Modeling of Subject Specific Arterial Segments Using 3D Fluid Structure Interaction and a 1D-0D Arterial Tree Network Boundary Condition
Magnus Andersson, Jonas Lantz , Matts Karlsson
Department of Management and Engineering, Linköping University, SE-581 83 Linköping, Sweden
In recent years it has been possible to simulate 3D blood flow through CFD including the dilatation effect in elastic arteries using Fluid-Structure Interaction (FSI) to better match in vivo data. Patient specific imposed boundary condition (BC) is often used as the velocity profiles at the inlets. However, for the outlet BC a time-resolved pressure is required and often lacking as it is obtained by an invasive procedure. Numerous models have been developed for capturing the main effects of the vascular bed at these sites, which have been shown crucial and difficult to implement accurately. This work focus on a full scaled FSI simulation at an arterial section including the abdominal aorta, renal arteries and iliac bifurcations, obtained from MRI of an healthy individual. The outlet BC at the iliac arteries is connected with a 1D systemic arterial tree which is truncated with a 0D lumped model. This 3D-(0D-1D) connection can provide the essential features of the peripheral flow and, in contrast to the imposed BC, the 1D-0D coupling allow for investigation of cardiovascular diseases including stenoses and/or hypertension.
The MRI images were segmented using an in-house software to obtain a 3D surface of the vessel lumen, Figure 1. The surfaces were meshed with high quality hexahedral element using ANSYS ICEM CFD 12.0 (ANSYS Inc, Canonsburg, PA, USA). A PC-MRI time-resolved massflow at the descending aorta were used as inlet BC, where 22% of the flow was forced into the renal bifurcations assuming negligible pressure wave reflection. The wall was modelled with an isotropic elastic model with addition of an elastic support mimicking the damping effect of the surrounding tissue. The 1D model is based on transmission-line theory which involves an impedance model for the pressure-flow relationship. The arterial topology was extracted from literature and only the central arteries after the iliacs was considered. At the truncation sites a 3-element Windkessel model (known as RRC) was implemented and is the most common model of choice for describing the main effects of all the distal vessels. The 1D system solves the Fourier frequency impedance coefficients over one heart cycle accounting for wave reflection by using the 15 first harmonics to obtain the corresponding pressure. The 3D-1D connection is done offline, which allows for an independent and more stable 3D simulation. This step is iteratively repeated until convergence is reach between the present 3D outlet flow and previous implemented 1D outlet flow. The simulation was utilized in ANSYS CFX, ANSYS Mechanical, and coupled by ANSYS Multi-Field.
The (0D-1D)-3D model showed convergence of pressure/flow at the iliac outlets, Figure 2. The method provides realistic pressure and flow responses based on the input parameters and even capture the relative difference in flow/pressure distribution between the right and left illiac artery due to subject specific geometric variability. Parameters such as velocity profiles and WSS can be extracted in the 3D domain.
This method allows for a better insight of large scale vascular networks effect of the local 3D flow features and also gives a better representation of the peripheral flow compared to a pure 0D (lumped parameter/Windkessel) model. PC-MRI will provide data for validation of velocity profiles in the 3D model. Future work includes a subject specific 1D vascular topology to be combined with the 3D model.
The 6th international symposium on biomechanics in vascular biology and cardiovascular disease