An analytical model for solute transport from blood to tissue

For narrow tubes, red blood cells concentrate in the core region, leaving an annular zone called cell-free layer. This has an impact on both the tube hematocrit level (Fåhraeus effect) and the apparent blood viscosity (Fåhraeus–Lindqvist effect). Blood flow, mass transfer across the microvessel membrane, and diffusion in the tissue affect the solute concentration profiles. The Krogh tissue cylinder concept, limiting mass transfer to a cylinder around each microvessel, and the marginal zone concept (introduced by Haynes to analyze blood flow dynamics in narrow tubes) are both used to develop a model for solute transfer from blood in microvessels to the surrounding tissues, based on fundamentals. The analysis accounts for advection and diffusion in each zone of the microvessel, solute transport in the microvessel membranes, and diffusion and reaction in the tissues. The present investigation provides an analytical solution. The approach can be extended to treat other kinetic models, while accounting for Fåhraeus and Fåhraeus–Lindqvist effects in blood microvessels. The model is validated against published results for glucose transport from blood to tissue.