Starling equation

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The Starling principle holds that extracellular fluid movements between blood and tissues are determined by differences in hydrostatic pressure and colloid osmotic pressure (oncotic pressure) between plasma inside microvessels and interstitial fluid outside them. The Starling equation, proposed many years after the death of Starling, describes that relationship in mathematical form and can be applied to many biological and non-biological semipermeable membranes. The classic Starling principle and the equation that describes it have in recent years been revised and extended.

Every day around 8 litres of water (solvent) containing a variety of small molecules (solutes) leaves the blood stream of an adult human and perfuses the cells of the various body tissues. Interstitial fluid drains by afferent lymph vessels to one of the regional lymph node groups, where around 4 litres per day is reabsorbed to the blood stream. The remainder of the lymphatic fluid is rich in proteins and other large molecules and rejoins the blood stream via the thoracic duct which empties into the great veins close to the heart.^[1] Filtration from plasma to interstitial (or tissue) fluid occurs in microvascular capillaries and post-capillary venules. In most tissues the micro vessels are invested with a continuous internal surface layer that includes a fibre matrix now known as the endothelial glycocalyx whose interpolymer spaces function as a system of small pores, radius circa 5 nm. Where the endothelial glycocalyx overlies a gap in the junction molecules that bind endothelial cells together (inter endothelial cell cleft), the plasma ultrafiltrate may pass to the interstitial space, leaving larger molecules reflected back into the plasma.

A small number of continuous capillaries are specialised to absorb solvent and solutes from interstitial fluid back into the blood stream through fenestrations in endothelial cells, but the volume of solvent absorbed every day is small.

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 (${\displaystyle P_{c}}$) and interstitial protein osmotic pressure (${\displaystyle \pi _{i}}$), and two absorptive forces, plasma protein osmotic pressure (${\displaystyle \pi _{p}}$) and interstitial pressure (${\displaystyle P_{i}}$). 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.^[2][3] The second Kedem–Katchalsky equation explains the trans endothelial transport of solutes, ${\displaystyle J_{s}}$.