Numerical simulation of liver perfusion: from CT scans to FE model

Abstract —We use a collection of Python programs for numerical simulationof liver perfusion. We have an application for semi-automatic generation ofa finite element mesh of the human liver from computed tomography scansand for reconstruction of the liver vascular structure. When the real vasculartrees can not be obtained from the CT data we generate artificial trees usingthe constructive optimization method. The generated FE mesh and vasculartrees are imported into SfePy (Simple Finite Elements in Python) and numericalsimulations are performed in order to get the pressure distribution and perfusionflows in the liver tissue. In the post-processing steps we calculate transport of acontrast fluid through the liver parenchyma. Index Terms —segmentation, liver perfusion, multicompartment model, finiteelement method, finite volume method 1 I NTRODUCTION A patient specific numerical modelling of liver perfusionrequires cooperation of people with different specializations.Our research group consists of cyberneticians, informaticians,mechanicians and physicians who formulate problems to besolved and who are able to judge the outcomes of mathemati-cal models and simulations from the point of view of medicine.The research is motivated by the needs of surgeons, they wouldlike to have efficient tools for better planning of liver surgeriesand who would also appreciate to be able to predict changes ofliver perfusion caused by diseases or after surgical resections.The task of numerical modelling of a human liver canbe divided into two sub-problems. First of all, the geometryof larger vascular structures and hepatic parenchyma mustbe identified from data obtained by computed tomography(CT) or magnetic resonance imaging (MRI) examinations.With the knowledge of liver shape and vascular structures,the numerical simulations of liver perfusion can be performedusing different mathematical models of blood flow at differentspatial scales. The question, how to obtain all the necessaryparameters of our models (permeabilities, etc.) is out ofthe scope of this paper. More information can be found in[Roh12b] or [Coo12].The mathematical model of tissue perfusion presented inthis paper has been already used for similar problems, e.g. for