the tissue
along the length of the spine. Further studies should use multi-slice scans of the entire
vertebra which would allow for a complete analysis of the surrounding soft-tissue
distribution in the DXA scan region. Unfortunately the findings of this study could not
be validated in actual DXA scans since the width of the scan region in our DXA machine
cannot be altered beyond 114 mm (most optimal ROIs of the subjects in this study
exceeded 114 mm). Further research is necessary to clarify whether patient-specific
ROIs can reduce the amount of soft-tissue error in DXA measures. It may also be
interesting to perform longitudinal analyses. The effect of a patient-specific ROI may be
more robust over time.
In summary, we have analyzed the soft-tissue content across the width of the
trunk in a 10 mm cross-section through L3. Differences in cumulative soft-tissue density
in the DXA soft-tissue region and bone region averaged zero using the three ROI
techniques: fixed distance, percentage of trunk width, and multiple of vertebral body
width. Each of the ROIs also showed a similar range and standard deviation in soft-tissue
differences that was similar to the original fixed ROI.
71
Chapter 7: Impact of the vertebral posterior elements in DXA
Chapters 5 and 6 discussed soft-tissue inhomogeneity in the dual energy x-ray
absorptiometry (DXA) scan region and proposed solutions to reduce the associated
errors. This chapter evaluates the impact of the vertebral posterior elements contained in
DXA anterior-posterior (AP) lumbar spine scans.
Bone strength in the vertebra is associated with the vertebral body, including the
vertebral cortex and cancellous bone within. The posterior elements do not play a
significant role in vertebral compressive or crush fractures, but are included in DXA
scans. Since the posterior elements are composed of cortical bone, their inclusion greatly
increases DXA bone measures. As a result, DXA measures may misrepresent bone
strength or resistance to fracture. This important limitation of DXA has not been
previously studied in vivo.
This study uses quantitative computed tomography (QCT) to measure the
contribution of the posterior elements. Their contribution is analyzed before and after
puberty and by gender. DXA bone measures are also compared with QCT measures.
Based on these analyses, the meaning and interpretation of DXA measures are clarified,
with regard to the posterior elements.
7.1 Background
Dual energy x-ray absorptiometry (DXA) is the most commonly used method of
assessing bone density in a clinical setting. Advantages of DXA include its low
radiation, low cost, fast scan time, and precision (Blake & Fogelman, 2007). However,
because DXA is a projection technique, its accuracy is limited by the inability to quantify
72
bone volume (Antonacci, Hanson, & Heggeness, 1996), by inhomogeneity of the extra-
osseous tissues, and by inclusion of the cortical-rich, non-weight-bearing vertebral
posterior elements in anterior-posterior (AP) spine scans (Myers et al., 1994; Zmuda,
Cauley, Glynn, & Finkelstein, 2000). These factors may be especially confounding in
studies of growing children (Binkovitz, Henwood, & Sparke, 2008; Gordon et al., 2008)
and those undergoing dynamic changes in bone size and morphology (Leonard, Shults, &
Zemel, 2006; Molgaard, Thomsen, & Michaelsen, 1999).
In DXA, x-rays pass through the body, and a cumulative attenuation is measured.
Therefore, in the DXA bone region, the measured attenuation represents a combination of
all soft-tissue and bone in the path of the beams. The attenuation values are used to
generate a two-dimensional projection image and to calculate areal bone mineral density
(aBMD, g/cm
2
). Commercial DXA scanners also report the projected bone area and bone
mineral content (BMC, g).
Quantitative computed tomography (QCT) is an established and accurate
alternative densitometry method. In contrast to DXA’s projection technique, QCT data
are reconstructed as three-dimensional voxels represented by a linear attenuation
coefficient, which can be converted into volumetric density. Further, QCT images can be
separated into different types of tissue, such as lean and adipose, as well as cortical and
cancellous bone. Volumetric bone mineral density (vBMD, mg/cm
3
) and BMC are
conventionally measured in a cancellous region or the isolated vertebral body, since these
are assumed to be the regions most strongly related to compressive fractures.
73
DXA bone measures are only moderately correlated with bone measures from
QCT (Wren et al., 2005a; Wren, Liu, Pitukcheewanont, & Gilsanz, 2005b). As a result, it
is not uncommon for a subject to have conflicting bone measures or Z-scores from DXA
and QCT (Wren et al., 2005b). Some disagreement between DXA and QCT outcomes
might be expected since AP DXA measures include the posterior elements, while QCT
measures generally exclude the posterior elements. Other differences in technique and
the regions measured may also affect the accuracy and comparison of DXA and QCT
vertebral measures, such as the assumption of a homogeneous extra-osseous soft-tissue
region (Formica et al., 1995; Hangartner & Johnston, 1990; Tothill & Pye, 1992) in DXA
measures and variations in marrow fat composition (Kuiper, van Kuijk, Grashuis,
Ederveen, & Schutte, 1996; Mazess, 1983; Mirsky & Einhorn, 1998) in both measures.
The effect of the vertebral posterior elements, as well as aortic calcifications, can
be eliminated using lateral DXA scans. However, this method is less commonly used
since lateral projections of the spine may include the ribs, particularly in the upper
vertebrae (T1-L2). In addition, lateral scans are still subject to DXA’s other
shortcomings, including traversing a larger amount of soft-tissue in the medial-lateral
direction. It is not clear whether the ability to avoid the posterior elements outweighs
these limitations; studies comparing the efficacy of lateral and AP DXA have reported
conflicting conclusions (Bjarnason, Hassager, & Christiansen, 1994; Bjarnason,
Hassager, Svendsen, Stang, & Christiansen, 1996; Blake, Herd, & Fogelman, 1996;
Finkelstein et al., 1994; Guglielmi, Grimston, Fischer, & Pacifici, 1994; Maricic, Tesser,
Chen, Lund, & Gluck, 1998; Sran et al., 2005). Currently, lateral DXA scans are used for
74
monitoring patients with vertebral deformities (Lewiecki et al., 2008) and detecting
abdominal aortic calcifications (Schousboe, Wilson, & Kiel, 2006), but not for clinical
measurements of bone density.
The goal of this study is to use QCT to quantify the impact of the posterior
elements in DXA AP spine scans. The amount of bone in the vertebra with and without
the posterior elements will be evaluated with QCT, and the effects of different analysis
regions will be assessed. We hypothesize that there will be good agreement between
QCT and DXA bone measures when the modalities measure the same bone region
(including the posterior elements) and that greater disparities will arise when typical QCT
measures which exclude the posterior elements are considered.
7.2 Methods
7.2.1 Clinical study
DXA and QCT scans of the lumbar vertebrae were performed in 574 subjects
(294 female, 280 male), age 6 – 25 yr (15.5 ± 3.6). All subjects were healthy, and
prospective participants were excluded if they had any recent history of serious disorders
or were taking medications that could affect bone, muscle, or growth. The Institutional
Review Board for clinical investigations
at Childrens Hospital Los Angeles approved the
protocols for this study, and written informed consent was obtained from
all parents
and/or participants (for minors, parents provided consent and participants provided
assent). The quantitative CT protocol
was designed to keep radiation exposure to a level
roughly equivalent
to the exposure during a round-trip airplane flight across North
America (Cann, 1991; Kalender, 1992), making its use in healthy subjects possible.
