Mathematical Modeling of Breast Tumor Destruction Using Fast Heating during Radiofrequency Ablation

Abstract

In oncology, hyperthermia is understood as a planned, controlled technique of heating cancerous changes in order to destroy their cells or stop their growth. In clinical practice, hyperthermia is used in combination with radiotherapy, chemotherapy, or immunological therapy. During the hyperthermia, the tissue is typically exposed to a temperature in the range of 40-45 • C, the exception is thermoablation, during which the temperatures reach much higher values. Thermoablation is characterized by the use of high temperatures up to 90 • C. The electrode using the radiofrequency is inserted into the central area of the tumor. Interstitial thermoablation is used to treat, among others, breast and brain cancer. The therapy consists of inducing coagulation necrosis in an area that is heated to very high temperatures. Mathematical modeling is based on the use of a coupled thermo-electric model, in which the electric field is described by means of the Laplace equation, while the temperature field is based on the Pennes equation. Coupling occurs at the level of the additional source function in the Pennes equation. The temperature field obtained in this way makes it possible to calculate the Arrhenius integral as a determinant of the destruction of biological tissue. As a result of numerical calculations regarding the temperature field and the Arrhenius integral, it can be concluded that, with the help of numerical tools and mathematical modeling, one can simulate the process of destroying cancerous tissue.

Plasmonic Nanocomposite Implants for Interstitial Thermotherapy: Experimental and Computational Analysis

“… (W m K ) is the temperature dependent thermal conductivity, which is assumed to be a linear function that is defined by [ 36 ]: where T (K) and (K) are the normal body and arbitrary temperatures, respectively. is the density of blood, , the specific heat capacity of blood, and is the coefficient of blood perfusion that is assumed to be dependent on the cell damage, , and is defined by [ 37 , 38 ]: ( ) is the baseline coefficient of blood perfusion. (W m ) is the metabolic heat.…”

“…where T (K) and T b (K) are the normal body and arbitrary temperatures, respectively. ρ b is the density of blood, c b , the specific heat capacity of blood, and ω b (Ω) is the coefficient of blood perfusion that is assumed to be dependent on the cell damage, Ω, and is defined by [37,38]:…”

“…Thermo-physical properties of the biological domains that were used in the simulation. The values were obtained from Refs [38,39]. …”

A Comprehensive Narrative Review on the Evolving Role of Endoscopic Ultrasound in Focal Solid Liver Lesions Diagnosis and Management

“…The application of EUS-guided RFA in patients with focal liver lesions is again reserved for HCC patients who are not candidates for definitive therapy and patients who failed previous minimally invasive therapies, such as trans-arterial chemoembolization (TACE) [57,58]. RFA is a low-risk minimally invasive procedure, which acts by delivering heat waves (in the range of 350-500 kHz) [59] that subsequently cause burning of the tumorous tissue, an effect that is mediated via coagulation necrosis [60]. A specifically designed needle tip electrode for performing EUS-RFA (EUSRA RF Electrode, STARmed, Koyang, Korea) with a designed internally cooled needle electrode was used for the first time in 2012 [61].…”

Numerical analysis of the temperature impact to the oxygen distribution in the biological tissue

“…where w(Arr) and w 0 denote damage-dependent and initial perfusion coefficients [s -1 ] respectively, while Arr is the tissue damage degree estimated on the basis of Arrhenius injury integral [15][16][17]…”