A Novel Patient-Specific Computational Fluid Dynamics Study of the Activation of Primary Collateral Pathways in the Circle of Willis During Vasospasm

Measurement of transcranial Doppler insonation angles from three-dimensional reconstructions of CT angiography scans

Blood velocities measured by Transcranial Doppler (TCD) are dependent on the angle between the incident ultrasound beam and the direction of blood flow (known as the Doppler angle). However, when TCD examinations are performed without imaging the Doppler angle for each vessel segment is not known. We have measured Doppler angles in the basal cerebral arteries examined with TCD using three-dimensional (3D) vessel models generated from computed tomography angiography (CTA) scans. This approach produces angle statistics that are not accessible during non-imaging TCD studies. We created 3D models of the basal cerebral arteries for 24 vasospasm patients. Standard acoustic windows were mapped to the specific anatomy of each patient. Virtual ultrasound transmit beams were generated that originated from the acoustic window and intersected the centerline of each arterial segment. Doppler angle measurements were calculated and compiled for each vessel segment. Doppler angles were smallest for the middle cerebral artery M1 segment (median 24.6°) and ophthalmic artery (median 25.0°), and largest for the anterior cerebral artery A2 segment (median 76.4°) and posterior cerebral artery P2 segment (median 75.8°). The ophthalmic artery had the highest proportion of Doppler angles that were less than 60° (99%) while the anterior cerebral artery A2 segment had the lowest proportion of Doppler angles that were less than 60° (10%). These angle measurements indicate the expected deviation between measured and true velocities in the cerebral arteries, highlighting specific segments that may be prone to underestimation of velocity.

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

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.

Influence of circle of Willis modeling on hemodynamic parameters in anterior communicating artery aneurysms and recommendations for model selection

Computational fluid dynamics (CFD) has been utilized to calculate hemodynamic parameters in anterior communicating artery aneurysm (AComA), which is located at a junction between left and right A1 and A2 segments. However, complete or half circle of Willis (CoW) models are used indiscriminately. This study aims to suggest recommendations for determining suitable CoW model. Five patient-specific CoW models with AComA were used, and each model was divided into complete, left-half, and right-half models. After validating the CFD using a flow experiment, the hemodynamic parameters and flow patterns in five AComAs were compared. In four out of five cases, inflow from one A1 side had a dominant influence on the AComA, while both left and right A1 sides affected the AComA in the remaining case. Also, the average difference in time-averaged wall shear stress between the complete and half models for four cases was 4.6%, but it was 62% in the other case. The differences in the vascular resistances of left and right A1 and A2 segments greatly influenced the flow patterns in the AComA. These results may help to enhance clinicians' understanding of blood flow in the brain, leading to improvements in diagnosis and treatment of cerebral aneurysms.