A theoretical model for water flux through the artery wall

A two layer model for water flux through the artery is studied using a mathematical model based on the theory for the consolidation of water saturated soils. The matrix is considered to be constituted by two layers with different permeabilities and different elastic constants and the two systems of equations are coupled with the condition of continuity of pressure, total stress, solid displacement and fluid seepage velocity at the interface. The luminal pressure is considered to be harmonic in time. Exact solutions are obtained for displacements and pressures in both the layers. For large consolidation times, large pressure gradients are found to exist near the boundaries and at the interface. The heterogeneous model may not only be useful to understand the mechanics of transport in the physiological system but it will also help the bioengineers to choose proper implant materials to design artificial vascular organs for the purpose of prosthesis.