Biomedical Engineering Reference
In-Depth Information
Since the interstitial pore fluid pressure in the porosity with the largest lineal
dimension,thePV,isalwayslow;themiddleporosity- thePLC- appearstobethe
most important porosity for the consideration of mechanical and mechanosensory
effects in the bone. The interstitial pore fluid pressure in the PLC can be, transiently,
much higher. The PLC is the primary porosity scale associated with the relaxation of
the excess pore pressure due to mechanical loading. This relaxation of the interstitial
pore fluid pressure was illustrated by Wang
et al
. [78]. In this work, the interstitial
pore fluid pressure distributions across a bone are calculated using an idealized
bone microstructural model consisting of six abutting square osteons with circular
osteonal canals (Figure 9.8). This idealized model is shown in Figure 9.8(a,b); it
has a length of 1200 µm and a width of 200 µm. The interstitial pore fluid pressure
profiles are given for different conditions of loading and of permeability of the
cement line that forms the outer boundary of the osteon. The completely free flow
across the osteonal cement line represents 100% coupling of the osteon with its
neighboring osteons, and 0% osteonal coupling is the case in which there is no
flow across the cement line. In Figure 9.8(c,d) the interstitial pore fluid pressure
profiles for a bone model specimen with 40
m osteonal canals were subjected
to an external loading applied at 1.5 Hz for 100% coupling (Figure 9.8c) and for
0% osteonal coupling (Figure 9.8d). In Figure 9.8(c,d), the interstitial pore fluid
pressure profiles are plotted along lines whose
x
distance is expressed as a multiple
of the osteonal canal diameter
d
; the interstitial pore fluid pressure profiles along
the line
x
µ
=
0 are the profiles along a line passing through the canal centers;
x
4 are interstitial pore fluid pressure profiles along a line halfway between
the canal centers and the cement line;
x
=
d
/
=
/
2 are interstitial pore fluid pressure
profiles along a line passing through the cement lines. In Figure 9.8(e), the local
interstitial pore fluid pressure gradients for 0% coupling and 100% coupling are
compared in the case
x
=
0. In Figure 9.8(f ), the effects of the different sized
osteonal canals (
d
d
m) on the pressure profiles and the transcortical
interstitial pore fluid pressure difference are illustrated for 100% osteonal coupling
with the loading applied at 1.5 Hz. In Figure 9.8(g), the effects of two different
=
0, 40, or 60
µ
Figure 9.8
Dimensionless pressure distribu-
tions from one surface of the bone specimen
(
y
=−
600
µ
m) to the other surface (
y
=
600
µ
m) for different conditions. (a) and (b)
the spacing of the osteonal lumen across
the test section. (c) and (d) Pressure pro-
files for a specimen with 40
µ
mosteonal
canals with the external loading applied at
1.5 Hz for 100% osteonal coupling (c) and
for 0% osteonal coupling (d).
x
=
0: pro-
file along a line passing through the canal
centers;
x
=
d
/
4: profile along a line halfway
between the canal centers and the cement
line;
x
=
d
/
2: profile along a line passing
through the cement lines. (e) Comparison
of the local pressure gradients for 0% cou-
pling and 100% coupling (
x
=
0). (f) Effects
of the size of the osteonal canals (
d
c=0,
40, or 60
µ
m) on the pressure profiles and
the transcortical pressure difference (
p
)for
100% osteonal coupling with the loading ap-
plied at 1.5 Hz. The transcortical pressure
difference is the pressure difference between
the points marked ''
∇
”, ''x” or ''O” on the
external surfaces. (g) Comparison of the
local pressure gradients and transcortical
pressure difference between loading applied
at 1.5 and 15 Hz.
