Validation of an open source framework for the simulation of blood flow in rigid and deformable vessels.

We discuss the validation of an open source framework for the solution of problems arising in hemodynamics. The proposed framework is assessed through experimental data for steady flow in an idealized medical device with rigid boundaries and a numerical benchmark for flow in compliant vessels. In 2004, the U.S. Food and Drug Administration (FDA) launched a ``Critical Path Initiative'' program aimed, among other things, at improving the use and validating CFD techniques in the evaluation of medical devices. A benchmark nozzle model was developed which contains all the features commonly encountered in medical devices (flow contraction and expansion, recirculation zones etc.) and three laboratories were asked to perform flow visualization experiments on fabricated models for flow rates spanning laminar, transitional, and turbulent regimes. This resulted in benchmark data available online to the scientific community for the validation of CFD simulations. Our goal is two-fold: (i) validate an open source CFD framework for the solution of problems of interest in hemodynamics and (ii) provide the details of the methodology that we use, to make our experiences reproducible. To achieve this goal we refer to (a) the FDA benchmark; (b) a fluid-structure interaction (FSI) test case presented in [1]. The former is intended to assess the code capabilities in simulating steady fluid flow in a rigid domain representative of a medical device. The latter is intended to evaluate the performance of the software in simulating fluid flow in deformable domains, which is of utmost relevance for cardiovascular problems. In particular - in absence of a FSI analogue of the FDA benchmark - the FSI test deals with the propagation of a pressure wave in a fluid-filled elastic cylindrical vessel for which an analytical solution for the wave speed and frequency of oscillation are provided. The core of the open-source framework is LifeV, an open source library of algorithms and data structures for the numerical solution of partial differential equations with high performance computing (HPC) technologies; LifeV is a C++ software project distributed under the LGPL license. As part of the framework we also consider open source mesh generators, such as Netgen and Gmsh, and software for visualization and post processing such as ParaView. Both Netgen and Gmsh provide several algorithms for 3D mesh generation and mesh refinement. Their scripting languages allow to have a fine control on the features of the mesh when dealing with simple geometries (in particular axisymmetric domains). Netgen is distributed under the LGPL license and Gmsh under the GPL license. ParaView is a large software project based on VTK. In this context, it is recalled for offering several filters to operate on the data from numerical simulation. ParaView is released under its own (BSD-style) ParaView License. The numerical results for the flow in the idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion) are in good quantitative agreement with the measured axial components of the velocity and pressures for three different flow rates corresponding to laminar, transitional, and turbulent regimes. We emphasize the crucial role played by the accuracy in performing numerical integration, mesh, and time step to match the measurements. Concerning the numerical FSI benchmark, the computed pressure wave speed and frequency of oscillations, and the axial velocity of the fluid on the tube axis are close to the values predicted by the analytical solution associated with the benchmark. This represents a first step towards making the CFD framework under consideration a reliable tool for flow simulations in medical devices or biomechanics problems. Nonetheless, we also draw some conclusions (e.g. on which methods and algorithms work best in the different flow regimes) that are not restricted to this specific framework, but rather are general and could be used as guidelines for similar CFD studies with different softwares. REFERENCES [1] Greenshields C, Weller H. A unified formulation for continuum mechanics applied to fluid-structure interaction in flexible tubes. Int. J. Numer. Methods Eng. 2005; 64:1575--1593.