Annals of Biomedical Engineering

, Volume 42, Issue 4, pp 787–796 | Cite as

Contrast Agent Bolus Dispersion in a Realistic Coronary Artery Geometry: Influence of Outlet Boundary Conditions

  • Karsten SommerEmail author
  • Regine Schmidt
  • Dirk Graafen
  • Hanns-Christian Breit
  • Laura M. Schreiber


Myocardial blood flow (MBF) quantification using contrast-enhanced first-pass magnetic resonance imaging relies on the precise knowledge of the arterial input function (AIF). Due to vascular transport processes, however, the shape of the AIF may change from the left ventricle where the AIF is measured to the myocardium. We employed computational fluid dynamics simulations in a realistic model of the left circumflex artery to investigate the degree to which this effect corrupts MBF quantification. Different outlet boundary conditions were applied to examine their influence on the solution. Our results indicate that vascular transport processes in realistic coronary artery geometries give rise to non-negligible systematic errors in the MBF values. The magnitude of these errors differs considerably between the outlets of the 3D model. Moreover, outlet boundary conditions are shown to have a significant influence on the outflows at the outlets of the 3D model. In particular, the employed boundary conditions respond differently to an artificially inserted stenosis and to hyperemia condition. Finally, outlet boundary conditions are shown to have an influence on the resulting MBF value. Since MBF errors are different under rest and under hyperemia conditions, overestimation of myocardial perfusion reserve values may occur as well.


Perfusion MRI MBF Vascular transport Computational fluid dynamics Stenosis Arterial input function 



This work was supported by a Carl Zeiss Foundation Dissertation Fellowship for Karsten Sommer and by the Max Planck Graduate Center with the Johannes Gutenberg-Universität Mainz (MPGC). The authors would like to thank Mette Olufsen from the Department of Mathematics, North Carolina State University for advice regarding the efficient implementation of the structured tree model, as well as Tamás Sebestény from the Institute for Microscopic Anatomy and Neurobiology, University Medical Center Mainz for providing the corrosion cast specimen.

Conflict of Interest

No benefits in any form have been or will be received from a commercial party related directly or indirectly to the subject of this manuscript.

Supplementary material

The supplemental video shows the transport of an injected contrast agent bolus for the resistance boundary condition without vasodilation at physical rest condition and without stenosis. For better visualization of contrast agent dispersion, a “delta bolus”, i.e., a very short version (approximately 0.5 s) of the original bolus is used as inlet boundary condition. (AVI 49033 kb)