75
Figure 7-1: Sample images from the same subject with QCT (left) and DXA (right). The QCT scan
location and thickness (10 mm) are shown in a shaded region on the L3 DXA scan.
For each subject, the DXA and QCT scans were done on the same day by a single
radiology technologist. A DXA AP scan was performed on a Hologic Delphi W DXA
scanner (Bedford, MA) using the Fast Scan protocol (Figure 7-1, right), and a transverse
10 mm cross-section through the mid-section of L3 was obtained with QCT using a
General Electric LightSpeed QC/i scanner (Waukesha, WI) (Figure 7-1, left). The
specific techniques employed have been described previously (Gilsanz et al., 1988; Wren
et al., 2007).
7.2.2 DXA analysis
The whole lumbar spine was scanned using four vertebral sub-regions (L1-L4).
Two regions of interest (ROI) were defined for L3 using the Hologic QDR Software
v11.2. The width of both ROIs was set at the default width of 116 lines (or 105 mm).
The first ROI included the entire L3 vertebra. The second ROI adjusted the L3 sub-
region height to 10 mm centered about the mid-section of the vertebra, which
76
corresponds to the QCT slice (Figure 7-1). Positioning of the ROIs was performed
manually by the same technologist for all subjects. The Hologic software calculates
aBMD, BMC, and projected area for each ROI (entire L3 and QCT region) according to
standard DXA calculations.
7.2.3 QCT analysis
QCT data from L3 were analyzed using custom software developed in MATLAB
2006b (MathWorks Inc., Natick, MA). An algorithm was designed to automatically
extract the vertebral shape and to separate the vertebral body from the posterior elements.
Reported measures include vBMD and BMC of the cancellous bone region, the vertebral
body excluding the posterior elements, and the vertebral body including the posterior
elements (Figure 7-2).
Figure 7-2: Regions of interest for the CT images. Left to right: cancellous bone region; isolated vertebral
body; vertebral body including the posterior elements.
The vertebra is first identified by thresholding the image using the peak bone
signal. Since there is high contrast between bone and the surrounding soft-tissue,
contours of the vertebra are easily extracted via edge detection. Efforts were taken to
extract only the regions included in the DXA bone area, avoiding lateral aspects of the
transverse processes. Thus, DXA’s bone region was defined within two anterior-
77
posterior lines through the lateral edges of the vertebral body, which are found by
extending a tangent from the anterior edge of the vertebral foramen to the lateral edges of
the vertebra. The same tangent line through the foramen serves to separate the vertebral
body from the posterior elements, which include the spinous process, superior/inferior
articular processes, and pedicels (Figure 7-2).
The cross-sectional area (CSA) of each ROI was calculated by taking the integral
of the region’s contour. vBMD was determined by averaging the Hounsfield Units (HU)
contained in the CSA and converting HU to hydroxyapatite equivalent density using a
mineral phantom simultaneously imaged with the subject. BMC was derived by
multiplying vBMD by the product of CSA and slice thickness (10 mm). The contribution
of the posterior elements to bone mass was calculated by dividing the posterior element
BMC by the total BMC (vertebral body plus posterior elements).
7.2.4 Statistical analysis
Statistical analysis was performed using MATLAB 2006b (MathWorks Inc.,
Natick, MA). Pearson correlation coefficients were calculated to determine the
relationship between the DXA and QCT measures, including both BMD and BMC, and
between posterior element contribution and age. For the latter analysis, separate analyses
were performed for mature and immature age groups. Since Tanner stage was not
recorded for all subjects, subjects were assumed to be sexually mature at age 16 for
females and age 17 for males. The Student’s t-test was used to compare the posterior
element contribution between females and males.
78
7.3 Results
The posterior elements accounted for 51.4 ± 4.2% (38.8% – 65.0%) of the total
bone content in the DXA scan region. There was a significant difference between
females and males (females: 52.8 ± 3.9%, males: 49.9 ± 4.0%; p < 0.001). Additionally,
the proportion of total BMC from the posterior elements increased with age for both
younger females and males (p < 0.001), but did not change after age 16 in females and
age 17 in males (p > 0.1) (Figure 7-3).
Figure 7-3: Posterior element contribution as a function of age.
Conventional measures of DXA aBMD (entire L3) and QCT vBMD (cancellous
region) correlated only moderately (R = 0.66) (Figure 7-4, Table 7-1). This trend was the
same in both the females (R = 0.67) and males (R = 0.65). The correlation improved for
QCT vBMD of the vertebral body, which includes the vertebral body’s cortical shell
(R = 0.77). The correlation improved further (R = 0.83) for QCT vBMD of the entire
vertebra (including the posterior elements, but not the transverse processes). Similar
results were observed when the DXA scan region was adjusted to match the 10 mm QCT
scan region, with comparable or slightly higher correlation coefficients.
79
Figure 7-4: Comparisons of DXA and QCT measures.
80
Pearson R correlation
DXA QCT
Total L3 10 mm Cancellous
Vertebral
body
Total
vertebra
Total (n = 574)
DXA
Total L3 0.94 0.79 0.87 0.93
10 mm 0.92 0.80 0.87 0.93
QCT
Cancellous 0.66 0.68 0.94 0.86
Vertebral
body
0.77 0.78 0.96 0.95
Total
vertebra
0.83 0.84 0.82 0.91
Females (n = 294)
DXA
Total L3 0.95 0.77 0.87 0.93
10 mm 0.93 0.80 0.89 0.93
QCT
Cancellous 0.67 0.66 0.91 0.83
Vertebral
body
0.79 0.78 0.95 0.94
Total
vertebra
0.85 0.85 0.79 0.90
Males (n = 280)
DXA
Total L3 0.93 0.81 0.89 0.94
10 mm 0.92 0.84 0.89 0.93
QCT
Cancellous 0.65 0.71 0.94 0.89
Vertebral
body
0.74 0.79 0.96 0.95
Total
vertebra
0.80 0.86 0.86 0.93
Table 7-1: Correlations between DXA/QCT BMD (underlined) and BMC (italicized).
81
Higher correlation coefficients, but similar patterns, were observed when
comparing BMC between DXA and QCT (Figure 7-4). The correlation progressively
increased as QCT measures moved from the cancellous region (R = 0.79) to the vertebral
body (R = 0.87) to the entire vertebra (R = 0.93) (Table 7-1). Correlations also increased
or did not change significantly when the 10 mm DXA region was used.
7.4 Discussion
We found that the posterior elements contributed approximately half of the total
bone content in the vertebra. Others have found similar results in vitro using ash weight
analysis (Nottestad, Baumel, Kimmel, Recker, & Heaney, 1987). Nottestad et al. found
that approximately half of the mineral of L3 is in the vertebral body (43% for females and
51% for males) and that of the bone within the L3 vertebral body, trabecular bone
accounts for less than half (39% for females, 27% for males). The results in this report
corroborate those previous studies in adult cadavers and extend their conclusions to
children. Although females had a slightly higher proportion of bone mass in the posterior
elements than males, the variability of the posterior element contribution was small in
both sexes (standard deviations around 4%). In addition, the influence of the posterior
elements stabilizes after puberty (Figure 7-3). Therefore, adjustments to remove or avoid
the posterior elements, such as with lateral DXA, may not be necessary for DXA bone
measures in young, healthy subjects after puberty.
