MATHEMATICAL-MODEL OF WATER FLUX THROUGH AORTIC TISSUE

Water flux in porcine aortic segments produced by the sudden application of a hydrostatic pressure gradient has been described in a recent paper by Harrison and Massaro (1976). A mathematical model is developed here to explain the results obtained when pressure is applied to either covered or uncovered samples. The model predicts that the rate of exudation in both instances should be substantially identical for a period of time ∼ 0.2τ, where τ is the consolidation time. The consolidation time is proportional to the hydraulic resistance to liquid flow, and inversely proportional to the compressive stiffness of the artery. The existence of a time-dependent water flux in an artery in vivo during periodic pressurization is predicted by the mathematical model if the resistance to water flow at the endothelium is not excessive. The pore pressure within the bulk of the media is predicted to pulsate in a highly unexpected fashion. These predictions follow naturally from the fact that the consolidation phenomenon in large arteries, as determined by the compression tests of Harrison and Massaro, is of long duration, much longer than the period of a heartbeat. Pressure gradients in vivo in interstitial fluid are then confined to a very small fraction of the total arterial wall thickness. A potential for plasma sloshing" across the endothelial junctions exists. The convective flux of water across an endothelial layer may therefore be of a pulsatile character in normal arteries in vivo. © 1979 Society for Mathematical Biology."