Annals of Biomedical Engineering

, Volume 43, Issue 1, pp 41–58 | Cite as

Lagrangian Postprocessing of Computational Hemodynamics

  • Shawn C. Shadden
  • Amirhossein Arzani


Recent advances in imaging, modeling, and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries, and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows.


Advection Blood flow Coherent structures Computational fluid dynamics Modeling Particle tracking Platelets Transport 



The authors acknowledge support of the NIH National Heart, Lung, and Blood Institute (Grant No. HL108272) and the National Science Foundation (Grant No. 1354541, 1358118, 1407834).

Conflict of interest

The authors do not have conflicts of interest relevant to this manuscript.


  1. 1.
    Alemu, Y., and D. Bluestein. Flow-induced platelet activation and damage accumulation in a mechanical heart valve: numerical studies. Artif. Org. 31(9):677–688, 2007.Google Scholar
  2. 2.
    Anand, M., K. Rajagopal, and K. R. Rajagopal. A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood: review article. J. Theor. Med. 5(3–4):183–218, 2003.Google Scholar
  3. 3.
    Apel, J., R. Paul, S. Klaus, T. Siess, and H. Reul. Assessment of hemolysis related quantities in a microaxial blood pump by computational fluid dynamics. Artif. Org. 25(5):341–347, 2001.Google Scholar
  4. 4.
    Argyris, J. H., G. Faust, and M. Haase. An Exploration of Chaos: An Introduction for Natural Scientists and Engineers. Amsterdam: Elsevier Science Ltd., 1994.Google Scholar
  5. 5.
    Arzani, A., A. S. Les, R. L. Dalman, and S. C Shadden. Effect of exercise on patient specific abdominal aortic aneurysm flow topology and mixing. Int. J. Numer. Methods Biomed. Eng. 30(2):280–295, 2014.Google Scholar
  6. 6.
    Arzani, A., and S.C. Shadden. Characterization of the transport topology in patient-specific abdominal aortic aneurysm models. Phys. Fluids. 24(8):1901, 2012.Google Scholar
  7. 7.
    Arzani, A., G. Y. Suh, M. V. McConnell, R. L. Dalman, and S. C. Shadden. Progression of abdominal aortic aneurysm: effect of lagrangian transport and hemodynamic parameters. In: ASME 2013 Summer Bioengineering Conference, pp. V01AT01A004--V01AT01A004, 2013.Google Scholar
  8. 8.
    Astorino, M., J. Hamers, S. C. Shadden, and J. Gerbeau. A robust and efficient valve model based on resistive immersed surfaces. Int. J. Numer. Methods Biomed. Eng. 28(9):937–959, 2012.PubMedGoogle Scholar
  9. 9.
    Avrahami, I., M. Rosenfeld, and S. Einav. The hemodynamics of the berlin pulsatile VAD and the role of its MHV configuration. Ann. Biomed. Eng. 34(9):1373–1388, 2006.PubMedGoogle Scholar
  10. 10.
    Bächler, P., N. Pinochet, J. Sotelo, G. Crelier, P. Irarrazaval, C. Tejos, and S. Uribe. Assessment of normal flow patterns in the pulmonary circulation by using 4d magnetic resonance velocity mapping. Magn. Reson. Imaging 31(2):178–188, 2013.PubMedGoogle Scholar
  11. 11.
    Basciano, C., C. Kleinstreuer, S. Hyun, and E. A. Finol. A relation between near-wall particle-hemodynamics and onset of thrombus formation in abdominal aortic aneurysms. Ann. Biomed. Eng. 39(7):2010–2026, 2011.PubMedCentralPubMedGoogle Scholar
  12. 12.
    Bellofiore, A., and N. J. Quinlan. High-resolution measurement of the unsteady velocity field to evaluate blood damage induced by a mechanical heart valve. Ann. Biomed. Eng. 39(9):2417–2429, 2011.PubMedGoogle Scholar
  13. 13.
    Bluestein, D., Y. M. Li, and I. B. Krukenkamp. Free emboli formation in the wake of bi-leaflet mechanical heart valves and the effects of implantation techniques. J. Biomech. 35(12):1533–1540, 2002.PubMedGoogle Scholar
  14. 14.
    Bluestein, D., E. Rambod, and M. Gharib. Vortex shedding as a mechanism for free emboli formation in mechanical heart valves. J. Biomech. Eng. 122(2):125–134, 2000.PubMedGoogle Scholar
  15. 15.
    Bockman, M. D., A. P. Kansagra, S. C. Shadden, E. C. Wong, and A. L. Marsden. Fluid mechanics of mixing in the vertebrobasilar system: comparison of simulation and MRI. Cardiovasc. Eng. Technol. 3(4):450–461, 2012.Google Scholar
  16. 16.
    Bogren, H. G., and M. H. Buonocore. 4d magnetic resonance velocity mapping of blood flow patterns in the aorta in young vs. elderly normal subjects. J. Magn. Reson. Imaging 10(5):861–869, 1999.PubMedGoogle Scholar
  17. 17.
    Bogren, H. G., M. H. Buonocore, and R. J. Valente. Four-dimensional magnetic resonance velocity mapping of blood flow patterns in the aorta in patients with atherosclerotic coronary artery disease compared to age-matched normal subjects. J. Magn. Reson. Imaging 19(4):417–427, 2004.Google Scholar
  18. 18.
    Bolger, A. F., E. Heiberg, M. Karlsson, L. Wigström, J. Engvall, A. Sigfridsson, T. Ebbers, J. P. E. Kvitting, C. J. Carlhäll, and B. Wranne. Transit of blood flow through the human left ventricle mapped by cardiovascular magnetic resonance. J. Cardiovasc. Magn. Reson. 9(5):741–747, 2007.PubMedGoogle Scholar
  19. 19.
