Marcela Szopos

Blood flow in the cerebral venous system: modeling and simulation

Abstract The development of a software platform incorporating all aspects, from medical imaging data, through three-dimensional reconstruction and suitable meshing, up to simulation of blood flow in patient-specific geometries, is a crucial challenge in biomedical engineering. In the present study, a fully three-dimensional blood flow simulation is carried out through a complete rigid macrovascular circuit, namely the intracranial venous network, instead of a reduced order simulation and partial vascular network. The biomechanical modeling step is carefully analyzed and leads to the description of the flow governed by the dimensionless Navier–Stokes equations for an incompressible viscous fluid. The equations are then numerically solved with a free finite element software using five meshes of a realistic geometry obtained from medical images to prove the feasibility of the pipeline. Some features of the intracranial venous circuit in the supine position such as asymmetric behavior in merging regions are discussed.

3D CFD in complex vascular systems: A case study

Modeling the flowing blood in vascular structures is crucial to perform in silico simulations in various clinical contexts. This remains however an emerging and challenging research field, that raises several open issues. In particular, a compromise is generally made between the completeness of the simulation and the complicated architecture of the vasculature: reduced order simulations (lumped parameter models) represent vascular networks, whereas detailed models are devoted to small regions of interest. However, technical improvements enable targeting of compartments of the blood circulation rather than focusing on vascular branched segments. This article aims at investigating the cerebral flow in the entire venous drainage that can be reconstructed from medical imaging.

Energy-based operator splitting approach for the time discretization of coupled systems of partial and ordinary differential equations for fluid flows: The Stokes case

Abstract The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The proposed algorithm is based on a semi-discretization in time based on operator splitting, whose design is guided by the rationale of ensuring that the physical energy balance is maintained at the discrete level. As a result, unconditional stability with respect to the time step choice is ensured by the implicit treatment of interface conditions within the Stokes substeps, whereas the coupling between Stokes and ODE substeps is enforced via appropriate initial conditions for each substep. Notably, unconditional stability is attained without the need of subiterating between Stokes and ODE substeps. Stability and convergence properties of the proposed algorithm are tested on three specific examples for which analytical solutions are derived.

From Real MRA to Virtual MRA: Towards an Open-Source Framework

Angiographic imaging is a crucial domain of medical imaging. In particular , Magnetic Resonance Angiography (MRA) is used for both clinical and research purposes. This article presents the first framework geared toward the design of virtual MRA images from real MRA images. It relies on a pipeline that involves image processing, vascular modeling, computational fluid dynamics and MR image simulation, with several purposes. It aims to provide to the whole scientific community (1) software tools for MRA analysis and blood flow simulation ; and (2) data (computational meshes, virtual MRAs with associated ground truth), in an open-source / open-data paradigm. Beyond these purposes, it constitutes a versatile tool for progressing in the understanding of vascular networks, especially in the brain, and the associated imaging technologies.