Biomedical Engineering Reference
In-Depth Information
be shown to solve the diffusion equation. Here, the diffusion coefficient of the solute
is then analogous to the kinematic viscosity of the underlying fluid [ 80 ]:
1
3
1
2
=
D
τ
(8)
g
Note that the relaxation rate of the gas solute and underlying fluid are independent,
hence the notation
τ g .
5.3
Interstitial Convection and Diffusion
LBM techniques have been applied successfully to the study of complex porous
media [ 17 ]. The idea is to specify a computation domain consisting of open “fluid”
nodes bounded by “solid” nodes that represent a porous medium. Though simple
and effective, the lattice resolution must be on the order of the smallest pore or
conduit in the material being studied. It also implicitly requires one to know the
pore-space geometry, which might be infeasible. Instead, a partial bounce-back
(PBB) rule can be employed to simulate a mesoscale permeability [ 94 ]:
f out
n s f in
t )
α =(
)
f α (
,
)+
α (
,
1
n s
x
t
x
(9)
Note, that this revised partial bounce-back rule is similar to the mid-plane rule
introduced above, except that a fraction n s of the distribution before collision (note
the t ) is added to the distribution after collision. Further, when the solid fraction is
unity, the partial bounce-back rule actually recovers the original mid-plane boundary
condition. Similarly, for a solid fraction of zero, the standard collision rule is in
effect.
By utilizing PBB, the entire computational domain becomes open to both
flow and solute transport. Thus, we are able to study interstitial convection and
diffusion at the mesoscale level. Further, local spatial modulation of the PBB is
ideal for simulating phenomenon-like vessel wall permeability and can be used
to independently control diffusion in plasma and the interstitium. Naturally, since
each component of the flow has a separate distribution function, permeability can
be tailored independently.
5.4
Incorporation of RBC Particles and Oxygen Release
As presented thus far, the basic LBM approach is unable to capture the physiological
effects that red blood cells (RBCs) have on the transport of oxygen in blood.
For example, at oxygen partial pressures typical in arterioles (20-60 mm Hg),
the oxygen content of hemoglobin in a volume of blood at 30 % hematocrit is
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