Comparison of solving algorithms for a mathematical model of filtration-diffusion transfer in the medium of spherical moisture-saturated microporous particles

The article considers the use an analytical and numerical approaches for finding solutions of mathematical model of diffusion mass transfer in the medium of particles of microporous structure. The special software developed based on both approaches and these software were used for computer simulation of pressures in particles and interparticle space for spatial and temporal parameters of the filtration process, and the results were compared taking into account their accuracy and speed of production. Considered algorithms showed approximately the same accuracy in finding the pressure profiles. Analytical solution-based software has demonstrated the higher efficiency for calculating unit pressure values at given parameters, in turn, numerical techniques have been found to be convenient for building high-resolution profiles.

Microvascular permeability, ultrafiltration, and restricted diffusion

This essay looks at the historical significance of two APS classic papers that are freely available online: Pappenheimer JR and Soto-Rivera A. Effective osmotic pressure of the plasma proteins and other quantities associated with the capillary circulation in the hindlimbs of cats and dogs. Am J Physiol 152: 471–491, 1948 ( http://ajplegacy.physiology.org/cgi/reprint/152/3/471 ). Pappenheimer JR, Renkin EM, and Borrero LM. Filtration, diffusion and molecular sieving through peripheral capillary membranes: a contribution to the pore theory of capillary permeability. Am J Physiol 167: 13–46, 1951 ( http://ajplegacy.physiology.org/cgi/reprint/167/1/13 ).

THE FINE STRUCTURE OF CAPILLARIES AND SMALL ARTERIES

Details of capillary endothelia of the mammalian heart are described and compared with capillaries of other organs and tissues. Continuous invagination and pinching off of the plasma membrane to form small vesicles which move across the cytoplasm are suggested as constituting a means of active and selective transmission through capillary walls (12). This might be designated as cytopempsis (transmission by cell). The fine structure of the different layers in the walls of small heart arteries is demonstrated. Endothelial protrusions extend through windows of the elestica interna to make direct contact with smooth muscle plasma membranes. The elastica interna appears to vary greatly in both thickness and density, and probably restricts filtration, diffusion, and osmosis to such an extent that windows and the transport mechanisms described (cytopempsis) are necessary for the functional integrity of the smooth muscle layer. The contractile material consists of very fine, poorly oriented filaments.