The Role of Circle of Willis Anatomy Variations in Cardio-embolic Stroke: A Patient-Specific Simulation Based Study

Abstract

We describe a patient-specific simulation based investigation on the role of Circle of Willis anatomy in cardioembolic stroke. Our simulation framework consists of medical image-driven modeling of patient anatomy including the Circle, 3D blood flow simulation through patient vasculature, embolus transport modeling using a discrete particle dynamics technique, and a sampling based approach to incorporate parametric variations. A total of 24 (four patients and six Circle anatomies including the complete Circle) models were considered, with cardiogenic emboli of varying sizes and compositions released virtually and tracked to compute distribution to the brain. The results establish that Circle anatomical variations significantly influence embolus distribution to the six major cerebral arteries. Embolus distribution to MCA territory is found to be least sensitive to the influence of anatomical variations. For varying Circle topologies, differences in flow through cervical vasculature are observed. This incoming flow is recruited differently across the communicating arteries of the Circle for varying anastomoses. Emboli interact with the routed flow, and can undergo significant traversal across the Circle arterial segments, depending upon their inertia and density ratio with respect to blood. This interaction drives the underlying biomechanics of embolus transport across the Circle, explaining how Circle anatomy influences embolism risk.

This is a preview of subscription content, log in to check access.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8

References

  1. 1.

    Akins, P.T., A.P. Amar, R.S. Pakbaz, and J.D. Fields. Complications of endovascular treatment for acute stroke in the SWIFT trial with Solitaire and Merci devices. Am. J. Neuroradiol 35(3):524–528, 2014.

    Article  PubMed  CAS  Google Scholar 

  2. 2.

    Alastruey, J., K.H. Parker, J. Peiró, S.M. Byrd, and S.J. Sherwin. Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. J. Biomech. 40(8):1794–1805, 2007.

    Article  PubMed  CAS  Google Scholar 

  3. 3.

    Alnæs, M.S., J. Isaksen, K.A. Mardal, B. Romner, M.K. Morgan, and T. Ingebrigtsen. Computation of hemodynamics in the circle of Willis. Stroke 38(9):2500–2505, 2007.

    Article  PubMed  Google Scholar 

  4. 4.

    Alpers, B.J., and R.G. Berry. Circle of Willis in cerebral vascular disorders: the anatomical structure. Arch. Neurol,-Chicago 8(4):398–402, 1963.

    Article  PubMed  CAS  Google Scholar 

  5. 5.

    Alpers, B.J., R.G. Berry, and R.M. Paddison. Anatomical studies of the circle of Willis in normal brain. AMA Arch. Neurol. Psychiatry 81(4):409–418, 1959.

    Article  PubMed  CAS  Google Scholar 

  6. 6.

    Arboix, A., and J. Alioc. Cardioembolic stroke: clinical features, specific cardiac disorders and prognosis. Curr. Cardiol. Rev. 6(3):150–161, 2010.

    Article  PubMed  PubMed Central  Google Scholar 

  7. 7.

    Carr, I.A., N. Nemoto, R.S. Schwartz, and S.C. Shadden. Size-dependent predilections of cardiogenic embolic transport. Am. J. Physiol.-Heart C 305(5):H732–H739, 2013.

    Article  CAS  Google Scholar 

  8. 8.

    Cassot, F., Vergeur, V., Bossuet, P., Hillen, B., Zagzoule, M., and Marc-Vergnes, J.P. Effects of anterior communicating artery diameter on cerebral hemodynamics in internal carotid artery disease: a model study. Circulation 92(10):3122–3131, 1995.

    Article  PubMed  CAS  Google Scholar 

  9. 9.

    DeVault, K., P.A. Gremaud, V. Novak, M.S. Olufsen, G. Vernieres, and P. Zhao. Blood flow in the circle of Willis: modeling and calibration. Multiscale Model. Sim. 7(2):888–909, 2008.

    Article  Google Scholar 

  10. 10.

    Ferro, J.M. Cardioembolic stroke: an update. Lancet Neurol. 2(3):177–188, 2003.

    Article  PubMed  Google Scholar 

  11. 11.

    Ferro, J.M., A.R. Massaro, and J.L. Mas. Aetiological diagnosis of ischaemic stroke in young adults. Lancet Neurol. 9(11):1085–1096, 2010.

    Article  PubMed  Google Scholar 

  12. 12.