In contrast, caution should be exercised when interpreting DXA aBMD values in
growing children since growth of the vertebrae is disproportional. Before age 17 for
females and age 16 for males, the proportion of bone mass in the posterior elements
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appears to increase with age. This may contribute to increasing DXA aBMD values even
though cancellous density in the vertebral body remains relatively constant in prepubertal
children (Gilsanz et al., 1988).
Our results comparing DXA and QCT are consistent with other studies which
have found a moderate correlation between DXA aBMD and QCT vBMD (Wren et al.,
2005a, 2005b). Previous reports comparing DXA and QCT have acknowledged
mismatched bone regions and other sources of error (Ebbesen, Thomsen, Beck-Nielsen,
Nepper-Rasmussen, & Mosekilde, 1998; Wren et al., 2007; Wren et al., 2005a, 2005b) as
contributors to discrepancies between DXA and QCT measures, but have not focused on
the impact of the posterior elements in DXA measures. We found that much of the
discrepancy between the two modalities is due to the exclusion of the posterior elements
in QCT analyses of the vertebra. When the posterior elements were included, we
observed a stronger relationship between DXA and QCT measurements (vertebral body
only: R = 0.67; vertebral body with posterior elements: R = 0.83).
Agreement between DXA and QCT bone measures was further improved by
using the same unit of measure. Lack of the dimension along the path of the beam in
DXA scans can cause size bias, an effect that reports different areal densities in bones of
different sizes despite having the same volumetric density (Carter et al., 1992). This
error can be prominent in genders studies, since males tend to have larger vertebrae than
females (Gilsanz et al., 1994; Mosekilde & Mosekilde, 1990), and in pediatric studies
since bone grows non-uniformly. While it is possible to convert areal density to
volumetric density via geometric or anthropometric scaling (Carter et al., 1992), this may
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also introduce another source of error, particularly in children, whose bones grow
disproportionately.
Instead, we converted both DXA aBMD and QCT vBMD to the same quantity,
BMC (grams), eliminating the confounding effect of comparing areal density with
volumetric density and allowing for a clear understanding of the impact of the posterior
elements. The correlation between DXA BMC and QCT BMC increased when the
posterior elements were included (R = 0.87 to R = 0.93). This affirms the analysis based
on density, which also showed a large increase in correlation with the inclusion of the
posterior elements. The higher correlation between DXA and QCT using BMC
corroborates other studies (Leonard et al., 2004; Wren et al., 2005a) that have suggested
DXA BMC as a more reliable measure than DXA aBMD. We agree that BMC
normalized for stature or body mass may be more informative than aBMD in evaluating
skeletal status. Whole body BMC may also prove useful since it measures a much larger
region. Ultimately, a comparison of bone measures in a prospective study of fracture risk
is needed to identify the most clinically useful measures.
A limitation of this study is that the QCT measurement covered only a 10 mm
section through the middle of L3. The vertebral posterior elements are highly irregular
structures, and the morphology may be different in other vertebrae (Scoles, Linton,
Latimer, Levy, & Digiovanni, 1988). The impact of the posterior elements observed in
the 10 mm midsection of L3 studied may not apply to the ends of L3 or to other posterior
elements along the spine. While it is possible to evaluate entire vertebrae with multi-slice
QCT scans, the additional radiation exposure is not recommended.
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In summary, the contribution of the posterior elements increases with age through
the end of puberty, but is relatively consistent in older adolescents and young adults.
Therefore, the posterior elements have a negligible effect on DXA measures in these
older subjects, but further study is needed to reveal the extent of their contribution in
growing populations. Adding the vertebral posterior elements to QCT measures of the
vertebral body resulted in a stronger relationship with DXA measures, especially for
BMC. This supports DXA as a good measure of total bone in older adolescents and
young adults.
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Chapter 8: Automated bone cross-section extraction with MRI
This chapter explores the use of magnetic resonance imaging (MRI) to measure
geometric parameters of long bones, such as in the femur or tibia. A program designed to
process MRI images is described and its outcomes are compared with equivalent
measures from quantitative computed tomography (QCT).
MRI is not traditionally used to image bone due to low contrast from the lack of
water (and therefore spin detection of hydrogen protons). However, MRI’s non-ionizing
technique is a major advantage over QCT. In this chapter, the possibility of using MRI to
characterize bone geometry that is traditionally measured with QCT is investigated.
There have been several studies that use MRI to examine bone which have
required manual tracing or semi-automatic methods. These techniques are prone to
operator error and may not offer better reproducibility than QCT techniques. This unique
study introduces an entirely automated algorithm that detects the contours of bone and
calculates the geometric parameters.
8.1 Background
Principles from mechanical and civil engineering have often been used to quantify
bone strength (Bartel et al., 2006). By applying beam theory to a bone’s cross-sectional
geometry, parameters can be derived that provide insight to a bone’s strength, its
resistance to stress, and the implications of changes in bone morphology.
Traditionally, cross-sectional images of bone are obtained with QCT or pQCT.
Bone voxels appear bright in contrast with the surrounding soft-tissue, and so extraction
of bone geometry is easily performed with edge or contour detection. Third-party and
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custom software can quickly analyze bone geometry and report useful measures.
However, a significant disadvantage of QCT scans is the high dose of radiation (Brenner
& Hall, 2007), particularly in multi-slice and periodic studies.
In contrast, MRI does not use ionizing radiation. Unfortunately, there is generally
low bone tissue contrast in MRI scans, even in bone optimized pulse sequences (Figure
8-1). Contours of bone are not clearly delineated, and therefore manual tracing is
required. The process is tedious and error prone, since reproducibility depends on the
operator’s ability to trace contours against an ambiguous contrast of bone and lean tissue.
Nonetheless, there is a growing interest in non-ionizing methods (Hong et al., 2000;
Schmid & Magnenat-Thalmann, 2008), especially in patients requiring frequent scans. It
would be advantageous to develop an efficient and reliable technique for measuring
cross-sectional properties of bone in MRI.
Figure 8-1: Low bone contrast in MRI image.
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The goal of this study was to create an automated technique that detects bone
contours in transverse cross-sections of long bones and calculates cross-sectional
geometry and structural properties, including area and moments of inertia, from MRI
scans. Additionally, a graphical user interface implementing these calculations would
minimize analysis time. The extracted data was then compared and validated with
equivalent QCT cross-sections and software.
8.2 Methods
8.2.1 Data acquisition
A small pilot group of subjects recruited from hospital staff (n = 7) were scanned
with both QCT (General Electric LightSpeed QX/i, Waukesha, WI) and MRI (1.5T
General Electric LX/CVi, Milwaukee, WI) on the same day. QCT parameters were
80 kVp, 70 mA, and 2 s; MRI used a T1 weighted pulse sequence. A 10 mm slice was
measured with QCT, and a 5 mm slice was measured with MRI. In both, efforts were
taken to position the scan at the mid-femur. MRI was used to image one femur at a time,
whereas QCT imaged both femurs simultaneously. The resolution for both was
approximately the same (QCT: 0.8789 or 0.9375 cm/pixel, MRI: 0.8594 cm/pixel).
A graphical user interface, MRI Viewer, implementing the tissue segmentation
algorithm was coded in MATLAB 2006b (MathWorks Inc., Natick, MA) (Appendix C).
The program also calculates the cross-sectional properties using equations found in
Appendix A. The program requires an operator to select a file for analysis and to visually
approve the automatic image segmentation.
