**2.8 Treatment planning of clinical application of thermotherapy**

The term treatment planning for clinical application of the thermotherapy means mathematical and experimental modeling of the effective treatment timing to determine the four-dimensional (4D) distribution of temperature (i.e., 3D in space + temperature behavior with respect to time) during the scheduled treatment (both within the treatment area and in its surroundings).

When preparing a particular type of clinical application, it is necessary to perform a series of experiments and model calculations to create a specific idea about the actual distribution of temperature (with respect to SAR) in the treated area. It is a highly complex problem that is not yet fully resolved. This is due to several factors, of which the most important may be considered:


In the case of treatment planning, first, we need to do the calculation of SAR 3D distribution and after to do the calculation of the temperature 3D distribution. This distribution inside the treated area (heated by microwave energy *q*) can be expressed from the well-known Pennes Bioheat Eq. (1948):

$$
\rho \mathbf{C}\_p \frac{\partial T}{\partial t} = \nabla \bullet (k \nabla T) + \rho \mathbf{b}\_b \mathbf{C}\_{p,b} (T\_d - T) + q\_m + \rho \mathbf{S} \mathbf{A} \mathbf{R}.\tag{9}
$$

where *T* is tissue temperature (K), *t* is time (s), *ρ* tissue density (kg/m<sup>3</sup> ), *C*<sup>p</sup> specific heat capacity of tissue (J/kg/K), *C*p,b specific heat capacity of blood (J/kg/K), k thermal conductivity (W/m/K), *ω<sup>b</sup>* volumetric blood flow rate (kg/s/m<sup>3</sup> ) of the specific tissue,*Ta* arterial blood temperature (usually 37°C), and *qm* metabolic heat source rate (W/m3 ).

The possibilities of an analytical solution to this equation are limited to a few cases e.g., the "one-dimensional" case of plane wave penetrating homogeneous phantom. Therefore, computers are to be used to solve this equation to obtain the temperature *T x*ð Þ , *y*, *z*, *t* time dependence and 3D space distribution. For the treatment planning of microwave thermotherapy, it is possible to use commercially available SW products, e.g., SEMCAD X, Sim4Life, Comsol Multiphysics, and CST Microwave Studio.

In general, it is necessary to solve the time dependence of the temperature *T x*ð Þ , *y*, *z*, *t* at different points in complex three-dimensional space with the inhomogeneous structure of the biological tissue whose blood supply changes depending on heating. This is not analytically solvable in general, only partially in the case of simplified geometric models.

The versatile option is to apply numerical methods using very powerful computers. The numerical solution then typically uses differential methods or finite element

methods. The biggest problem then acts precisely, defining and modeling the bloodstream and its responses to cool or heat certain areas of the human body. The situation is further complicated dramatically by the topology of the heated area. The topology can be a good guess for subsurface treatment in clinical applications. However, the more complicated is the situation for deep regional heating when mapping the treated area requires a CT and/or MRI.
