Biomedical Engineering Reference
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loading decreased in the disuse state. In this analysis, the changes of the BMU activation threshold
and mechanical loading were assumed as exponential functions. The coefficients were chosen to
make the simulated changes of BMD correspond with the experimental data from ovariectomy
and hind-limb suspension. The combined effects of changes of the BMU activation threshold and
mechanical loading were simulated by assuming that the values were the same when both factors
changed as when each factor changed alone.
25.2.2.2 model validation for the Computational
Simulation of Cortical bone remodeling
The computational simulation algorithm of cortical bone remodeling (Equations 25.3, 25.5, 25.6,
25.10, and 25.11) was validated by the pQCT data showing the relationship between the duration
of paralysis and bone structure of spinal-cord-injured patients by Eser et al. (2004) as an example
of mechanical disuse. Eighty-nine men with injury to the motor complex of the spinal cord
(24 tetraplegics and 65 paraplegics) with a duration of paralysis between 2 months and 50 years
were included. The age range was 41.5 ± 14.2 for all subjects. The reference group comprised
21 healthy able-bodied men of the same age range.
The remodeling behaviors of cortical bone in the femur and tibia were simulated. The represen-
tative cross section of the femur cortical bone was located at 25% of the total bone length from the
distal end for the femur, and at 38% for the tibia, mirroring the locations of the diaphyseal scans in
Eser et al. (2004). For simplification, the cortical bone volume was assumed to be cylindrical and
the endosteal surface and periosteal surface were assumed to be concentric circles (Figure 25.1).
The geometrical and mechanical conditions of the two cortical samples are shown in Table 25.5.
table 25.5
geometrical and mechanical Properties of the representative rectangular Slices for
Femur and tibia Cortical models
tibia
Femur
notes
Initial cortical thickness
h
0
(mm)
5.84
3.33
From Eser et al. (2004).
Length
l
(mm)
1
1.64
The length of the tibia model was
chosen to guarantee a small slice and
that of the femur model was chosen
such that both models occupied the
same percentage of total cortical area,
i.e., approximately 1.69%.
Initial area
A
0
of the
model (mm
2
)
5.84
5.46
From equation
.
Ahl
=⋅
0
0
Equilibrium strain ε
0
(
μ
ε)
500
From Beaupré et al. (1990) and Turner
et al. (1997).
Porosity
p
0
(%)
4.43
From Hazelwood et al. (2001). Eser
et al. (2004), found no decrease in
cortical BMD of the diaphyses with
time after injury. Hence, the cortical
porosity in this analysis was held
constant.
Elastic modulus
E
(MPa)
18000
From the relationship between elastic
modulus and porosity of cortical bone
proposed by Currey (1988):
(23440
5.74
E
=
×
(1
−
p
)
)
MPa
.
0
Equilibrium load
F
0
(N)
52.770
49.336
From equation
0
F
=⋅
A
⋅
E
.
0
0
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