Lumped parameter modeling of changes in liver hemodynamics due to cirrhosis

This numerical study employs a computational model of human hepatic blood flow to investigate the hemodynamic consequences of cirrhosis. The liver receives blood through a dual-inlet system (portal vein and hepatic artery) that perfuses a complex network of sinusoids; however, cirrhosis-induced fibrosis distorts these channels, increasing hydraulic resistance. In turn, portal pressure is elevated, leading to the potential recanalization of portosystemic collaterals. We extended a lumped parameter hydraulic network model of the human liver, with demarcation of Couinaud segments, to capture the effects of fibrosis by incorporating a portosystemic collateral pathway and an "apparent viscosity" formulation that accounts for the non-Newtonian properties of blood. Our simulations indicate that segment-wise reductions in mean sinusoid conductance, combined with increased heterogeneity, drive the flow redistribution characteristic of the clinical "atrophy-hypertrophy complex". This results in diminished perfusion and wall shear stress in right-lobe segments, while flow and wall shear stress is preserved or even elevated in the left lobe. Sensitivity analysis suggests that the onset of portal hypertension is driven primarily by the reduction of mean sinusoid conductance, not increased heterogeneity. However, increased heterogeneity likely exacerbates liver dysfunction, as the model predicts that a disproportionately large fraction of blood passes through the relatively few sinusoids with the lowest hydraulic resistance. Additionally, results demonstrate that while the dilatation of portosystemic collaterals effectively offloads the portal system, it leads to a substantial increase in overall blood flow, contributing to hyperdynamic circulation (a hallmark feature of cirrhosis). These predictions provide quantitative, mechanistic insights into the hemodynamic and anatomical alterations of cirrhosis, offering a computational framework that helps explain clinical observations and may assist in future patient-specific surgical planning.