Fig. 7
a Heatmap showing influence of metabolic load and cell death sensitivity parameters on the threshold of liver failure in terms of fraction of resection that is safe. Black cross markers represent the virtual patients for the corresponding phase portraits in panels b-f. b Phase plane for metabolic load (M) = 2.293 and cell death sensitivity (βap) = 0.071, yielding a threshold of failure at 58% resection. This scenario corresponds to the critical transition from high threshold to low threshold of liver failure on the heatmap in panel a. c M = 2.293 and βap = 0.053, yields a threshold of failure at 79% resection. d M = 2.293 and βap = 0.085, yields a virtual patient for whom all levels of resection lead to failure. e M = 1.139 and βap = 0.071, yields a threshold of failure of 87%. f M = 3.447 and βap = 0.071, yields a virtual patient for whom all levels of resection resulted in a failure. The circular markers in the phase portraits represent different levels of resection and the red curves denote the critical level of resection above which the system progresses towards the failure mode