Biomedical Engineering Reference
In-Depth Information
table 25.3
State variables in the Computational Simulation of Cortical bone
remodeling
State variable
h
N
R
N
F
fa
ε
Φ
Cortical thickness (mm)
Number of resorbing BMUs (BMUs/mm
2
)
Number of refilling BMUs (BMUs/mm
2
)
BMU activation frequency (BMUs/mm
2
/day)
Strain (μ ε)
Mechanical stimulus (MPa)
table 25.4
Constants in the Computational Simulation of Cortical bone remodeling
Constant
nominal values
A
T
r
T
i
T
f
f
a(max)
kb
kc
f
a
Φ
0
Cross-sectional area of each BMU (mm
2
)
Resorption period (days)
Reversal period (days)
Refilling period (days)
Maximum BMU activation frequency (BMUs/mm
2
/day)
Dose-response coefficient (Pa
−1
)
Dose-response coefficient (Pa)
Maximum BMU activation frequency (BMUs/mm
2
/day)
Initial mechanical stimulus (Pa)
2.84×10
−2
a
24
b
8
b
64
b
0.299
c
0.005759
c
1129.493
c
4.8768×10
−4
d
2258.986
Note:
The nominal values are for the example in Section 25.2.2.2 about bone loss simulations of
the cortical bone of the femur and tibia in paralysis state measured in Eser et al., Bone, 34,
869-80, 2004.
a
Based on Parfitt,
Bone Histomorphometry: Techniques and Interpretation
, 143-223, CRC Press, Boca
Raton, FL, 1983.
b
From Hazelwood et al.,
Journal of Biomechanics
, 34, 299-308, 2001, based on several histomorphometric
studies.
c
Parametrical sensitivity analyses were done for the coefficients to fit the curves within known experimental
data ranges. (Eser et al.,
Bone
, 34, 869-80, 2004.)
d
Based on Equation 25.3.
Hence
dh t
dt
()
=
hQtN t
(()()
−
QtN t
( )())
(25.10)
0
r
R
f
F
N
R
(
t
) and N
F
(
t
) are the populations of resorbing BMUs and refilling BMUs, respectively, and were
calculated according to Equations 25.5 and 25.6, respectively, and
f
a
(
t
) is the BMU activation fre-
quency. The relationship between BMU activation frequency and mechanical load was assumed to
be sigmoidal, similar to the response found in pharmacological applications (Hazelwood et al., 2001):
f
e
a
kb
(max)
(()
fit
()
=
(25.11)
a
1
+
ϕ−
t
c
)
Mechanical stimulus
f
(
t
) was described by strain energy density, having the same form as
Equation 25.3.
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