Computational Modeling of Macromolecule Transport in the Arterial Wall

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Abstract
In the present study a numerical model for the convective-diffusive transport of macromolecules in the various layers of the arterial wall is developed. The model considers the transport in the endothelium, intima, internal elastic lamina (TEL) and media of a straight axisymmetric arterial segment. The transport processes in the various wall layers and in the arterial lumen are coupled using appropriate conditions. The blood flow in the arterial lumen is mathematically modeled using the Navier-Stokes equations, the filtration velocities in the wall are calculated applying Darcy's law. The description of the mass transport in the lumen uses the convection-diffusion equation, the transport in the porous intima and media is modeled applying the volume-averaged convection-diffusion-reaction equation. The flux across the endothelium and IEL is described using the Kedem-Katchalsky equations. The transport parameters of the various porous wall layers are obtained from suitable pore models and fiber matrix models. The numerical solution of the Navier-Stokes equations and of the mass transport equations applies the finite element method and an upwind stabilization procedure. The study demonstrates, that the numerical model developed can be easily used to investigate the sensitivity of the mural macromolecule accumulation dependence on parameters, such as the molecule size, the degree of endothelial injury, the conditions at the media-adventitia interface, occurrence of smooth muscle cells within the intima, and chemical reactions.