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The Starling equation describes the net flow of fluid across a semipermeable membrane. It is named after
Ernest Starling Ernest Henry Starling (17 April 1866 – 2 May 1927) was a British physiologist who contributed many fundamental ideas to this subject. These ideas were important parts of the British contribution to physiology, which at that time led the world ...
. It describes the balance between capillary pressure, interstitial pressure, and osmotic pressure. The classic Starling equation has in recent years been revised. The Starling principle of fluid exchange is key to understanding how plasma fluid (
solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
) within the
bloodstream The blood circulatory system is a system of organs that includes the heart, blood vessels, and blood which is circulated throughout the entire body of a human or other vertebrate. It includes the cardiovascular system, or vascular system, tha ...
(
intravascular fluid Blood plasma is a light amber-colored liquid component of blood in which blood cells are absent, but contains proteins and other constituents of whole blood in suspension. It makes up about 55% of the body's total blood volume. It is the intra ...
) moves to the space outside the bloodstream (
extravascular space The blood vessels are the components of the circulatory system that transport blood throughout the human body. These vessels transport blood cells, nutrients, and oxygen to the tissues of the body. They also take waste and carbon dioxide away ...
). 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
glycocalyx The glycocalyx, also known as the pericellular matrix, is a glycoprotein and glycolipid covering that surrounds the cell membranes of bacteria, epithelial cells, and other cells. In 1970, Martinez-Palomo discovered the cell coating in animal c ...
of the plasma membrane of the
endothelium The endothelium is a single layer of squamous endothelial cells that line the interior surface of blood vessels and lymphatic vessels. The endothelium forms an interface between circulating blood or lymph in the lumen and the rest of the vesse ...
, 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 ( P_c ) and interstitial protein osmotic pressure ( \pi_i ), and two absorptive forces, plasma protein osmotic pressure ( \pi_p ) and interstitial pressure ( 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. The second Kedem–Katchalsky equation explains the trans endothelial transport of solutes, J_s .


The equation

The classic Starling equation reads as follows: :\ J_v = L_\mathrm S ( _\mathrm - P_\mathrm- \sigma pi_\mathrm - \pi_\mathrm) where: * J_v is the trans endothelial solvent filtration volume per second (SI units of m3·s−1). * _\mathrm - P_\mathrm- \sigma pi_\mathrm - \pi_\mathrm is the net driving force (SI units of Pa = kg·m−1·s−2, often expressed as mmHg), ** P_c is the capillary
hydrostatic pressure Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an imme ...
** P_i is the interstitial hydrostatic pressure ** \pi_p is the plasma protein
oncotic pressure Oncotic pressure, or colloid osmotic-pressure, is a form of osmotic pressure induced by the proteins, notably albumin, in a blood vessel's plasma (blood/liquid) that causes a pull on fluid back into the capillary. Participating colloids displace ...
** \pi_i is the interstitial oncotic pressure ** L_p is the hydraulic conductivity of the membrane (SI units of m2·s·kg−1, equivalent to m·s−1·mmHg−1) ** S is the surface area for filtration (SI units of m2) *** the product L_p · S is defined as the filtration coefficient (SI units of m4·s·kg−1, or equivalently in m3·s−1·mmHg−1) ** \sigma is Staverman's reflection coefficient (adimensional) 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 A lymph node, or lymph gland, is a kidney-shaped organ of the lymphatic system and the adaptive immune system. A large number of lymph nodes are linked throughout the body by the lymphatic vessels. They are major sites of lymphocytes that inclu ...
and the
thoracic duct In human anatomy, the thoracic duct is the larger of the two lymph ducts of the lymphatic system. It is also known as the ''left lymphatic duct'', ''alimentary duct'', ''chyliferous duct'', and ''Van Hoorne's canal''. The other duct is the righ ...
. 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: :\ J_v = L_\mathrm S ( _\mathrm - P_\mathrm- \sigma pi_\mathrm - \pi_\mathrm) where: * J_v is the trans endothelial solvent filtration volume per second. * _\mathrm - P_\mathrm- \sigma pi_\mathrm - \pi_\mathrm is the net driving force, ** P_c is the capillary
hydrostatic pressure Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an imme ...
** P_i is the interstitial hydrostatic pressure ** \pi_p is the plasma protein
oncotic pressure Oncotic pressure, or colloid osmotic-pressure, is a form of osmotic pressure induced by the proteins, notably albumin, in a blood vessel's plasma (blood/liquid) that causes a pull on fluid back into the capillary. Participating colloids displace ...
** \pi_g is the subglycocalyx oncotic pressure ** L_p is the hydraulic conductivity of the membrane ** S is the surface area for filtration ** \sigma is Staverman's reflection coefficient 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).