    Gallo, D., Vardoulis, O., Monney, P., Piccini, D., Antiochos, P., Schwitter, J., Stergiopoulos, N., and Morbiducci, U. Cardiovascular morphometry with high-resolution 3D magnetic resonance: First application to left ventricle diastolic dysfunction. Med. Eng. Phys. 47:64–71, 2017.

    Article  PubMed  Google Scholar 

  13. 13.

    Gottesman, R.F., P.M. Sherman, M.A. Grega, D.M. Yousem, L.M. Borowicz, O.A. Selnes, W.A. Baumgartner, and G.M. McKhann. Watershed strokes after cardiac surgery. Stroke 37(9):2306–2311, 2006.

    Article  PubMed  Google Scholar 

  14. 14.

    Grinberg, L., Anor, T., Cheever, E., Madsen, J.R., and Karniadakis, G.E. Simulation of the human intracranial arterial tree. Philos. Trans. R. Soc. A 367(1896):2371–2386, 2009.

    Article  Google Scholar 

  15. 15.

    Hart, R.G., H.C. Diener, S.B. Coutts, J.D. Easton, C.B. Granger, M.J. O’Donnell, R.L. Sacco, S.J. Connolly, Cryptogenic Stroke/ESUS International Working Group, et al. Embolic strokes of undetermined source: the case for a new clinical construct. Lancet Neurol. 13(4):429–438, 2014.

    Article  Google Scholar 

  16. 16.

    Hendrikse, J., Hartkamp, M.J., Hillen, B., Mali, W.P., and Van der Grond, J. Collateral ability of the Circle of Willis in patients with unilateral internal carotid artery occlusion: border zone infarcts and clinical symptoms. Stroke 32(12):2768–2773, 2001.

    Article  PubMed  CAS  Google Scholar 

  17. 17.

    Hillen, B., Hoogstraten, H.W., and Post, L. A mathematical model of the flow in the Circle of Willis. J. Biomech. 19(3):187–194, 1986.

    Article  PubMed  CAS  Google Scholar 

  18. 18.

    Hillen, B., Drinkenburg, B.A.H., Hoogstraten, H.W., and Post, L. Analysis of flow and vascular resistance in a model of the Circle of Willis. J. Biomech. 21(10):807–814, 1988.

    Article  PubMed  CAS  Google Scholar 

  19. 19.

    Hoksbergen, A.W.J., B. Fülesdi, D.A. Legemate, and L. Csiba. Collateral configuration of the circle of Willis. Stroke 31(6):1346–1351, 2000.

    Article  PubMed  CAS  Google Scholar 

  20. 20.

    Hoksbergen, A.W.J., D.A. Legemate, L. Csiba, G. Csati, P. Siro, and B. Fülesdi. Absent collateral function of the circle of Willis as risk factor for ischemic stroke. Cerebrovasc. Dis. 16(3):191–198, 2003.

    Article  PubMed  CAS  Google Scholar 

  21. 21.

    Hoksbergen, A.W.J., D.A. Legemate, D.T. Ubbink, and M.J.H.M. Jacobs. Collateral variations in circle of Willis in atherosclerotic population assessed by means of transcranial color-coded duplex ultrasonography. Stroke 31(7):1656–1660, 2000.

    Article  PubMed  CAS  Google Scholar 

  22. 22.

    Kapoor, K., B. Singh, and I.J. Dewan. Variations in the configuration of the circle of Willis. Anat. Sci. Int. 83(2):96–106, 2008.

    Article  PubMed  Google Scholar 

  23. 23.

    Kim, G.E., Y.P. Cho, and S.M. Lim. The anatomy of the circle of Willis as a predictive factor for intra-operative cerebral ischemia (shunt need) during carotid endarterectomy. Neurol. Res. 24(3):237–240, 2002.

    Article  PubMed  Google Scholar 

  24. 24.

    Kim, H.J., J.M. Song, S.U. Kwon, B.J. Kim, D.H. Kang, J.K. Song, J.S. Kim, and D.W. Kang. Right-left propensity and lesion patterns between cardiogenic and aortogenic cerebral embolisms. Stroke 42(8):2323–2325, 2011.

    Article  PubMed  Google Scholar 

  25. 25.

    Kluytmans, M., J. Van der Grond, K.J. Van Everdingen, C.J.M. Klijn, L.J. Kappelle, and M.A. Viergever. Cerebral hemodynamics in relation to patterns of collateral flow. Stroke 30(7):1432–1439, 1999.

    Article  PubMed  CAS  Google Scholar 

  26. 26.