    Born, S., M. Pfeifle, M. Markl, M. Gutberlet, and G. Scheuermann. Visual analysis of cardiac 4d MRI blood flow using line predicates. IEEE Trans. Vis. Comput. Graph. 19(6):900–912, 2013.PubMedGoogle Scholar
  20. 20.
    Buchanan, J. R., and C. Kleinstreuer. Simulation of particle-hemodynamics in a partially occluded artery segment with implications to the initiation of microemboli and secondary stenoses. J. Biomech. Eng. 120(4):446–454, 1998.PubMedGoogle Scholar
  21. 21.
    Buchanan, J. R., C. Kleinstreuer, S. Hyun, and G. A. Truskey. Hemodynamics simulation and identification of susceptible sites of atherosclerotic lesion formation in a model abdominal aorta. J. Biomech. 36(8):1185–1196, 2003.PubMedGoogle Scholar
  22. 22.
    Buchanan, Jr., J. R. C. Kleinstreuer, and J. K. Comer. Rheological effects on pulsatile hemodynamics in a stenosed tube. Comput. Fluids 29(6):695–724, 2000.Google Scholar
  23. 23.
    Buonocore, M. H. Visualizing blood flow patterns using streamlines, arrows, and particle paths. Magn. Reson. Med. 40(2):210–226, 1998.PubMedGoogle Scholar
  24. 24.
    Buonocore, M. H., and H. G. Bogren. Analysis of flow patterns using MRI. Int. J. Card. Imaging 15(2):99–103, 1999.Google Scholar
  25. 25.
    Butty, V. D., K. Gudjonsson, P. Buchel, V. B. Makhijani, Y. Ventikos, and D. Poulikakos. Residence times and basins of attraction for a realistic right internal carotid artery with two aneurysms. Biorheology 39(3):387–393, 2002.PubMedGoogle Scholar
  26. 26.
    Cao, J., and S. E. Rittgers. Particle motion within in vitro models of stenosed internal carotid and left anterior descending coronary arteries. Ann. Biomed. Eng. 26(2):190–199, 1998.PubMedGoogle Scholar
  27. 27.
    Caro, C. G., T. J. Pedley, R. C. Schroter, and W. A. Seed. The Mechanics of the Circulation. Oxford: Oxford University Press, 2012.Google Scholar
  28. 28.
    Carr, I. A., N. Nemoto, R. S. Schwartz, and S. C. Shadden. Size-dependent predilections of cardiogenic embolic transport. Am. J. Physiol. Heart Circ. Physiol. 305(5):H732–H739, 2013.PubMedGoogle Scholar
  29. 29.
    Charonko, J. J., R. Kumar, K. Stewart, W. C. Little, and P. P. Vlachos. Vortices formed on the mitral valve tips aid normal left ventricular filling. Ann. Biomed. Eng. 41(5):1049–1061, 2013.PubMedGoogle Scholar
  30. 30.
    Clift, R., J. R. Grace, and M. E. Weber. Bubbles, Drops, and Particles. New York, NY: Dover, 2005.Google Scholar
  31. 31.
    Cookson, A. N., D. J. Doorly, and S. J. Sherwin. Mixing through stirring of steady flow in small amplitude helical tubes. Ann. Biomed. Eng. 37(4):710–721, 2009.PubMedGoogle Scholar
  32. 32.
    Cookson, A. N., D. J. Doorly, and S. J. Sherwin. Using coordinate transformation of navier-stokes equations to solve flow in multiple helical geometries. J. Comput. Appl. Math. 234(7):2069–2079, 2010.Google Scholar
  33. 33.
    De Gruttola, S., K. Boomsma, and D. Poulikakos. Computational simulation of a non-newtonian model of the blood separation process. Artif. Org. 29(12):949–959, 2005.Google Scholar
  34. 34.
    De Tullio, M. D., A. Cristallo, E. Balaras, and R. Verzicco. Direct numerical simulation of the pulsatile flow through an aortic bileaflet mechanical heart valve. J. Fluid Mech. 622:259–290, 2009.Google Scholar
  35. 35.
    De Tullio, M. D., J. Nam, G. Pascazio, E. Balaras, and R. Verzicco. Computational prediction of mechanical hemolysis in aortic valved prostheses. Eur. J. Mech. B 35:47–53, 2012.Google Scholar
  36. 36.
    DePaola, N., M. A. Gimbrone, P. F. Davies, and C. F. Dewey. Vascular endothelium responds to fluid shear stress gradients. Arterioscler. Thromb. Vasc. Biol. 12(11):1254–7, 1992.Google Scholar
  37. 37.
    Deplano, V., Y. Knapp, L. Bailly, and E. Bertrand. Flow of a blood analogue fluid in a compliant abdominal aortic aneurysm model: experimental modelling. J. Biomech. 47(6):1262–1269, 2014.PubMedGoogle Scholar
  38. 38.
    Doorly, D. J., S. J. Sherwin, P. T. Franke, and J. Peiró. Vortical flow structure identification and flow transport in arteries. Comput. Methods Biomech. Biomed. Eng. 5(3):261–273, 2002.Google Scholar
  39. 39.
    Dumont, K., J. Vierendeels, R. Kaminsky, G. Van Nooten, P. Verdonck, and D. Bluestein. Comparison of the hemodynamic and thrombogenic performance of two bileaflet mechanical heart valves using a CFD/FSI model. J. Biomech. Eng. 129(4):558–565, 2007.PubMedGoogle Scholar
  40. 40.
