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Starling equation

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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 pressure and colloid osmotic pressure (oncotic pressure) on either side of a semipermeable barrier that sieves the filtrate, keeping larger molecules such as proteins within the blood stream. 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.[1] 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 equation

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

where:

  • is the trans endothelial solvent filtration volume per second.
  • is the net driving force,
    • is the capillary hydrostatic pressure
    • is the interstitial hydrostatic pressure
    • is the plasma protein oncotic pressure
    • is the subglycocalyx oncotic pressure, which varies inversely with and so stabilises .
    • is the hydraulic conductivity of the membrane
    • is the surface area for filtration, determined by gaps in the "tight junction" glue that binds endothelial cells at their edges.
    • is Staverman's reflection coefficient, determined by the condition of the endothelial glycocalyx over the junction gaps.

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).

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.[2][3] The second Kedem–Katchalsky equation explains the trans endothelial transport of solutes, .

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. Briefly, the average colloid osmotic pressure of the interstitial fluid has been found to have no effect on and the colloid osmotic pressure difference that opposes filtration is now known to be π'p minus the subglycocalyx , 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.

Filtration coefficient

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

Reflection coefficient

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Staverman's reflection coefficient, σ, is a unitless constant that is specific to the permeability of a membrane to a given solute.[4]

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.[5]

σn corrects for the partial permeability of a semipermeable membrane to a solute n.[5]

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.[5]

  • Glomerular capillaries have a reflection coefficient close to 1 as normally no protein crosses into the glomerular filtrate.
  • In contrast, hepatic sinusoids have no reflection coefficient as they are fully permeable to protein. Hepatic interstitial fluid within the Space of Diss has the same colloid osmotic pressure as plasma and so hepatocyte synthesis of albumin can be regulated.

Approximate values

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Following are typical values for the variables in the Starling equation which regulate net to about 0.1ml per second, 5-6 ml per minute or about 8 litres per day.

Location Pc (mmHg)[6] Pi (mmHg)[6] σπc (mmHg)[6] σπg (mmHg)[6]
arteriolar end of capillary +35 −2 +28 depends on local
venule +15 −2 +28 depends on local

Specific organs

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Kidneys

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Glomerular capillaries have a continuous glycocalyx layer in health and the total transendothelial filtration rate of solvent () to the renal tubules is normally around 125 ml/ min (about 180 litres/ day). Glomerular capillary is more familiarly known as the glomerular filtration rate (GFR).

Lungs

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The Starling equation can describe the movement of fluid from pulmonary capillaries to the alveolar air space.[7][8]

Clinical significance

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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.[9] 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.

History

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The Starling equation is named for the British physiologist Ernest Starling, who is also recognised for the Frank–Starling law of the heart.[10] 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.[10]

See also

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References

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  1. ^ Curry, F. E.; Michel, C. C. (1980-07-01). "A fiber matrix model of capillary permeability". Microvascular Research. 20 (1): 96–99. doi:10.1016/0026-2862(80)90024-2. ISSN 0026-2862.
  2. ^ Staverman, A. J. (1951). "The theory of measurement of osmotic pressure". Recueil des Travaux Chimiques des Pays-Bas. 70 (4): 344–352. doi:10.1002/recl.19510700409. ISSN 0165-0513.
  3. ^ Kedem, O.; Katchalsky, A. (February 1958). "Thermodynamic analysis of the permeability of biological membranes to non-electrolytes". Biochimica et Biophysica Acta. 27 (2): 229–246. doi:10.1016/0006-3002(58)90330-5. ISSN 0006-3002. PMID 13522722.
  4. ^ Zelman, A. (1972-04-01). "Membrane Permeability: Generalization of the Reflection Coefficient Method of Describing Volume and Solute Flows". Biophysical Journal. 12 (4): 414–419. Bibcode:1972BpJ....12..414Z. doi:10.1016/S0006-3495(72)86093-4. ISSN 0006-3495. PMC 1484119. PMID 5019478.
  5. ^ a b c Michel, C. Charles; Woodcock, Thomas E.; Curry, Fitz-Roy E. (2020). "Understanding and extending the Starling principle". Acta Anaesthesiologica Scandinavica. 64 (8): 1032–1037. doi:10.1111/aas.13603. ISSN 1399-6576. PMID 32270491.
  6. ^ a b c d Boron, Walter F. (2005). Medical Physiology: A Cellular And Molecular Approaoch. Elsevier/Saunders. ISBN 978-1-4160-2328-9.
  7. ^ Pal, Pramod K.; Chen, Robert (2014-01-01), Aminoff, Michael J.; Josephson, S. Andrew (eds.), "Chapter 1 - Breathing and the Nervous System", Aminoff's Neurology and General Medicine (Fifth Edition), Boston: Academic Press, pp. 3–23, doi:10.1016/b978-0-12-407710-2.00001-1, ISBN 978-0-12-407710-2, S2CID 56748572, retrieved 2020-11-28
  8. ^ Nadon, A. S.; Schmidt, E. P. (2014-01-01), McManus, Linda M.; Mitchell, Richard N. (eds.), "Pathobiology of the Acute Respiratory Distress Syndrome", Pathobiology of Human Disease, San Diego: Academic Press, pp. 2665–2676, doi:10.1016/b978-0-12-386456-7.05309-0, ISBN 978-0-12-386457-4, retrieved 2020-11-28
  9. ^ Woodcock, T. E.; Woodcock, T. M. (29 January 2012). "Revised Starling equation and the glycocalyx model of transvascular fluid exchange: an improved paradigm for prescribing intravenous fluid therapy". British Journal of Anaesthesia. 108 (3): 384–394. doi:10.1093/bja/aer515. PMID 22290457.
  10. ^ a b Starling, Ernest H. (1896-05-05). "On the Absorption of Fluids from the Connective Tissue Spaces". The Journal of Physiology. 19 (4): 312–326. doi:10.1113/jphysiol.1896.sp000596. PMC 1512609. PMID 16992325.
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