A time-dependent multi-layered mathematical model of filtration and solute exchange, the revised Starling principle and the Landis experiments

Cell oxygenation and nutrition is vitally important for human and animal life. Oxygen and nutrients are transported by the blood stream and cross microvessel walls to penetrate the cell’s membrane. Pathological alterations in the transport of oxygen, and other nutrition elements, across microvessel walls may have serious consequences to cell life, possibly leading to localized cell necrosis. We present a transient model of plasma filtration and solute transport across microvessel walls by coupling flow and transport equations, the latter being non-linear in solute concentration. The microvessel wall is modeled through the superimposition of two or more membranes with different physical properties, representing key structural elements. With this model, the combined effect of the endothelial cells, the glycocalyx and other coating membranes specific of certain microvessels, can be analyzed. We investigate the role of transient external pressures in the study of trans-vascular filtration and solute exchange during the drop of blood capillary pressure due to the pathological decrease of blood volume called hypovolaemia, as well as hemorrhage. We discuss the advantage of using a multi-layered model, rather than a model considering the microvessel wall as a single and homogeneous membrane.