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Effects of Vessel Tortuosity on Coronary Hemodynamics: An Idealized and Patient-Specific Computational Study

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Abstract

Although coronary tortuosity can influence the hemodynamics of coronary arteries, the relationship between tortuosity and flow has not been thoroughly investigated partly due to the absence of a widely accepted definition of tortuosity and the lack of patient-specific studies that analyze complete coronary trees. Using a computational approach we investigated the effects of tortuosity on coronary flow parameters including pressure drop, wall shear stress, and helical flow strength as measured by helicity intensity. Our analysis considered idealized and patient-specific geometries. Overall results indicate that perfusion pressure decreases with increased tortuosity, but the patient-specific results show that more tortuous vessels have higher physiological wall shear stress values. Differences between the idealized and patient-specific results reveal that an accurate representation of coronary tortuosity must account for all relevant geometric aspects, including curvature imposed by the heart shape. The patient-specific results exhibit a strong correlation between tortuosity and helicity intensity, and the corresponding helical flow contributes directly to the observed increase in wall shear stress. Therefore, helicity intensity may prove helpful in developing a universal parameter to describe tortuosity and assess its impact on patient health. Our data suggest that increased tortuosity could have a deleterious impact via a reduction in coronary perfusion pressure, but the attendant increase in wall shear stress could afford protection against atherosclerosis.

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References

  1. Alastruey, J., A. W. Khir, K. S. Matthys, P. Segers, S. J. Sherwin, P. R. Verdonck, et al. Pulse wave propagation in a model human arterial network: assessment of 1-D visco-elastic simulations against in vitro measurements. J. Biomech. 44(12):2250–2258, 2011.

    Article  PubMed  PubMed Central  Google Scholar 

  2. Alastruey, J., J. H. Siggers, V. Peiffer, D. J. Doorly, and S. J. Sherwin. Reducing the data: analysis of the role of vascular geometry on blood flow patterns in curved vessels. Phys. Fluids 24(3):031902, 2012.

    Article  Google Scholar 

  3. Aristokleous, N., I. Seimenis, G. C. Georgiou, Y. Papaharilaou, B. C. Brott, A. Nicolaides, et al. Impact of head rotation on the individualized common carotid flow and carotid bifurcation hemodynamics. IEEE J. Biomed. Health Inf. 18(3):783–789, 2014.

    Article  Google Scholar 

  4. Barilla, F., F. Romeo, G. M. C. Rosano, A. Valente, and A. Reale. Coronary artery loops and myocardial ischemia. Am. Heart J. 122(1):225–226, 1991.

    Article  CAS  PubMed  Google Scholar 

  5. Berger, S. A., L. Talbot, and L. S. Yao. Flow in Curved Pipes. Annu. Rev. Fluid Mech. 15(1):461–512, 1983.

    Article  Google Scholar 

  6. Bullitt, E., G. Gerig, S. M. Pizer, W. Lin, and S. R. Aylward. Measuring tortuosity of the intracerebral vasculature from MRA images. IEEE Trans. Med. Imaging 22(9):1163–1171, 2003.

    Article  PubMed  PubMed Central  Google Scholar 

  7. Caro, C. G. Discovery of the role of wall shear in atherosclerosis. Arterioscler. Thromb. Vasc. Biol. 29(2):158–161, 2009.

    Article  CAS  PubMed  Google Scholar 

  8. Caro, C. G., N. J. Cheshire, and N. Watkins. Preliminary comparative study of small amplitude helical and conventional ePTFE arteriovenous shunts in pigs. J. R. Soc. Interface 2(3):261–266, 2005.

    Article  PubMed  PubMed Central  Google Scholar 

  9. Chatzizisis, Y. S., A. U. Coskun, M. Jonas, E. R. Edelman, C. L. Feldman, and P. H. Stone. Role of endothelial shear stress in the natural history of coronary atherosclerosis and vascular remodeling—molecular, cellular, and vascular behavior. J. Am. Coll. Cardiol. 49(25):2379–2393, 2007.

