Biomedical Engineering Reference
In-Depth Information
evaluation of the references reporting the low PV permeabilities revealed that they
were very rough estimates.
9.8.6
Implications for the Determination of the Permeabilities
The measurement of the permeability of the PV has not been accomplished
with sufficient accuracy to date, primarily because of the topological intertwin-
ing of the PV with the PLC. The pore fluid pressures in both the PLC and
the PV depend upon the permeability of their own porosity as well as upon
the permeability of the other porosities. The PV permeabilities reported in the
past are thought to be significant underestimates, because these previous val-
ues represent a PLC and PV lumped permeability measurement rather than
a PV or PLC measurement alone. The fact that, in general, the pore pres-
sure in each porosity depends upon the permeability of the other porosities
means that special strategies should be designed for the experimental deter-
mination of each porosity's permeability. Traditional permeability measurement
techniques based on Darcy's technique of measuring the volume of flow per unit
area per unit time across a porous layer and dividing by the pore pressure
gradient across the layer requires modification for porous media structured
hierarchically.
Thetwoporositiesofthebonetissueoccupythesamethree-dimensionalvolume
of the bone tissue. In the cross section of the bone shown in Figure 9.5, the
PV channels are the central lumens of the osteons and the region immediately
surrounding the osteon is part of the PLC. Thus, it is impossible to obtain a
reasonably sized specimen of bone tissue that contains some PV porosity, without
containing any PLC porosity. This topological fact makes it difficult to design an
experiment to measure the permeability of the PV. The analytical basis for a number
of different approaches to this measurement technique for the measurement of
the permeability of the PV was provided by Cowin
et al
. [91]. From this discussion,
it is clear that previous measurements of the permeability of the PV were not
accurate as they were based on models that did not include the interchange of
interstitial fluid with the PLC. This is one reason why we have not honored the
reported measurements of the permeability of the PV that are present in the
literature - permeabilities as low as 10
−
14
m
2
. As noted in the previous section,
the results of this study suggest a PV permeability lower than 10
−
9
m
2
and perhaps
a little greater than 10
−
8
m
2
. The second reason is that permeabilities as low as
10
−
14
m
2
predict PV pore pressures that are too high as the results in [91] and [95]
show.
We now turn to the question of measurement of the permeability of the PLC.
The entire content of a single osteon that is considered as a hollow circular
cylinder is composed of the PLC porosity and no PV porosity; this may be used to
measure the permeability of the PLC. This has been accomplished [57] by isolating
single osteons, imposing a compressive stress on them, and measuring the
time-dependent axial strain. The PLC permeability determined was on the order
