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

Haipeng Liu, Defeng Wang, Xinyi Leng, Dingchang Zheng, Fei Chen, Lawrence Ka Sing Wong, Lin Shi, Thomas Wai Hong Leung

    Research output: Contribution to journalReview articlepeer-review

    29 Citations (Scopus)
    81 Downloads (Pure)


    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 as 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.
    Original languageEnglish
    Article number9134441
    Pages (from-to)156261 - 156273
    Number of pages13
    JournalIEEE Access
    Publication statusPublished - 7 Jul 2020

    Bibliographical note

    This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see


    • Brain modeling
    • computational modeling
    • circle of Willis (CoW)
    • Windkessel effect
    • pulse wave
    • computational fluid dynamics (CFD)
    • cerebral blood flow
    • intracranial arteries

    ASJC Scopus subject areas

    • Engineering(all)
    • Materials Science(all)
    • Computer Science(all)


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