Filtration coefficient

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


Reflection coefficient

Staverman's reflection coefficient, ''σ'', is a unitless constant that is specific to the permeability of a membrane to a given solute. 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. ''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. *
Glomerular capillaries The glomerulus (plural glomeruli) is a network of small blood vessels (capillaries) known as a ''tuft'', located at the beginning of a nephron in the kidney. Each of the two kidneys contains about one million nephrons. The tuft is structurally s ...
have a reflection coefficient close to 1 as normally no protein crosses into the glomerular filtrate. * In contrast,
hepatic sinusoids A liver sinusoid is a type of capillary known as a sinusoidal capillary, discontinuous capillary or sinusoid, that is similar to a fenestrated capillary, having discontinuous endothelium that serves as a location for mixing of the oxygen-rich blo ...
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. Albumin and other proteins in the interstitial spaces return to the circulation via lymph.


Approximated values

Following are typically quoted values for the variables in the classic Starling equation: It is reasoned that some albumin escapes from the capillaries and enters the interstitial fluid where it would produce a flow of water equivalent to that produced by a hydrostatic pressure of +3 mmHg. Thus, the difference in protein concentration would produce a flow of fluid into the vessel at the venous end equivalent to 28 − 3 = 25 mmHg of hydrostatic pressure. The total oncotic pressure present at the venous end could be considered as +25 mmHg. In the beginning (arteriolar end) of a
capillary A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter. Capillaries are composed of only the tunica intima, consisting of a thin wall of simple squamous endothelial cells. They are the smallest blood vessels in the body: ...
, there is a net driving force ( _\mathrm - P_\mathrm- \sigma pi_\mathrm - \pi_\mathrm/math>) outwards from the capillary of +9 mmHg. In the end (venular end), on the other hand, there is a net driving force of −8 mmHg. 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 The lymphatic system, or lymphoid system, is an organ system in vertebrates that is part of the immune system, and complementary to the circulatory system. It consists of a large network of lymphatic vessels, lymph nodes, lymphatic or lymphoid o ...
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.


Specific organs


Kidneys

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


Lungs

The Starling equation can describe the movement of fluid from
pulmonary capillaries A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter. Capillaries are composed of only the tunica intima, consisting of a thin wall of simple squamous endothelial cells. They are the smallest blood vessels in the body: ...
to the alveolar air space.


Clinical significance

The principles behind the equation are useful for explaining physiological phenomena in
capillaries A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter. Capillaries are composed of only the tunica intima, consisting of a thin wall of simple squamous endothelial cells. They are the smallest blood vessels in the body: ...
, such as the formation of
edema Edema, also spelled oedema, and also known as fluid retention, dropsy, hydropsy and swelling, is the build-up of fluid in the body's Tissue (biology), tissue. Most commonly, the legs or arms are affected. Symptoms may include skin which feels t ...
. 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.{{cite journal, last=Woodcock, first=T. E., author2=Woodcock, T. M. , title=Revised Starling equation and the glycocalyx model of transvascular fluid exchange: an improved paradigm for prescribing intravenous fluid therapy, journal=British Journal of Anaesthesia, date=29 January 2012, volume=108, issue=3, pages=384–394, doi=10.1093/bja/aer515, pmid=22290457, doi-access=free


History

The Starling equation is named for the British physiologist
Ernest Starling Ernest Henry Starling (17 April 1866 – 2 May 1927) was a British physiologist who contributed many fundamental ideas to this subject. These ideas were important parts of the British contribution to physiology, which at that time led the world ...
, who is also recognised for the Frank–Starling law of the heart. 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.


See also

* Renal function


References


External links

* Derangedphysiology.com: Starling's Principle of Transvascular Fluid Dynamic
Starling's principle of transvascular fluid dynamics , Deranged Physiology
Equations of fluid dynamics Cardiovascular physiology Mathematics in medicine