Indirect Contributions to Tumor Dynamics in the First Stage of the Avascular Phase

Abstract

A continuum model for tumor invasion in a two-dimensional spatial domain based on the interaction of the urokinase plasminogen activation system with a model for cancer cell dynamics is proposed. The arising system of partial differential equations is numerically solved using the finite element method. We simulated a portion of biological tissue imposing no flux boundary conditions. We monitored the cancer cell dynamics, as well the degradation of an extra cellular matrix representative, vitronectin, and the evolution of a specific degrading enzyme, plasmin, inside the biological tissue. The computations were parameterized as a function of the indirect cell proliferation induced by a plasminogen activator inhibitor binding to vitronectin and of the indirect plasmin deactivation due to the plasminogen activator inhibitor binding to the urokinase plasminogen activator. Their role during the cancer dynamical evolution was identified, together with a possible marker helping the mapping of the cancer invasive front. Our results indicate that indirect cancer cell proliferation biases the speed of the tumor invasive front as well as the heterogeneity of the cancer cell clustering and networking, as it ultimately acts on the proteolytic activity supporting cancer formation. Because of the initial conditions imposed, the numerical solutions of the model show a symmetrical dynamical evolution of heterogeneities inside the simulated domain. Moreover, an increase of up to about 12% in the invasion speed was observed, increasing the rate of indirect cancer cell proliferation, while increasing the plasmin deactivation rate inhibits heterogeneities and networking. As cancer cell proliferation causes vitronectin consumption and plasmin formation, the intensities of the concentration maps of both vitronectin and plasmin are superimposable to the cancer cell concentration maps. The qualitative imprinting that cancer cells leave on the extra cellular matrix during the time evolution as well their activity area is identified, framing the numerical results in the context of a methodology aimed at diagnostic and therapeutic improvement.