Biomedical Engineering Reference
In-Depth Information
200
100
95
90
85
80
75
70
65
60
55
50
190
180
170
160
150
140
130
120
110
100
0
5
10
15
20
25
30
0
5
10
15
20
25
30
Time (d)
Time (d)
(a)
(b)
FIgure 25.3
Percentage changes in the mechanical loading and BMU activation threshold in the simula-
tions relative to their magnitudes at equilibrium. (a) Mechanical loading and (b) BMU activation threshold.
Figure 25.3 shows the relative percentage changes of the mechanical loading and BMU acti-
vation threshold in the simulations relative to their magnitudes at equilibrium. The mechani-
cal loading decreased to 54.59% at the end of the experiment and followed the equation
()
Ft
=
2.42
−
t
/44.0
F
(0)0
≤
t
≤
30 days
. The BMU activation threshold increased to 197.55% and
followed the equation
akfa
()
t
=−
2.0 .6
−
t
/3.8
0
≤≤
t
30days
.
25.3.2 r
eSultS
for
c
ortical
B
one
l
oSS
a
SSociated
WitH
m
ecHanical
d
iSuSe
Figure 25.4 shows the numerical outcomes of the cortical thickness of the femur and tibia models.
The simulated cortical bone thicknesses for both models were consistent with the clinical data
measured by Eser et al. (2004). The correlation coefficients between the clinical data points and
the simulated values at the same time points were
R
2
= 0.43 (
p
< .001) for the femur model, and
R
2
= 0.33 (
p
< .001) for the tibia model. The simulated steady state cortical thicknesses in both
models were close to the clinical measurements. For the femur model, the simulated steady state
cortical thickness was 2.038 mm and 2.17 mm according to the clinical data. For the tibia model,
the simulated steady state value was 4.134 mm and 3.94 mm from the clinical data.
Figure 25.5 shows the changes of the mechanical load for both models. The mechanical load in
the tibia model followed the equation
Ft
()
=
Fe
tibia
⋅
−
0.2
t
with
t
= time (year) and that in the femur
0
model followed the equation
Ft
()
=
F
⋅
e
−
0.3
t
with
t
= time (year). The values of
F
tibia
and
0
femur
F
femur
are listed in Table 25.5.
25.4 aPPlICatIonS oF the model
Mechanical disuse and estrogen deficiency are two main causes of osteoporosis. The human muscu-
loskeletal system has evolved under the continuous influence of Earth's gravity. Removal of gravity
during long-duration space flight results in a loss of homeostasis in the musculoskeletal system. In
the general population, skeletal muscle forces decrease significantly by 20%-40% with aging (Frost
1999; Polla et al., 2004). Loads on bones generate strain-dependent signals (Martin, 2000; Jones
et al., 1991). Frost (1983) used the minimum effective strain (MES) as a threshold or mechanical
set point to describe bone's adaptation to its mechanical environment. When dynamic strains stay
below a lower remodeling threshold range (MESr), “disuse-mode” remodeling removes bone next to
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