    Korin, N., M. Kanapathipillai, B.D. Matthews, M. Crescente, A. Brill, T. Mammoto, K. Ghosh, S. Jurek, S.A. Bencherif, D. Bhatta, et al. Shear-activated nanotherapeutics for drug targeting to obstructed blood vessels. Science 337(6095):738–742, 2012.

    Article  PubMed  CAS  Google Scholar 

  27. 27.

    Krishnaswamy, A., J.P. Klein, and S.R. Kapadia. Clinical cerebrovascular anatomy. Catheter. Cardio. Intervent. 75(4):530–539, 2010.

    Google Scholar 

  28. 28.

    Les, A.S., S.C. Shadden, C.A. Figueroa, J.M. Park, M.M. Tedesco, R.J. Herfkens, R.L. Dalman, and C.A. Taylor. Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamics. Ann. Biomed. Eng. 38(4):1288–1313, 2010.

    Article  PubMed  Google Scholar 

  29. 29.

    Liebeskind, D.S. Collateral circulation. Stroke 34(9):2279–2284, 2003.

    Article  PubMed  Google Scholar 

  30. 30.

    Lubicz, B., L. Collignon, G. Raphaeli, J.P. Pruvo, M. Bruneau, O. De Witte, and X. Leclerc. Flow-diverter stent for the endovascular treatment of intracranial aneurysms. Stroke 41(10):2247–2253, 2010.

    Article  PubMed  Google Scholar 

  31. 31.

    MacDonald, M.E., and R. Frayne. Phase contrast MR imaging measurements of blood flow in healthy human cerebral vessel segments. Physiol. Meas. 36(7):1517–1527, 2015.

    Article  PubMed  Google Scholar 

  32. 32.

    Marosfoi, M.G., N. Korin, M.J. Gounis, O. Uzun, S. Vedantham, E.T. Langan, A.L. Papa, O.W. Brooks, C. Johnson, A.S. Puri, et al. Shear-activated nanoparticle aggregates combined with temporary endovascular bypass to treat large vessel occlusion. Stroke 46(12):3507–3513, 2015.

    Article  PubMed  CAS  Google Scholar 

  33. 33.

    Maxey, M.R., and J.J. Riley. Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26(4):883–889, 1983.

    Article  Google Scholar 

  34. 34.

    Morbiducci, U., Ponzini, R., Gallo, D., Bignardi, C., and Rizzo, G. Inflow boundary conditions for image-based computational hemodynamics: impact of idealized versus measured velocity profiles in the human aorta. J. Biomech. 46:102–109, 2013.

    Article  PubMed  Google Scholar 

  35. 35.

    Mukherjee, D., N.D. Jani, K. Selvaganesan, C.L. Weng, and S.C. Shadden. Computational assessment of the relation between embolism source and embolus distribution to the circle of Willis for improved understanding of stroke etiology. J. Biomech. Eng. 138(8):081008, 2016.

    Article  Google Scholar 

  36. 36.

    Mukherjee, D., J. Padilla, and S.C. Shadden. Numerical investigation of fluid-particle interactions for embolic stroke. Theor. Comp. Fluid Dyn. 30(1–2):23–39, 2016.

    Article  Google Scholar 

  37. 37.

    Mukherjee, D., and S.C. Shadden. Inertial particle dynamics in large artery flows-Implications for modeling arterial embolisms. J. Biomech. 52:155–164, 2017.

    Article  PubMed  Google Scholar 

  38. 38.

    Olufsen, M.S., Peskin, C.S., Kim, W.Y., Pedersen, E.M., Nadim, A., and Larsen, J. Numerical simulation and experimental validation of blood flow iin arteries with structured-tree outflow conditions. Ann. Biomed. Eng. 28(11):1281–1299, 2000.

    Article  PubMed  CAS  Google Scholar 

  39. 39.

    Patel, N., M.A. Horsfield, C. Banahan, J. Janus, K. Masters, J. Morlese, V. Egan, and E.M.L. Chung. Impact of perioperative infarcts after cardiac surgery. Stroke 46:680–686, 2015.

    Article  PubMed  Google Scholar 

  40. 40.

    Ringelstein, E.B., C. Weiller, M. Weckesser, and S. Weckesser. Cerebral vasomotor reactivity is significantly reduced in low-flow as compared to thromboembolic infarctions: the key role of the circle of Willis. J. Neurol. Sci. 121(1):103–109, 1994.

    Article  PubMed  CAS  Google Scholar 

  41. 41.

