Numerical simulation of avascular tumor growth

A mathematical and numerical model for the description of different aspects of microtumor development is presented. The model is based in the solution of a system of partial differential equations describing an avascular tumor growth. A detailed second-order numeric algorithm for solving this system is described. Parameters are swiped to cover a range of feasible physiological values. While previous published works used a single set of parameters values, here we present a wide range of feasible solutions for tumor growth, covering a more realistic scenario. The model is validated by experimental data obtained with a multicellular spheroid model, a specific type of in vitro biological model which is at present considered to be optimum for the study of complex aspects of avascular microtumor physiology. Moreover, a dynamical analysis and local behaviour of the system is presented, showing chaotic situations for particular sets of parameter values at some fixed points. Further biological experiments related to those specific points may give potentially interesting results