    Article  CAS  PubMed  Google Scholar 

  10. Cheung, C. Y.-L., Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, et al. Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors. Ophthalmology. 118(5):812–818, 2011.

    Article  PubMed  Google Scholar 

  11. Chiastra, C., S. Morlacchi, D. Gallo, U. Morbiducci, R. Cárdenes, I. Larrabide, et al. Computational fluid dynamic simulations of image-based stented coronary bifurcation models. J. R. Soc./Interface/R. Soc. 10(84):20130193, 2013.

    Article  Google Scholar 

  12. Chien, S. Effects of disturbed flow on endothelial cells. Ann. Biomed. Eng. 36(4):554–562, 2008.

    Article  PubMed  PubMed Central  Google Scholar 

  13. Choi, G., C. P. Cheng, N. M. Wilson, and C. A. Taylor. Methods for quantifying three-dimensional deformation of arteries due to pulsatile and nonpulsatile forces: implications for the design of stents and stent grafts. Ann. Biomed. Eng. 37(1):14–33, 2009.

    Article  PubMed  Google Scholar 

  14. Davies, J. E., K. H. Parker, J. Mayet, Z. I. Whinnett, D. P. Francis, C. H. Manisty, et al. Evidence of a dominant backward-propagating “suction” wave responsible for diastolic coronary filling in humans, attenuated in left ventricular hypertrophy. Circulation 113(14):1768–1778, 2006.

    Article  PubMed  Google Scholar 

  15. Dean, W. R. Note on the motion of fluid in a curved pipe. Lond. Edinb. Dublin Philos. Mag. J. Sci. 4(20):208–223, 1927.

    Article  Google Scholar 

  16. Dean, W. R. LXXII The stream-line motion of fluid in a curved pipe (Second paper). Philos. Mag. Ser. 7. 5(30):673–695, 1928.

    Article  Google Scholar 

  17. Del Corso, L., D. Moruzzo, B. Conte, M. Agelli, A. M. Romanelli, F. Pastine, et al. Tortuosity, kinking, and coiling of the carotid artery: expression of atherosclerosis or aging? Angiology. 49(5):361–371, 1998.

    Article  PubMed  Google Scholar 

  18. Dougherty, G., and M. J. Johnson. Clinical validation of three-dimensional tortuosity metrics based on the minimum curvature of approximating polynomial splines. Med. Eng. Phys. 30(2):190–198, 2008.

    Article  PubMed  Google Scholar 

  19. Dougherty, G., M. J. Johnson, and M. D. Wiers. Measurement of retinal vascular tortuosity and its application to retinal pathologies. Med. Biol. Eng. Compu. 48(1):87–95, 2010.

    Article  Google Scholar 

  20. Gaibazzi, N., F. Rigo, and C. Reverberi. Severe coronary tortuosity or myocardial bridging in patients with chest pain, normal coronary arteries, and reversible myocardial perfusion defects. Am. J. Cardiol. 108(7):973–978, 2011.

    Article  PubMed  Google Scholar 

  21. Gallo, D., D. A. Steinman, and U. Morbiducci. An insight into the mechanistic role of the common carotid artery on the hemodynamics at the carotid bifurcation. Ann. Biomed. Eng. 43(1):68–81, 2015.

  22. Gallo, D., D. A. Steinman, P. B. Bijari, and U. Morbiducci. Helical flow in carotid bifurcation as surrogate marker of exposure to disturbed shear. J. Biomech. 45(14):2398–2404, 2012.

    Article  PubMed  Google Scholar 

  23. Germano, M. On the effect of torsion on a helical pipe flow. J. Fluid Mech. 125(1):1–8, 1982.

    Article  Google Scholar 

  24. Han, H. C. Twisted blood vessels: symptoms, etiology and biomechanical mechanisms. J. Vasc. Res. 49(3):185–197, 2012.

