Page 74 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

HEAT TRANSFER APPLICATIONS IN BIOLOGICAL SYSTEMS 51

For the limiting case of an infinitesimally small probe with an infinitesimally short heating pulse, the
solution for Eq. (2.20) for the interval of temperature decay takes the form

0 t
2
ts
(
r
− )]
θ = λ 2 ∫ (ts −15 . e − ω − ) e − /[ 4 λ 1 (ts ds (2.21)
− )
0
1.5
0.5
1.5
where λ = P(ρC) /(8π ) and λ =α /(k t ). In this theoretical analysis, there are two unknowns,
0.5
1 2 t p
k and α. A least square residual fit allows one to find a set of values of k and ω that will lead to the
t t
best fit of the theoretical predictions to the experimentally measured temperature decay.
The temperature pulse decay technique has been used to measure both the in vivo and in vitro
thermal conductivity and blood flow rate in various tissues (Xu et al., 1991, 1998). The specimen
does not need to be cut from the body, and this method minimizes the trauma by sensing the tem-
perature with a very small thermistor bead. For the in vitro experimental measurement, the mea-
surement of thermal conductivity is simple and relatively accurate. The infinitively large tissue area
surrounding the probe implies that the area affected by the pulse heating is very small in comparison
with the tissue region. This technique also requires that the temperature distribution before the pulse
heating should reach steady state in the surrounding area of the probe.
2.4.3 Blood Perfusion Measurement
Blood perfusion rate is defined as the amount of blood supplied to a certain tissue region per minute
per 100 g tissue weight. In most of the situation, it is representing the nutrient need in that tissue
area. High blood perfusion is also associated with heat dissipation during exercise or thermal stress.
In humans, there are several tissue regions, such as kidney, heart, and choriocapillaris in the eye, pos-
sessing a high blood perfusion rate. The measured blood perfusion rate in the kidney is approxi-
mately 500 mL/min/100 g tissue (Holmes, 1997). In the heart, the blood perfusion rate is around
300 mL/min/100 g which serves for the energy need of pumping the heart. The choriocapillaris in
the eyes is a meshed structure within two thin sheets. Its blood perfusion rate is very high and can
be as much as 8000 mL/min/100 g tissue. In addition to providing oxygen and other nutrients to the
retina, the choriocapillaris also may play a role in stabilizing the temperature environment of the retina
and retinal pigment epithelium (Aurer and Carpenter, 1980). In addition to its physiological role,
blood perfusion measurement is important in theoretical modeling of the temperature distribution
during various therapeutic and diagnostic applications.
Radio-Labeled Microsphere Technique. Measurement of blood flow has become an integral part
of the physiologic study of humans. While many methods have been utilized in measuring tissue
blood flow, the one most often practiced today is dependent on injection of radioactively labeled
microspheres. The reason for its overwhelming acceptance is due, in part, to the shortcomings of
many of the alternative methods of blood flow determination.
In principle, small particles are uniformly mixed with blood and allowed to circulate freely until
they impact in a vessel smaller in diameter than themselves. The tissue or organ is then removed and
its radioactivity measured. In such a system, the number of particles impacted in a given tissue is
assumed proportional to the volume of particle-containing blood perfusing that tissue. If the number
of particles in the tissue sample is determined, and an adequate blood flow reference established, a
tissue blood flow can be derived.
Calculating the blood flow rate is straightforward; it is based on the assumption that the number
of microspheres in each organ should be directly proportional to blood flow to that organ, e.g.,

Bloodflow toorganA bloodflow toorganB cardiacoutput
f
t
= = (2.22)
MicrospheresinorganA microspheresinorganB totalmicrospheresinjected
The cardiac output of the animal is obtained by another independent method.