A generalized multilayer reaction–diffusion model for tumor dynamics under hyperthermic therapy with spatial heterogeneity

Local hyperthermia is an effective treatment for advanced malignant tumors, whose multilayer structure and physiological heterogeneity strongly influence their response to therapy. In this work, a generalized multilayer reaction-diffusion model is developed to study tumor-volume dynamics under localized hyperthermic treatment. The tumor is represented as a set of interacting biological layers, allowing spatial variation in key parameters such as diffusion and proliferation. The model is formulated with appropriate initial, interface and boundary conditions and solved using the finite element method. Simulations are carried out for planar, cylindrical and spherical tumor geometries to examine the effects of heterogeneity, geometry and hyperthermia. The results show a clear reduction in tumor volume under thermal therapy, with stronger effects observed in spherical tumors due to enhanced diffusion. Sensitivity analysis and comparison with published data further support the reliability of the model. Overall, the proposed work provides a simple and flexible approach for analyzing tumor behavior under hyperthermic treatment. This work can support future treatment planning studies.