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Cardiovascular Engineering and Technology

, Volume 10, Issue 4, pp 648–659 | Cite as

Embolus Transport Simulations with Fully Resolved Particle Surfaces

  • Patrick M. McGahEmail author
Article
  • 34 Downloads

Abstract

Purpose

There has been interest in recent work in using computational fluid dynamics with Lagrangian analysis to calculate the trajectory of emboli-like particles in the vasculature. While previous studies have provided an understanding of the hemodynamic factors determining the fates of such particles and their relationship to risk of stroke, most analyses have relied on a particle equation of motion that assumes the particle is “small” e.g., much less than the diameter of the vessel. This work quantifies the limit when a particle can no longer be considered “small”.

Methods

The motion of embolus-like particles are simulated using an overset mesh technique. This allows the fluid stresses on the particle surface to be fully resolved. Consequently, the particles can be of arbitrary size or shape. The trajectory of resolved particles and “small” particles are simulated through a patient-specific carotid artery bifurcation model with particles 500, 1000, and 2000 μm in diameter. The proportions of particles entering the internal carotid artery are treated as the outcome of the particle fate, and statistical comparisons are made to ascertain the importance of non-small particle effects.

Results

For the 2000 μm embolus, the proportion of particles traveling to the internal carotid artery is 74.7 ± 1.3% (mean ± 95% confidence margin) for the “small” particle model and is 85.7 ± 5.4% for a resolved particle model. The difference is statistically significant, \(p< 0.05\), based on the binomial test for the particle outcomes. No statistically discernible differences are found for the smaller diameter particles.

Conclusions

Quantitative differences are observable for the 2000 μm trajectories between the “small” and resolved particle models which is a particle diameter 27% relative to the common carotid artery diameter. A fully resolved particle model ought to be considered for emboli trajectory simulations when the particle size ratio is ≳ 20%.

Notes

Acknowledgments

Thanks to Bradley Davidson, Kristian Debus, and Ehsan Rajabi for helpful comments during the preparation of the manuscript.

Conflict of interest

P. M. McGah is an employee of Siemens PLM Software Inc., the company that produces and sells Simcenter STAR-CCM+.

Human Subjects and Animal Subjects Ethical Statement

No animal studies were conducted by the author for this article. No human studies were conducted by the author for this article.

Supplementary material

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Supplementary material 1 (AVI 1933 kb)
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Supplementary material 3 (AVI 1849 kb)

