Inverse Problem of Estimation of the Blood Perfusion Coefficient in Cancerous Tissues

The success of the treatment of malignant tumors by hyperthermia calls for the knowledge of the temperature field for both healthy and cancerous tissues. This medical procedure consists in exposing malignant cells to temperatures in the range of 42°C to 45 ° C in order to retard, stop or reverse the growth of tumors. Although susceptible to the increase in temperature, the normal cells do not exhibit the same degree of sensitivity as the malignant cells and therefore the potential of induced hyperthermia as a therapy for cancer has been long considered for both local and global treatments. For the case of local hyperthermia, it is important to predict and control the thermal fields generated by the external medical device responsible for increasing local temperature. However, the task of controlling both temperature levels and duration of the heating process cannot be satisfactory accomplished based solely on measurements because only a few localized temperature readings can be monitored during the therapy. Therefore, mathematical models commonly employed in engineering are often used in the simulation of the heat transfer in living tissues, furnishing temperature profiles that may guide the physician before and after the treatment. One of these models is the bioheat transfer equation proposed by Pennes [1] that consists in a heat diffusion equation together with an energy sink term that accounts for the effect of the temperature difference between the blood supply and the tissue. The source term of this equation carries a combined effect of the internal metabolic heat generation and the external irradiation of the treatment. In this work, a parameter estimation produce based on several optimization methods [2, 3] was employed, in order to determine the perfusion coefficient of Pennes ’ model