Starling equation

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 pressures and colloid osmotic pressures (oncotic pressure) on either side of a semipermeable barrier that sieves the filtrate, retarding larger molecules such as proteins from leaving the blood stream. As all blood vessels allow a degree of protein leak, true equilibrium across the membrane cannot occur and there is a continuous flow of water with small solutes. 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. 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

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

J

v

=

L

p

S

(

[

P

c

−

P

i

]

−

σ

[

π

p

−

π

g

]

)

{\displaystyle \ J_{v}=L_{\mathrm {p} }S([P_{\mathrm {c} }-P_{\mathrm {i} }]-\sigma [\pi _{\mathrm {p} }-\pi _{\mathrm {g} }])}

where:

J

v

{\displaystyle J_{v}}

is the trans endothelial solvent filtration volume per second.

L

p

{\displaystyle L_{p}}

is the hydraulic conductivity of the membrane

S

{\displaystyle S}

is the surface area for filtration, determined by gaps in the "tight junction" glue that binds endothelial cells at their edges.

[

P

c

−

P

i

]

−

σ

[

π

p

−

π

g

]

{\displaystyle [P_{\mathrm {c} }-P_{\mathrm {i} }]-\sigma [\pi _{\mathrm {p} }-\pi _{\mathrm {g} }]}

is the net driving force,

P

c

{\displaystyle P_{c}}

is the capillary hydrostatic pressure

P

i

{\displaystyle P_{i}}

is the interstitial hydrostatic pressure

π

p

{\displaystyle \pi _{p}}

is the plasma protein oncotic pressure

π

g

{\displaystyle \pi _{g}}

is the subglycocalyx oncotic pressure, which varies inversely with

J

v

{\displaystyle J_{v}}

and so stabilises

J

v

{\displaystyle J_{v}}

.

σ

{\displaystyle \sigma }

is Staverman's reflection coefficient, determined by the condition of the endothelial glycocalyx over the junction gaps.

Pressures are customarily measured in millimetres of mercury (mmHg), and the filtration coefficient in millilitres per minute per millimetre of mercury (ml·min−1·mmHg−1).