Uncertainty quantification in FEM simulation of human liver: sensitivity analysis, Gradient-Enhanced Kriging, and Monte Carlo simulation

The numerical simulation of metabolic processes in the human liver involves challenges related to model accuracy, physiological representation, and data uncertainty. Soft tissue models must capture complex, multiphase, and time-dependent behavior. However, the high computational cost of such analyses often restricts them to simplified deterministic scenarios that neglect biological variability and uncertainty. In this paper, the deterministic foundation of a liver perfusion-function model based on the Finite Element Method (FEM) is extended to incorporate material variability. To this end, a workflow is presented that integrates sensitivity analysis, surrogate modeling based on a Gradient-Enhanced Kriging (GEK) model, and uncertainty quantification. This approach enables the identification of critical parameters, enhances the interpretability of the model, and provides probabilistic outcome assessments for FEM-based simulations. The FEM model represents liver tissue on the lobule scale, incorporating metabolically active cells and vascular systems through a poroelastic multiscale framework with spatially coupled function-perfusion dynamics. It simulates liver-related conditions, such as tumor growth due to metabolic associated fatty liver disease (MAFLD), which affects microperfusion. Aleatoric uncertainties in material parameters are accounted for, and a local sensitivity analysis identifies critical nodes as a foundation for a GEK metamodel. Monte Carlo (MC) methods on the surrogate enable fast propagation of input uncertainty and probabilistic assessment of predicted outcomes. Rather than assuming deterministic accuracy, this approach offers a systematic way to explore and interpret model behavior under uncertainty.