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Modelling of tumor cells regression in response to chemotherapeutic treatment


The proposed model describes the interaction among normal, immune and tumor cells in a tumor with a chemotherapeutic drug, using a system of four coupled partial differential equations. The dimensions of the tumor and initial conditions of tumor cells are chosen under the assumption that the tumor is already large enough in size to be detectable with the available clinical devices. The pattern of distribution of tumor cells is drafted on the basis of clinical observations. The stability of the system is established with tumor and tumor-free equilibria. The process of tumor regression with the introduction of different diffusion coefficients of tumor and immune cells is considered along with normal cells of tissue without any diffusive movement. It is shown that the results of chemotherapy treatment are in agreement with Jeff’s phenomenon. The response of three different levels of immune system strength to the pulsed chemotherapy are investigated. It is observed that the tumor performs better if a chemotherapeutic drug is injected near the invasive fronts of the tumor.