Starling equation

The Starling equation for fluid filtration is named for the British physiologist Ernest Starling, who is also recognised for the Frank–Starling law of the heart. The classic Starling equation has in recent years been revised. The Starling principle of fluid exchange is key to understanding how plasma fluid (solvent) within the bloodstream (intravascular fluid) moves to the space outside the bloodstream (extravascular space). Starling can be credited with identifying that the "absorption of isotonic salt solutions (from the extravascular space) by the blood vessels is determined by this osmotic pressure of the serum proteids." (1896)

Transendothelial fluid exchange occurs predominantly in the capillaries, and is a process of plasma ultrafiltration across a semi-permeable membrane. It is now appreciated that the ultrafilter is the endothelial glycocalyx layer whose interpolymer spaces function as a system of small pores, radius circa 5 nm. Where the endothelial glycocalyx overlies an inter endothelial cell cleft, the plasma ultrafiltrate may pass to the interstitial space. Some continuous capillaries may feature fenestrations that provide an additional subglycocalyx pathway for solvent and small solutes. Discontinuous capillaries as found in sinusoidal tissues of bone marrow, liver and spleen have little or no filter function.

The rate at which fluid is filtered across vascular endothelium (transendothelial filtration) is determined by the sum of two outward forces, capillary pressure (Pc) and interstitial protein osmotic pressure (πi), and two absorptive forces, plasma protein osmotic pressure (πp) and interstitial pressure (Pi). The Starling equation describes these forces in mathematical terms. It is one of the Kedem Katchalski equations which bring nonsteady state thermodynamics to the theory of osmotic pressure across membranes that are at least partly permeable to the solute responsible for the osmotic pressure difference (Staverman 1951; Kedem and Katchalsky 1958). The second Kedem Katchalsky equation explains the trans endothelial transport of solutes, Js.

Glomerular capillaries have a continuous glycocalyx layer in health and the total transendothelial filtration rate of solvent (Jv) to the renal tubules is normally around 125 ml/ min (about 180 litres/ day). Glomerular capillary Jv is more familiarly known as the glomerular filtration rate (GFR). In the rest of the body's capillaries, Jv is typically 5 ml/ min (around 8 litres/ day), and the fluid is returned to the circulation via afferent and efferent lymphatics.

The classic Starling equation reads as follows:

where:

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