A biphasic computational model of the mechanics of the blood-perfused liver*

Modeling the mechanics of injured soft tissues is important for medical applications. The current study focuses on the liver and aims to simulate its material and hemo-dynamic response. The liver is considered as a dynamic poro-hyperelastic material with blood-filled voids. A biphasic formulation—effectively, a generalization of Darcy’s law---is utilized, treating the phases as occupying fractions of the same volume. A Stokes-like friction force and a pressure that penalizes deviations from volume fractions summing to unity serve as the interaction force between solid and liquid phases. The conservation equations are discretized by the method of Smoothed Particle Hydrodynamics. Inflow conditions are obtained from a systemic cardiovascular model with regulatory response, automatically adapting to hemorrhage and other disturbances. Simulations of the mechanics under baseline conditions will be demonstrated. Ongoing progress in modeling the liver under injuries and surgical conditions will be discussed.