Impact of radiation therapy on healthy and cancerous cell dynamics: a Mathematical analysis

This study proposes a novel therapeutic model for cancer treatment with radiation therapy by analyzing the interactions among cancer, immune and healthy cells through a system of three ordinary differential equations. In this model, the natural influx rate of mature immune cells is assumed constant and is denoted by, a. The overall effect of radiation therapy on cancer cells is represented by a parameter, s; which is the surviving fraction of cells as determined by the Linear Quadratic (LQ) model. Conditions for the stability of equilibria in the interaction model modified to include the surviving fraction, are systematically established in terms of the dose and model parameters. Numerical simulations are performed in Wolfram MATHEMATICA software, investigating a spectrum of initial cell population values irradiated with ⁶⁰Co $$-ray Low-LET radiation and High-LET 165 $$ Ni-ion radiation to facilitate improved visualization and in-depth analysis. By analyzing the model, this study identifies threshold values for the absorbed dose D for particular values of the model and radiation parameters for both High Linear Energy Transfer (high-LET) and Low Linear Energy Transfer (low-LET) radiations that ensure either eradication or minimization of cancer cells from a patient's body, providing valuable insights for designing effective cancer treatments.