Journal
of Computer Modelling
and Simulation in Medicine
Volume 1
Issue 2
June 2000
Osteoporosis
and Bone Measurement
Abstracts
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Simulation
of Cancellous Bone Remodelling, Structure and Biomechanical Stresses
associated with Osteoporosis: A Review
C
A Dobson, C M Langton, M J Fagan
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79-97 |
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Over recent years a
number of mathematical, analytical and finite element models of
cancellous bone have been developed and used to aid our understanding
of its growth, behaviour and structural function. In particular,
models have been used to explore the processes and effects of normal
bone renewal through osteoclast and osteoblast remodelling activities;
the structural properties of cancellous bone resulting from the
complex and variable geometry of its constituent trabeculae; and the
overall effects of the cancellous bone structure on the properties and
performance of individual bones in the skeleton. This paper reviews
the current status of these models and assesses their relevance and
applicability to the specific problem of osteoporosis, which is now
one of the most important health issues in the developed world.
Prediction
of Trabecular Bone Failure Parameters using a Tissue Failure Criterion
and m FE Analysis
B
van Rietbergen, W Pistoia, D Ulrich, R Huiskes
and P. Rüegsegger
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98-101 |
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We investigated if
failure behavior of trabecular bone at the apparent level as measured
in compression tests can be predicted from tissue loading conditions
and a tissue yield criterion. Micro- finite element models of 5 bone
specimens were made using a micro-CT scanner. The failure behavior of
these specimens was measured in compression tests and simulated with
non-linear micro- finite element analyses assuming elastic-perfectly
plastic tissue yield behavior. It was found that the ultimate stress
could be predicted within 15% of the measured values, the ultimate
strain, however was underestimated by 35%-49%. Although a more
realistic description of tissue yield behavior is likely necessary to
improve agreement, it is concluded that the approach introduced here
is feasible.
A
Continuous Stochastic Simulation of Cancellous Bone Remodelling
R
Eastwood and C M Langton
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102-111 |
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Throughout life,
cancellous bone is remodelled through a cellular process of osteoclast
resorption and osteoblast deposition, a negative imbalance resulting
in the development of osteoporosis. Remodelling occurs at specific
trabecular surface foci, basic multi-cellular units (BMU), and
consists of four phases: resorption, reversal, formation and
mineralisation.
A BMU-based
stochastic simulation of cancellous bone remodelling has been
successfully developed operating continuously with time. Remodelling
parameter data from a clinical study of control and osteoporotic
subjects has been incorporated in the form of median along with 10th
and 90th percentile values. Random values for the various
remodelling parameters were obtained via interpolation of normally
distributed probability curves. The simulation was repeated five times
for both control and osteoporotic states, over a five year period. The
mean relative bone tissue volume reductions for control and
osteoporotic states were 6.1+0.8% and 13.7+0.7 %
respectively.
This computer
simulation offers an improved physiological representation of
cancellous bone remodelling along with the ability to accurately
implement various treatment regimes; for example, anti-resorptive and
bisphosphonate therapies, which have differing effects on the
resorption and formation processes.
Review
of Fractal Paradigms to Simulate Cancellous Bone Structure and
Validation of the Random Walk Method
C
R Percy and C M Langton
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112-122 |
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Fractal theory is a
recent development in mathematical geometry with particular relevance
to the growth and form of biological systems. The structure of
cancellous bone may be considered to be fractal and hence could be
simulated in 3D using fractal concepts. The feasibility of applying
several fractal paradigms (cellular automata, reaction and diffusion
mechanisms, diffusion limited aggregation, percolation and epidemic
models, and random walk) has been considered, concluding that a random
walk is most appropriate. A flexible 3D simulator has been developed
where probability weightings may be applied to various parameters
including line width, probability of a particular move and anisotropy.