    Duvernois, V., A. L. Marsden, and S. C. Shadden. Lagrangian analysis of hemodynamics data from FSI simulation. Int. J. Numer. Methods Biomed. Eng. 29(4):445–461, 2013.PubMedGoogle Scholar
  41. 41.
    Ehrlich, L. W., and M. H. Friedman. Particle paths and stasis in unsteady flow through a bifurcation. J. Biomech. 10(9):561–568, 1977.PubMedGoogle Scholar
  42. 42.
    Eriksson, J., C. J. Carlhall, P. Dyverfeldt, J. Engvall, A. F. Bolger, and T. Ebbers. Semi-automatic quantification of 4d left ventricular blood flow. J. Cardiovasc. Magn. Reson. 12(9):12, 2010.Google Scholar
  43. 43.
    Espa, S., M. G. Badas, S. Fortini, G. Querzoli, and A. Cenedese. A lagrangian investigation of the flow inside the left ventricle. Eur. J. Mech. B 35:9–19, 2012.Google Scholar
  44. 44.
    Fabbri, D., Q. Long, S. Das, and 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.PubMedCentralPubMedGoogle Scholar
  45. 45.
    Falahatpisheh, A., and A. Kheradvar. High-speed particle image velocimetry to assess cardiac fluid dynamics in vitro: from performance to validation. Eur. J. Mech. B 35:2–8, 2012.Google Scholar
  46. 46.
    Filipovic, N., and H. Schima. Numerical simulation of the flow field within the aortic arch during cardiac assist. Artif. Org. 35(4):E73–E83, 2011.Google Scholar
  47. 47.
    Freund, J. B. Numerical simulation of flowing blood cells. Annu. Rev. Fluid Mech. 46:67–95, 2014.Google Scholar
  48. 48.
    Frydrychowicz, A., R. Arnold, D. Hirtler, C. Schlensak, A. F. Stalder, J. Hennig, M. Langer, and M. Markl. Multidirectional flow analysis by cardiovascular magnetic resonance in aneurysm development following repair of aortic coarctation. J. Cardiovasc. Magn. Reson. 10(1):30, 2008.PubMedCentralPubMedGoogle Scholar
  49. 49.
    Fyrenius, A., L. Wigström, T. Ebbers, M. Karlsson, J. Engvall, and A. F. Bolger. Three dimensional flow in the human left atrium. Heart 86(4):448–455, 2001.PubMedCentralPubMedGoogle Scholar
  50. 50.
    Gambaruto, A. M., A. Moura, and A. Sequeira. Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty. Int. J. Numer. Methods Biomed. Eng. 26(7):926–953, 2010.Google Scholar
  51. 51.
    Gatignol, R. The Faxen formulae for a rigid particle in an unsteady non-uniform Stokes flow. Journal de Mecanique Theorique et Appliquee, 2(2):143–160, 1983.Google Scholar
  52. 52.
    Gharib, M., E. Rambod, A. Kheradvar, D. J. Sahn, and J. O. Dabiri. Optimal vortex formation as an index of cardiac health. Proc. Natl. Acad. Sci. 103(16):6305–6308, 2006.Google Scholar
  53. 53.
    Giersiepen, M., L. J. Wurzinger, R. Opitz, and H. Reul. Estimation of shear stress-related blood damage in heart valve prostheses-in vitro comparison of 25 aortic valves. Int. J. Artif. Org. 13(5):300–306, 1990.Google Scholar
  54. 54.
    Govindarajan, V., H. S. Udaykumar, L. H. Herbertson, S. Deutsch, K. B Manning, and K. B. Chandran. Impact of design parameters on bi-leaflet mechanical heart valve flow dynamics. J. Heart Valve Dis. 18(5):535, 2009.PubMedCentralPubMedGoogle Scholar
  55. 55.
    Grigioni, M., C. Daniele, U. Morbiducci, G. D’Avenio, G. Di Benedetto, and V. Barbaro. The power-law mathematical model for blood damage prediction: analytical developments and physical inconsistencies. Artif. Org. 28(5):467–475, 2004.Google Scholar
  56. 56.
    Grigioni, M., C. Daniele, U. Morbiducci, C. Del Gaudio, G. D’Avenio, A. Balducci, and V. Barbaro. A mathematical description of blood spiral flow in vessels: application to a numerical study of flow in arterial bending. J. Biomech. 38(7):1375–1386, 2005.PubMedGoogle Scholar
  57. 57.
    Grigioni, M., U. Morbiducci, G. D’Avenio, G. Di Benedetto, and C. Del Gaudio. A novel formulation for blood trauma prediction by a modified power-law mathematical model. Biomech. Model. Mechanobiol. 4(4):249–260, 2005.PubMedGoogle Scholar
  58. 58.
    Gundert, T. J., S. C. Shadden, A. R. Williams, B. K. Koo, J. A. Feinstein, and J. F. LaDisa, Jr. A rapid and computationally inexpensive method to virtually implant current and next-generation stents into subject-specific computational fluid dynamics models. Ann. Biomed. Eng. 39(5):1423–1437, 2011.PubMedGoogle Scholar
  59. 59.
    Hardman, D., B. J. Doyle, S. I. K. Semple, J. M. J. Richards, D. E. Newby, W. J. Easson, and P. R. Hoskins. On the prediction of monocyte deposition in abdominal aortic aneurysms using computational fluid dynamics. Proc. Inst. Mech. Eng. Part H 227(10):1114–1124, 2013.Google Scholar
  60. 60.
