A General Set of Bioheat Transfer Equations Based on the Volume Averaging Theory - Porous Media: Applications in Biological Systems and Biotechnology - page 2

1.7 Application of Bioheat Equation to Cryoablation Therapy ................ 26

1.7.1 Related Work ....................................................... 26

1.7.2 Bioheat Equation for Cryoablation ................................. 29

1.7.3 Numerical Analysis Based on Enthalpy Method ................... 30

1.7.4 Analytical Treatment Based on Integral Method ................... 32

1.7.5 Limiting Radius for Freezing a Tumor during Cryoablation ....... 36

1.8 Conclusions ................................................................. 38

1.9 Nomenclature ............................................................... 39

1.10 References ................................................................... 41

1.1 Introduction
There has been considerable interest in developing sound and accurate thermal
models that describe heat transfer within a living tissue with blood perfusion.
Since the landmark paper by Pennes (1948), a number of bioheat transfer
equations for living tissue have been proposed to remedy possible shortcom-
ings in his equation. Although Pennes' model is often adequate for roughly
describing the effect of blood flow on the tissue temperature, there exist some
serious shortcomings in his model due to its inherent simplicity, as pointed out
by Wulff (1974), namely, assuming uniform perfusion rate without accounting
for blood flow direction, neglecting the important anatomical features of the
circulatory network system such as countercurrent arrangement of the system,
and choosing only the venous blood stream as the fluid stream equilibrated
with the tissue.
To overcome these shortcomings, a considerable number of modifications
have been proposed by various researchers. Wulff (1974) and Klinger (1978)
considered the local blood mass flux to account the blood flow direction, while
Chen and Holmes (1980) examined the effect of thermal equilibration length
on the blood temperature and added the dispersion and microcirculatory per-
fusion terms to the Klinger equation.
All foregoing papers concerned mainly with the cases of isolated vessels
and the surrounding tissue. The effect of countercurrent heat transfer between
closely spaced arteries and veins in the tissue must be taken into full consid-
eration when the anatomical configuration of the main supply artery and vein
in the limbs is treated. Following the experimental study conducted by Bazett
and his colleagues (1948a,b), Scholander and Krog (1957), and Mitchell and
Myers (1968) investigated such an effect and successfully demonstrated that
the countercurrent heat exchange reduces heat loss from the extremity to the
surroundings, which could be quite significant because of a large surface to
volume ratio. Keller and Seiler (1971) established a bioheat transfer model
equation to include the countercurrent heat transfer, using a one-dimensional
configuration for the subcutaneous tissue region with arteries, veins, and cap-
illaries. Weinbaum and Jiji (1979) proposed a new model, which is based