    Article  PubMed  PubMed Central  Google Scholar 

  25. Hart, W. E., M. Goldbaum, B. Côté, P. Kube, and M. R. Nelson. Measurement and classification of retinal vascular tortuosity. Int. J. Med. Informatics 53(2–3):239–252, 1999.

    Article  CAS  Google Scholar 

  26. Himburg, H. A., D. M. Grzybowski, A. L. Hazel, J. A. LaMack, X.-M. Li, and M. H. Friedman. Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability. Am. J. Physiol. Heart Circ. Physiol. 286(5):H1916–H1922, 2004.

    Article  CAS  PubMed  Google Scholar 

  27. Hoi, Y., Y.-Q. Zhou, X. Zhang, R. M. Henkelman, and D. A. Steinman. Correlation between local hemodynamics and lesion distribution in a novel aortic regurgitation murine model of atherosclerosis. Ann. Biomed. Eng. 39(5):1414–1422, 2011.

    Article  PubMed  Google Scholar 

  28. Hutchins, G. M., M. M. Miner, and B. H. Bulkley. Tortuosity as an index of the age and diameter increase of coronary collateral vessels in patients after acute myocardial infarction. Am. J. Cardiol. 41(2):210–215, 1978.

    Article  CAS  PubMed  Google Scholar 

  29. Jackson, Z. S., D. Dajnowiec, A. I. Gotlieb, and B. L. Langille. Partial off-loading of longitudinal tension induces arterial tortuosity. Arterioscler. Thromb. Vasc. Biol. 25(5):957–962, 2005.

    Article  CAS  PubMed  Google Scholar 

  30. Jakob, M., D. Spasojevic, O. N. Krogmann, H. Wiher, R. Hug, and O. M. Hess. Tortuosity of coronary arteries in chronic pressure and volume overload. Cathet. Cardiovasc. Diagn. 38(1):25–31, 1996.

    Article  CAS  PubMed  Google Scholar 

  31. Kaplan, A. D., A. J. Jaffa, I. E. Timor, and D. Elad. Hemodynamic analysis of arterial blood flow in the coiled umbilical cord. Reprod. Sci. 17(3):258–268, 2010.

    Article  PubMed  Google Scholar 

  32. Ku, D. N., D. P. Giddens, C. K. Zarins, and S. Glagov. Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arterioscler. (Dallas, Tex). 5(3):293, 1985.

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  34. Lee, S.-W., L. Antiga, and D. A. Steinman. Correlations among indicators of disturbed flow at the normal carotid bifurcation. J. Biomech. Eng. 131(6):061013–061017, 2009.

    Article  PubMed  Google Scholar 

  35. Li, Y., C. X. Shen, Y. N. Ji, Y. Feng, G. S. Ma, and N. F. Liu. Clinical implication of coronary tortuosity in patients with coronary artery disease. PLoS ONE 6(8):e24232, 2011.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Li, Y., Z. Shi, Y. Cai, Y. Feng, G. Ma, C. Shen, et al. Impact of coronary tortuosity on coronary pressure: numerical simulation study. PLoS ONE 7(8):e42558, 2012.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Lyne, W. H. Unsteady viscous flow in a curved pipe. J. Fluid Mech. 45:13–31, 1971.

    Article  Google Scholar 

  38. Malek, A. M., S. L. Alper, and S. Izumo. Hemodynamic shear stress and its role in atherosclerosis. JAMA:J. Am. Med. Assoc. 282(21):2035–2042, 1999.

    Article  CAS  Google Scholar 

  39. Malvè, M., A. M. Gharib, S. K. Yazdani, G. Finet, M. A. Martínez, R. Pettigrew, et al. Tortuosity of coronary bifurcation as a potential local risk factor for atherosclerosis: CFD steady state study based on in vivo dynamic CT measurements. Ann. Biomed. Eng. 43(1):82–93, 2015.