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8.2.2 Image segmentation
The goal of image segmentation in MRI was to differentiate tissues and extract
meaningful measures. Generally, the image contrast was adjusted to highlight and isolate
tissue features. The contrast thresholds were found by applying the following algorithm.
The program detects and crops the region of interest, which contains only bone
and soft-tissue. A cropped image is preferred since the entire cross-sectional image may
contain artifacts. Also, by decreasing the image dimensions, computation time is
decreased while improving the likelihood of successful bone contour extraction.
This is done by first isolating the femoral cross-section and removing the
surrounding air. An image histogram is generated and a peak detection function finds the
most probable peaks for adipose and lean tissue (Figure 8-2). The peak detection process
involves convolving the image histogram with a unit step function, normalizing,
computing the extended-maxima transform, and fitting Gaussian curves to the maxima.
The image contrast is thresholded such that all voxels with intensities greater than the
lean tissue peak are set to one, while voxels with lesser intensities remain dampened (less
than one) (Figure 8-3). This highlights bone as dark voxels, with some faint remnants of
lean tissue.
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Figure 8-2: Image histogram showing detected peaks of bone, lean (muscle), and adipose (fat) tissues from
a sampled region of interest.
Figure 8-3: Isolated cortical bone from femur: original contrast (left) and new contrast (right).
90
A median filter was applied to the image to remove pixel noise, and bone
contours were then extracted via the contour function from the Image Processing Toolbox
Version 5.3 (MathWorks Inc., Natick, MA). The contour algorithm performs a basic
linear interpolation of neighboring points on a mesh to connect line segments between
likely candidates (Watson, 1992). This method was preferred over other edge detection
algorithms since it was computationally efficient and able to detect contours reliably.
Ideally, only two contours should be discovered, that of the periosteum and
endosteum. However, there may be other contours detected, such as bone lesions and
artifacts. In the event of three or more contours, the algorithm takes into account the size
and location of the contour and determines which are most likely to be from bone. For
example, the endosteal contour must be within the periosteum contour, and contours of
the femur must be larger than the tibia. If an incorrect contour is selected, the user may
manually select the correct contour. It is also possible that the cortex is so thin that it
appears discontinuous and results in broken contours. In this case, the contours cannot be
extracted due to the lack of resolution to discern a measurable thickness.
To extract adipose and lean tissue data, a sample of soft-tissue surrounding the
extracted bone is measured and a histogram generated. The program was designed to
sample an area around the bone to measure a comparable amount of tissue exterior to the
bone (lean tissue) and interior to the bone (adipose tissue). By doing so, both lean and
adipose tissue peaks should be detected in an image histogram using the previously
described algorithm. Occasionally, the magnitude of the adipose tissue peak is too small
and avoids maxima detection. To account for this, the midpoint between the lean tissue
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peak and the missing adipose peak is estimated by adding eight times the distance
between the inflection point of the lean tissue Gaussian curve to the lean tissue peak.
With the midpoint between the peaks of the two soft-tissues (Figure 8-2), their respective
areal regions in the entire femoral cross-section can be accounted for. All voxels with
intensity less than the soft-tissue midpoint are defined as lean tissue (not including bone
voxels), while all voxels with intensity greater than the soft-tissue midpoint are defined as
adipose tissue.
8.2.3 Cross-sectional properties
Using the bone contours, cross-sectional properties can be calculated.
Conventionally, these measures are expressed as integrals. However, a summation was
used since the contours were defined using vertices. The equations for these parameters
can be found in Appendix A.
The following parameters from cross-sections of long bones were extracted: area
(cross-sectional, intramedullary canal, cortical bone, lean tissue, adipose tissue, mm
2
),
circumference (periosteal, endosteal, mm), cortex thickness (max, min, mean, mm),
centroid, distance from edge to centroid (max, min, mean, mm), product moment of area
(mm
4
), principal moment (max, min, mm
4
), polar moment (mm
4
), and section moduli
(max, min, polar, mm
3
).
Cortical bone area is a basic measure that describes the quantity of bone in a
given cross-section. Area is also related to compression or tension in the basic uniaxial
stress equation:
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A
F
= σ Equation 8-1
where σ is axial stress, F is the load applied (N), and A is area (m
2
). This equation
describes the bone’s resistance to axial stress.
Second moment of area, commonly known as area moment, is related to the
bone’s resistance to bending. The equation for bending stress is:
x
I
My
= σ Equation 8-2
where σ is bending stress, M is the moment about the neutral axis (Nm), y is the
perpendicular distance (m) from the measurement site to the neutral axis, and I
x
is the
area moment about the neutral axis (mm
4
). This formula is valid for simple and
symmetrical bending, and should not be applied to asymmetrical cases such as cross-
sections of bone. It is possible however to transform cortical bone’s cross-sectional
geometry into concentric ellipses, which are symmetrical and can be applied to classical
bending. In asymmetric cases, the following formula is used:
y
I I I
I M I M
x
I I I
I M I M
xy y x
xy y y x
xy y x
xy x x y
z 2 2
) ( ) (
−
−
−
−
−
− = σ Equation 8-3
where σ
z
is bending stress about the z-axis, M is the bending moment about the centroid
axes (Nm), I is the second moment of area about the axes (mm
4
), I
xy
is the product
moment of area (mm
4
), and x and y correspond to the point on the cross-section where the
stress is measured.
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Polar moment of inertia is a measure that characterizes the cross-section’s ability
to resist torsion. The larger the polar moment, the more resistant is the object against a
given torque:
J
Tr
= σ Equation 8-4
where σ is shear stress, T is torque (Nm), r is the distance from the centroid to the
measurement site (m), and J is polar moment (mm
4
).
Moments are useful for predicting fracture risk, particularly under the influence of
bending and/or torsion. Moments also can be used to calculate section modulus, which
describes the cross-section’s flexural strength in bending. Section modulus is calculated
by taking the ratio of the second moment of area to the maximum distance from the
measuring point to the centroid.
Geometric parameters derived from imaged cross-sections of bone shed valuable
insight on resistance to stress. They describe the bone’s strength in a way that cannot be
evaluated by superficial observations and would otherwise require mechanical testing.
These values are only an estimation of the long bone’s strength since cross-sections of
bone are asymmetrical and not uniform along the length. Precise stress equations
describing whole bones require more scans and computationally intensive models
(Eswaran et al., 2007). Nevertheless, these are well understood cross-sectional
parameters and can be used to describe cortical bone strength.
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8.2.4 Validation with QCT
For comparison and validation, established methods were used to evaluate QCT
images (CT Viewer) for the same parameters calculated in the MRI program including
bone, lean and adipose tissue area, as well as moments of inertia for bone geometry
(maximum principal, minimum principal, and polar). Pearson’s correlation coefficients
were calculated for the measurements by QCT and MRI data for both left and right limbs
(n = 14).
8.3 Results
The MRI program successfully extracted femoral contours in all seven subjects in
both legs per subject (Figure 8-4). The program calculated geometric parameters
including the conventional measurements of bone and soft-tissue area, and moments of
inertia for bone (maximum principal, minimum principal, and polar).
Figure 8-4: Contours from femoral mid-shaft (left); segmented into adipose and lean tissues (right).
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The reported measures from MRI Viewer were highly correlated with analogous
measurements from QCT (Table 8-1), except intramedullary canal area, lean tissue area,
endosteal circumference, and minimum cortical thickness, which were moderately
correlated.
