Abstract
This work is focused on the study of the first stages of atherosclerosis development as an inflammatory disease. The mathematical model on which this research is based is given by a system of two-dimensional nonlinear reaction-diffusion equations with a nonlinear source term in one of the equations, that was proposed originally in [1]. In addition, this model incorporates a nonlinear nonhomogeneous Neumann boundary condition which represents the recruitment of immune cells through the upper boundary as a response to the production of cytokines. In this work a new model is proposed considering nonlinear porous-medium type diffusion. The model is solved using a finite volume scheme with dimension-by-dimension WENO reconstruction in space, using entire polynomials, unlike the pointwise WENO reconstruction commonly used, and a third order Runge-Kutta TVD scheme for time integration. The evolution of the inflammation is studied according to the results of the numerical simulation, depending on the values of the bio-physical parameters and the size of the initial inflammation.
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