Wall stress equals pressure times radius divided by twice the wall thickness
Mnemonic
“Tension equals pressure times radius, divided by wall thickness”:
T = (P x r) / (2h) for a sphere.
Three consequences run the whole of cardiac mechanics:
- A dilated ventricle has a larger radius, so it needs more wall tension to generate the same pressure, and therefore consumes more oxygen. This is why dilatation is self-perpetuating in heart failure
- Hypertrophy reduces wall stress by increasing h, which is the adaptive response to pressure overload in aortic stenosis and hypertension
- Afterload reduction with ACE inhibitors and vasodilators works partly by reducing wall tension, allowing reverse remodelling
In the lung, the same law explains why surfactant is essential: small alveoli would otherwise generate higher pressures than large ones and empty into them. Surfactant reduces surface tension more in small alveoli, equalising the pressures.
In vessels, it explains why aneurysms enlarge progressively: as radius grows, tension rises, which drives further growth.
Expansion
Wall stress = (pressure x radius) / (2 x wall thickness)
Three consequences:
- Dilatation is costly. A larger radius raises wall stress for the same pressure, so a dilated ventricle needs more oxygen to generate the same output
- Hypertrophy is compensatory. Thickening the wall reduces stress; pressure overload such as aortic stenosis therefore produces concentric hypertrophy
- Volume overload such as mitral regurgitation produces eccentric hypertrophy, with dilatation and proportionate wall thickening
The same law explains why the thin-walled right ventricle tolerates volume loading well but copes badly with acute pressure loading, as in massive pulmonary embolism.
It also applies to vessels: an aneurysm with a larger radius has higher wall tension, so it expands and ruptures at an accelerating rate.