Haemodynamics (flow, pressure and resistance)
Also known as: hemodynamics, Poiseuille's law, vascular resistance, laminar flow, turbulent flow, Reynolds number, Laplace's law, compliance
Haemodynamics is the physics of blood flow. Flow equals the pressure gradient divided by resistance, resistance depends very steeply on vessel radius (Poiseuille's law), and the speed of blood varies inversely with the total cross-sectional area of the vessels.
Overview
Flow and resistance. Flow (Q) = ΔP ÷ R. This is the haemodynamic equivalent of Ohm's law. For the whole systemic circulation it becomes MAP − RAP = CO × TPR.
Poiseuille's law. Resistance R = 8ηL ÷ πr⁴, where η is viscosity, L is vessel length and r is radius. Because of the fourth power, halving the radius increases resistance sixteenfold. This is why the arterioles, by changing their radius, control the distribution of flow.
Series and parallel resistances. Resistances in series add together. Organ circulations are mostly arranged in parallel, and parallel resistances combine to a total lower than any single one. This means total peripheral resistance is lower than the resistance of any individual organ, and each organ can control its own flow without disturbing the others.
Viscosity. Viscosity rises with haematocrit. Polycythaemia increases resistance, while anaemia lowers viscosity and favours turbulence. In very narrow vessels the apparent viscosity of blood falls, because red cells gather in the centre of the stream (the Fåhræus–Lindqvist effect).
Velocity. Mean velocity v = Q ÷ A, where A is the total cross-sectional area. Blood moves at a mean of about 20–30 cm/s in the aorta, peaking at about 1 m/s, but at only about 0.3 mm/s in the capillaries.
Laminar and turbulent flow. Flow is normally laminar, in smooth layers. It becomes turbulent when the Reynolds number (Re = ρvD ÷ η) exceeds about 2000. Turbulence is audible as murmurs, bruits and Korotkoff sounds. It is promoted by high velocity, stenoses, wide vessels and low viscosity.
Compliance. Compliance (C = ΔV ÷ ΔP) describes how much a vessel's volume rises for a given rise in pressure. Veins are about 24 times more compliant than arteries.
Laplace's law. Wall tension T = P × r in a cylinder. In a thick-walled sphere, wall stress σ = P × r ÷ 2h, where h is wall thickness. This explains why an aneurysm, once enlarged, tends to keep enlarging. It also explains why dilated ventricles need more oxygen, and why hypertrophy brings wall stress back toward normal.
Simplified Bernoulli equation. The pressure gradient across a narrowed valve ΔP ≈ 4v², where v is the peak velocity in m/s. Echocardiography uses this to estimate valve gradients.
Function
- Explains how pressure, flow, resistance and vessel geometry are related throughout the circulation.
Clinical significance
Critical stenosis
At rest, flow through an artery falls only once its diameter is reduced by about 70%, because the vessels downstream dilate to compensate. During exercise, when those vessels are already dilated, a less severe stenosis becomes limiting. This is why angina first appears on exertion.
Bruits and murmurs
Turbulence across a narrowed carotid, renal or femoral artery produces a bruit. Turbulence across a heart valve produces a murmur. Severe anaemia can produce flow murmurs, because low viscosity and high cardiac output both favour turbulence.
Compiled from standard anatomy and physiology references — see the Cardiovascular System sources. For education only; not medical advice.