Characterization of Thermal Damage Due to Two-Temperature High-Order Thermal Lagging in a Three-Dimensional Biological Tissue Subjected to a Rectangular Laser Pulse

The use of lasers and thermal transfers on the skin is fundamental in medical and clinical treatments. In this paper, we constructed and applied bioheat transfer equations in the context of a two-temperature heat conduction model in order to discuss the three-dimensional variation in the temperature of laser-irradiated biological tissue. The amount of thermal damage in the tissue was calculated using the Arrhenius integral. Mathematical difficulties were encountered in applying the equations. As a result, the Laplace and Fourier transform technique was employed, and solutions for the conductive temperature and dynamical temperature were obtained in the Fourier transform domain.

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

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.

Tumor Shrinkage Study in Magnetic Nanoparticle Hyperthermia Based on Designed Heating Protocols

Magnetic nanoparticle hyperthermia has attracted growing attentions recently due to its ability of confining nanoparticle-induced heating in targeted tumor region. Our recent studies have identified an injection strategy to achieve repeatable and controllable nanoparticle deposition patterns in PC3 tumors using microCT scans. Based on the injection strategy, simulation of temperature elevations in tumors is conducted to design heating protocols to induce irreversible thermal damage to the entire tumors. In this study, in vivo heating experiments are performed on PC3 tumors implanted on mice following the designed heating protocols. The tumors in the control group without heating triple their sizes over a period of eight weeks. The tumors in the heating groups are heated for either 25 minutes or 12 minutes, representing that the Arrhenius integral is equal to or larger than 4 or 1 in the entire tumors, respectively. The tumors in the heating group of 25 minutes disappear completely after the 3rd days, and the site maintains the disappearance for over eight weeks. The sizes of the tumors in the heating group of 12 minutes decrease in the first ten days, however, the tumors re-grow afterwards, and by the end of the 8th week, they are approximately 60% larger than their initial size. This study demonstrates the importance of imaging-based design for individualized treatment planning. The success of the designed heating protocol in complete damaging PC3 tumors validates the theoretical models used in planning the heating treatment in magnetic nanoparticle hyperthermia.