Starling equation

The Starling equation is an equation that illustrates the role of hydrostatic and oncotic forces (the so-called Starling forces) in the movement of fluid across capillary membranes.

Capillary fluid movement may occur as a result of two processes:

• diffusion
• filtration

Starling's equation only refers to fluid movement across the capillary membrane that occurs as a result of filtration. In the glomerular capillaries, there is a net fluid filtration of 125 ml/min (about 180 litres/day). In the rest of the body's capillaries, there is a total net transcapillary fluid movement of 20 ml/min (about 28.8 litres/day) as a result of filtration. This is several orders of magnitude lower than the total diffusional water flux at the capillary membrane, as that is about 80,000 litres/day.

The Starling equation was formulated in 1896 by the British physiologist Ernest Starling.

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The equation

The Starling equation reads as follows:

J_v = K_f([P_c − P_i] − σ[π_c − π_i])

where:

• ([P_c − P_i] − σ[π_c − π_i]) is the net driving force,
• K_f is the proportionality constant, and
• J_v is the net fluid movement between compartments.

By convention, outward force is defined as positive, and inward force is defined as negative. The solution to the equation is known as the net filtration or net fluid movement (J_v). If positive, fluid will tend to leave the capillary (filtration). If negative, fluid will tend to enter the capillary (absorption). This equation has a number of important physiologic implications, especially when pathologic processes grossly alter one or more of the variables.

The variables

According to Starling's equation, the movement of fluid depends on six variables:

1. Capillary hydrostatic pressure ( P_c )
2. Interstitial hydrostatic pressure ( P_i )
3. Capillary osmotic pressure ( π_c )
4. Interstitial osmotic pressure ( π_i )
5. Filtration coefficient ( K_f )
6. Reflection coefficient ( σ )

Pressures are often measured in millimeters of mercury (mmHg), and the filtration coefficient in milliliters per minute per millimeter of mercury (ml·min^-1·mmHg^-1).

In essence the equation says that the net filtration (J_v) is proportional to the net driving force. The first four variables in the list above are the forces that contribute to the net driving force.

Filtration coefficient

The filtration coefficient is the constant of proportionality. A high value indicates a highly water permeable capillary. A low value indicates a low capillary permeability.

The filtration coefficient is the product of two components:

• capillary surface area
• capillary hydraulic conductance

Reflection coefficient

The reflection coefficient is often thought of as a correction factor. The idea is that the difference in oncotic pressures contributes to the net driving force because most capillaries in the body are fairly impermeable to the large molecular weight proteins. (The term ultrafiltration is usually used to refer to this situation where the large molecules are retained by a semipermeable membrane but water and low molecular weight solutes can pass through the membrane).

Many body capillaries do have a small permeability to proteins (such as albumins). This small protein leakage has two important effects:

• the interstitial fluid oncotic pressure is higher than it would otherwise be in that tissue
• not all of the protein present is effective in retaining water so the effective capillary oncotic pressure is lower than the measured capillary oncotic pressure.

Both these effects decrease the contribution of the oncotic pressure gradient to the net driving force. The reflection coefficient (σ) is used to correct the magnitude of the measured gradient to 'correct for' for the ineffectiveness of some of the oncotic pressure gradient. It can have a value from 0 up to 1.

• Glomerular capillaries have a reflection coefficient close to 1 as normally no protein crosses into the glomerular filtrate.

• In contrast, hepatic sinusoids have a low reflection coefficient as they are quite permeable to protein. This is advantageous because albumin is produced in hepatocytes and can relatively freely pass from these cells into the blood in the sinusoids. The predominant pathway for albumin and other proteins to enter the circulation is via the lymph.

Approximated values

Following are approximated values for the variables in the equation for both arterioles and venules:

In the beginning (arteriolar end) of a capillary, there is a net driving force (([P_c − P_i] − σ[π_c − π_i])) outwards from the capillary of +12 mm Hg. In the end (venilar end), on the other hand, there is a net driving force of -5 mm Hg.

Assumed that the net driving force declines linearily, 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.

Clinical usefulness

The equation is very useful for explaining what is happening at the capillary, but has very limited clinical usefulness. Mostly this reflects the impossibility of easily measuring all six variables together in actual patients.

See also

• Glomerular filtration rate#Calculation using Starling equation