**2.5 Regional hyperthermia**

The term "Regional hyperthermia" means treating deep-seated tumors of the pelvis or lower extremities, etc. The so-called regional applicators can perform treatment, i.e., usually, an array of phase-controlled radiating elements typically working in the frequency range of 50–150 MHz. As radiating elements again, waveguides or dipoles are mostly being used. They surround the whole circumference; all possible directions are employed to deliver EM energy into the treated volume. The higher number of antennas and higher the frequency have the potential to control the heating 3D pattern. Several rings of antennas directed to the patient axis can be used to enable flexibility with respect to the anatomical structures for optimization.

A system for regional hyperthermia consists of a microwave (MW) or radiofrequency (RF) multichannel power generator (multiple power generators), an array of MW applicators for focusing EM power into the area to be treated (tumor), a multichannel thermometer with several probes for measurements of temperature in the tumor and its surroundings, and the main computer; see the schematics in **Figure 3**.

Applicators are positioned upon the area to be treated and coupled to the tissue by a water bolus. The water temperature in the water bolus is possible to control, so it is possible to modify the temperature profile in the area to be treated, like in the case of local hyperthermia. In the case of regional hyperthermia, the water temperature in the water bolus is usually below 10°C.

From a physical point of view, we mostly want to create the best possible approximation of a cylindrical or spherical EM wave irradiated from several (typically from 4

**Figure 3.** *Schematics of microwave system for regional or part-body hyperthermia.* up to 12) single applicators situated around the patient. Superposition of the waves from these single applicators then creates inward propagating cylindrical or spherical waves, enabling the focus EM power in the area to be treated. Thus we can get the best approximation of the tumor dimensions and shape by dimensions and shape of the SAR distribution and thus, the best approximation of temperature distribution.

In discussed case, when we have a cylindrical phantom surrounded by several above mentioned applicators, then for the thermotherapy, the most important component of the EM field will be longitudinal component Ez, which in the discussed case can be expressed by equation.

$$\mathbf{E}\_{\mathbf{z}}(r) = \mathbf{K} \mathbf{H}\_0^{(2)}(\mathcal{yr}),\tag{3}$$

where Hð Þ<sup>2</sup> <sup>0</sup> is the Hankel function of zero order and second kind, *K* is a constant, *r* is a radius vector, *γ* is a complex propagation constant. Hankel function Hð Þ<sup>2</sup> <sup>0</sup> can be calculated as a linear combination of the Bessel function J0 and the Neumann function N0:

$$\mathbf{H}\_0^{(2)}(\mathcal{yr}) = \mathbf{J}\_0(\mathcal{yr}) \text{--jN}\_0(\mathcal{yr}),\tag{4}$$

As cylindrical agar phantom is mimicking muscle tissue, i.e., lossy medium, then the argument of Hankel function is a complex number. In **Figure 3**, there are three basic cases of temperature distribution inside an area treated by regional hyperthermia, which follows from the behavior of the Hankel function (see the narrow colored strips signed by letters *a*, *b,* and *c*):


Given examples of frequency bands are valid either for the human body of average dimensions or for agar phantom with similar dimensions and dielectric parameters with values near to values valid for muscle tissue.

### **2.6 Part-body hyperthermia**

Part-body hyperthermia is a technique derived from the regional approach and developed to heat a selected anatomical region in an extended manner up to 41–42°C under careful MR monitoring. From a physical point of view, we want mostly to

create the best possible approximation of a spherical EM wave irradiated from several (typically from 12 up to 24) single applicators situated around the patient.

Superposition of the waves from these single applicators then creates inward propagating spherical waves enabling the focus EM power in the area to be treated. Thus, we can get the best approximation of the tumor dimensions and shape by dimensions and shape of the SAR distribution and thus, the best approximation of temperature distribution.

Due to safety reasons, the use of MR monitoring (to measure online temperature and perfusion) and a planning system is required at these higher power levels. Systems for part-body hyperthermia are called "hybrid systems" because they are based on the MR-compatible integration of a multiantenna applicator into an MR tomograph.