R p value
Cross-sectional area (mm
2
) 0.99 p < 0.001
Intramedullary canal area (mm
2
) 0.74 p = 0.002
Cortical bone area (mm
2
) 0.95 p < 0.001
Lean tissue area (mm
2
) 0.72 p = 0.004
Periosteal circumference (mm) 0.94 p < 0.001
Endosteal circumference (mm) 0.77 p = 0.001
Adipose tissue area (mm
2
) 0.92 p < 0.001
Edge to centroid (max, mm) 0.93 p < 0.001
Edge to centroid (min, mm) 0.95 p < 0.001
Cortical thickness (max, mm) 0.88 p < 0.001
Cortical thickness (min, mm) 0.70 p = 0.006
Cortical thickness (mean, mm) 0.81 p = 0.004
Product moment of area (mm
4
) 0.80 p = 0.005
Principal moment (max, mm
4
) 0.98 p < 0.001
Principal moment (min, mm
4
) 0.99 p < 0.001
Polar moment (mm
4
) 0.99 p < 0.001
Section modulus (max, mm
3
) 0.98 p < 0.001
Section modulus (min, mm
3
) 0.98 p < 0.001
Section modulus (polar, mm
3
) 0.99 p < 0.001
Table 8-1: Regression coefficients of area, moments of inertia, and other geometric parameters comparing
QCT and MRI measurements.
MRI area measures were generally less than QCT data: 4% for cross-sectional
area, 21% for cortical bone area, 26% for lean tissue area, and 9% for adipose tissue area.
The differences were less when comparing areas as percentages of the total area
(sum of bone, muscle, and adipose tissues). MRI data was greater than QCT data in
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femur cross-sectional area (0.46%) and adipose tissue (4.50%); QCT was greater than
MRI data in cortical bone area (0.05%) and lean tissue (4.96%).
8.4 Discussion
The MRI Viewer program was able to extract bone strength measures in all
subjects. Investigators have previously evaluated properties of the femoral mid-shaft
using tracing (Hogler, Blimkie, Cowell, Kemp, Briody, Wiebe, Farpour-Lambert,
Duncan, & Woodhead, 2003), deformable models (Schmid & Magnenat-Thalmann,
2008), and semi-automatic algorithms (Modlesky, Kanoff, Johnson, Subramanian, &
Miller, 2008). The technique introduced in this study differs by being fully automatic.
Measurement errors, if any, would be consistent and not influenced by the operator.
The results indicate that the tissue segmentation algorithm and bone geometry
equations used in MRI Viewer generally reflect the bone measures reported by traditional
QCT analyses. Measures related to the endosteum, such as the circumference and canal
area were only moderately correlated. Secondary measures including adipose and lean
tissue area were also analyzed. Adipose tissue relationship between the two modalities
was strong, but lean tissue was not.
Although there is discrepancy between some measures, it is unclear which
modality is superior. QCT and DXA are fundamentally different. In QCT, image
contrast is based on the distribution of x-ray attenuations, whereas in MRI, image
contrast is based on proton NMR signal. As a result, tissue contrasts will be different,
even though they depict the same cross-section. Especially with MRI, interfaces between
tissue transitions may behave differently depending on the types of tissues. It is also
97
possible that the two scanners were not positioned at exactly the same anatomical
location. If the locations were inconsistent, the associated error may be negligible for
bone measures since cross-sections of the femur do not change dramatically along the
length. On the other hand, cross-sectional area of lean and adipose tissue vary
considerably along the length of the bone. These elastic tissues may change during
contraction, deform when placed in the coil, or between scans.
Geometric distortions in MRI may be a likely explanation for the differences with
QCT. The localization of the image depends on magnetic field intensities. Gradient field
non-linearity and magnetic field inhomogeneity can cause non-linear distortions in the
acquired image (Sumanaweera, Glover, Song, Adler, & Napel, 1994). In contrast, QCT
uses line-of-sight ray optics, which avoids significant distortions. Nonetheless, the
relative differences between the areal measurements are less than 5% for soft-tissues and
less than 1% for bone, which suggest that these variations are minimal. Further analysis
with a phantom in simultaneous MRI and QCT studies may lead to more precise
identification of any differences.
One of the limitations of this study is that the images were not acquired with the
same thickness. The QCT slice was twice as thick as the MRI slice, which may result in
errors due to volume averaging. This study was also limited by a low sample size.
With more subjects, differences, if any, may be more apparent. Nonetheless, the results
showed significant results.
Advances in MRI imaging have enabled bone analyses on a micron level in a
large volume, enabling a clear depiction of trabecular microarchitecture. This high
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resolution MRI (HR-MRI) technology reports measures similar to histomorphometric
studies that describe trabeculae, including trabecular number (Tb. N), trabecular
thickness (Tb. Th), trabecular spacing (Tb. Sp), and bone volume fraction (BV/TV or
bone volume over total volume), analogous to bone density (Majumdar et al., 1998).
Although promising, the cost and technique restricts HR-MRI to research purposes.
In summary, we were able to successfully extract cross-sections of the femur
automatically with MRI and assess bone geometry and strength. Bone measures reported
by the MRI analyses correlate with bone measures reported by QCT, but further study is
necessary before substituting QCT bone scans with MRI or using them interchangeably
in clinical settings.
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Chapter 9: Conclusions and future work
The goals of these studies were to improve methods of bone assessment in
children and adolescents by quantifying their fundamental limitations and minimizing
errors. Specifically, this thesis addressed some of the major assumptions and potential
inaccuracies of popular imaging modalities including peripheral quantitative computed
tomography’s (pQCT) lack of reproducibility due to metaphyseal density gradients and
dual energy x-ray absorptiometry’s (DXA) technical principles (soft-tissue based errors,
region of interest, and inclusion of the vertebral posterior elements). These problems can
significantly impact bone measures and may result in misrepresentations of skeletal
health. Changes in bone morphology and body composition can also drastically and
artificially skew bone measures, especially in children and adolescents. There is no
simple solution that corrects for these issues, but the studies presented in this dissertation
have isolated specific problems. Chapters 4 – 8 have introduced several optimizations to
minimize errors and new ways of assessing pediatric bone. Their conclusions are
summarized here along with possible future steps.
9.1 pQCT – Peripheral quantitative computed tomography
In Chapter 4, pQCT’s shortcoming of obtaining density measurements from a
gradient of cancellous bone from the appendicular skeleton was examined. Single slices
are prone to errors since cancellous bone density varies along the length of the
metaphysis. To understand the behavior of bone within the metaphysis, a semi-
automated technique was developed to evaluate the entire region of cancellous bone. It
was found that the density gradient within the metaphysis is unique for all subjects and
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changes over time. Density changed throughout the gradient on an average of 7 mg/cm
3
per 1 mm, which is also the precision error from positioning of the scan. To minimize
errors from offset scans, measures of the total density in the metaphysis were reported
including average density, length of metaphysis, and total cumulative density.
Additionally, we identified an optimal single slice containing an amount of cancellous
bone reflective of the average density at approximately 50% of the metaphysis length,
which was not as effective over time.
This study has highlighted a significant limitation of pQCT scans using a single
slice. Previous studies using a single slice protocol based on a percentage of tibial length
could not be validated since tibia length data was not collected in our subjects.
Nevertheless, it is important for investigators to be aware of the behavior of metaphyseal
density gradients and minimize positioning precision error.
