Biomedical Engineering Reference
In-Depth Information
affected for a longer time by the mechanical loading of the whole bone, the bone
fluid pressure in the PV is hardly affected because the PV relaxes the pressure
pulse very rapidly by diffusion.
9.8.5
Interchange of Interstitial Fluid between the Vascular and Lacunar-Canalicular
Porosities
Using the hierarchical scheme described in the previous subsection, a model was
formulated in [91] for the transport of bone interstitial fluid between the PV and
PLC porosity levels in the osteonal cortical bone. A section of this bone is illustrated
in Figure 9.5. The osteon at the top of this figure is entirely PLC porosity except for
its central lumen, called the
osteonal canal
or
Haversian canal
,whichispartofthe
PV porosity. The PV porosity consists of the volume of all the tunnels in bones that
contain blood vessels and includes all the osteonal canals and all the Volkmann
canals, less the volume of the tunnels occupied by the blood vessels.
The PV and the PLC are both modeled as poroelastic hollow circular cylinders.
The poroelastic hollow circular cylinder model of the PLC connects through its
inner cylindrical wall to the PV; the hollow part of this cylinder is actually part of
the PV. The inner surface of the cylinder representing the PLC is the surface across
which the two porosities exchange pore fluids. The PLC is assumed to permit
flow across its inner radial boundary, but not across its outer radial boundary.
While other assumptions are possible, an earlier study [78] showed that this is
a reasonable assumption. The PV is assumed to permit flow across both of its
radial boundaries. The PLC hollow cylinder is the osteon of Figure 9.5. The PV
hollow cylinder is the entire bone of Figure 9.5 with central lumen of the whole
bone, the medullary canal, constituting the hollow part of the PV model. Both of
these models are continuum models and the transport connection between is the
outflow-influx across the osteonal or Volkmann inner wall between the PLC and
the PV [92]. In the domain between the inner surface and outer surface of the PV
cylinder, there are areal sources-sinks that permit interchange of fluid between
the two continuum models representing the PV and PLC.
In this model, the fluid movement will be driven by two force systems. The
whole bone and its surrounding soft tissue structures are assumed to be cyclically
strained in the long bone direction by the axial strain
o
e
i
ω
t
. This straining
occurs as a result of environmental loading and muscle stimulation. At the
endosteum, the wall of the central lumen of the whole bone, the medullary
canal, the pore fluid pressure is assumed to be the same as the blood pressure,
p
BP
o
e
i
t
ε
(
t
)
=
ε
where
p
BP
o
60 mmHg. We assume that the periosteum is impermeable;
it has been identified as a barrier to the interstitial fluid flow [61]. We note that
lymphatic circulation is unlikely to play a role in bone fluid transport in the
normal bone, because lymphatic vessels are absent in the bone (see Section 9.6
above).
As a first step in describing the results in [91], the generic poroelastic hollow
circular cylinder model of this section is specialized to the PLC. As a second step,
=