    Article  PubMed  Google Scholar 

  40. Morbiducci, U., R. Ponzini, D. Gallo, C. Bignardi, and G. Rizzo. Inflow boundary conditions for image-based computational hemodynamics: impact of idealized versus measured velocity profiles in the human aorta. J. Biomech. 46(1):102–109, 2013.

    Article  PubMed  Google Scholar 

  41. O’Flynn, P. M., G. O’Sullivan, and A. S. Pandit. Methods for three-dimensional geometric characterization of the arterial vasculature. Ann. Biomed. Eng. 35(8):1368–1381, 2007.

    Article  PubMed  Google Scholar 

  42. Papanastasiou, T. C., G. C. Georgiou, and A. N. Alexandrou. Viscous Fluid Flow. Boca Raton, Fla: CRC Press, 2000.

    Google Scholar 

  43. Pedley, T. J. The Fluid Mechanics of Large Blood Vessels. Cambridge; NY: Cambridge University Press, 1980.

    Book  Google Scholar 

  44. Piccinelli, M., A. Veneziani, D. A. Steinman, A. Remuzzi, L. Antiga. A framework for geometric analysis of vascular structures: application to cerebral aneurysms. IEEE Trans. Med. Imaging. 28; 31(8):1141–1155, 2009.

  45. Pietrabissa, R., S. Mantero, T. Marotta, and L. Menicanti. A lumped parameter model to evaluate the fluid dynamics of different coronary bypasses. Med. Eng. Phys. 18(6):477–484, 1996.

    Article  CAS  PubMed  Google Scholar 

  46. Pletcher, B. A., J. E. Fox, R. A. Boxer, S. Singh, D. Blumenthal, T. Cohen, et al. Four sibs with arterial tortuosity: description and review of the literature. Am. J. Med. Genet. 66(2):121–128, 1996.

    Article  CAS  PubMed  Google Scholar 

  47. Prosi, M., K. Perktold, Z. Ding, and M. H. Friedman. Influence of curvature dynamics on pulsatile coronary artery flow in a realistic bifurcation model. J. Biomech. 37(11):1767–1775, 2004.

    Article  PubMed  Google Scholar 

  48. Qiao, A. K., X. L. Guo, S. G. Wu, Y. J. Zeng, and X. H. Xu. Numerical study of nonlinear pulsatile flow in S-shaped curved arteries. Med. Eng. Phys. 26(7):545–552, 2004.

    Article  CAS  PubMed  Google Scholar 

  49. Sangalli, L. M., P. Secchi, S. Vantini, and A. Veneziani. A case study in exploratory functional data analysis: geometrical features of the internal carotid artery. J. Am. Stat. Assoc. 104(485):37–48, 2009.

    Article  CAS  Google Scholar 

  50. Seo, T., L. G. Schachter, and A. I. Barakat. Computational study of fluid mechanical disturbance induced by endovascular stents. Ann. Biomed. Eng. 33(4):444–456, 2005.

    Article  PubMed  Google Scholar 

  51. Siggers, J. H., and S. L. Waters. Steady flows in pipes with finite curvature. Phys. Fluids 17(7):77102, 2005.

    Article  Google Scholar 

  52. Smedby, Ö., and L. Bergstrand. Tortuosity and atherosclerosis in the femoral artery: what is cause and what is effect? Ann. Biomed. Eng. 24(4):474–480, 1996.

    Article  CAS  PubMed  Google Scholar 

  53. Soikkonen, K., J. Wolf, and K. Mattila. Tortuosity of the lingual artery and coronary atherosclerosis. Br. J. Oral Maxillofac. Surg. 33(5):309–311, 1995.

    Article  CAS  PubMed  Google Scholar 

  54. Sutter, F. K. P., and H. Helbig. Familial retinal arteriolar tortuosity: a review. Surv. Ophthalmol. 48(3):245–255, 2003.

    Article  PubMed  Google Scholar 

  55. Turgut, O., A. Yilmaz, K. Yalta, B. Yilmaz, A. Ozyol, O. Kendirlioglu, et al. Tortuosity of coronary arteries: an indicator for impaired left ventricular relaxation? Int. J. Cardiovasc. Imaging 23(6):671–677, 2007.

