State-of-the-Art Computational Models of Circle of Willis With Physiological Applications: A Review

Abstract

Background: Various computational models of the circle of Willis (CoW) have been developed to non-invasively estimate the blood flow and hemodynamic parameters in intracranial arteries for the assessment of clinical risks such as aneurysms, ischemia, and atherosclerotic plaque growth. This review aims to categorize the latest computational models of CoW and summarize the innovative techniques. Summary of Review: In traditional computational models of CoW, the computational complexity increased from zero-dimensional models to one-dimensional and three-dimensional models. The applications extend from estimating certain hemodynamic parameters to simulating local flow field. The innovative techniques include the combination of models with different dimensions, the extension of vascular structure including heart and veins, as well the addition of distal fractality, cerebral autoregulation, and intracranial pressure. There are some nontraditional models based on fluid-solid-interaction, control theory, and in-vitro experiments. In all kinds of models, the in-vivo data and non-Newtonian rheological models of blood have been widely applied to improve the accuracy of hemodynamic simulation. Conclusion: Firstly, the selection of model depends on its application scenario. The balance between computational complexity and physiological accuracy deserves further investigation. Secondly, the improvement of CoW models relies on the large-scale validations and the combination of various innovative modeling techniques. INDEX TERMS brain modeling, computational modeling, Circle of Willis (CoW), Windkessel effect, pulse wave, computational fluid dynamics (CFD), cerebral blood flow, intracranial arteries.

The Comparison of Different Constitutive Laws and Fiber Architectures for the Aortic Valve on Fluid–Structure Interaction Simulation

“…Although this 3-element Windkessel model has limitations to predict spatially distributed flow quantities, it is simple and accurate to predict the ventricular after-load as discussed by Westerhof et al ( 2008 ). There are many blood flow models ranging from the zero-dimensional models (lumped-parameter models) (Liu et al, 2020 ), the one-dimensional models (Olufsen et al, 2000 ; Chen et al, 2016 ; Duanmu et al, 2019 ), and the three-dimensional models (Lee et al, 2016 ). Interested reader can refer to Shi et al ( 2011 ); Morris et al ( 2016 ) for reviews on blood flow modeling.…”

Development of Novel Fractal Method for Characterizing the Distribution of Blood Flow in Multi-Scale Vascular Tree

“…Nowadays, the RCL model has been developed for hemodynamic simulation in which the resistance (R), capacitance (C), and inductance (L) elements were used to mimic the effects of vessel resistance, vessel compliance, and blood inertia, respectively ( Muller and Toro, 2014 ; Zhang et al, 2014 ). And models from 0D to 3D were established ( Arciero et al, 2017 ; Liu et al, 2020 ). In the present hemodynamic model of microcirculation, only the resistance element for a vessel segment was considered.…”

Geometric features of middle cerebral artery are associated with spontaneous basal ganglia intracerebral haemorrhage

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