On the performance and accuracy of PFEM-2 in the solution of biomedical benchmarks

Abstract

In recent years, the biomedical industry has shown increased interest in using numerical methods to assist in the R&D of medical devices. The long-term goal is to reduce the costly and lengthy process that clinical trials take for the US Food and Drug Administration (FDA) to approve a medical device. For this reason, both the FDA and academia are working together to create laboratory experiments that will help the industry gain confidence in numerical techniques as well as provide software developers with insights into the strengths and weaknesses of numerical software. In this article, three benchmarks proposed by the FDA are used to compare experimental results with those of a finite element method formulation and enhanced particle finite element method (PFEM-2). The first benchmark problem is the flow in a nozzle containing both, a gradual and a sudden change in diameter with the goal of predicting hemolysis (not studied in this work). The second problem studies the flow in a simplified centrifugal blood pump under various operation conditions. Finally, the third benchmark studies the steady flow in a patient-averaged inferior vena cava. PFEM-2 is regarded as a tool with great potential, mainly because no stabilization is needed for the Galerkin approximation of the advection term in the transport equations. This could be a big advantage in problems with flows at high Reynolds number. The improved time integration along streamlines provide a more accurate way to analyze a problem with a large time step. This paper is an effort to test PFEM-2 in engineering applications.