    Hendabadi, S., J. Bermejo, Y. Benito, R. l Yotti, F. Fernández-Avilés, J. C. del Álamo, and S. C Shadden. Topology of blood transport in the human left ventricle by novel processing of doppler echocardiography. Ann. Biomed. Eng. 41(12):2603–2616, 2013.PubMedGoogle Scholar
  61. 61.
    M. D., Hope, S. J. Wrenn, and P. Dyverfeldt. Clinical applications of aortic 4d flow imaging. Curr. Cardiovasc. Imaging Rep. 6(2):128–139, 2013.Google Scholar
  62. 62.
    Hope, T. A., M. Markl, L. Wigström, M. T. Alley, D. C. Miller, and R. J. Herfkens. Comparison of flow patterns in ascending aortic aneurysms and volunteers using four-dimensional magnetic resonance velocity mapping. J. Magn. Reson. Imaging 26(6):1471–1479, 2007.PubMedGoogle Scholar
  63. 63.
    Hsu, U. K., and P. J. Lu. Dynamic simulation and hemolysis evaluation of the regurgitant flow over a tilting-disc mechanical heart valve in pulsatile flow. World J. Mech. 3:160, 2013.Google Scholar
  64. 64.
    Humphrey, J. D. Mechanisms of arterial remodeling in hypertension: coupled roles of wall shear and intramural stress. Hypertension 52:195–200, 2008.PubMedCentralPubMedGoogle Scholar
  65. 65.
    Hyun, S., C. Kleinstreuer, and J. P. Archie, Jr. Hemodynamics analyses of arterial expansions with implications to thrombosis and restenosis. Med. Eng. Phys. 22(1):13–27, 2000.Google Scholar
  66. 66.
    Hyun, S., C. Kleinstreuer, and J. P. Archie, Jr. Computational particle-hemodynamics analysis and geometric reconstruction after carotid endarterectomy. Comput. Biol. Med. 31(5):365–384, 2001.PubMedGoogle Scholar
  67. 67.
    Hyun, S., C. Kleinstreuer, P. W. Longest, and C. Chen. Particle-hemodynamics simulations and design options for surgical reconstruction of diseased carotid artery bifurcations. J. Biomech. Eng. 126(2):188–195, 2004.PubMedGoogle Scholar
  68. 68.
    Jensen, M. H., G. Paladin, and A. Vulpiani. Dynamical Systems Approach to Turbulence. Cambridge: Cambridge University Press, 2005.Google Scholar
  69. 69.
    Jin, W., and C. Clark. Experimental investigation of unsteady flow behaviour within a sac-type ventricular assist device (VAD). J. Bbiomech. 26(6):697–707, 1993.Google Scholar
  70. 70.
    Karmeshu, J. Entropy Measures, Maximum Entropy Principle and Emerging Applications, Vol. 119. Berlin: Springer, 2003.Google Scholar
  71. 71.
    Kheradvar, A., J. Kasalko, D. Johnson, and M. Gharib. An in vitro study of changing profile heights in mitral bioprostheses and their influence on flow. ASAIO J. 52(1):34–38, 2006.PubMedGoogle Scholar
  72. 72.
    Kim, M. C., J. H. Nam, and C. S. Lee. Near-wall deposition probability of blood elements as a new hemodynamic wall parameter. Ann. Biomed. Eng. 34(6):958–970, 2006.PubMedGoogle Scholar
  73. 73.
    Kleinstreuer, C., and Y. Feng. Computational analysis of non-spherical particle transport and deposition in shear flow with application to lung aerosol dynamics—a review. J. Biomech. Eng. 135(2):021008, 2013.PubMedGoogle Scholar
  74. 74.
    Kozerke, S., J. M. Hasenkam, E. M. Pedersen, and P. Boesiger. Visualization of flow patterns distal to aortic valve prostheses in humans using a fast approach for cine 3d velocity mapping. J. Magn. Reson. Imaging 13(5):690–698, 2001.PubMedGoogle Scholar
  75. 75.
    Krishnan, H., C. Garth, J. Guhring, M. A. Gulsun, A. Greiser, and K. I. Joy. Analysis of time-dependent flow-sensitive PC-MRI data. IEEE Trans. Vis. Comput. Graph. 18(6):966–977, 2012.Google Scholar
  76. 76.
    Krishnan, S., H. S. Udaykumar, J. S. Marshall, and K. B. Chandran. Two-dimensional dynamic simulation of platelet activation during mechanical heart valve closure. Ann. Biomed. Eng. 34(10):1519–1534, 2006.PubMedGoogle Scholar
  77. 77.
    Kunov, M. J., D. A. Steinman, and C. R. Ethier. Particle volumetric residence time calculations in arterial geometries. J. Biomech. Eng. 118(2):158–164, 1996.PubMedGoogle Scholar
  78. 78.
    Longest, P. W., and C. Kleinstreuer. Comparison of blood particle deposition models for non-parallel flow domains. J. Biomech. 36(3):421–430, 2003.Google Scholar
  79. 79.
    Longest, P. W., and C. Kleinstreuer. Numerical simulation of wall shear stress conditions and platelet localization in realistic end-to-side arterial anastomoses. J. Biomech. Eng. 125(5):671–681, 2003.PubMedGoogle Scholar
  80. 80.
    Longest, P. W., and C. Kleinstreuer. Particle-hemodynamics modeling of the distal end-to-side femoral bypass: effects of graft caliber and graft-end cut. Med. Eng. Phys. 25(10):843–858, 2003.Google Scholar
  81. 81.
    Longest, P. W., C. Kleinstreuer, and J. P. Archie, Jr. Particle hemodynamics analysis of miller cuff arterial anastomosis. J. Vasc. Surg. 38(6):1353–1362, 2003.PubMedGoogle Scholar
  82. 82.