It is possible that the only way to avoid this error is to extract cancellous data
from the entire metaphysis. However, more research is necessary to understand the value
of using total bone measurements such as average density or total density (area under the
curve). These measures may or may not relate to skeletal health or fracture risk.
Additionally, this study only characterized the behavior of cancellous bone in cerebral
palsy subjects. It is not known if density gradients differ in normal populations. Future
studies should also measure the length of the tibia to evaluate current pQCT protocols
based on tibial length. However, the likelihood of positioning errors, especially over
time, may negate the usefulness of any optimal slice based on tibial length.
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9.2 DXA – Dual energy x-ray absorptiometry
DXA has several confounding factors that limit its interpretability in pediatric
populations, including the assumption of soft-tissue homogeneity surrounding the bone
and the inclusion of the vertebral posterior elements. The soft-tissue content surrounding
the bone, specifically the proportion of adipose and lean tissue in the two DXA scan
regions, is assumed be homogeneous for accurate DXA measures. In Chapter 5, the error
due to inhomogeneity (11% difference in adipose tissue content) was quantified and a
correction equation based on trunk circumference was generated and validated in a
separate group of subjects. The average error was reduced with the equation to zero, but
the range of error remained the same. Additionally in Chapter 6, the possibility of
altering the DXA region of interest (ROI) was explored, such that the soft-tissue density
from the region lateral to the vertebra matches the soft-tissue density overlying and
underlying the vertebra. The results of this study show that a fixed ROI width of 169 mm
and patient-specific ROIs (63% of trunk width and 4x vertebral body width) shifted the
average error to zero. However these optimal ROIs did not offer a smaller range of error
than the default DXA ROI. Even though the corrections applied in Chapters 5 and 6 did
not reduce the range of errors, the error may remain consistent over time when using
patient specific methods. Lastly in Chapter 7, the impact of the vertebral posterior
elements was evaluated and determined to contribute to half of the total bone content,
which increases during growth and is relatively consistent in sexually mature subjects.
The inclusion of the posterior elements with the vertebral body in QCT showed a strong
relationship with DXA measures, supporting DXA as a good measure of total bone. We
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also found that BMC measures were the most related between DXA and QCT, rather than
aBMD (DXA) and vBMD (QCT).
DXA’s limitations have previously been identified, but have not been fully
characterized. These studies offer strong, but simplified analyses of apparent soft-tissue
content in the DXA scan region and proportion of bone mass from the vertebral posterior
elements. The main strength of these studies is the use of quantitative computed
tomography (QCT) data, which was acquired on the same day with the DXA data. We
were able to visualize and account for soft-tissue and bone in ways DXA could not.
Another strength of these studies was their large sample size. With 574 children, we
were able to easily detect trends with statistical significance. However, these studies
have only examined a 10 mm cross-section through L3. The surrounding soft-tissue and
the vertebral posterior elements are not uniform along the length of the spine and may
vary considerably. So although these studies compared DXA and QCT in the same bone
region, the results may not remain consistent throughout the spine.
Future work should aim to measure the entire vertebra and surrounding soft-tissue
region measured in DXA with QCT. These analyses would require more QCT cross-
sections along the spine, which will expose the subjects to more radiation. However,
exposure levels can be decreased without considerable sacrifice to resolution. There only
needs to be sufficient resolution to discern the major features of bone and soft-tissue.
With the entire DXA scan region available in three-dimensions (QCT data), the volume
of bone can be measured, including the complete contribution of the posterior elements.
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Complete vertebral volumes can also provide insight into the differences between
volumetric density and areal density. Essentially this enables a full simulation of DXA.
It may also be worthwhile to merge the different corrections and optimizations
described in this thesis and in other studies together. Theoretically and potentially, a
combination of a thorough set of corrections for each limitation will result in the most
accurate DXA measurement. Further, the effectiveness of these corrections in children
may be fully realized in longitudinal studies.
9.3 MRI – Magnetic resonance imaging
Chapter 8 presented an image processing technique that uses the image histogram
to detect tissue peaks and isolate bone contours. The algorithm was successful in
automatically extracting bone and calculating geometric properties. Comparisons with
equivalent QCT images showed an excellent relationship. This study suggests that MRI
is a possible alternative to conventional QCT scans which expose the subject to ionizing
radiation.
Since this was the first fully automated MRI bone feature extraction algorithm,
further study is warranted. Comparisons with existing MRI analysis software, including
semi-automatic programs and those requiring tracing could further validate the method
presented here. Also, different MRI pulse sequences may yield different results. A
survey of various sequences would lead to the most optimal protocol for bone feature
extraction. Use of a phantom may also correct for image distortions or susceptibilities of
the gradient. Lastly, this study only examined seven volunteers; a larger cohort in a
longitudinal study would test the robustness of the program.
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9.4 GUIs – Graphical user interfaces
All the data collected for the studies in this thesis were analyzed using custom
built graphical user interfaces. Screenshots and general walk-throughs of the GUIs can
be found in Appendix C. All programming was performed in MATLAB R2006b
(MathWorks Inc., Natick, MA). Stand-alone GUI applications were created using the
MATLAB Compiler Version 4.5 (MathWorks Inc., Natick, MA) and can be run on any
computer after a one time installation of MATLAB data library files. These GUIs were
created to assist in image processing, which is both time consuming and prone to error
when analyzed manually.
In all GUIs, the general goal was to automate the analyses as much as possible.
There is a basic file system which enables the operator to select the appropriate images,
instead of typing in file names in a command prompt. Then the image is displayed with
options and header information that is available on professional radiology software.
There is also an automatic phantom calibration, with manual options as a backup.
Various types of image processing techniques are then performed, depending on the
application. These include filtering, segmenting, edge detection, peak finding, and fitting
Gaussian curves to image histograms. The result of these analyses requires a quick visual
approval by the operator. If the automatic processing algorithm fails (usually due to
insufficient resolution), there are manual methods as well. The extracted data can then be
copied and pasted into a spreadsheet or automatically saved to a database for further
analysis. The entire process is simple enough for any operator to use given the proper
105
instructions, and the automated algorithms produce consistent results regardless of
operator.
A comparison of basic bone measurements from QCT data obtained from existing
software (RAD Version 1.80, © 1996 – 2002, Craig Schlaman) and the software
developed for this research showed an excellent correlation (R > 0.98 for femoral cortical
bone area, R > 0.96 for vertebral cancellous bone density; n = 250, p < 0.001). A
separate validation is recommended to confirm the accuracy of outcomes that are
exclusive to the studies described here. Many of these programs are in their first
versions. Future revisions may lead to more efficient algorithms and better features.
9.5 Concluding remarks
There is a growing interest in bone measures in children and adolescents. As new
technologies emerge, it is necessary to thoroughly investigate the reliability and
usefulness of their outcomes and achieve the most accurate and precise measures. To
this end, this dissertation has highlighted the limitations of bone imaging modalities and
contributed to the advancement of pediatric bone assessment by proposing corrections
and alternative measures. Investigators using pQCT and DXA in pediatric populations
should take note of the shortcomings and potential errors of the methodologies reported
here, and exercise caution when interpreting bone measures.
While care has been taken to validate these methods and optimizations, it is
important that they are continued and refined. Future studies may add to this body of
work or use it in combination with other optimizations to further improve pediatric bone
measures, and ultimately enhance the quality life for children and adolescents.
