Computational hemodynamics framework for the analysis of cerebral aneurysms

Abstract

Assessing the risk of rupture of intracranial aneurysms is important for clinicians because the natural rupture risk can be exceeded by the small but significant risk carried by current treatments. To this end numerous investigators have used image-based computational fluid dynamics models to extract patient-specific hemodynamics information, but there is no consensus on which variables or hemodynamic characteristics are the most important. This paper describes a computational framework to study and characterize the hemodynamic environment of cerebral aneurysms in order to relate it to clinical events such as growth or rupture. In particular, a number of hemodynamic quantities are proposed to describe the most salient features of these hemodynamic environments. Application to a patient population indicates that ruptured aneurysms tend to have concentrated inflows, concentrated wall shear stress distributions, high maximal wall shear stress and smaller viscous dissipation ratios than unruptured aneurysms. Furthermore, these statistical associations are largely unaffected by the choice of physiologic flow conditions. This confirms the notion that hemodynamic information derived from image-based computational models can be used to assess aneurysm rupture risk, to test hypotheses about the mechanisms responsible for aneurysm formation, progression and rupture, and to answer specific clinical questions.

Effects of Flow-Diverting Device Oversizing on Hemodynamics Alteration in Cerebral Aneurysms

“…14 Pulsatile CFD simulations were performed for 2 cardiac cycles, and the results are presented for the second cycle. The results of these CFD computations were postprocessed to calculate the following aneurysmal hemodynamic quantities: 15 1) inflow rate into the aneurysm, 2) flow velocity averaged over the aneurysm volume, 3) shear rate averaged over the aneurysm volume, and 4) wall shear stress averaged over the aneurysm surface. Subsequently, the reduction of these quantities from the prestenting configuration to each of the stented models was calculated, and the minimum, maximum, and mean of these changes over the cardiac cycle were computed and compared.…”

Deflated preconditioned conjugate gradients applied to a Petrov-Galerkin generalized least squares finite element formulation for incompressible flows with heat transfer

“…Algorithm 1 -Edge-by-edge matrix-vector product It is known that iterative Krylov solvers such as CG are very efficient at minimizing errors associated with higher frequency modes but can be rather slow for lower frequency ones (Aubry et al, 2008;Frank and Vuik, 2001;Löhner et al, 2011;Nicolaides, 1987;Vermolen et al, 2002), which in other words translates as the smaller the spectral condition number, that is, the ratio between the largest and smallest eigenvalues of the matrix, the faster convergence will be. The use of deflation aims to accelerate solution convergence by reducing the spectral condition number in comparison with the original system Mut, 2008), with Nicolaides (1987) presenting its mathematical proof, later discussed again by Frank and Vuik (2001). For a generic system of linear equations A·x ¼ b, given a deflation space W, of order n × m, rank m and m ≪ n, the projector P, of order n × n, mapping A −1 orthogonally onto W is:…”

“…However, one can easily infer that if the smallest eigenvalue is too small, the number of iterations necessary may become less affordable, especially with larger systems of linear equations. Mut (2008) and then Aubry et al (2011) have shown that the adoption of deflation helps speed up the convergence of the solution by reducing the spectral condition number of the deflated system. The deflation space is then built in a way to remove from the solution the smallest eigenvalues, responsible for slowing convergence.…”

3D Cine Phase-Contrast MRI at 3T in Intracranial Aneurysms Compared with Patient-Specific Computational Fluid Dynamics

“…Despite these drawbacks, CFD has recently been used to associate intra-aneurysmal hemodynamics with rupture. 15 The enormous advancements in MR imaging technology in the past decade now allow direct measurement of intra-aneurys-mal flow by using 3D PC-MR imaging. 19 Moreover, the technique was validated against CFD in a real-size phantom.…”