    Longest, P. W., C. Kleinstreuer, and J. R. Buchanan. Efficient computation of micro-particle dynamics including wall effects. Comput. Fluids 33(4):577–601, 2004.Google Scholar
  83. 83.
    Longest, P. W., C. Kleinstreuer, and J. R. Buchanan, Jr. A new near-wall residence time model applied to three arterio-venous graft end-to-side anastomoses. Comput. Methods Biomech. Biomed. Eng. 4(5):379–397, 2001.Google Scholar
  84. 84.
    Longest, P. W., C. Kleinstreuer, and A. Deanda. Numerical simulation of wall shear stress and particle-based hemodynamic parameters in pre-cuffed and streamlined end-to-side anastomoses. Ann. Biomed. Eng. 33(12):1752–1766, 2005.PubMedGoogle Scholar
  85. 85.
    Longest, P. W., C. Kleinstreuer, G. A. Truskey, and J. R. Buchanan. Relation between near-wall residence times of monocytes and early lesion growth in the rabbit aorto-celiac junction. Ann. Biomed. Eng. 31(1):53–64, 2003.PubMedGoogle Scholar
  86. 86.
    Lonyai, A., A. M. Dubin, J. A. Feinstein, C. A. Taylor, and S. C. Shadden. New insights into pacemaker lead-induced venous occlusion: simulation-based investigation of alterations in venous biomechanics. Cardiovasc. Eng. 10(2):84–90, 2010.PubMedGoogle Scholar
  87. 87.
    Maiti, S., K. Chaudhury, D. DasGupta, and S. Chakraborty. Alteration of chaotic advection in blood flow around partial blockage zone: role of hematocrit concentration. J. Appl. Phys. 113(3):034701, 2013.Google Scholar
  88. 88.
    Markl, M., M. T. Draney, M. D. Hope, J. M. Levin, F. P. Chan, M. T. Alley, N. J. Pelc, and R. J Herfkens. Time-resolved 3-dimensional velocity mapping in the thoracic aorta: visualization of 3-directional blood flow patterns in healthy volunteers and patients. J. Comput. Assist. Tomogr. 28(4):459–468, 2004.Google Scholar
  89. 89.
    Markl, M., M. T. Draney, D. C. Miller, J. M. Levin, E. E. Williamson, N. J. Pelc, D. H. Liang, and R. J. Herfkens. Time-resolved three-dimensional magnetic resonance velocity mapping of aortic flow in healthy volunteers and patients after valve-sparing aortic root replacement. J. Thorac. Cardiovasc. Surg. 130(2):456–463, 2005.PubMedGoogle Scholar
  90. 90.
    Markl, M., P. J. Kilner, and T. Ebbers. Comprehensive 4d velocity mapping of the heart and great vessels by cardiovascular magnetic resonance. J. Cardiovasc. Magn. Reson. 13(1):1–22, 2011.Google Scholar
  91. 91.
    Marsden, A. L., V. M. Reddy, S. C. Shadden, F. P. Chan, C. A. Taylor, and J. A. Feinstein. A new multiparameter approach to computational simulation for fontan assessment and redesign. Congenit. Heart Dis. 5(2):104–117, 2010.PubMedGoogle Scholar
  92. 92.
    Marshall, I. Targeted particle tracking in computational models of human carotid bifurcations. J. Biomech. Eng. 133(12):124501, 2011.PubMedGoogle Scholar
  93. 93.
    Massai, D., G. Soloperto, D. Gallo, X. Y. Xu, and U. Morbiducci. Shear-induced platelet activation and its relationship with blood flow topology in a numerical model of stenosed carotid bifurcation. Eur. J. Mech. B 35:92–101, 2012.Google Scholar
  94. 94.
    Mathew, G., I. Mezić, and L. Petzold. A multiscale measure for mixing. Physica D 211(1):23–46, 2005.Google Scholar
  95. 95.
    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.Google Scholar
  96. 96.
    McLaughlin, J. B. The lift on a small sphere in wall-bounded linear shear flows. J. Fluid Mech. 226:249–265, 1993.Google Scholar
  97. 97.
    Michaelides, E. E. Hydrodynamic force and heat/mass transfer from particles, bubbles, and drops–The Freeman Scholar Lecture. J. Fluids Eng. 125(2):209–238, 2003.Google Scholar
  98. 98.
    Moffatt, H. K., and A. Tsinober. Helicity in laminar and turbulent flow. Annu. Rev. Fluid Mech. 24(1):281–312, 1992.Google Scholar
  99. 99.
    Morbiducci, U., D. Gallo, D. Massai, R. Ponzini, M. A. Deriu, L. Antiga, A. Redaelli, and F. M. Montevecchi. On the importance of blood rheology for bulk flow in hemodynamic models of the carotid bifurcation. J. Biomech. 44(13):2427–2438, 2011.PubMedGoogle Scholar
  100. 100.
    Morbiducci, U., D. Gallo, R. Ponzini, D. Massai, L. Antiga, F. M. Montevecchi, and A. Redaelli. Quantitative analysis of bulk flow in image-based hemodynamic models of the carotid bifurcation: the influence of outflow conditions as test case. Ann. Biomed. Eng. 38(12):3688–3705, 2010.PubMedGoogle Scholar
  101. 101.
    Morbiducci, U., R. Ponzini, M. Grigioni, and A. Redaelli. Helical flow as fluid dynamic signature for atherogenesis risk in aortocoronary bypass. A numeric study. J. Biomech. 40(3):519–534, 2007.PubMedGoogle Scholar
  102. 102.
