Numerical simulation of growth of an atherosclerotic lesion with a moving boundary

We consider a mathematical model of the formation of an atherosclerotic lesion that is based on a simplification of Russell Ross' paradigm of atherosclerosis as a chronic inflammatory response. Atherosclerosis is characterized by the accumulation of lipid-laden cells in the arterial wall that can result in lesions within the artery. Such lesions can cause an occlusion of the artery resulting in heart attack. The presented mathematical model describes, among others, a response of immune and smooth muscle cells to biochemical signals of chemoattractants and a build up of debris. It results in a coupled system of four nonlinear reaction-convection-diffusion equations including a free inner boundary that is permitted to move due to an additional evolution equation. We perform a numerical study of the problem using fully implicit finite volume discretization methods. The moving boundary is described implicitly using an evolution of a level set function. In such a way, a grid used in numerical simulation can remain fixed during the whole computations. In this report, we present preliminary results that demonstrates that our numerical model captures certain observed features such as the localization of immune cells, the build-up of debris, the isolation of a lesion by smooth muscle cells, and an occlusion of the artery

Maximum Principle And Local Mass Balance For Numerical Solutions Of Transport Equation Coupled With Variable Density Flow

. A parabolic convection-diffusion equation of the transport in porous media strongly coupled with a flow equation through a variable fluid density is studied from the point of view of the qualitative properties of numerical solution. A numerical discretization is based on "node-centered" finite volume methods with a clear form for a local mass balance property. Numerical solutions of the discrete conservation laws fulfill a discrete maximum (and minimum) principle. The presented results are an extension of ones in [12], [7] and [1] for the case of transport equation coupled with variable density flow including the source/sink terms, inflow/outflow boundary conditions and anisotropic diffusion and for the case of upwind algorithms applied to a general class of finite volume meshes. 1. Introduction and Mathematical Model A motivation of the following mathematical problem arises from the area of modelling the groundwater flows near salt domes where the fluid is supposed to be a mixture ..

Consistent Velocity Approximation for Density Driven Flow and Transport

The flow and transport problems that include the variation of the fluid density are much more difficult to solve numerically as the problems with constant density. The artificial numerical velocities that have no counterpart in the analytical situation are the most typical difficulty that has to be anticipated here. The topic will be presented for a general class of models with density driven velocities including new improved algorithms of consistent velocity approximation

Semi-analytical solutions for contaminant transport with nonlinear sorption in 1D

SIGLEAvailable from TIB Hannover: RR 1606(2002,24) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany); Bundesministerium fuer Bildung und Forschung, Berlin (Germany)DEGerman