Differential equation models for tumor growth dynamics

Growth of tumors is a complex process that is regulated by cellular proliferation, the availability of nutrients and the development of blood vessels, as well as by the tumor's environment.This research builds a mathematical model based on differential equations to analyze the dynamics of tumor growth and the related control of tumor angiogenesis.Proposed model represents tumour cell population and carrying capacity by coupled nonlinear differential equations along with the intrinsic proliferation, growth limitation, vascular support and tumour-induced angiogenesis.Systematically biological assumptions and model variables are expressed to set up realistic relations between the expansion of the tumor and the availability of resources.A numerical solution algorithm is used to explore the changes in tumor volume and vascular carrying capacity for various parameter values.Results of the simulations show typical growth phases: a period of fast growth which leads to a period of slower growth where environmental factors are limiting growth.The framework allows for quantitative analysis of the tumor progression, equilibrium and parameter sensitivity.The proposed model is a flexible mathematical framework for the understanding of the dynamics of a tumor and the computational evaluation of therapeutic strategies.