Biomedical Engineering Reference
In-Depth Information
×
10
6
9
w
t
=
0.2
p
8
7
w
t
=
0.28
p
w
p
w
t
=
0.45
p
t
=
0.36
6
5
4
3
2
1
0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
l
Figure 9.9
A plot of the pore pressure in the PLC,
p
L
(
λ
,
t
)
as a function of the dimensionless radial coordinate of the
model osteon
λ
, at various temporal points in the cyclic
oscillation; this plot is for the special case when the pore
pressure in the PV vanishes. The values of parameters used
in the plot are listed in Table 9.1. (From Cowin
et al
.[91].)
the volume of the fluid leaving the PLC and moving to the PV in one cycle is
described. As a third step, the generic poroelastic hollow circular cylinder model of
this section is specialized to the PV, accounting for the influx from/outflow to the
PLC.
The pore pressure in the PLC as a function of the dimensionless radial coordinate
of the model osteon
, at various temporal points in the cyclic oscillation, is shown
in Figure 9.9; this plot is for the special case when the pore pressure in the
PV vanishes. A plot of
V
total due to
ε
o
(
λ
), the fluid volume exchanged between the
PLC and the PV in the case of zero PV pressure, against the driving frequency
ω
ω
, the PLC porosity, equal to 0.05, 0.1, and 0.15 is shown in
Figure 9.10. Since the nonzero PV pressure reduces
V
total due to
ε
o
(
for values of
φ
ω
), the case of
zero PV pressure yields the maximum value of
V
total
.
Expressions relating the pore pressure field in the PV to the two driving forces,
the cyclic mechanical straining with amplitude
ε
o
and a frequency
ω
and the
blood pressure with amplitude
p
BP
o
and a frequency
, are plotted in Figures 9.11
and 9.12. A plot of the pore pressure in the PV,
p
V
(
β
,
t
), is shown in Figure 9.11 as
a function of the dimensionless radial coordinate of the model bone
at various
temporal points in the cyclic oscillation. Figure 9.12 is again a plot of the same
equation for the pore pressure in the PV, but with the PV permeability reduced
by 2 orders of magnitude, 6
β
.
35
×
10
−
8
m
2
, from that employed in Figure 9.11,
10
−
10
m
2
. Notice from Figure 9.11 that the peak pressure is near 15 MPa for
a PV permeability of 6
.
×
6
35
10
−
10
m
2
, and from Figure 9.12, it is found to be about
9.5 kPa for a PV permeability of 6
.
35
×
10
−
8
m
2
. Since 8 kPa is about 60 mmHg, the
.
35
×