  1. 1.
    Baek, H., M. V. Jayaraman, and G. E. Karniadakis. Wall shear stress and pressure distribution on aneurysms and infundibulae in the posterior communicating artery bifurcation. Ann. Biomed. Eng. 37:2469–2487, 2009.PubMedCrossRefGoogle Scholar
  2. 2.
    Ballyk, P. D., D. A. Steinman, and C. R. Ethier. Simulation of non-Newtonian blood flow in an end-to-side anastomosis. Biorheology 31:565–586, 1994.PubMedGoogle Scholar
  3. 3.
    Berthier, B., R. Bouzerar, and C. Legallais. Blood flow patterns in an anatomically realistic coronary vessel: influence of three different reconstruction methods. J. Biomech. 35:1347–1356, 2002.PubMedCrossRefGoogle Scholar
  4. 4.
    Calamante, F., P. J. Yim, and J. R. Cebral. Estimation of bolus dispersion effects in perfusion MRI using image-based computational fluid dynamics. Neuroimage 19:341–353, 2003.PubMedCrossRefGoogle Scholar
  5. 5.
    Cousins, W., and P. A. Gremaud. Boundary conditions for hemodynamics: the structured tree revisited. J. Comput. Phys. 231:6086–6096, 2012.CrossRefGoogle Scholar
  6. 6.
    Fenchel, M., U. Helber, O. P. Simonetti, N. I. Stauder, U. Kramer, C. N. Nguyen, J. P. Finn, C. D. Claussen, and S. Miller. Multislice first-pass myocardial perfusion imaging: Comparison of saturation recovery (SR)-TrueFISP-two-dimensional (2D) and SR-TurboFLASH-2D pulse sequences. J. Magn. Reson. Imaging 19:555–563, 2004.PubMedCrossRefGoogle Scholar
  7. 7.
    Fritz-Hansen, T., J. D. Hove, K. F. Kofoed, H. Kelbaek, and H. B. Larsson. Quantification of MRI measured myocardial perfusion reserve in healthy humans: a comparison with positron emission tomography. J. Magn. Reson. Imaging 27:818–824, 2008.PubMedCrossRefGoogle Scholar
  8. 8.
    Gatehouse, P. D., J. Keegan, L. A. Crowe, S. Masood, R. H. Mohiaddin, K. F. Kreitner, and D. N. Firmin. Applications of phase-contrast flow and velocity imaging in cardiovascular MRI. Eur. Radiol. 15:2172–2184, 2005.PubMedCrossRefGoogle Scholar
  9. 9.
    Gijsen, F. J. H., E. Allanic, F. N. Van de Vosse, and J. D. Janssen. The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube. J. Biomech. 32:705–713, 1999.PubMedCrossRefGoogle Scholar
  10. 10.
    Go, A. S., D. Mozaffarian, V. L. Roger, E. J. Benjamin, J. D. Berry, W. B. Borden, M. B. Turner, et al. Heart disease and stroke statistics-2013 update a report from the American Heart Association. Circulation 127(6):245, 2013.Google Scholar
  11. 11.
    Graafen, D., J. Hamer, S. Weber, and L. M. Schreiber. Quantitative myocardial perfusion magnetic resonance imaging: the impact of pulsatile flow on contrast agent bolus dispersion. Phys. Med. Biol. 56:5167–5185, 2011.PubMedCrossRefGoogle Scholar
  12. 12.
    Graafen, D., K. Münnemann, S. Weber, K. F. Kreitner, and L. M. Schreiber. Quantitative contrast-enhanced myocardial perfusion magnetic resonance imaging: simulation of bolus dispersion in constricted vessels. Med. Phys. 36:3099–3106, 2009.PubMedCrossRefGoogle Scholar
  13. 13.
    Groden, C., J. Laudan, S. Gatchell, and H. Zeumer. Three-dimensional pulsatile flow simulation before and after endovascular coil embolization of a terminal cerebral aneurysm. J. Cereb. Blood Flow Metab. 21:1464–1471, 2001.PubMedCrossRefGoogle Scholar
  14. 14.
    Hozumi, T., K. Yoshida, Y. Ogata, T. Akasaka, Y. Asami, T. Takagi, and S. Morioka. Noninvasive assessment of significant left anterior descending coronary artery stenosis by coronary flow velocity reserve with transthoracic color Doppler echocardiography. Circulation 97:1557–1562, 1998.PubMedCrossRefGoogle Scholar
  15. 15.
    Hsu, L. Y., D. W. Groves, A. H. Aletras, P. Kellman, and A. E. Arai. A quantitative pixel-wise measurement of myocardial blood flow by contrast-enhanced first-pass CMR perfusion imaging. JACC Cardiovasc. Imaging 5:154–166, 2012.PubMedCentralPubMedCrossRefGoogle Scholar
  16. 16.
