This monograph provides a comprehensive review of mathematical modeling of kidney transport. It sits at the intersection of mathematical biology and renal physiology. The content is organized according to multiscale model development: from membrane transporters, to polarized cell construction, cell function within epithelia, elaboration of kidney tubule segments, configuration of the whole nephron, and finally formulation of a kidney consisting of nephrons and blood vessels. The concluding chapter reviews several outstanding unsolved problems in mathematical modeling of kidney function and offers a possible approach for future workers.

Alan M. Weinstein is a graduate of Princeton University and Harvard Medical School. He is currently Emeritus Professor of Physiology and Biophysics and Emeritus Professor of Medicine at Weill Cornell Medicine. From 1981 to 2024, he was the Principal Investigator of an NIH-supported project, RO1-DK29857, “Theory of solute and water transport across epithelia”. The principal aim of that work was creation of mathematical models and computer simulation of renal function.