Starling equation

Formulated in 1896 by the British physiologist Ernest Starling, the Starling equation illustrates the role of hydrostatic and oncotic forces (also called Starling forces) in the movement of flow through the capillary membranes. It allows to predict the net filtration pressure for a certain liquid in the capillaries. The equation is:

Q=Kf([chuckles]Pc− − Pi]− − R[chuckles]π π c− − π π i]){displaystyle Q=K_{f}([P_{c}-P_{i}]]-R[pi _{c}-pi _{i})}

Symbol	Name	Unit
Q{displaystyle Q}	Filtration of trans endotelial solvent	m3 / s
Kf{displaystyle K_{f}}	Filling coefficient	m3 / (s mmHg)
Pc{displaystyle P_{c}}	Hydrostatic capillary pressure	mmHg
Pi{displaystyle P_{i}}	Interstitial hydrostatic pressure	mmHg
R{displaystyle R}	Staverman's Reflection Coefficient
π π c{displaystyle pi _{c}}	Onchotic capillary pressure	mmHg
π π i{displaystyle pi _{i}}	Interstitial onchotic pressure	mmHg

The filtration coefficient (Kf{displaystyle K_{f}}) expresses the permeability of the capillary wall for liquids.

The coefficient of reflection (R{displaystyle R}) is the Index of the efficacy of the capillary wall to prevent the passage of proteins and that, in normal conditions, it is admitted that it is equal to 1, which means that it is totally impermeable to the same and in pathological situations less than 1, to reach the value 0 when it can be crossed by them without difficulty

All pressures are measured in millimeters of mercury (mm Hg), and the filtration coefficient is measured in milliliters per minute per millimeter of mercury (mL min^-1 mm Hg^-1). For example:

• Arteriolar hydrostatic pressure (Pc) =37 mm Hg
• Venular hydrostatic pressure (Pc) = 17 mm Hg

According to the equation, arteriolar P(Q)=(37-1)-(25-0)=11 and venular P(Q)= (17-0)-(25-0)= -9. Filtration is therefore greater than reabsorption. The difference is then recovered by the lymphatic system to return to circulation.

The solution to the equation is the flow of water from the capillaries to the gap (Q). If it is positive, the flow will tend to leave the capillary (leakage). If it is negative, the flow will tend to enter the capillary (reabsorption). This equation has an important number of physiological implications, especially when pathological processes considerably alter one or more of these variables.

Starling forces on seepage pressure

Glomerular filtration is determined by:

1. The sum of hydrostatic and colloidosmotic forces through the glomerular membrane, which gives rise to the net filtration pressure.
2. The Kf glomerular coefficient.

The net filtration pressure represents the sum of the hydrostatic and colloidosmotic forces that favor or oppose the filtration through the glomerular capillaries. 

• Hydrostatic pressure within the glomerular capillaries (glomerular hydrostatic pressure, PG), which favors filtration through the glomerular membrane; it is estimated that in the human being it should be 60mmHg.
• Hydrostatic pressure in the Bowman capsule (PB) outside the capillaries, which opposes filtration, it is estimated that in the human being it must be 18mmHg.
• The colloidosmotic pressure of plasma proteins in glomerular capillary (πG), which opposes filtration, (onchotic); is estimated to be 32mmhg. This force is the one that exerts plasma proteins to contain water and solutes in the intravascular space, which contributes to the permanent microcirculation of the body, and regulates the amount of water contained in the tissues.
• The colloidosmotic pressure of proteins in the Bowman capsule (πB), which favors filtration. (In normal conditions, protein concentration in glomerular filtration is so low that colloidosmotic pressure in the Bowman capsule liquid is considered zero.)

Net filtration pressure: determines the passage of the liquid through the glomerular membrane, being equal to the glomerular pressure less the sum of the plasma colloidosmotic pressure and the capsular pressure. PF = PG-POG-PC