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Starling equation

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Starling equation

The Starling principle holds that fluid movement across a semi-permeable blood vessel such as a capillary or small venule is determined by the hydrostatic pressures and colloid osmotic pressures (oncotic pressure) on either side of a semipermeable barrier that sieves the filtrate, retarding larger molecules such as proteins from leaving the blood stream. As all blood vessels allow a degree of protein leak , true equilibrium across the membrane cannot occur and there is a continuous flow of water with small solutes. The molecular sieving properties of the capillary wall reside in a recently discovered endocapillary layer rather than in the dimensions of pores through or between the endothelial cells. This fibre matrix endocapillary layer is called the endothelial glycocalyx.The Starling equation describes that relationship in mathematical form and can be applied to many biological and non-biological semipermeable membranes.

The Starling equation as applied to a blood vessel wall reads as

where:

Pressures are customarily measured in millimetres of mercury (mmHg), and the filtration coefficient in millilitres per minute per millimetre of mercury (ml·min−1·mmHg−1).

The rate at which fluid is filtered across vascular endothelium (transendothelial filtration) is determined by the sum of two outward forces, capillary pressure () and colloid osmotic pressure beneath the endothelial glycocalyx (), and two absorptive forces, plasma protein osmotic pressure () and interstitial pressure (). The Starling equation is the first of two 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. The second Kedem–Katchalsky equation explains the trans endothelial transport of solutes, .

It is now known that the average colloid osmotic pressure of the interstitial fluid has no effect on . The colloid osmotic pressure difference that opposes filtration is now known to be π'p minus the subglycocalyx .The subglycocalyx space is a very small but vitally important micro domain of the total interstitial fluid space. The concentration of soluble proteins in that microdomain, which determines , is close to zero while there is adequate filtration to flush them out of the interendothelial clefts. For this reason is much less than previously calculated and is tightly regulated . Any transient rise in plasma colloid osmotic pressure or fall in capillary hydrostatic pressure sufficient to allow reverse (negative) causes unopposed diffusion of interstitial proteins to the subglycocalyx space, reducing the colloid osmotic pressure difference that was driving absorption of fluid to the capillary. The dependence of upon the local has been called The Glycocalyx Model or the Michel-Weinbaum model, in honour of two scientists who, independently, described the filtration function of the glycocalyx. The Michel-Weinbaum Model explains how most continuous capillaries are in a steady state of filtration along their entire length most of the time. Transient disturbances of the Starling forces return rapidly to steady state filtration.

In some texts the product of hydraulic conductivity and surface area is called the filtration co-efficient Kfc.[citation needed]

Staverman's reflection coefficient, σ, is a unitless constant that is specific to the permeability of a membrane to a given solute.

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