Skip to main content

Advertisement

SpringerLink
Log in

Modeling Blood Flow Circulation in Intracranial Arterial Networks: A Comparative 3D/1D Simulation Study

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

We compare results from numerical simulations of pulsatile blood flow in two patient-specific intracranial arterial networks using one-dimensional (1D) and three-dimensional (3D) models. Specifically, we focus on the pressure and flowrate distribution at different segments of the network computed by the two models. Results obtained with 1D and 3D models with rigid walls show good agreement in massflow distribution at tens of arterial junctions and also in pressure drop along the arteries. The 3D simulations with the rigid walls predict higher amplitude of the flowrate and pressure temporal oscillations than the 1D simulations with compliant walls at various segments even for small time-variations in the arterial cross-sectional areas. Sensitivity of the flow and pressure with respect to variation in the elasticity parameters is investigated with the 1D model.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Alastruey, J., S. M. Moore, K. H. Parker, J. Peiró, T. David, and S. J. Sherwin. Reduced modeling of blood flow in the cerebral circulation: coupling 1-D, 0-D and cerebral auto-regulation models. Int. J. Numer. Methods Fluids 56(8):1061–1067, 2007.

    Article  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  3. Cassot, F., M. Zagzoule, and J. P. Marc-Vergnes. Hemodynamic role of the circle of Willis in stenoses of internal carotid arteries. An analytical solution of a linear model. J. Biomech. 33:395–405, 2000.

    Article  CAS  PubMed  Google Scholar 

  4. Chen, J., and X. Y. Lu. Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch. J. Biomech. 39(5):818–832, 2006.

    Article  PubMed  Google Scholar 

  5. Chen, J., X. Lu, and W. Wang. Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses. J. Biomech. 39(11):1983–1995, 2006.

    Article  PubMed  Google Scholar 

  6. Das, B., P. Johnson, and A. Popel. Computational fluid dynamic studies of leukocyte adhesion effects on non-Newtonian blood flow through microvessels. Biorheology 37:239–258, 2000.

    CAS  PubMed  Google Scholar 

  7. Fahrig, R., H. Nikolov, A. J. Fox, and D. W. Holdsworth. A three dimensional cerebrovascular flow phantom. Med. Phys. 26:1589–1599, 1999.

    Article  CAS  PubMed  Google Scholar 

  8. Frahm, J., A. Haase, and D. Matthaei. Rapid NMR imaging of dynamic processes using the FLASH technique. Magn. Reson. Med. 3:321–327, 1986.

    Article  CAS  PubMed  Google Scholar 

  9. Fontanella, M. M., W. Valfré, F. Benech, C. Carlino, D. Garbossa, M. F. Ferrio, R. Perez, M. Berardino, G. B. Bradac, and A. Ducati. Vasospasm after SAH due to aneurysm rupture of the anterior circle of Willis: value of TCD monitoring. Neurol. Res. 30(3):256, 2008.

    Article  PubMed  Google Scholar 

  10. Formaggia, L., D. Lamponi, M. Tuveri, and A. Veneziani. Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart. Comput. Methods Biomech. Biomed. Eng. 9(5):273–288, 2006.

    Article  Google Scholar 

  11. Gonzalez, N. R., W. J. Boscardin, T. Glenn, F. Vinuela, and N. A. Martin. Vasospasm probability index: a combination of transcranial Doppler velocities, cerebral blood flow, and clinical risk factors to predict cerebral vasospasm after aneurysmal subarachnoid hemorrhage. J. Neurosur. 107(6):1101–1112, 2007.

    Article  Google Scholar 

  12. Greitz, D. Cerebrospinal fluid circulation and associated intracranial dynamics. A radiologic investigation using MR imaging and radionuclide cisternography. Acta Radiol. Suppl. 386:1–23, 1993.

    CAS  PubMed  Google Scholar 

  13. Grinberg, L. Topics in Ultrascale Scientific Computing with Application in Biomedical Modeling. PhD thesis, Brown University, 2009.

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

    Article  Google Scholar 

  15. Grinberg, L., and G. E. Karniadakis. Outflow boundary conditions for arterial networks with multiple outlets. Ann. Biomed. Eng. 36(9):1496–1514, 2008.

    Article  PubMed  Google Scholar 

  16. Grinberg, L., and G. E. Karniadakis. A new domain decomposition method with overlapping patches for ultrascale simulations: application to biological flows. J. Comput. Phys. 229:5541–5563, 2010.

    Article  CAS  Google Scholar 

  17. Huo, Y., J. S. Choy, M. Svendsen, A. K. Sinha, and G. S. Kassab. Effects of vessel compliance on flow pattern in porcine epicardial right coronary arterial tree. J. Biomech. 42:594–602, 2009.

    Article  PubMed  Google Scholar 

  18. Isaksen, J. G., Y. Bazilevs, T. Kvamsdal, Y. Zhang, J. H. Kaspersen, K. Waterloo, B. Romner, and T. Ingebrigtsen. Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke 39(12):3172–3178, 2008.

