Formulae for Afferent and Efferent Arteriolar Resistance in the Human Kidney: An Application to the Effects of Spinal Anesthesia

Glomerular dynamics are steadily becoming more coinprehensible as the trenchant methods for studying renal physiology developed by Homer Smith and his coworkers (1, 2) are further extended.Their recent analysis of the problem, using the current conception of the glomerulus as a pure ultra-filter operated by the hydrostatic pressure of the blood, is based on various pre- sumptions-some of them explicit and supported by evidence, others tacit or not supported by evidence ( 2).An examination of these basic questions leads to formulae, different in certain respects from those developed by these workers, which can be applied clinically to determine the actual afferent and efferent arteriolar resistance of human kid- neys.We shall first present these formulae, with an example of a clinical application, before proceeding much further with their detailed derivation.Fundamentally, the essence of a quantitative description of resistance, whether applied to flow of fluid or electricity, is the representation of resistance in terms of flow and pressure, the cus- tomarily measured quantities.In electricity, Ohm's law defines resistance as the ratio of the potential drop, in volts, along the resistor, to the electric current flow in it, in amperes.In hydraulics, Poiseuille, who was brought to the problem by his interest in the resistance of the blood vessels to the circulation of the blood, has similarly defined resistance as the ratio of the fall in pressure from one end to the other of a continuous wetted tube, to the rate of flow through it, after being multiplied by the viscosity of the fluid.Thus: Resistance = drop in pressure rate of flow X viscosity It is, of course, applicable in the simple form only if certain conditions are fulfilled.For ex-