References

  1. 1.
    Abolfazli, E., N. Fatouraee, and B. Vahidi. Dynamics of motion of a clot through an arterial bifurcation: a finite element analysis. Fluid Dyn. Res. 46(5):055505, 2014.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aliseda, A., V. K. Chivukula, P. M. Mcgah, A. R. Prisco, J. A. Beckman, G. J. Garcia, N. A. Mokadam, and C. Mahr. LVAD outflow graft angle and thrombosis risk. ASAIO J. 63(1):14–23, 2017.CrossRefGoogle Scholar
  3. 3.
    Arboix, A., and J. Alioc. Cardioembolic stroke: clinical features, specific cardiac disorders and prognosis. Curr. Cardiol. Rev. 6(3):150–161, 2010.CrossRefGoogle Scholar
  4. 4.
    Aycock, K. I., R. L. Campbell, K. B. Manning, and B. A. Craven. A resolved two-way coupled CFD/6-DOF approach for predicting embolus transport and the embolus-trapping efficiency of IVC filters. Biomech. Model. Mechanobiol. 16(3):851–869, 2017.CrossRefGoogle Scholar
  5. 5.
    Barbut, D., F. S. F. Yao, Y. W. Lo, R. Silverman, D. N. Hager, R. R. Trifiletti, and J.P. Gold. Determination of size of aortic emboli and embolic load during coronary artery bypass grafting. Ann. Thorac. Surg. 63(5):1262–1265, 1997.CrossRefGoogle Scholar
  6. 6.
    Benjamin, E. J., S. S. Virani, C. W. Callaway, A. M. Chamberlain, A. R. Chang, S. Cheng, S. E. Chiuve, M. Cushman, F. N. Delling, and R. Deo, et al. Heart disease and stroke statistics 2018 update: a report from the American Heart Association. Circulation 137(12):e67–e492, 2018.CrossRefGoogle Scholar
  7. 7.
    Bushi, D., Y. Grad, S. Einav, O. Yodfat, B. Nishri, and D. Tanne. Hemodynamic evaluation of embolic trajectory in an arterial bifurcation: an in-vitro experimental model. Stroke 36(12):2696–2700, 2005.CrossRefGoogle Scholar
  8. 8.
    Carr, I. A., N. Nemoto, R. S. Schwartz, S. C. Shadden. Size-dependent predilections of cardiogenic embolic transport. Am. J. Physiol. Heart Circ. Physiol. 305(5):H732, 2013.CrossRefGoogle Scholar
  9. 9.
    Chung, E. M., J. P. Hague, M. A. Chanrion, K. V. Ramnarine, E. Katsogridakis, and D. H. Evans. Embolus trajectory through a physical replica of the major cerebral arteries. Stroke 41(4):647–652, 2010.CrossRefGoogle Scholar
  10. 10.
    Fabbri, D., Q. Long, S. Das, M. Pinelli. Computational modelling of emboli travel trajectories in cerebral arteries: influence of microembolic particle size and density. Biomech. Model. Mechanobiol. 13(2):289–302, 2014.CrossRefGoogle Scholar
  11. 11.
    Hadžić, H. Development and application of finite volume method for the computation of flows around moving bodies on unstructured, overlapping grids. Ph.D. thesis, Technische Universität Hamburg, 2006.Google Scholar
  12. 12.
    Haller, G. and T. Sapsis. Where do inertial particles go in fluid flows? Physica D 237(5):573–583, 2008.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Happel, J. and H. Brenner. Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media. New York: Springer, 1981.CrossRefGoogle Scholar
  14. 14.
    Holdsworth, D., C. Norley, R. Frayne, D. Steinman, and B. Rutt. Characterization of common carotid artery blood-flow waveforms in normal human subjects. Physiol. Meas. 20(3):219, 1999.CrossRefGoogle Scholar
  15. 15.
    Ling, Y., M. Parmar, and S. Balachandar. A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows. Int. J. Multiph. Flow 57:102–114, 2013.CrossRefGoogle Scholar
  16. 16.
    Manning, W. J., R. M. Weintraub, C. A. Waksmonski, J. M. Haering, P. S. Rooney, A. D. Maslow, R. G. Johnson, and P.S. Douglas. Accuracy of transesophageal echocardiography for identifying left atrial thrombi: a prospective, intraoperative study. Ann. Intern. Med. 123(11):817–822, 1995.CrossRefGoogle Scholar
  17. 17.
    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.CrossRefGoogle Scholar
  18. 18.
    Mei, R. Velocity fidelity of flow tracer particles. Exp. Fluids 22(1):1–13, 1996.MathSciNetCrossRefGoogle Scholar
  19. 19.
    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.CrossRefGoogle Scholar
  20. 20.
    Mukherjee, D., J. Padilla, S. C. Shadden. Numerical investigation of fluid–particle interactions for embolic stroke. Theor. Comput. Fluid Dyn. 30(1–2):23–39, 2016.CrossRefGoogle Scholar
  21. 21.
    Proudman, I. and J. R. A. Pearson. Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2(3):237–262, 1957.MathSciNetCrossRefGoogle Scholar
  22. 22.
    Reichenspurner, H., J. A. Navia, G. Berry, R. C. Robbins, D. Barbut, J. P. Gold, and B. Reichart. Particulate emboli capture by an intra-aortic filter device during cardiac surgery. J. Thorac. Cardiovasc. Surg. 119(2);233–241, 2000.CrossRefGoogle Scholar
  23. 23.
    Swaminathan, T. N., H. H. Hu, and A. A. Patel. Numerical analysis of the hemodynamics and embolus capture of a Greenfield vena cava filter. J. Biomech. Eng. 128(3):360–370, 2006.CrossRefGoogle Scholar
  24. 24.
    Temkin, S. Suspension Acoustics: An Introduction to the Physics of Suspensions. Cambridge: Cambridge University Press, 2005.CrossRefGoogle Scholar
  25. 25.
    Van Hinsberg, M. A. T., J. H. M. ten Thije Boonkkamp, and H. J. H. Clercx. An efficient, second order method for the approximation of the Basset history force. J. Comput. Phys. 230(4):1465–1478, 2011.CrossRefGoogle Scholar
  26. 26.
    Westerhof, N., J. W. Lankhaar, and B. E. Westerhof. The arterial Windkessel. Med. Biol. Eng. Comput. 47(2):131–141, 2009.CrossRefGoogle Scholar
  27. 27.
    Zierler, R. E., D. F. Leotta, K. Sansom, A. Aliseda, M. D. Anderson, and F. H. Sheehan. Development of a duplex ultrasound simulator and preliminary validation of velocity measurements in carotid artery models. Vasc. Endovasc. Surg. 50(5):309–316, 2016.CrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2019

Authors and Affiliations

  1. 1.Siemens PLM Software Inc.BellevueUSA

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