    Article  PubMed  Google Scholar 

  19. Kim C.S., C. Kiris, and D. Kwak. Numerical models of human circulatory system under altered gravity: brain circulation. AIAA Paper No. 2004-1092, AIAA 42nd Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2004.

  20. Ku, D. N. Blood flow in arteries. Annu. Rev. Fluid Mech. 29:399–434, 1997.

    Article  Google Scholar 

  21. Lee, S. W., L. Antiga, J. D. Spence, and D. A. Steinman. Geometry of the carotid bifurcation predicts its exposure to disturbed flow. Stroke 39(8):2341–2347, 2008.

    Article  PubMed  Google Scholar 

  22. Matthys, K. S., J. Alastruey, J. Peiró, A. W. Khir, P. Segers, P. R. Verdonck, K. H. Parker, and S. J. Sherwin. Pulse wave propagation in a model human arterial network: assessment of 1D numerical simulations against in-vitro measurements. J. Biomech. 40(15):3476–3486, 2007.

    Article  PubMed  Google Scholar 

  23. Moore, S. M., K. T. Moorhead, J. G. Chase, T. David, and J. Fink. One-dimensional and three-dimensional models of cerebrovascular flow. J. Biomech. Eng. 127(3):440–449, 2005.

    Article  CAS  PubMed  Google Scholar 

  24. Olufsen, M. S. Structured tree outflow condition for blood flow in larger systemic arteries. Am. J. Physiol. 276:H257–H268, 1999.

    CAS  PubMed  Google Scholar 

  25. Perktold, K., and G. Rappitsch. Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. J. Biomech. 28(7):845–856, 1995.

    Article  CAS  PubMed  Google Scholar 

  26. Reymond, P., F. Merenda, F. Perren, D. Rufenacht, and N. Stergiopulos. Validation of a one-dimensional model of the systematic arterial tree. Am. J.Physiol. Heart Circ. Physiol. 297:208–222, 2009.

    Article  Google Scholar 

  27. Sherwin, S. J., V. Franke, J. Peiró, and K. Parker. 1D modeling of a vascular network in space-time variable. J. Eng. Math. 47:217–250, 2003.

    Article  Google Scholar 

  28. Sherwin, S. J., and G. E. Karniadakis. Spectral/hp Element Methods for CFD, 2nd ed. Oxford: Oxford University Press, 2005.

    Google Scholar 

  29. Smith, N. P., A. J. Pullan, and P.J. Hunter. An anatomically based model of transient coronary blood flow in the heart. SIAM J. Appl. Math. 62:990–1018, 2001.

    Article  Google Scholar 

  30. Spilker, R., J. Feinstein, D. Parker, V. Reddy, and C. Taylor. Morphometry-based impedance boundary conditions for patient-specific modeling of blood flow in pulmonary arteries. Ann. Biomed. Eng. 35(4):546–559, 2007.

    Article  PubMed  Google Scholar 

  31. Stanfield, C. L. Principles of Human Physiology. San Francisco, CA: Benjamin Cummings, 2008.

    Google Scholar 

  32. Stergiopulos, N., D. Young, and T. Rogge. Computer simulation of arterial flow with applications to arterial and aortic stenoses. J. Biomech. 25:1477–1488, 1992.

    Article  CAS  PubMed  Google Scholar 

  33. Taylor, C. A., and M. T. Draney. Experimental and computational methods in cardiovascular fluid mechanics. Annu. Rev. Fluid Mech. 36:197–231, 2004.

    Article  Google Scholar 

  34. White, H., and B. Venkatesh. Applications of transcranial Doppler in the ICU: a review. Intensive Care Med. 32(7):981–994, 2007.

    Article  Google Scholar 

  35. www.pointwise.com

  36. Xiu, D. B., and J. S. Hesthaven. High order collocation methods for differential equations with random inputs. SIAM J. Sci. Comput. 27(3):1118–1139, 2005.

    Article  Google Scholar 

  37. Xiu, D. B., and G. E. Karniadakis. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24(2):619–644, 2002.

    Article  Google Scholar 

  38. Xiu, D. B., and S. J. Sherwin. Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network. J. Comput. Phys. 226:1385–1407, 2007.

    Article  Google Scholar 

Download references

Acknowledgments

This study was supported by the NSF under Grants OCI-0636336 and NSF OCI-0904288. T. Anor and J. R. Madsen would like to thank the Webster Family for supporting their study. Supercomputer resources were provided by the National Institute for Computational Sciences at University of Tennessee.

Author information

Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 182 George St., Providence, RI, 02912, USA

    L. Grinberg, E. Cheever & G. E. Karniadakis

  2. Children’s Hospital, Harvard Medical School, Boston, MA, 02115, USA

    T. Anor & J. R. Madsen

Authors
  1. L. Grinberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Cheever
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Anor
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. R. Madsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. E. Karniadakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Grinberg.

Additional information

Associate Editor Aleksander S. Popel oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grinberg, L., Cheever, E., Anor, T. et al. Modeling Blood Flow Circulation in Intracranial Arterial Networks: A Comparative 3D/1D Simulation Study. Ann Biomed Eng 39, 297–309 (2011). https://doi.org/10.1007/s10439-010-0132-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-010-0132-1

Keywords

Search

Navigation