Liver resection causes marked perfusion alterations in the liver remnant both on the organ scale (vascular anatomy) and on the microscale (sinusoidal blood flow on tissue level). These changes in perfusion affect hepatic functions via direct alterations in blood supply and drainage, followed by indirect changes of biomechanical tissue properties and cellular function. Changes in blood flow impose compression, tension and shear forces on the liver tissue. These forces are perceived by mechanosensors on parenchymal and non-parenchymal cells of the liver and regulate cell-cell and cell-matrix interactions as well as cellular signaling and metabolism. These interactions are key players in tissue growth and remodeling, a prerequisite to restore tissue function after PHx. Their dysregulation is associated with metabolic impairment of the liver eventually leading to liver failure, a serious post-hepatectomy complication with high morbidity and mortality. Though certain links are known, the overall functional change after liver surgery is not understood due to complex feedback loops, non-linearities, spatial heterogeneities and different time-scales of events. Computational modeling is a unique approach to gain a better understanding of complex biomedical systems. This approach allows (i) integration of heterogeneous data and knowledge on multiple scales into a consistent view of how perfusion is related to hepatic function; (ii) testing and generating hypotheses based on predictive models, which must be validated experimentally and clinically. In the long term, computational modeling will (iii) support surgical planning by predicting surgery-induced perfusion perturbations and their functional (metabolic) consequences; and thereby (iv) allow minimizing surgical risks for the individual patient. Here, we review the alterations of hepatic perfusion, biomechanical properties and function associated with hepatectomy. Specifically, we provide an overview over the clinical problem, preoperative diagnostics, functional imaging approaches, experimental approaches in animal models, mechanoperception in the liver and impact on cellular metabolism, omics approaches with a focus on transcriptomics, data integration and uncertainty analysis, and computational modeling on multiple scales. Finally, we provide a perspective on how multi-scale computational models, which couple perfusion changes to hepatic function, could become part of clinical workflows to predict and optimize patient outcome after complex liver surgery.

The liver is a unique parenchymal organ with a regenerative capacity allowing it to restore up to 70% of its volume. Although knowledge of this phenomenon dates back to Greek mythology (the story of Prometheus), many aspects of liver regeneration are still not understood. A variety of different factors, including inflammatory cytokines, growth factors, and bile acids, promote liver regeneration and control the final size of the organ during typical regeneration, which is performed by mature hepatocytes, and during alternative regeneration, which is performed by recently identified resident stem cells called "hepatic progenitor cells". Hepatic progenitor cells drive liver regeneration when hepatocytes are unable to restore the liver mass, such as in cases of chronic injury or excessive acute injury. In liver maintenance, the body mass ratio is essential for homeostasis because the liver has numerous functions; therefore, a greater understanding of this process will lead to better control of liver injuries, improved transplantation of small grafts and the discovery of new methods for the treatment of liver diseases. The current review sheds light on the key molecular pathways and cells involved in typical and progenitor-dependent liver mass regeneration after various acute or chronic injuries. Subsequent studies and a better understanding of liver regeneration will lead to the development of new therapeutic methods for liver diseases.