    Article  PubMed  Google Scholar 

  56. Van Canneyt, K., U. Morbiducci, S. Eloot, G. De Santis, P. Segers, and P. Verdonck. A computational exploration of helical arterio-venous graft designs. J. Biomech. 46(2):345–353, 2013.

    Article  PubMed  Google Scholar 

  57. van der Giessen, A. G., H. C. Groen, P.-A. Doriot, P. J. de Feyter, A. F. W. van der Steen, F. N. van de Vosse, et al. The influence of boundary conditions on wall shear stress distribution in patients specific coronary trees. J. Biomech. 44(6):1089–1095, 2011.

    Article  PubMed  Google Scholar 

  58. Wood, N. B., S. Z. Zhao, A. Zambanini, M. Jackson, W. Gedroyc, S. A. Thom, et al. Curvature and tortuosity of the superficial femoral artery: a possible risk factor for peripheral arterial disease. J. Appl. Physiol. (Bethesda, Md: 1985) 101(5):1412–1418, 2006.

    Article  CAS  Google Scholar 

  59. Xie, X., Y. Wang, and H. Zhou. Impact of coronary tortuosity on the coronary blood flow: a 3D computational study. J. Biomech. 46(11):1833–1841, 2013.

    Article  PubMed  Google Scholar 

  60. Xie, X., Y. Wang, H. Zhu, and J. Zhou. Computation of hemodynamics in tortuous left coronary artery: a morphological parametric study. J. Biomech. Eng. 136(10):101006, 2014.

    Article  PubMed  Google Scholar 

  61. Xie, X., Y. Wang, H. Zhu, H. Zhou, and J. Zhou. Impact of coronary tortuosity on coronary blood supply: a patient-specific study. PLoS ONE 8(5):e64564, 2013.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  62. http://meshlab.sourceforge.net/.

  63. Yushkevich, P. A., J. Piven, H. C. Hazlett, R. G. Smith, S. Ho, J. C. Gee, et al. User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. NeuroImage. 31(3):1116–1128, 2006.

    Article  PubMed  Google Scholar 

  64. Zegers, E. S., B. T. J. Meursing, E. B. Zegers, and A. J. M. O. Ophuis. Coronary tortuosity: a long and winding road. Neth. Heart J. 15(5):191–195, 2007.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgments

Pavlos Vlachos acknowledges partial support by NIH NHLBI Grant No HL106276-01A1. Claudio Chiastra is partially supported by the ERC starting grant (310457, BioCCora).

Conflict of Interest

Authors Natalya Vorobtsova, Claudio Chiastra, Mark A. Stremler, David C. Sane, Francesco Migliavacca, Pavlos Vlachos have no conflicts of interest to report. No human studies were carried out by the authors for this article. No animal studies were carried out by the authors for this article.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA

    Natalya Vorobtsova

  2. Laboratory of Biological Structure Mechanics (LaBS), Department of Chemistry, Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, Milan, Italy

    Claudio Chiastra & Francesco Migliavacca

  3. Department of Biomedical Engineering, Thoraxcenter, Erasmus University Medical Center, Rotterdam, The Netherlands

    Claudio Chiastra

  4. Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, VA, USA

    Mark A. Stremler

  5. Section of Cardiology, Carilion Clinic, Virginia Tech Carilion School of Medicine, Roanoke, VA, USA

    David C. Sane

  6. School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN, USA

    Pavlos Vlachos

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Associate Editor Umberto Morbiducci oversaw the review of this article.

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Vorobtsova, N., Chiastra, C., Stremler, M.A. et al. Effects of Vessel Tortuosity on Coronary Hemodynamics: An Idealized and Patient-Specific Computational Study. Ann Biomed Eng 44, 2228–2239 (2016). https://doi.org/10.1007/s10439-015-1492-3

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