Fast numerical solutions of patient‐specific blood flows in 3D arterial systems

Abstract

The study of hemodynamics in arterial models constructed from patient-specific medical images requires the solution of the incompressible flow equations in geometries characterized by complex branching tubular structures. The main challenge with this kind of geometries is that the convergence rate of the pressure Poisson solver is dominated by the graph depth of the computational grid. This paper presents a deflated preconditioned conjugate gradients (DPCG) algorithm for accelerating the pressure Poisson solver. A subspace deflation technique is used to approximate the lowest eigenvalues along tubular domains. This methodology was tested with an idealized cylindrical model and three patient-specific models of cerebral arteries and aneurysms constructed from medical images. For these cases, the number of iterations decreased by up to a factor of 16, while the total CPU time was reduced by up to 4 times when compared with the standard PCG solver.

Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms

“…If the fluid and structure meshes at the fluid-structure interface are identical, then the projections given by Equations (26), (27) and (29) simplify to 'direct substitution'.…”

“…Here ( , h h 1I and h h 2I (the fluid velocity, fluid stress and structural stress at the fluid-structure interface) are treated as separate unknowns, and Equations (27), (28) and (29) can be seen as corresponding to these three unknowns, respectively. The structural displacement rate at the interface, u h 2I , is derived from y h .…”

“…Although this detail was not discussed in [9,21,52], the two projection equations given by Equations (27) and (29) are solved by 'numerical substitution', which essentially consists of sublevel GMRES iterations.…”

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

“…These equations were numerically solved by using an implicit finite-element formulation and a deflated conjugate-gradients algorithm to accelerate the convergence. 11 The stent wires were treated with an immersed boundary approach on the refined unstructured grids. 12 Because patient-specific flow conditions were not available, typical flow waveforms measured in healthy subjects were used to specify the inflow boundary conditions.…”

Special issue on patient‐specific computational modelling

“…Effect of prestressed patient-specific geometries is discussed by Gee et al [3]. A fast solution strategy for long patient-specific fluid domains is suggested in [4]. The importance and application of adaptive methods in biological problems are described by Botti et al [5].…”