What does computational fluid dynamics tell us about intracranial aneurysms? A meta-analysis and critical review

Abstract

Despite the plethora of published studies on intracranial aneurysms (IAs) hemodynamic using computational fluid dynamics (CFD), limited progress has been made towards understanding the complex physics and biology underlying IA pathophysiology. Guided by 1733 published papers, we review and discuss the contemporary IA hemodynamics paradigm established through two decades of IA CFD simulations. We have traced the historical origins of simplified CFD models which impede the progress of comprehending IA pathology. We also delve into the debate concerning the Newtonian fluid assumption used to represent blood flow computationally. We evidently demonstrate that the Newtonian assumption, used in almost 90% of studies, might be insufficient to describe IA hemodynamics. In addition, some fundamental properties of the Navier-Stokes equation are revisited in supplementary material to highlight some widely spread misconceptions regarding wall shear stress (WSS) and its derivatives. Conclusively, our study draws a roadmap for next-generation IA CFD models to help researchers investigate the pathophysiology of IAs.

Keywords: CFD; Cerebral aneurysm; cerebrovascular blood flow; fluid dynamics; non-Newtonian fluids.

Figure 1.

The rise of simplified CFD models of IA hemodynamics during the past two decades. (a) Exponential growth in the use of CFD as a research tool in aneurysm hemodynamics based on Scopus® database. Search query available in the supplementary materials. (b) Comparison of the citation counts (2000–2018) from Scopus® bibliographic database between the early in vitro works reporting complex IA flow physics (black column indicates total annual citations for references^,,) and subsequent CFD models adopting simplified assumed flow physics (blue outlined column indicates total annual citations of references^,,).

Figure 2.

The parameters and assumptions which define the complexity of CFD models. The meshing resolution of the flow domain, boundary conditions as well as the viscosity models and solver numerical settings define the flow physics predicted by the CFD model and whether or not it could model transitional and turbulent features of the flow.

Figure 3.

Classification of published studies on intracranial anereurysm hemodynamics with respect to physical assumptions in the CFD models, as revealed by Scopus® bibliographic databases. A total number of 1733 publications was found by searching Scopus® on 14 October 2018. This classification was conducted using sequential searches via Scopus® analytic tools. Classification methodology is explained in the methods section. Articles using CFD as a method of investigation comprised 47% of the literature on aneurysm hemodynamics (a). Of these CFD-based articles, only 10% used the non-Newtonian viscocity assumption to investigate aneurysm hemodynamic features (b), 31% used unsteady and pulsatile models (c) and only 4% investigated turbulence and transition to turbulence (d).

Figure 4.

Box plots of WSS as calculated by Newtonian and five different non-Newtonian models in different intracranial arteries which are known for harboring IAs. Box plots were computed using m means for a total of n measurements by artery. The red midline in the box plots represents the median of WSS per artery per model for all studies. Models compared: Newtonian (N), Power-law (PL), Carreau (C), Carreau-Yasuda (C-Y), Casson (CS) and Cross (CR).

Figure 5.

WSS estimation difference $(\mathit{WS}{S}_N-\mathit{WS}{S}_{\mathit{NN}})$ as calculated for different non-Newtonian models. Measurements of diameter and flow rate of different intracranial arteries as compiled from the meta-analysis with colors showing different arteries.