### **2.7 EM waves in biological tissue**

The most important effect from the point of view of microwave thermotherapy is the propagation of EM waves through the biological tissue to be treated. It can be classified as lossy dielectrics. So the power (energy) of propagating EM wave will be changed into thermal power (energy). For more details, see [1–20].

EM energy turns to heat, particularly due to the following mechanism: When the alternate field takes effect, vibrating electric particles lag behind the exciting intensity of the electric field; the current is not entirely in phase with electric field intensity. It is possible to describe this phase mathematically in a way that we virtually split up the movement of electrons into:


The first component mentioned above determines the real part of permittivity *ε*<sup>0</sup> . The other one is the cause of loss of current heating up the dielectric and determining the imaginary (conductive) part of permittivity *ε*00. From this, relative permittivity depends on the polarization charge value of the dipole, and alternate losses depend on the weight and volume of moving particles. The dielectric quality is thus given by the ratio of particle charge and particle mass.

When the electromagnetic energy goes through the biological tissue, it is absorbed and turned into heat, resulting in a temperature increase of biological tissue within the irradiated area. Spatial distribution of temperature induced the way mentioned above (with respect to depth of EM wave penetration and depth of efficient treatment) depends on various factors.

The interaction of the EM field with biological tissue studied from a physical point of view is well described in several references, e.g. [1–20], so we do not need to go into the details here. When studying these interactions to be used in clinical applications of thermotherapy, then usually it is necessary to determine by calculations or measurements following 3D or 4D distributions:

• The 3D spatial distribution of the values of the EM field main quantities (e.g., vector of electric field strength **E**(*x*,*y*,*z*), vector of magnetic field strength **H** (*x*,*y*,*z*), etc.) in a certain area of the biological tissue—area to be treated.

• The 3D spatial distribution of power *P*<sup>a</sup> absorbed in a given biological object can be for a single point or elementary volume (voxel) calculated as

$$P\_a(\mathbf{x}, \mathbf{y}, \mathbf{z}) = \frac{\sigma}{2} |\mathbf{E}(\mathbf{x}, \mathbf{y}, \mathbf{z})|^2. \tag{5}$$

The 3D spatial distribution of specific absorption rate—the SAR [W/kg] indicates the EM energy absorbed in the biological tissue and, as shown by the unit, it is the power absorbed per 1 kg of tissue

$$SAR = \frac{\delta}{\delta t} \left( \frac{\delta W}{\delta m} \right) = \frac{\delta}{\delta t} \left( \frac{\delta W}{\rho \delta V} \right) = \frac{\delta P}{\delta m} = \frac{\delta P}{\rho \delta V},\tag{6}$$

where *W* is the electromagnetic energy absorbed in the biological tissue, *t* is the time, and m denotes mass. *P* is the power of the electromagnetic wave that spreads the biological tissue, *ρ* is the density of the tissue, and *V* is the volume. By introducing the spatial distribution of the intensity of the electric field E (x, y, z), the relationship is as follows:

$$SAR = \frac{\sigma}{\rho} \frac{\left| E(x, y, z) \right|^2}{2} \tag{7}$$

Which can be further modified as *SAR* = *P*a/ρ. In case of experimental evaluation of the SAR, we can measure the temperature increase Δ*T* after heating by EM-power in time interval Δ*t.*

$$SAR = c \frac{\delta T(\mathbf{x}, y, z, t)}{\delta t} = c \frac{\Delta T(\mathbf{x}, y, z, t)}{\Delta t},\tag{8}$$

where *c* is the specific heat of the biological tissue or its phantom and SAR very well defines the level of exposure of the biological tissue.

• The 4D—i.e., spatial and time-dependent distribution of temperature *T* (*x*,*y*,*z*,*t*) in a given biological object, which can be calculated from the so-called Penne's Bioheat Equation, see in part 2.9 of this chapter.

High-frequency electromagnetic fields can penetrate the human body and propagate through. During the propagation of EM waves through biological tissues, their energy is gradually absorbed and converted into heat, thereby increasing the temperature of the irradiated area. To such a wave, biological tissues behave as a lossy dielectric. In such a case, permittivity and permeability become to be complex numbers. The spatial distribution of temperature depends on many factors, the most important of which are:

