Mathematical Modeling of Cancer Inhibition Through Localized Radiation Therapy

This study investigates the possibility of halting the spread of cancer within tissue by acting on a small, targeted area through radiation therapy. Using reaction-diffusion equations, we model the dynamics of cancer proliferation, which are represented by traveling wave solutions. These waves illustrate how cancer cells invade healthy tissue. We propose a method to block this invasion by calculating the critical gap length L∗, which represents the minimum area where radiation can effectively stop the wave of cancerous growth. By adapting the geometric approach of Lewis and Keener, we apply a localized dose of radiation, creating a barrier to the spread of cancer cells. Numerical simulations are performed to support our theoretical findings, offering potential applications to improve localized radiation treatments to prevent the progression of cancer within affected tissues.