106
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118
Appendix A: Cross-sectional geometry formulas & calculations
∫
= dA y I
x
2
∫
= dA x I
y
2
∫
− = xydA I
xy
) 2 sin( ) 2 cos(
2 2
φ φ
xy
y x y x
x
I
I I I I
I +
−
+
+
= ′
) 2 sin( ) 2 cos(
2 2
φ φ
xy
y x y x
y
I
I I I I
I −
−
−
+
= ′
) 2 cos( ) 2 sin(
2
φ φ
xy
y x
xy
I
I I
I +
−
− = ′
y x
xy
I I
I
−
=
2
arctan
2
1
φ
2 2
min max
4 / ) ( 2 / ) ( ,
xy y x y x
I I I I I I I ′ + ′ − ′ + ′ + ′ =
∫
= dA r J
2
) (
2
a r CSMI × Σ =
max min, max,
min, max,
min, max,
r
I
S
polar
polar
=
max
2
/ ) (
r
ND CD a r
pSSI
× × Σ
=
where
I
i
= second moment of area about x or y axis
I
xy
= product moment of area
I′
i
= second moment of area about the centroid
I
max
, I
min
= second moment of area in principal directions
J = polar moment
r = distance from center of gravity to voxel
CSMI = cross-sectional moment of inertia (polar moment)
S = section modulus
pSSI = polar stress strain index, using discrete polar CSMI formula
a = area of a voxel
CD = measured cortical density
ND = normal cortical density (1200 mg/cm
3
)
119
Table A-1: Integral and summation equations for area and moments of inertia. Table courtesy of Dr. Joe Sommer.
120
Example summation:
∫
(2xy dx – x
2
dy) / 4 =
n
1 i=
Σ [ dy x dx xy 2
1 i
i
1 i
i
y
y
2
x
x
∫ ∫
+ +
− ] / 4
for polygonal sides use x = x
i
+ t Δx and y = y
i
+ t Δy over t = 0 to 1
where Δx = x
i+1
- x
i
and Δy = y
i+1
- y
i
=
n
1 i=
Σ [ dt x t x y dt y t y x t x x
i i i
∫ ∫
Δ + Δ − Δ + Δ + Δ
1
0
2
1
0
) ( ) )( ( 2 ] / 4
=
n
1 i=
Σ [ dt ) x t x x t 2 x ( y dt ) y x t ) x y y x ( t y x ( x 2
1
0
2 2
i
2
i
2
1
0
i i i i
∫ ∫
Δ + Δ + Δ − Δ Δ + Δ + Δ + Δ ] / 4
=
n
1 i=
Σ [
1
0 t
3 2 2
i
2
i
1
0 t
3 2
i i i i
) t x
3
1
t x x t x ( y ) t y x
3
1
t ) x y y x (
2
1
t y x ( x 2
= =
Δ + Δ + Δ − Δ Δ + Δ + Δ + Δ ] / 4
=
n
1 i=
Σ [ y x
3
1
x y x x y y x
3
2
x y x y x y x x 2
2
i
2
i
2
i i
2
i i
Δ Δ − Δ Δ − Δ − Δ Δ + Δ Δ + Δ + Δ ] / 4
=
n
1 i=
Σ [6Δx x
i
y
i
+ 3Δx
2
y
i
+ Δx
2
Δy - 3Δy x
i
2
] / 12
121
Appendix B: Derivation of DXA & soft-tissue error equations
DXA equation
The underlying basis of absorptiometry is the interaction of X-ray or gamma-ray
photons with material. The attenuation of a single energy through a homogenous
material can be represented by:
x
e I I
α −
=
0
(1)
where I
0
is the original intensity of the photon and I is the intensity after passing through
a material with linear attenuation coefficient α and distance x. Mass attenuation
coefficient μ is defined as linear attenuation normalized by volumetric density ρ.
Therefore, Equation 1 can be rewritten as:
x
e I I
μρ −
=
0
or
μσ −
= e I I
0
(2)
Areal density σ is the product of volumetric density and beam path length:
x Δ = ρ σ (3)
where Δx is the distance traversed by the photons in the material. Linear attenuation
coefficient μ is normalized by density ρ, which is known as the mass attenuation
coefficient. For simplicity, mass attenuation coefficient will use the symbol μ from now
on, and linear attenuation coefficient will not be used.
In human subjects, the contents traversed by photons are not homogenous and are
made up of many materials and combinations of materials. Therefore to accommodate
different materials, mass attenuation coefficient and areal density from Equation 2 is
expressed as the summation of all materials:
∑
=
=
−
N
i
i i
e I I
1
0
σ μ
(4)
where N represents the number of components in an heterogeneous material.
DXA makes the assumption that the body is composed of two materials: soft-
tissue and bone. Since there are two energies attenuated by the body, there are now two
paired equations with two tissue variables:
) (
0
b b s s
e I I
σ μ σ μ − −
= (5)
) (
0
b b s s
e I I
σ μ σ μ ′ − ′ −
′ = ′ (6)
122
where s represents soft-tissue and b represents bone. The prime symbol denotes values at
a higher photon energy. By combining the two equations, σ
b
can be isolated:
) / (
) / ln( ) / ln( ) / (
0 0
s s b b
s b
b
I I I I
μ μ μ μ
μ μ
σ
′ ′ −
− ′ ′ ′
= (7)
Equation 7 can be reduced by representing mass attenuation coefficients of soft-
tissue as a function of fat percentage of soft-tissue:
R
I I R I I R
b b
b
μ μ
σ
′ −
− ′ − − ′
=
) ln ln ( ) ln ln (
0 0
, where
s
s
R
μ
μ
′
= (8)
where R is the only unknown. Intensities are known though the X-ray detectors, as well
as standard mass attenuation coefficients of bone at different energies (Berger et al.,
2005; ICRU, 1989). To completely solve Equation 8, R is used from the soft-tissue
region, lateral to the bone, which is assumed to have the same composition as the soft-
tissue overlying and underlying the bone (Figure 5-1). Equation 8 is solved for on a line-
by-line basis, stacking saggital lines along the height of the vertebra. The result is a
projection image in the frontal plane similar to a standard x-ray (Figure 5-1).
Derivation of a soft-tissue error equation
To derive a soft-tissue error equation (Hangartner & Johnston, 1990), the
derivative of areal BMD (σ
b
) is taken with respect to R:
2
0 0 0
) (
)] ln ln ( ) ln ln [( ) )( ln (ln
R
I I R I I R R I I
R
b b
b b b
μ μ
μ μ μ σ
′ −
′ − ′ − − ′ + ′ − ′ − ′
=
∂
∂
(9)
Which reduces to:
R R
I I
R
b b
b b
b b
b
μ μ
μ σ
μ μ
σ
′ −
′
+
′ −
′ − ′
=
∂
∂
0
ln ln
, sub:
b b s s
I
I
I I σ μ σ μ ′ − ′ =
′
′
= ′ − ′
0
0
ln ln ln (10)
R R
b b
s s b
μ μ
σ μ σ
′ −
′ −
=
∂
∂
(11)
where ∂R is discretized to ΔR or R
soft-tissue region
– R
bone region
.
This error equation describes the change in aBMD, as a function of the difference
in the ratio of soft-tissue attenuation coefficient from DXA’s soft-tissue and bone
regions.
