Biomedical Engineering Reference
In-Depth Information
For the microcirculation of peripheral tissue in which capillaries pro-
vide a continuous connection between the terminal artery and vein (i.e.,
arterial-venous anastomoses), as shown in Figure 1.4, we may readily set
ω a =
ω v such that the present energy equation (1.43) for the solid tissue
phase reduces to
(1
s
s
ε ) ρ s c s
T
∂x j
ε ) k s
T
(1
=
∂t
∂x j
a
s )+ a v h v (
v
s )
+ a a h a (
T
T
T
T
a
v )+(1
+ ρ f c p f ω a (
T
T
ε ) S m
(1.48)
1.5.3 Keller and Seiler Model
Most existing bioheat transfer models for countercurrent bioheat transfer
already reside in the present model based on the theory of porous media.
Let us revisit some of the existing models and try to generate them from the
present general model.
Keller and Seiler (1971) noted that the axial temperature gradient in the
limb is much higher than the transverse one and considered an energy bal-
ance within a control volume for the idealized one-dimensional steady case, as
illustrated in Figure 1.5, for which they proposed
s
ε ) k s d 2
T
a
s )+ a v h v (
v
s )
(1
+ a a h a (
T
T
T
T
dx 2
a
s )+(1
+ ρ f c p f ω (
T
T
ε ) S m = 0
(1.49)
which is almost identical to what we would get for the one-dimensional
case from our multidimensional expression (1.48), except that the temper-
ature difference in the perfusion term somewhat differs from ours. Keller and
Veins
Capillaries
Tissue space
Arteries
FIGURE 1.5
One-dimensional model for countercurrent heat exchange.
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