Biomedical Engineering Reference
In-Depth Information
10000
9500
9000
8500
8000
7500
7000
6500
6000
5500
5000
w
t
=
0.20
p
w
t
=
0.28
p
t
0.36
t
0.44
w
=
p
w
=
p
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
1
b
Figure 9.12
A plot of the pore pressure in the PV,
p
V
(
β
,
t
)
using a PV permeability on the order of 10
−
8
m
2
,asafunc-
tion of the dimensionless radial coordinate of the model
bone
β
at various temporal points in the cyclic oscilla-
tion. The values of parameters used in the plot are listed
in Table 9.1. (From Cowin
et al
.[91].)
peak blood pressure, a PV pore pressure in the range of 8 kPa is a more reasonable
result for several reasons. First, as the comparison of Figures 9.11 and 9.12 shows,
the gradient of the PV pore pressure across the bone cortex is smaller in the case of
the lower PV permeability; the bone pressure is almost uniform across the cortex.
Since the gradient is small at the endosteal surface, there is less flow in and out of
the medullary canal; there is no known physiological advantage for interstitial flow
in and out of the medullary canal. Last, the pore pressure in the PV cannot exceed
a pore pressure that would collapse the blood vessels present for any significant
length of time. Figure 9.13 is a plot of the pore pressure due to blood pressure in
the PV,
p
V
(
,
t
), as a function of the dimensionless radial coordinate of the model
bone
β
, at various temporal points in the cyclic oscillation. Figure 9.13a is at a
scale that obscures the small spatial gradient in the blood pressure; Figure 9.13b
expands the scale for a single time point in the oscillation so that the small gradient
is apparent. These considerations concerning the plots in Figures 9.11 and 9.12
suggest a PV permeability lower than 10
−
9
m
2
β
and perhaps a little greater than
10
−
8
m
2
.
The interpretation in [91] of results presented in a recent paper [95] reinforces
the point made at the end of the previous paragraph concerning a PV permeability
lower than 10
−
9
m
2
and perhaps a little greater than 10
−
8
m
2
.In[95],afinite
element model whose geometry was generated from a quantitatively computed
tomography scan of a section of human tibia was employed. The fluid velocities
and the pore fluid pressure in the PLC and in the PLC
+
PV were calculated for
