Computational modeling of bone and bone remodeling 257
d
d
mx
t
t
rr
ob
r
r
oc
rr
,
(
)
=
r
r
[8.2]
The Young’s modulus E ( x , t ) at each location can be expressed as:
Ex
tE
mx
t
r
,,
tE
mx
ma
x
(
)
×
E
E
(
)
⎡
⎣
⎡
⎡
⎤
⎦
⎤
⎤
[8.3]
where E
max
was the maximum tissue level Young’s modulus, and E
max
and r
can be obtained from experiments.
Numerical approach and example
The schematic representation of the bone remodeling algorithm in combi-
nation with nite element analysis is shown in Fig. 8.11.
A simpli ed two-dimensional nite element model of a 2 mm × 2 mm
portion of bone volume with a thickness of 0.02 mm was used here as an
example to show the ...
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