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Numerical Modeling of Flow in the Cerebral Vasculature: Understanding Changes in Collateral Flow Directions in the Circle of Willis for a Cohort of Vasospasm Patients Through Image-Based Computational Fluid Dynamics

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Abstract

The Circle of Willis (CoW) is a ring-like network of blood vessels that perfuses the brain. Flow in the collateral pathways that connect major arterial inputs in the CoW change dynamically in response to vessel narrowing or occlusion. Vasospasm is an involuntary constriction of blood vessels following subarachnoid hemorrhage (SAH), which can lead to stroke. This study investigated interactions between localization of vasospasm in the CoW, vasospasm severity, anatomical variations, and changes in collateral flow directions. Patient-specific computational fluid dynamics (CFD) simulations were created for 25 vasospasm patients. Computed tomographic angiography scans were segmented capturing the anatomical variation and stenosis due to vasospasm. Transcranial Doppler ultrasound measurements of velocity were used to define boundary conditions. Digital subtraction angiography was analyzed to determine the directions and magnitudes of collateral flows as well as vasospasm severity in each vessel. Percent changes in resistance and viscous dissipation were analyzed to quantify vasospasm severity and localization of vasospasm in a specific region of the CoW. Angiographic severity correlated well with percent changes in resistance and viscous dissipation across all cerebral vessels. Changes in flow direction were observed in collateral pathways of some patients with localized vasospasm, while no significant changes in flow direction were observed in others. CFD simulations can be leveraged to quantify the localization and severity of vasospasm in SAH patients. These factors as well as anatomical variation may lead to changes in collateral flow directions. Future work could relate localization and vasospasm severity to clinical outcomes like the development of infarct.

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Acknowledgements

We would like to thank Shumaila Ahmed, Karen Velderrain-Lopez, and François Ramon for creating patient-specific segmentations, François Ramon for creating the PyTec scripts to calculate resistance, and Erin Espeland for generating CFD models from patient-specific data. We are grateful for Katie Paulson, Ameer Dharamshi, and Ethan Ashby, who provided guidance and insight into presenting the statistical results in an intuitive way.

Funding

This work was funded by the National Science Foundation Graduate Research Fellowship Program (NSF GRFP) AHRQ (Grant No. 1 R18 HS 026690; Funder ID: 10.13039/100000133), the Royalty Research Fund at the University of Washington, the CRBT Strategic Research Investment through the Seattle Children’s Research Institute, the Locke Trust through a gift to the Division of Cardiology of the University of Washington, the American Heart Association via a Postdoctoral fellowship (19POST34450082), and the National Institute of Health Grants R01NS105692 and R25NS079200. This work was facilitated through the use of advanced computational, storage, and networking infrastructure provided by the Hyak supercomputer system and funded by the Student Technology Fund at the University of Washington.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Washington, Seattle, WA, USA

    Angela Straccia, Michael C. Barbour & Alberto Aliseda

  2. INSERM U1059 Sainboise, Mines Saint-Étienne, Saint-Étienne, France

    Fanette Chassagne

  3. Department of Neurological Surgery, University of Washington, Seattle, WA, USA

    David Bass, Guilherme Barros & Michael R. Levitt

  4. Applied Physics Laboratory, University of Washington, Seattle, WA, USA

    Daniel Leotta

  5. Department of Medicine, University of Washington, Seattle, WA, USA

    Florence Sheehan

  6. Department of Anesthesiology and Pain Medicine, University of Washington, Seattle, WA, USA

    Deepak Sharma

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Appendices

Appendix A

Definition of Antegrade Collateral Flow Directions

See Fig. 9.

Fig. 9
figure 9

Definition of antegrade flow in the collateral pathways of the CoW

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Mesh Independence Study

The mesh independence study was performed by comparing the percent changes in resistance and dissipation between the baseline and vasospasm conditions across four mesh resolutions: a base size of 0.6 mm (3.5 million elements during baseline and 2.8 million elements during vasospasm), 0.35 mm (4.4 million elements during baseline and vasospasm), 0.2 mm (13 million elements during baseline and 10.5 million elements during vasospasm), and 0.15 mm (33 million elements during baseline and 22 million elements during vasospasm). The percent changes in resistance and dissipation were compared between each of the meshes. The differences in percent change in resistance between the coarsest and finest meshes were below 15 in vessels exhibiting an absolute change below 1000%, below 100 in vessels with an absolute change between 1000% and 1200%, and below 500 for one vessel with greater than 3000% absolute change. The differences in percent change in dissipation between the coarsest and finest meshes were below 50 in vessels exhibiting an absolute change below 800%, below 100 in vessels with an absolute change between 800% and 2000%, and below 100 for vessels with greater than 2000% absolute change. Given the relatively small differences between the percent changes in resistance and dissipation compared to their absolute values, the CFD results were considered to be insensitive to mesh resolution in the range of base sizes between 0.6 mm and 0.15 mm.

The base size of 0.55 mm was selected because a previous mesh study showed that the collateral flow rates were consistent between this sizing and the finer meshes [43].

Determination of CFD Metric Threshold for Discretizing Severity

See Fig. 10.

Fig. 10
figure 10

Least squares error between the quantized CFD metrics and angiographic severity given a range of thresholds for resistance (left) and dissipation (right)

Full size image

Comparison Between CFD Metrics with Angiographic Severity Across Patients

See Table 1.

Table 1 The percentage of blood vessels for a given patient that agree within one level of the angiographic severity given the CFD metrics of percent change in resistance and dissipation
Full size table

Collateral Flow Directions

See Figs. 11, 12, 13 and 14.

Fig. 11
figure 11

Flow direction and magnitude in the collateral pathways for patients 1 and 2 during baseline and vasospasm

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Fig. 12
figure 12

Flow direction and magnitude in the collateral pathways for patients 3 and 4 during baseline and vasospasm

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Fig. 13
figure 13

Flow direction and magnitude in the collateral pathways for patients 5 and 6 during baseline and vasospasm

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Fig. 14
figure 14

Flow direction and magnitude in the collateral pathways for patients 7 and 8 during baseline and vasospasm

Full size image

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Straccia, A., Barbour, M.C., Chassagne, F. et al. Numerical Modeling of Flow in the Cerebral Vasculature: Understanding Changes in Collateral Flow Directions in the Circle of Willis for a Cohort of Vasospasm Patients Through Image-Based Computational Fluid Dynamics. Ann Biomed Eng (2024). https://doi.org/10.1007/s10439-024-03533-w

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