**5. RF penetration depth**

Penetration depth of RF energy depends on the electrode geometry and divergence of the RF current inside the tissue. We will determine RF penetration depth as the depth where RF energy is decreased by exponential factor (*e = 2.71* … ) and analyze a few typical cases (**Figure 5**).

The first case in **Figure 5** illustrates small electrode distant from the return electrode. The RF current density and consequently electric field in vicinity of the electrode diverges spherically and current density drops as square of distance from electrodes. Taking into the account that heat is proportional to square of electric field. Therefore, heat created by RF energy can be represented as following:

$$H = \sigma E\_o \left(\frac{r\_0}{r\_0 + d}\right)^4 \tag{5}$$

Where *E0* is electric field on the surface of semispherical electrode, r0 is radius of electrode and d is distance from the electrode. It is easy to calculate that heating drops by exponential factor at *d = 0.28 r0*. For the electrosurgical electrode having tip with radius about 0.5 mm the RF penetration into the tissue is about 140 microns. Such small RF penetration depth allows to cut the tissue with minimal thermal damage.

**Figure 5.** *RF current distribution for typical geometries of electrodes.*

**Figure 5b** shows two long electrodes having cylindrical surface contacting the tissue. The distance between the electrodes is larger than an electrode size. In this case the heat distribution near the electrode can be calculated using the following equation:

$$H = \sigma E\_o \left(\frac{r\_0}{r\_0 + d}\right)^2\tag{6}$$

The heating drops by exponential factor at the distance of *d = 0.64 r0*. Such configuration of esthetic devices is commonly used, but the penetration depth is limited and most of the energy is concentrated near the electrode.

The case shown in **Figure 5c** represents two parallel electrodes having size comparable with the distance between them. Analysis of heat distribution required computer simulation but RF penetration depth can be estimated as half distance between the electrodes [10].

The thermal measurements conducted for the three cases described above are shown in **Figure 6**.

Thermal experiments were conducted using porcine tissue and a RF generator with the frequency of 1 MHz and 50 W power. The thermal camera FLIR A320 was used for thermography of tissue during RF application.

Heat conductivity, real geometry of electrodes and non-uniformity of tissue effect the thermal imaging but measurements correlate well with theoretical consideration.

#### **6. Tissue conductivity and impedance**

The electrical properties of tissue play important role in understanding of RFtissue interaction.

Tissue conductivity is a strong function of tissue type. The fundamental article of Gabriel et al. [12] summarized data on electrical conductivity for different types of tissue. **Figure 7** shows tissue conductivity of fat and skin in broad range of frequencies.

In the RF range, the tissue conductivity is a weak function of frequency. The tissue has resistive and capacitive properties. The capacitance of tissue in RF diapason is determined by recharging of cell membrane.

The properties of different types of tissue are presented in **Table 1**.

Our measurements in-vivo for tumesced adipose tissue show that fat's conductivity is very similar to the one of skin and is in the range of 1 to 2 S m�<sup>1</sup> .

Conductivity of tissue is a function of temperature and is changed in the range of sub-necrotic heating by 2%/o C [13]. Our measurements of tissue conductivity

**Figure 6.**

*Thermal measurements of tissue temperature generated by RF current for typical geometries of electrodes.*

*The Basic Science of Radiofrequency-Based Devices DOI: http://dx.doi.org/10.5772/intechopen.96652*

**Figure 7.** *Electrical conductivity of skin and fat as a function of frequency of electrical current.*


#### **Table 1.**

*Tissue conductivity at 1 MHz [12].*

**Figure 8.**

*Impedance of tissue measured between two electrodes applied to the skin surface.*

between two electrodes in-vivo showed smaller change for the temperature close to the normal body temperature and larger change when tissue temperature deviated more (**Figure 8**). The tissue was pre-heated to 43 °C during 15 min and then tissue impedance was measured for short RF pulses during two hours as skin cooled down.

As tissue is heated to higher temperatures resulting in tissue coagulation and dehydration, the tissue impedance is increased dramatically [10]. Schematic change of tissue impedance as function of temperature is shown in **Figure 9**.

### **Figure 9.** *Schematic impedance behavior as function of temperature.*

As mentioned above regarding conductivity, heating of tissue reduces its impedance with a rate of about 2% per degree Centigrade [13]. This change is related to reduction of tissue viscosity which is reduced with temperature increase. Coagulation of the tissue causes a chemical change in tissue structure, subsequently changing the trend of impedance behavior. When heating up to 100 °C, the evaporation of liquids dehydrates the tissue, dramatically increasing tissue impedance. Additional heating of the tissue leads to its carbonization. Dependence of tissue conductivity on temperature is utilized by ELOS (Electro optical synergy) technology where tissue is preheated using optical energy creating a preferable path for RF current [14, 15]. This can provide treatment advantages for some applications.
