Biomedical Engineering Reference
In-Depth Information
The measurement technique consists of inserting the therm-
istor probe of nominal radius
a
into a target and allowing
an initial period of thermal equilibration. Then, a current is
supplied to the thermistor with a control to maintain a con-
stant temperature rise of the probe above the initial baseline,
=−
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TTT
o
. The Pennes equation is applied in spherical coordi-
nates to model the transient temperatures in the probe and in
the surrounding tissue:
1
2
+
−
∂
∂
T
t
∂
∂
T
r
∂
∂
ABt
a
+
p
p
2
ρ
c
=
k
r
for
r
<
(1.96)
pp
p
4
r
2
π
3
−ω
∂
∂
T
t
∂
∂
∂
∂
T
r
(
)
t
2
t
(1.97)
ρ
c
=
k
r
cT T
−
for
r <a
tt
t
bb
b
t
r
where the subscripts
p
and
t
refer to the probe and tissue. The
constants
A
and
B
are characteristics of the heating regime
applied to the thermistor. The initial power input to the therm-
istor to maintain
T
p
at a constant value is maximal, followed
by a decline to a steady state value in which there is an equi-
librium between the heating of the thermistor and the rate of
loss by conduction in the tissue and convection to perfused
blood. The solution of Equations 1.96 and 1.97 is complex, and
for details the reader may reference Valvano (1992) and Diller
et al. (2005).
Currently, there is no method to quantify simultaneously the
major three parameters: the intrinsic tissue thermal conductiv-
it y,
k
m
, the tissue thermal diffusivity, α
m
, and perfusion, ω. Either
the knowledge of
k
m
is required prior to the perfusion measure-
ment, or even when
k
m
is measured in the presence of perfusion,
the thermal diffusivity cannot be measured.
acknowledgments
This chapter was prepared with support from NSF Grant No.
CBET 0966998 and the Robert and Prudie Leibrock Professorship
in Engineering.
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