Page 264 - Computational Modeling in Biomedical Engineering and Medical Physics

Hyperthermia and ablation 253

temperature reaches the critical value (T h respectively T c ), and (2) the temperature
exceeds (hyperthermia) or decreases below (cryoablation) the critical value for a certain
time (t h , respectively t c ).
A damage tissue indicator, α d , and a necrosis time indicator, α t , are defined through

ð t ð t ð t ð t
1 1 1 1
α d 5 δ d;h T d;h dt 1 δ d;c T d;c dt; α n 5 δ n;h T n;h dt 1 δ n;c T n;c dt;
t d;h 0 t d;c 0 t n;h 0 t n;c 0
ð8:2Þ
where δ h 5 1 for T . T h , and 0 otherwise, and δ c 5 1 for T , T c and 0 otherwise.
The subscript “d” stands for damage, “n” for necrosis, “h” for hyperthermia, and “c”
for cryoablation (Comsol, 2010 2019). A concise expression for the overall fraction
of damaged tissue is

1 if α n . 0;
Ω 5 ð8:3Þ
min α d ; 1ð Þ otherwise:
Effective thermal conductivity, k eff 5 θ d k d 1 (1 θ d )k, and effective heat capacity at
constant pressure, (ρC p ) eff 5 θ d ρ d C p,d 1 (1 θ d ) ρC p , are introduced to account for the
tissue injury—here, ρ d is the mass density, C p , d , the heat capacity at constant pressure,
k d the thermal conductivity for the damaged tissue of the damaged tissue, and θ d is a
weight term.
As already discussed, numerical modeling may provide useful and unique information
on the underlying heat transfer paths and mechanisms in thermal therapy that could assist
the preoperational planning, improve the diagnosis, and could suggest therapeutic proto-
cols. In what follows, this chapter presents several localized hyperthermia and ablation
models with EMF and US power sources and emphasizes the effects of the local vascu-
larization upon the heat transfer balance. The optimization of the applicators, the control
of their location, and the adjustment of the heating protocols are currently possible, and
numerical simulation may bring a significant help in improving the procedures based on
the predictive analysis of the thermal behavior of tissues.

8.2 Radiofrequency thermotherapy

Radiofrequency localized hyperthermia ablation of tumors is a relatively new, promis-
ing, minimum invasive, and highly effective tumor extirpation procedure that may be
used to eradicate bone, lung, liver, and renal smaller tumors (Ramanathan et al.,
2010). The heat source is provided by the electrothermal (Joule) effect.
In RFA, high-frequency electrical currents flow through a needle electrode intro-
duced into the tumor to some ground pads positioned on the body, to create a focal