    Hundertmark-Zaušková, A., and M. Lukáčová-Medvid’ová. Numerical study of shear-dependent non-Newtonian fluids in compliant vessels. Comput. Math. Appl. 60:572–590, 2010.CrossRefGoogle Scholar
  17. 17.
    Jasak, H., H. G. Weller, and A. D. Gosman. High resolution NVD differencing scheme for arbitrarily unstructured meshes. Int. J. Numer. Methods Fluids 31:431–449, 1999.CrossRefGoogle Scholar
  18. 18.
    Jerosch-Herold, M., N. Wilke, Y. Wang, G. R. Gong, A. M. Mansoor, H. Huang, S. Gurchumelidze, and A. E. Stillman. Direct comparison of an intravascular and an extracellular contrast agent for quantification of myocardial perfusion. Int. J. Cardiac. Imaging 15:453–464, 1999.CrossRefGoogle Scholar
  19. 19.
    Jiang, J., C. Strother, K. Johnson, S. Baker, D. Consigny, O. Wieben, and J. Zagzebski. Comparison of blood velocity measurements between ultrasound Doppler and accelerated phase-contrast MR angiography in small arteries with disturbed flow. Phys. Med. Biol. 56:1755–1773, 2011.PubMedCentralPubMedCrossRefGoogle Scholar
  20. 20.
    Jin, S., Y. Yang, J. Oshinski, A. Tannenbaum, J. Gruden, and D. Giddens. Flow patterns and wall shear stress distributions at atherosclerotic-prone sites in a human left coronary artery—an exploration using combined methods of CT and computational fluid dynamics. In Proc. 26th Ann. Int. IEEE EMBS, 2004.Google Scholar
  21. 21.
    Kanyanta, V., A. Ivankovic, and A. Karac. Validation of a fluid–structure interaction numerical model for predicting flow transients in arteries. J. Biomech. 42:1705–1712, 2009.PubMedCrossRefGoogle Scholar
  22. 22.
    Kolandavel, M. K., E. T. Fruend, S. Ringgaard, and P. G. Walker. The effects of time varying curvature on species transport in coronary arteries. Ann. Biomed. Eng. 34:1820–1832, 2006.PubMedCentralPubMedCrossRefGoogle Scholar
  23. 23.
    Konstas, A. A., G. V. Goldmakher, T. Y. Lee, and M. H. Lev. Theoretic basis and technical implementations of CT perfusion in acute ischemic stroke, part 2: technical implementations. Am. J. Neuroradiol. 30:885–892, 2009.PubMedCrossRefGoogle Scholar
  24. 24.
    Kroll, K., N. Wilke, M. Jerosch-Herold, Y. Wang, Y. Zhang, R. J. Bache, and J. B. Bassingthwaighte. Modeling regional myocardial flows from residue functions of an intravascular indicator. Am. J. Physiol. Heart C 271:1643–1655, 1996.Google Scholar
  25. 25.
    Lally, C., A. J. Reid, and P. J. Prendergast. Elastic behavior of porcine coronary artery tissue under uniaxial and equibiaxial tension. Ann. Biomed. Eng. 32:1355–1364, 2004.PubMedCrossRefGoogle Scholar
  26. 26.
    Lee, J., and N. P. Smith. The multi-scale modelling of coronary blood flow. Ann. Biomed. Eng. 40:399–2413, 2012.Google Scholar
  27. 27.
    Lima, J. A., R. M. Judd, A. Bazille, S. P. Schulman, E. Atalar, and E. A. Zerhouni. Regional heterogeneity of human myocardial infarcts demonstrated by contrast-enhanced MRI Potential mechanisms. Circulation 92:1117–1125, 1995.PubMedCrossRefGoogle Scholar
  28. 28.
    Mischi, M., J. A. Den Boer, and H. H. M. Korsten. On the physical and stochastic representation of an indicator dilution curve as a gamma variate. Physiol. Meas. 29:281–294, 2008.PubMedCrossRefGoogle Scholar
  29. 29.
    Morris, L., P. Delassus, P. Grace, F. Wallis, M. Walsh, and T. McGloughlin. Effects of flat, parabolic and realistic steady flow inlet profiles on idealised and realistic stent graft fits through Abdominal Aortic Aneurysms (AAA). Med. Eng. Phys. 28:19–26, 2006.PubMedCrossRefGoogle Scholar
  30. 30.
    Nichols, W. W., and M. F. O’Rourke. McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles. Philadelphia: Lea & Febiger, p. 512, 1990.Google Scholar
  31. 31.
    Bratis, K., and E. Nagel. Variability in quantitative cardiac magnetic resonance perfusion analysis. J. Thorac. Dis. 5:357–359, 2013.PubMedCentralPubMedGoogle Scholar
  32. 32.
