Cardiovascular Engineering and Technology

, Volume 3, Issue 4, pp 450–461 | Cite as

Fluid Mechanics of Mixing in the Vertebrobasilar System: Comparison of Simulation and MRI

  • Matthew D. Bockman
  • Akash P. Kansagra
  • Shawn C. Shadden
  • Eric C. Wong
  • Alison L. Marsden


Recent magnetic resonance imaging (MRI) studies have demonstrated that perfusion to the posterior fossa of the brain can be surprisingly unilateral, with specific vascular territories supplied largely by a single vertebral artery (VA) rather than a mixture of the two. It has been hyposthesized that this is due to a lack of mixing in the confluence of the VA into the basilar artery (BA), however the local mechanisms of mixing (or lack thereof) have not been previously examined in detail. This study aims to assess the mixing characteristics and hemodynamics of the vertebrobasilar junction using subject specific computational fluid dynamics (CFD) simulations, and perform quantitative comparisons to arterial spin labeling (ASL) MRI measurements. Subject specific CFD simulations and unsteady particle tracking were performed to quantitatively evaluate vertebrobasilar mixing in four subjects. Phase-contrast MRI was used to assign inflow boundary conditions. A direct comparison of the fractional flow contributions from the VAs was performed against perfusion maps generated via vessel-encoded pseudo-continuous arterial spin labeling (VEPCASL) MRI. The laterality of VA blood supply in 7/8 simulated cerebellar hemispheres and 5/7 simulated cerebral hemispheres agree with ASL data. Whole brain laterality of the VA supply agrees within 5% for measured and computed values for all patients. However, agreement is not as strong when comparing perfusion to individual regions. Simulations were able to accurately predict laterality of VA blood supply in four regions of interest and confirm ASL results, showing that very little mixing occurs at the vertebrobasilar confluence. Additional particle tracking analysis using Lagrangian coherent structures is used to augment these findings and provides further physical insight that complements current in vivo imaging techniques. A quantitative mix-norm measure was used to compare results, and sensitivity analysis was performed to assess changes in the results with pertubations in the boundary condition values.


Computational fluid dynamics Arterial spin labeling MRI Lagrangian coherent structures Fluid mixing Vertebral artery Basilar artery 



Support for this work was provided by a Burroughs Wellcome Fund Career Award at the Scientific Interface, a UCSD Collaboratories Grant and NIH grant R01EB002096. The authors gratefully acknowledge the use of software from the Simvascular open source project (, and the convection-diffusion code written by Mahdi Esmaily Moghadam.


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Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  • Matthew D. Bockman
    • 1
  • Akash P. Kansagra
    • 2
  • Shawn C. Shadden
    • 3
  • Eric C. Wong
    • 4
    • 5
  • Alison L. Marsden
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaSan DiegoUSA
  2. 2.Department of Radiology and Biomedical ImagingUniversity of CaliforniaSan FranciscoUSA
  3. 3.Department of Mechanical, Materials, and Aerospace EngineeringIllinois Institute of TechnologyChicagoUSA
  4. 4.Department of RadiologyUniversity of CaliforniaSan DiegoUSA
  5. 5.Department of PsychiatryUniversity of CaliforniaSan DiegoUSA

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