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 (
Pc
\pii
\pip
Pi
Js
The classic Starling equation reads as follows:[4]
Jv=LpS([Pc-Pi]-\sigma[\pip-\pii])
where:
Jv
[Pc-Pi]-\sigma[\pip-\pii]
Pc
Pi
\pip
\pii
Lp
S
Lp
S
\sigma
By convention, outward force is defined as positive, and inward force is defined as negative. If Jv is positive, solvent is leaving the capillary (filtration). If negative, solvent is entering the capillary (absorption).
Applying the classic Starling equation, it had long been taught that continuous capillaries filter out fluid in their arteriolar section and reabsorb most of it in their venular section, as shown by the diagram.
However, empirical evidence shows that, in most tissues, the flux of the intraluminal fluid of capillaries is continuous and, primarily, effluent. Efflux occurs along the whole length of a capillary. Fluid filtered to the space outside a capillary is mostly returned to the circulation via lymph nodes and the thoracic duct.[5]
A mechanism for this phenomenon is the Michel-Weinbaum model, in honour of two scientists who, independently, described the filtration function of the glycocalyx. Briefly, the colloid osmotic pressure πi of the interstitial fluid has been found to have no effect on Jv and the colloid osmotic pressure difference that opposes filtration is now known to be π'p minus the subglycocalyx π, which is close to zero while there is adequate filtration to flush interstitial proteins out of the interendothelial cleft. Consequently, Jv is much less than previously calculated, and the unopposed diffusion of interstitial proteins to the subglycocalyx space if and when filtration falls wipes out the colloid osmotic pressure difference necessary for reabsorption of fluid to the capillary.
The revised Starling equation is compatible with the steady-state Starling principle:
Jv=LpS([Pc-Pi]-\sigma[\pip-\pig])
where:
Jv
[Pc-Pi]-\sigma[\pip-\pii]
Pc
Pi
\pip
\pig
Lp
S
\sigma
Pressures are often measured in millimetres of mercury (mmHg), and the filtration coefficient in millilitres per minute per millimetre of mercury (ml·min−1·mmHg−1).
See main article: article and Filtration coefficient. In some texts the product of hydraulic conductivity and surface area is called the filtration co-efficient Kfc.
Staverman's reflection coefficient, σ, is a unitless constant that is specific to the permeability of a membrane to a given solute.[6]
The Starling equation, written without σ, describes the flow of a solvent across a membrane that is impermeable to the solutes contained within the solution.[7]
σn corrects for the partial permeability of a semipermeable membrane to a solute n.
Where σ is close to 1, the plasma membrane is less permeable to the denotated species (for example, larger molecules such as albumin and other plasma proteins), which may flow across the endothelial lining, from higher to lower concentrations, more slowly, while allowing water and smaller solutes through the glycocalyx filter to the extravascular space.
Following are typically quoted values for the variables in the classic Starling equation:
| Location | Pc (mmHg)[9] | Pi (mmHg) | σπc (mmHg) | σπi (mmHg) | |
|---|---|---|---|---|---|
| +35 | −2 | +28 | +0.1 | ||
| venular end of capillary | +15 | −2 | +28 | +3 |
In the beginning (arteriolar end) of a capillary, there is a net driving force (
[Pc-Pi]-\sigma[\pic-\pii]
Assuming that the net driving force declines linearly, then there is a mean net driving force outwards from the capillary as a whole, which also results in that more fluid exits a capillary than re-enters it. The lymphatic system drains this excess.
J. Rodney Levick argues in his textbook that the interstitial force is often underestimated, and measurements used to populate the revised Starling equation show the absorbing forces to be consistently less than capillary or venular pressures.
Glomerular capillaries have a continuous glycocalyx layer in health and the total transendothelial filtration rate of solvent (
Jv
Jv
Jv
The Starling equation can describe the movement of fluid from pulmonary capillaries to the alveolar air space.
Woodcock and Woodcock showed in 2012 that the revised Starling equation (steady-state Starling principle) provides scientific explanations for clinical observations concerning intravenous fluid therapy.[10] Traditional teaching of both filtration and absorption of fluid occurring in a single capillary has been superseded by the concept of a vital circulation of extracellular fluid running parallel to the circulation of blood. New approaches to the treatment of oedema (tissue swelling) are suggested.
The Starling equation is named for the British physiologist Ernest Starling, who is also recognised for the Frank–Starling law of the heart.[11] 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 proteins" in 1896.