    Morbiducci, U., R. Ponzini, M. Nobili, D. Massai, F. M. Montevecchi, D. Bluestein, and A. Redaelli. Blood damage safety of prosthetic heart valves. shear-induced platelet activation and local flow dynamics: a fluid-structure interaction approach. J. Biomech. 42(12):1952–1960, 2009.PubMedGoogle Scholar
  103. 103.
    Morbiducci, U., R. Ponzini, G. Rizzo, M. Cadioli, A. Esposito, F. De Cobelli, A. Del Maschio, F. M. Montevecchi, and A. Redaelli. In vivo quantification of helical blood flow in human aorta by time-resolved three-dimensional cine phase contrast magnetic resonance imaging. Ann. Biomed. Eng. 37(3):516–531, 2009.PubMedGoogle Scholar
  104. 104.
    Morbiducci, U., R. Ponzini, G. Rizzo, M. Cadioli, A. Esposito, F. M. Montevecchi, and A. Redaelli. Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study. Biomech. Model. Mechanobiol. 10(3):339–355, 2011.PubMedGoogle Scholar
  105. 105.
    Nazemi, M., and C. Kleinstreuer. Analysis of particle trajectories in aortic artery bifurcations with stenosis. J. Biomech. Eng. 111(4):311–315, 1989.PubMedGoogle Scholar
  106. 106.
    Nobili, J., M. and Sheriff, U. Morbiducci, A. Redaelli, and D. Bluestein. Platelet activation due to hemodynamic shear stresses: damage accumulation model and comparison to in vitro measurements. ASAIO J. (American Society for Artificial Internal Organs: 1992), 54(1):64, 2008.Google Scholar
  107. 107.
    Osorio, A. F., R. Osorio, A. Ceballos, R. Tran, W. Clark, E. A. Divo, I. R. Argueta-Morales, Alain J. Kassab, and W. M DeCampli. Computational fluid dynamics analysis of surgical adjustment of left ventricular assist device implantation to minimise stroke risk. Comput. Methods Biomech. Biomed. Eng. 16(6):622–638, 2011.PubMedGoogle Scholar
  108. 108.
    Parashar, A., R. Singh, P. K. Panigrahi, and K. Muralidhar. Chaotic flow in an aortic aneurysm. J. Appl. Phys. 113(21):214909, 2013.Google Scholar
  109. 109.
    Peng, Y., Y. Wu, X. Tang, W. Liu, D. Chen, T. Gao, Y. Xu, and Y. Zeng. Numerical simulation and comparative analysis of flow field in axial blood pumps. Comput. Methods Biomech. Biomed. Eng. 17(7):723–727, 2012.PubMedGoogle Scholar
  110. 110.
    Perktold, K. On the paths of fluid particles in an axisymmetrical aneurysm. J. Biomech. 20(3):311–317, 1987.PubMedGoogle Scholar
  111. 111.
    Perktold, K., and D. Hilbert. Numerical simulation of pulsatile flow in a carotid bifurcation model. J. Biomed. Eng. 8(3):193–199, 1986.PubMedGoogle Scholar
  112. 112.
    Perktold, K., T. Kenner, D. Hilbert, B. Spork, and H. Florian. Numerical blood flow analysis: arterial bifurcation with a saccular aneurysm. Basic Res. Cardiol. 83(1):24–31, 1988.PubMedGoogle Scholar
  113. 113.
    Perktold, K., R. Peter, and M. Resch. Pulsatile non-newtonian blood flow simulation through a bifurcation with an aneurysm. Biorheology 26(6):1011–1030, 1988.Google Scholar
  114. 114.
    Phillips, R. J., R. C. Armstrong, R. A. Brown, A. L. Graham, and J. R. Abbott. A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids A 4:30–40, 1992.Google Scholar
  115. 115.
    Prosi, M., K. Perktold, and H. Schima. Effect of continuous arterial blood flow in patients with rotary cardiac assist device on the washout of a stenosis wake in the carotid bifurcation: a computer simulation study. J. Biomech. 40(10):2236–2243, 2007.PubMedGoogle Scholar
  116. 116.
    Purvis, Jr., N. B., and T. D. Giorgio. The effects of elongational stress exposure on the activation and aggregation of blood platelets. Biorheology 28(5):355, 1991.PubMedGoogle Scholar
  117. 117.
    Raz, S., S. Einav, Y. Alemu, and D. Bluestein. DPIV prediction of flow induced platelet activation-comparison to numerical predictions. Ann. Biomed. Eng. 35(4):493–504, 2007.PubMedGoogle Scholar
  118. 118.
    Schelin, A. B., Gy Károlyi, A. P. S. De Moura, N. A. Booth, and C. Grebogi. Chaotic advection in blood flow. Phys. Rev. E 80(1):016213, 2009.Google Scholar
  119. 119.
    Schelin, A. B., György Károlyi, A. P. S. De Moura, N. Booth, and C. Grebogi. Are the fractal skeletons the explanation for the narrowing of arteries due to cell trapping in a disturbed blood flow?. Comput. Biol. Med. 42(3):276–281, 2012.PubMedGoogle Scholar
  120. 120.
    Schelin, A. B., György Károlyi, Alessandro P. S. De Moura, N. A Booth, and C. Grebogi. Fractal structures in stenoses and aneurysms in blood vessels. Philos. Trans. R. Soc. A 368(1933):5605–5617, 2010.Google Scholar
  121. 121.
    Schima, H., B. Lackner, M. Prosi, and K. Perktold. Numerical simulation of carotid hemodynamics in patients with rotary blood pump cardiac assist. The International Journal of Artif. Org. 26(2):152–160, 2003.Google Scholar
  122. 122.
