Analysis and Simulation on a Model for the Evolution of Tumors under the Influence of Nutrient and Drug Application
This work provides a mathematical framework for understanding tumor dynamics under nutrient and drug influence, but it is an incremental contribution to existing tumor modeling literature.
The authors model tumor evolution using PDEs with nutrient and drug effects, showing that a necrotic core forms when nutrient levels drop below a critical threshold, and that tumor shrinkage or growth depends on the nutrient-drug balance.
We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application. Rigorous analysis and simulations are presented which show the role of nutrient and drug application in the progression of tumors. We construct an explicit convergent numerical scheme to approximate solutions of the nonlinear system of partial differential equations. Extensive numerical tests show that solutions exhibit a necrotic core when the nutrient level falls below a critical level in accordance with medical observations. The same numerical experiment is performed in the case of drug application for the purpose of comparison. Depending on the balance between nutrient and drug both shrinkage and growth of tumors can occur. The role of inhomogeneous boundary conditions, vascularization and anisotropies in the development of tumor shape irregularities are discussed.