Local hyperthermic treatment of an advanced in vivo malignant tumor: A compartmental cum mathematical model

Hyperthermia, also called as thermal ablation, is used to treat some advanced cancers. Numerous clinical trials indicate that hyperthermia, when combined with therapies like radiation and chemotherapy, can reduce tumor size and potentially enhance their ability to eradicate cancerous cells. Hence, it is of utmost importance to study the behavior and transmission dynamics of in vivo malignant tumors subjected to hyperthermia. To this purpose, a mathematical model has been formulated, primarily based on the reaction–diffusion equation, imposed with suitable initial and boundary conditions. As the advanced tumors usually consist of five layers, the domain is discretized into five compartments. The model is then solved analytically using the eigenvalue expansion method to determine the tumor cell volume profiles, in the presence and absence of hyperthermia. The main foci of the developed model are the discretization of the domain, variable nature of various physiological parameters involved, and its analytical solution, thereby aiming at strengthening the novelties of the present work. The model outcome and simulations obtained are compared with the previously published/clinical results to prove the validity and feasibility of the proposed work. This work is expected to provide an optimum mathematical model utilizing best mathematical techniques that can greatly aid researchers and biologists in the field of oncology to streamline the process and reduce costs associated with cancer treatment.