    Sengupta, D., A. M. Kahn, J. C. Burns, S. Sankaran, S. C. Shadden, and A. L. Marsden. Image-based modeling of hemodynamics in coronary artery aneurysms caused by kawasaki disease. Biomech. Model. Mechanobiol. 11(6):915–932, 2012.PubMedGoogle Scholar
  123. 123.
    Seo, J. H., and R. Mittal. Effect of diastolic flow patterns on the function of the left ventricle. Phys. Fluids 25(11):110801, 2013.Google Scholar
  124. 124.
    Shadden, S. C. Lagrangian coherent structures. In Transport and Mixing in Laminar Flows: from Microfluidics to Oceanic Currents. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2011.Google Scholar
  125. 125.
    Shadden, S. C., M. Astorino, and J. F. Gerbeau. Computational analysis of an aortic valve jet with Lagrangian coherent structures. Chaos 20:017512–1, 2010.PubMedGoogle Scholar
  126. 126.
    Shadden, S. C., J. O. Dabiri, and J. E. Marsden. Lagrangian analysis of fluid transport in empirical vortex rings. Phys. Fluids 18:047105, 2006.Google Scholar
  127. 127.
    Shadden, S. C., and S. Hendabadi. Potential fluid mechanic pathways of platelet activation. Biomech. Model. Mechanobiol. 12(3):467–474, 2013.PubMedCentralPubMedGoogle Scholar
  128. 128.
    Shadden, S. C., K. Katija, M. Rosenfeld, J. E. Marsden, and J. O. Dabiri. Transport and stirring induced by vortex formation. J. Fluid Mech. 593:315–331, 2007.Google Scholar
  129. 129.
    Shadden, S. C., F. Lekien, and J. E. Marsden. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212(3–4):271–304, 2005.Google Scholar
  130. 130.
    Shadden, S. C., and C. A. Taylor. Characterization of coherent structures in the cardiovascular system. Ann. Biomed. Eng. 36:1152–1162, 2008.PubMedGoogle Scholar
  131. 131.
    Siegel, J. M., J. N. Oshinski, R. I. Pettigrew, and D. N. Ku. Comparison of phantom and computer-simulated mr images of flow in a convergent geometry: implications for improved two-dimensional MR angiography. J. Magn. Reson. Imaging 5(6):677–683, 1995.PubMedGoogle Scholar
  132. 132.
    Simon, H. A., L. Ge, F. Sotiropoulos, and A. P. Yoganathan. Numerical investigation of the performance of three hinge designs of bileaflet mechanical heart valves. Ann. Biomed. Eng. 38(11):3295–3310, 2010.PubMedCentralPubMedGoogle Scholar
  133. 133.
    Sirois, E., and W. Sun. Computational evaluation of platelet activation induced by a bioprosthetic heart valve. Artif. Org. 35(2):157–165, 2011.Google Scholar
  134. 134.
    Smadi, O., I. Hassan, P. Pibarot, and L. Kadem. Numerical and experimental investigations of pulsatile blood flow pattern through a dysfunctional mechanical heart valve. J. Biomech. 43(8):1565–1572, 2010.PubMedGoogle Scholar
  135. 135.
    Song, X., A. L. Throckmorton, H. G. Wood, J. F. Antaki, and D. B. Olsen. Computational fluid dynamics prediction of blood damage in a centrifugal pump. Artif. Org. 27(10):938–941, 2003.Google Scholar
  136. 136.
    Song, X., A. L Throckmorton, H. G. Wood, J. F Antaki, and D. B Olsen. Quantitative evaluation of blood damage in a centrifugal VAD by computational fluid dynamics. J. Fluids Eng. 126(3):410–418, 2004.Google Scholar
  137. 137.
    Steinman, D. A. Simulated pathline visualization of computed periodic blood flow patterns. J. Biomech. 33(5):623–628, 2000.Google Scholar
  138. 138.
    Steinman, D. A., and B. K. Rutt. On the nature and reduction of plaque-mimicking flow artifacts in black blood MRI of the carotid bifurcation. Magn. Reson. Med. 39(4):635–641, 1998.PubMedGoogle Scholar
  139. 139.
    Steinman, D. A., J. B. Thomas, H. M. Ladak, J. S. Milner, B. K. Rutt, and J. D. Spence. Reconstruction of carotid bifurcation hemodynamics and wall thickness using computational fluid dynamics and MRI. Magn. Reson. Med. 47(1):149–159, 2002.PubMedGoogle Scholar
  140. 140.
    Suh, G. Y., A. S. Les, A. S. Tenforde, S. C. Shadden, R. L. Spilker, J. J. Yeung, C. P. Cheng, R. J. Herfkens, R. L. Dalman, and C. A. Taylor. Quantification of particle residence time in abdominal aortic aneurysms using magnetic resonance imaging and computational fluid dynamics. Ann. Biomed. Eng. 39:864–883, 2011.PubMedCentralPubMedGoogle Scholar
  141. 141.
    Suh, G. Y., A. S. Tenforde, S. C. Shadden, R. L. Spilker, C. P. Cheng, R. J. Herfkens, R. L. Dalman, and C. A. Taylor. Hemodynamic changes in abdominal aortic aneurysms with increasing exercise intensity using MR exercise imaging and image-based computational fluid dynamics. Ann. Biomed. Eng. 39:2186–2202, 2011.PubMedCentralPubMedGoogle Scholar
  142. 142.
    Tambasco, M., and D. A Steinman. On assessing the quality of particle tracking through computational fluid dynamic models. J. Biomech. Eng. 124(2):166–175, 2002.Google Scholar
  143. 143.
