Starling equation

Diagram of the classic Starling model. Note that the concentration of interstitial solutes (orange) increases proportionally to the distance from the arteriole.

The classic Starling equation reads as follows:[4]

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

where:

• ${\displaystyle J_{v}}$ is the trans endothelial solvent filtration volume per second (SI units of m³·s⁻¹).
• ${\displaystyle [P_{\mathrm {c} }-P_{\mathrm {i} }]-\sigma [\pi _{\mathrm {p} }-\pi _{\mathrm {i} }]}$ is the net driving force (SI units of Pa = kg·m⁻¹·s⁻², often expressed as mmHg),
  • ${\displaystyle P_{c}}$ is the capillary hydrostatic pressure
  • ${\displaystyle P_{i}}$ is the interstitial hydrostatic pressure
  • ${\displaystyle \pi _{p}}$ is the plasma protein oncotic pressure
  • ${\displaystyle \pi _{i}}$ is the interstitial oncotic pressure
  • ${\displaystyle L_{p}}$ is the hydraulic conductivity of the membrane (SI units of m²·s·kg⁻¹, equivalent to m·s⁻¹·mmHg⁻¹)
  • ${\displaystyle S}$ is the surface area for filtration (SI units of m²)
    • the product ${\displaystyle L_{p}}$·${\displaystyle S}$ is defined as the filtration coefficient (SI units of m⁴·s·kg⁻¹, or equivalently in m³·s⁻¹·mmHg⁻¹)
  • ${\displaystyle \sigma }$ is Staverman's reflection coefficient (adimensional)

By convention, outward force is defined as positive, and inward force is defined as negative. If J_v 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.[4]

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 and the thoracic duct.[5]

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 π_i 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.[4]

The revised Starling equation is compatible with the steady-state Starling principle:

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

where:

• ${\displaystyle J_{v}}$ is the trans endothelial solvent filtration volume per second.
• ${\displaystyle [P_{\mathrm {c} }-P_{\mathrm {i} }]-\sigma [\pi _{\mathrm {p} }-\pi _{\mathrm {i} }]}$ is the net driving force,
  • ${\displaystyle P_{c}}$ is the capillary hydrostatic pressure
  • ${\displaystyle P_{i}}$ is the interstitial hydrostatic pressure
  • ${\displaystyle \pi _{p}}$ is the plasma protein oncotic pressure
  • ${\displaystyle \pi _{g}}$ is the subglycocalyx oncotic pressure
  • ${\displaystyle L_{p}}$ is the hydraulic conductivity of the membrane
  • ${\displaystyle S}$ is the surface area for filtration
  • ${\displaystyle \sigma }$ 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).

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.[12] 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.

The Starling equation is named for the British physiologist Ernest Starling, who is also recognised for the Frank–Starling law of the heart.[13] 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.[13]

• Renal function

• Derangedphysiology.com: Starling's Principle of Transvascular Fluid Dynamics Starling's principle of transvascular fluid dynamics | Deranged Physiology