    Schomer, D.F., M.P. Marks, G.K. Steinberg, I.M. Johnstone, D.B. Boothroyd, M.R. Ross, N.J. Pelc, and D.R. Enzmann. The anatomy of the posterior communicating artery as a risk factor for ischemic cerebral infarction. N. Eng. J. Med. 330(22):1565–1570, 1994.

    Article  CAS  Google Scholar 

  42. 42.

    Smith, W.S., M.H. Lev, J.D. English, E.C. Camargo, M. Chou, S.C. Johnston, G. Gonzalez, P.W. Schaefer, W.P. Dillon, W.J. Koroshetz, and K.L. Furie. Significance of large vessel intracranial occlusion causing acute ischemic stroke and TIA. Stroke 40(12):3834–3840, 2009.

    Article  PubMed  PubMed Central  Google Scholar 

  43. 43.

    Steinman, D.A. Image-based computational fluid dynamics modeling in realistic arterial geometries. Ann. Biomed. Eng. 30(4):483–497, 2002.

    Article  PubMed  Google Scholar 

  44. 44.

    Szabo, K., R. Kern, A. Gass, J. Hirsch, and M. Hennerici. Acute stroke patterns in patients with internal carotid artery disease. Stroke 32(6):1323–1329, 2001.

    Article  PubMed  CAS  Google Scholar 

  45. 45.

    Tanaka, H., N. Fujita, T. Enoki, K. Matsumoto, Y. Watanabe, K. Murase, and H. Nakamura. Relationship between variations in the circle of willis and flow rates in internal carotid and basilar arteries determined by means of magnetic resonance imaging with semiautomated lumen segmentation: reference data from 125 healthy volunteers. Am. J. Neuroradiol. 27(8):1770–1775, 2006.

    PubMed  CAS  Google Scholar 

  46. 46.

    Taylor, C.A., and D.A. Steinman. Image-based modeling of blood flow and vessel wall dynamics: applications, methods and future directions. Ann. Biomed. Eng. 38(3):1188–1203, 2010.

    Article  PubMed  Google Scholar 

  47. 47.

    Torvik, A. The pathogenesis of watershed infarcts in the brain. Stroke 15(2):221–223, 1984.

    Article  PubMed  CAS  Google Scholar 

  48. 48.

    Updegrove, A., N.M. Wilson, J. Merkow, H. Lan, A.L. Marsden, and S.C. Shadden. SimVascular: an open source pipeline for cardiovascular simulation. Ann. Biomed. Eng.:1–17, 2016.

  49. 49.

    Van Seeters, T., J. Hendrikse, G.J. Biessels, B.K. Velthuis, W.P.T.M. Mali, L.J. Kappelle, Y. van der Graaf, SMART Study Group, et al. Completeness of the circle of Willis and risk of ischemic stroke in patients without cerebrovascular disease. Neuroradiology 57(12):1247–1251, 2015.

    Article  PubMed  PubMed Central  Google Scholar 

  50. 50.

    Zamir, M., Sinclair, P., and Wonnacott, T.H. Relation between diameter and flow in major branches of the arch of the aorta. J. Biomech. 25(11):1303–1310, 1992.

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

This work was supported by the American Heart Association Award: 13GRNT17070095. This research used the Savio computational cluster resource provided by the Berkeley Research Computing program at the University of California, Berkeley. NDJ acknowledges support from the Regent’s and Chancellor’s Research Fellowship at U.C. Berkeley. DM, NDJ, and SCS conceptualized the design of the study. DM developed the computational framework, performed the embolus dynamics, performed all statistical and data analysis, drafted the manuscript. NDJ devised the image-based modeling framework, computed all flow simulations, and contributed to embolus dynamics simulations. JN helped with data analysis, and contributed clinical and diagnostic connections to the simulation data. NDJ, SCS, and JN reviewed and edited the manuscript draft. Final manuscript version was in agreement with all Authors.

Conflict of interest

There are no conflicts of interest.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Debanjan Mukherjee.

Additional information

Associate Editor Ender A. Finol oversaw the review of this article.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Electronic supplementary material 2 (MP4 28204 kb)

Electronic supplementary material 1 (PDF 2594 kb)

Electronic supplementary material 2 (MP4 28204 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mukherjee, D., Jani, N.D., Narvid, J. et al. The Role of Circle of Willis Anatomy Variations in Cardio-embolic Stroke: A Patient-Specific Simulation Based Study. Ann Biomed Eng 46, 1128–1145 (2018). https://doi.org/10.1007/s10439-018-2027-5

Download citation

Keywords

  • Stroke
  • Embolus
  • Hemodynamics
  • Circle of Willis
  • Fluid–particle interaction