    Tambasco, M., and D. A. Steinman. Path-dependent hemodynamics of the stenosed carotid bifurcation. Ann. Biomed. Eng. 31(9):1054–1065, 2003.PubMedGoogle Scholar
  144. 144.
    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.PubMedGoogle Scholar
  145. 145.
    Töger, J., M. Kanski, M. Carlsson, S. J. Kovács, G. Söderlind, H. Arheden, and E. Heiberg. Vortex ring formation in the left ventricle of the heart: analysis by 4d flow MRI and lagrangian coherent structures. Ann. Biomed. Eng. 40(12):2652–2662, 2012.PubMedGoogle Scholar
  146. 146.
    Tsao, R., S. A. Jones, D. P. Giddens, C. K. Zarins, and S. Glagov. An automated three-dimensional particle tracking technique for the study of modeled arterial flow fields. J. Biomech. Eng. 117(2):211–218, 1995.PubMedGoogle Scholar
  147. 147.
    Turitto, V. T., A. M. Benis, and E. F. Leonard. Platelet diffusion in flowing blood. Ind. Eng. Chem. Fundam. 11(2):216–223, 1972.Google Scholar
  148. 148.
    Vétel, J., A. Garon, and D. Pelletier. Lagrangian coherent structures in the human carotid artery bifurcation. Exp. Fluids 46(6):1067–1079, 2009.Google Scholar
  149. 149.
    Wada, S., and T. Karino. Theoretical prediction of low-density lipoproteins concentration at the luminal surface of an artery with a multiple bend. Ann. Biomed. Eng. 30(6):778–791, 2002.PubMedGoogle Scholar
  150. 150.
    Wen, J., T. Zheng, W. Jiang, X. Deng, and Y. Fan. A comparative study of helical-type and traditional-type artery bypass grafts: numerical simulation. ASAIO J. 57(5):399–406, 2011.PubMedGoogle Scholar
  151. 151.
    Wigström, L., T. Ebbers, A. Fyrenius, M. Karlsson, J. Engvall, B. Wranne, and A. F. Bolger. Particle trace visualization of intracardiac flow using time-resolved 3d phase contrast MRI. Magn. Reson. Med. 41(4):793–799, 1999.PubMedGoogle Scholar
  152. 152.
    Wu, J., J. F. Antaki, T. A. Snyder, W. R. Wagner, H. S. Borovetz, and B. E. Paden. Design optimization of blood shearing instrument by computational fluid dynamics. Artif. Org. 29(6):482–489, 2005.Google Scholar
  153. 153.
    Wu, J., B. E. Paden, H. S. Borovetz, and J. F. Antaki. Computational fluid dynamics analysis of blade tip clearances on hemodynamic performance and blood damage in a centrifugal ventricular assist device. Artif. Org. 34(5):402–411, 2010.Google Scholar
  154. 154.
    Xenos, M., G. Girdhar, Y. Alemu, J. Jesty, M. Slepian, S. Einav, and D. Bluestein. Device thrombogenicity emulator (DTE)- design optimization methodology for cardiovascular devices: a study in two bileaflet MHV designs. J. Biomech. 43(12):2400–2409, 2010.PubMedCentralPubMedGoogle Scholar
  155. 155.
    Xu, Z., N. Chen, S. C. Shadden, J. E. Marsden, M. M. Kamocka, E. D. Rosen, and M. Alber. Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter 5(4):769–779, 2009.Google Scholar
  156. 156.
    Yang, W., J. A. Feinstein, S. C Shadden, I. E. Vignon-Clementel, and A. L. Marsden. Optimization of a Y-graft design for improved hepatic flow distribution in the Fontan circulation. J. Biomech. Eng. 135(1):011002, 2013.PubMedGoogle Scholar
  157. 157.
    Yang, W., I. E. Vignon-Clementel, G. Troianowski, V. M. Reddy, J. A. Feinstein, and A. L. Marsden. Hepatic blood flow distribution and performance in conventional and novel Y-graft Fontan geometries: a case series computational fluid dynamics study. J. Thorac. Cardiovasc. Surg. 143(5):1086–1097, 2012.PubMedGoogle Scholar
  158. 158.
    Yin, W., Y. Alemu, K. Affeld, J. Jesty, and D. Bluestein. Flow-induced platelet activation in bileaflet and monoleaflet mechanical heart valves. Ann. Biomed. Eng. 32(8):1058–1066, 2004.PubMedGoogle Scholar
  159. 159.
    Young, A. A., and J. L. Prince. Cardiovascular magnetic resonance: deeper insights through bioengineering. Annu. Rev. Biomed. Eng. 15:433–461, 2013.PubMedGoogle Scholar
  160. 160.
    Yun, B. M., J. Wu, H. A. Simon, S. Arjunon, F. Sotiropoulos, C. K. Aidun, and A. P. Yoganathan. A numerical investigation of blood damage in the hinge area of aortic bileaflet mechanical heart valves during the leakage phase. Ann. Biomed. Eng. 40(7):1468–1485, 2012.PubMedGoogle Scholar
  161. 161.
    Zarins, C. K., and S. Glagov. Vascular Surgery Principles and Practice, Chapter Pathophysiology of Human Atherosclerosis. New York, NY: McGraw-Hill, 1994.Google Scholar
  162. 162.
    Zheng, T., W. Wang, W. Jiang, X. Deng, and Y. Fan. Assessing hemodynamic performances of small diameter helical grafts: transient simulation. J. Mech. Med. Biol. 12(01), 2012.Google Scholar

Copyright information

© Biomedical Engineering Society 2014

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

Personalised recommendations