Hagen-Poiseuille's law: The link between cirrhosis, liver stiffness, portal hypertension and hepatic decompensation

The onset of hepatic decompensation in cirrhosis heralds an accelerated downhill course with poor outcome. The sole predictor of this decompensation in cirrhosis is increased hepatic vein to portal vein gradient hepatic venous pressure gradient (HVPG). Surrogate markers of liver function or hepatic reserve appear to be less relevant. The hepatic sinusoids become less elastic and more rigid as liver fibrosis and cirrhosis progress. We propose that the Hagen-Poiseuille's law, which applies to rigid, but not elastic vessels, determines the pressure-flow characteristics in the sinusoids. In the rigid cirrhotic liver, HVPG rises dramatically with any change in net surface area or radius, r(4) of the vasculature that follows surgical resection. This review relates liver stiffness to the risk of decompensation in patients with cirrhosis. The liver has a unique dual blood supply comprising a low pressure portal vein and high pressure hepatic artery. We compare the complexity of autoregulation in the normal elastic liver with that in the rigid cirrhotic liver. Therapeutic modalities to reduce portal pressure may reduce the risk of hepatic decompensation and improve outcomes in cirrhosis.