123
Appendix C: GUI documentation
This appendix documents the graphical user interfaces used in this thesis, tibiagui.m
(Chapter 4), fatgui.m (Chapter 5), fatgui2.m (Chapter 6), spinegui.m (Chapter 7), and
mriviewer.m (Chapter 8). For each GUI, a short description, a walkthrough, and
screenshots are provided. The source code is available upon request, which includes
custom functions called by the main GUI files that are not part of MATLAB.
Documentation for functions from the statistics, image processing, and optimization
toolboxes can be found online (www.mathworks.com), and are not included in the source
code. All programming was performed in MATLAB R2006b (MathWorks Inc., Natick,
MA). For more information, please contact: davidclee@alumni.usc.edu.
tibiagui.m
Description
Extracts a cylindrical core of cancellous bone from the metaphysis of the proximal tibia,
plots the density gradient, and outputs the area under the curve and length of the
metaphysis. This program was used in Chapter 4.
Walkthrough
1. Select folder using the pull down menu (dir_list)
2. Select the appropriate image (file_list) and label using the push buttons
a. “Middle” is the image containing the mid-shaft (middle_pushbutton)
b. “Start” is the approximate slice below the growth plate
(seriesstart_pushbutton)
c. “Stop” is the most distal cross-section (seriesstop_pushbutton)
3. Choose left or right tibia to analyze (left_button, right_button)
4. Calibrate the series of images (calibrate_pushbutton)
a. Crop a rectangle containing the entire phantom
b. Crop sample regions of each phantom (left to right)
5. Select “Go!” to start data processing (go_pushbutton)
6. Copy data from data dump (status_text)
124
Figure C-1: Screen shot of tibiagui.m – image selection.
Figure C-2: Screen shot of tibiagui.m – data output.
125
fatgui.m
Description
Finds the proportion of adipose and lean tissue in the DXA scan region, and calculates
the error in aBMD due to the soft-tissue inhomogeneity. This program was used in
Chapter 5.
Walkthrough
1. Select folder using the pull down menu (enterpath, dir_list)
2. Select image (such as L1, L2, or L3 cross-section) (file_list)
3. Calibrate image
a. Auto method (inspect regression for R > 0.99) (phantomauto_button)
b. Manual method requires cropping phantom regions (phantomman_button)
4. Rotate image to align spine in AP direction
a. Use slider bar to rotate (rotate_slider)
b. Select “Rotate: X deg” to set (rotate_button)
5. Isolate trunk
a. “Body ROI” detects trunk and crops (bodyroi_button)
b. “Poly Block” to manually crop and erase artifacts (e.g. phantom)
(block_button)
6. “Separate” segments the body into adipose, lean, and bone tissue
(separate_button)
7. “Find Spine” asks the user to double-click the anterior edge of the vertebral
foramen and begins the image processing (spine_button)
8. Copy data from data dump (status_text)
126
Figure C-3: Screen shot of fatgui.m – image segmentation.
Figure C-4: Screen shot of fatgui.m – data output.
127
fatgui2.m
Description
Finds the cumulative attenuation of soft-tissue in the AP direction along the width of the
trunk, and saves the results to a database. This program was used in Chapter 6.
Walkthrough
1. Select folder using the pull down menu (enterpath, dir_list)
2. Select image (such as L1, L2, or L3 cross-section) (file_list)
3. Calibrate image
a. Auto method (inspect regression for R > 0.99) (button_autophan)
b. Manual method requires cropping phantom regions (button_manualphan)
4. Isolate trunk
a. Auto method automatically detects trunk and crops (button_autobody)
b. Manual method to crop and erase artifacts (e.g., phantom)
(button_manualbody)
5. Rotate image to align spine in AP direction
a. Auto method aligns major axis of body with horizontal axis
(button_autorotate)
b. Manual method to adjust slider bar set with push button
(button_manualrotate)
6. Analyze soft-tissue
a. Auto method discovers spine and calculates results (button_autospine)
b. Manual method not necessary and was not programmed
(button_manualspine)
7. Save data to spreadsheet database (button_database)
128
Figure C-5: Screen shot of fatgui2.m – image selection.
Figure C-6: Screen shot of fatgui2.m – data output.
129
spinegui.m
Description
Extracts measures from the spine, including density and cross-sectional area of the
vertebral body and posterior elements. This program was used in Chapter 7.
Walkthrough
1. Select folder using the pull down menu (enterpath, dir_list)
2. Select image (such as L1, L2, or L3 cross-section) (file_list)
3. Calibrate image
a. Auto method (inspect regression for R > 0.99) (phantomauto)
b. Manual method requires cropping phantom regions (phantommanual)
4. Rotate image to align spine in AP direction
a. Use slider bar to rotate (rotateslider)
b. Select “Rotate: X deg” to set (rotatedcm)
5. Find spine and start vertebral analysis
a. Auto method discovers spine and calculates results (findspineauto)
b. Manual method requires locating anterior edge of foramen (findspineman)
6. “Spine Advance” separates and calculates density and cross-sectional area of the
total cancellous bone, total cortical bone, cortex, and posterior elements
(spineadvance)
130
Figure C-7: Screen shot of spinegui.m – regions of interest.
Figure C-8: Screen shot of spinegui.m – image processing.
131
mriviewer.m
Description
Finds bone contours in MRI images and extracts cross-sectional parameters. This
program was used in Chapter 8.
Walkthrough
1. Select folder using the pull down menu (enterpath, dir_list)
2. Select image (such as L1, L2, or L3 cross-section) (file_list)
3. ROI Select
a. Rectangle method asks user to crop a rectangle around the bone containing
approximately half bone and half soft-tissue (findarearect_button)
b. Polygon method asks user to crop a polygon around the bone containing
approximately half bone and half soft-tissue (findareapoly_button)
c. Auto method finds the bone region and calculates results (autothresh)
d. Any ROI zooms in on any cropped region (anyroi_button)
4. Multi-View enables viewing in three planes, given a volume of data
(radiobutton1)
5. Dixon Method (radiobutton2)
a. User must select Dixon fat data and water data folders (dixonmenu1,
dixonmenu2)
b. Use ROI select to find intramedullary canal for Dixon analysis
132
Figure C-9: Screen shot of mriviewer.m – image selection.
133
Figure C-10: Screen shot of mriviewer.m – data output.
Abstract (if available)
Abstract
Peripheral quantitative computed tomography (pQCT) and dual energy x-ray absorptiometry (DXA) are fundamental imaging technologies in the assessment of bone in children and adolescents. However, they may both produce misleading outcomes, particularly in growing subjects. The goal of this thesis is to quantify and minimize the shortcomings of pQCT and DXA. We have isolated factors that lead to potential errors in pQCT and DXA, offered corrections for those errors or alternative measures, and introduced an automated MRI (magnetic resonance imaging) bone feature extraction program.
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Asset Metadata
Creator
Lee, David Choen
(author)
Core Title
Optimizations in the assessment of pediatric bone
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Biomedical Engineering
Publication Date
03/11/2009
Defense Date
02/23/2009
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
bone,DXA,imaging,OAI-PMH Harvest,Orthopedics,Pediatrics
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Singh, Manbir (
committee chair
), Wren, Tishya A. (
committee chair
), Gilsanz, Vicente (
committee member
), McNitt-Gray, Jill L. (
committee member
)
Creator Email
davidcle@usc.edu,davidclee@alumni.usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m2018
Unique identifier
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215423
Document Type
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texts
Source
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(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
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Tags
DXA
imaging