Static variables include the boundary size of the structure, the
number of spawn sites and the random walk moves. Random walk
structures were created using 100,000 moves. Four profiles were
considered, separately incorporating: a) equal line width and move
probability in X, Y and Z directions; b) Z-direction line-width of +2;
c) probability of a Z-move weighting of *6; and d) the latter two
variables combined. The move probability and line-width weighting in
the Z-direction were incorporated to reflect the predominance of
thicker vertical (Z) trabeculae observed in the vertebral body. Each
profile was repeated five times. The absolute values (mean and 95%
confidence intervals) and variability (CV%) of bone-to-tissue volume
(BV/TV%) and fractal dimension were calculated for the 2D central
section images of each simulation. The fractal dimension of the 2D
central sections indicated comparable variability within a particular
profile and between different profiles. There was less variability in
the fractal dimension than the BV/TV% between profile settings,
consistent with other biological fractal phenomena. The relationship
between fractal dimension and BV/TV% was comparable to previously
reported data on human cancellous bone samples. In conclusion, a 3D
random walk simulator of cancellous bone structure has been
successfully developed and validated through analysis of 2D central
sections. The fractal forms represent cancellous bone not only in
appearance but also in their relation to quantitative structural
properties. Further work is required in 3D to fully explore these
relationships and hence determine the potential and utility of this
simulator.
Computer
Simulation and Experiments to Investigate the Effects of
Frequency-Dependent Attenuation and Dispersion on Speed of Sound
Estimates in Cancellous Bone
K
A Wear
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123-129 |
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A computer
simulation has been utilized to model the effects of
frequency-dependent attenuation and dispersion (frequency-dependent
phase velocity) on transit-time-based speed of sound estimates. The
simulation is based on, but does not require all the approximations
assumed in, a previously developed linear system model. Thirty human
calcaneus samples were interrogated in vitro in order to test the
simulation. Simulated and experimental transit-time-based speed of
sound estimates were compared. The simulation showed good quantitative
agreement with experimental results. In addition, the simulation
predicts that in cancellous bone, frequency-dependent attenuation is a
greater contributor to variations in transit-time-based speed of sound
estimates than dispersion. This approach may be used to adjust
previously acquired individual measurements so that speed of sound
data recorded with different devices using different algorithms may be
compared in a meaningful fashion.
Computer
and Experimental Simulation of a Cortical End-Plate Phase Cancellation
Artefact in the Measurement of BUA
at the Calcaneus
C
M Langton and M Subhan
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130-137 |
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It has been
experimentally demonstrated that for the measurement of broadband
ultrasound attenuation (BUA) at the human calcaneus, the cortical
end-plate creates an artefact of the order of 7 dB MHz-1.
It has been suggested that the origin of this artefact may be a phase
cancellation of the ultrasound pulse resulting from inconsistencies in
propagation time across the ultrasound beam.
Experimental and
computer simulations were performed on samples of varying degrees of
curvature and hence varying propagation times across the ultrasound
beam. The experimental simulation incorporated perspex samples of
35mm, 50mm and 75mm radius. The computer simulation was implemented
using Matlab and Simulink, the propagation time represented by a
transport delay. The wavelet-based simulation incorporated a digitised
transmitted ultrasound pulse derived from the experimental simulation.
The experimental and
computer derived frequency spectra for the varying radii samples were
comparable, demonstrating firstly, that there is a significant
dependence of measured BUA upon radius of curvature; and secondly,
that the response in measured BUA with radius of curvature is similar
in magnitude and trend for both experimental and computer simulations.
The current study suggests that the BUA artefact observed in vitro
corresponds to a radius of approximately 58mm. Although the radius of
curvature was not recorded in the original in vitro study, this value
appears to be reasonable.
This study indicates
that the assumptions within the computer simulation were manifested
within the experimental validation, and hence, the observed BUA
artefact is related to the presence of the calcaneal cortical
end-plate and is due to phase cancellation of the propagating
ultrasound.
Editor:
Dr Chris
Langton F.Inst.P., C.Phys., C.Eng.
Centre for Metabolic Bone Disease
Hull Royal Infirmary, Anlaby Road, Hull, HU3 2RW, UK
Email: c.m.langton@medschool.hull.ac.uk
Tel: 44 1482
675311
Fax: 44 1482 675301
ISSN 1470-2371 |
