The first step in urine formation is the ultrafiltration of blood in renal glomerular capillaries. The glomerular capillary wall is an exquisitely "well-engineered" barrier, which is normally very permeable to water and yet able to prevent all but very minute losses from the circulation of major plasma proteins such as albumin. Progress has been made in using hydrodynamic models to relate the permeability properties of this barrier to its structure, at the cellular and subcellular levels, in health and disease. These efforts will be reviewed, and certain unresolved problems will be discussed.

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1998-1999 Mathematics in Biology