    Olufsen, M. Structured tree outflow condition for blood flow in larger systemic arteries. Am. J. Physiol. Heart C. 276:257–268, 1999.Google Scholar
  33. 33.
    Pandit, A., X. Lu, C. Wang, and G. S. Kassab. Biaxial elastic material properties of porcine coronary media and adventitia. Am. J. Physiol. Heart C. 288:2581–2587, 2005.CrossRefGoogle Scholar
  34. 34.
    Pries, A. R., D. Neuhaus, and P. Gaehtgens. Blood viscosity in tube flow: dependence on diameter and hematocrit. Am. J. Physiol. Heart C 263:1770–1778, 1992.Google Scholar
  35. 35.
    Quarteroni, A., and L. Formaggia. Mathematical modelling and numerical simulation of the cardiovascular system. Handb. Numer. Anal. 12:3–127, 2004.Google Scholar
  36. 36.
    Schambach, S. J., S. Bag, L. Schilling, C. Groden, and M. A. Brockmann. Application of micro-CT in small animal imaging. Methods 50:2–13, 2010.PubMedCrossRefGoogle Scholar
  37. 37.
    Schmidt, R., D. Graafen, S. Weber, and L. M. Schreiber. Computational fluid dynamics simulations of contrast agent bolus dispersion in a coronary bifurcation: impact on MRI-based quantification of myocardial perfusion. Comput. Math. Methods Med. Article ID 513187, 2013.Google Scholar
  38. 38.
    Schmitt, M., G. Horstick, S. E. Petersen, A. Karg, N. Hoffmann, T. Gumbrich, N. Abegunewardene, and W. G. Schreiber. Quantification of resting myocardial blood flow in a pig model of acute ischemia based on first-pass MRI. Magn. Reson. Med. 53:1223–1227, 2005.PubMedCrossRefGoogle Scholar
  39. 39.
    Spaan, J. A. E., R. ter Wee, J. W. G. E. van Teeffelen, G. Streekstra, M. Siebes, C. Kolyva, H. Vink, D. S. Fokkema, and E. VanBavel. Visualisation of intramural coronary vasculature by an imaging cryomicrotome suggests compartmentalisation of myocardial perfusion areas. Med. Biol. Eng. Comput. 43:431–435, 2005.PubMedCrossRefGoogle Scholar
  40. 40.
    Spilker, R. L., J. A. Feinstein, D. W. Parker, V. M. Reddy, and C. A. Taylor. Morphometry-based impedance boundary conditions for patient-specific modeling of blood flow in pulmonary arteries. Ann. Biomed. Eng. 35:546–559, 2007.PubMedCrossRefGoogle Scholar
  41. 41.
    Stroud, J., S. Berger, and D. Saloner. Numerical analysis of flow through a severely stenotic carotid artery bifurcation. J. Biomech. Eng. T. ASME 124:9–20, 2002.CrossRefGoogle Scholar
  42. 42.
    Theodorakakos, A., M. Gavaises, A. Andriotis, A. Zifan, P. Liatsis, I. Pantos, and D. Katritsis. Simulation of cardiac motion on non-Newtonian, pulsating flow development in the human left anterior descending coronary artery. Phys. Med. Biol. 53:4875–4892, 2008.Google Scholar
  43. 43.
    Uren, N. G., J. A. Melin, B. De Bruyne, W. Wijns, T. Baudhuin, and P. G. Camici. Relation between myocardial blood flow and the severity of coronary-artery stenosis. New Engl. J. Med. 330:1782–1788, 1994.PubMedCrossRefGoogle Scholar
  44. 44.
    Varghese, S. S., and S. H. Frankel. Numerical modeling of pulsatile turbulent flow in stenotic vessels. J. Biomech. Eng. 125:445–460, 2003.PubMedCrossRefGoogle Scholar
  45. 45.
    Vignon-Clementel, I. E., C. Alberto Figueroa, K. E. Jansen, and C. A. Taylor. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput. Methods Appl. Mech. Eng. 195:3776–3796, 2006.CrossRefGoogle Scholar
  46. 46.
    Wang, J. C., S. L. T. Normand, L. Mauri, and R. E. Kuntz. Coronary artery spatial distribution of acute myocardial infarction occlusions. Circulation 110:278–284, 2004.PubMedCrossRefGoogle Scholar
  47. 47.
    Weber, S., A. Kronfeld, R. P. Kunz, K. Muennemann, G. Horstick, K. F. Kreitner, and W. G. Schreiber. Quantitative myocardial perfusion imaging using different autocalibrated parallel acquisition techniques. J. Magn. Reson. Imaging 28:51–59, 2008.PubMedCrossRefGoogle Scholar
  48. 48.
    Wellnhofer, E., J. Osman, U. Kertzscher, K. Affeld, E. Fleck, and L. Goubergrits. Flow simulation studies in coronary arteries—impact of side-branches. Atherosclerosis 213:475–481, 2010.PubMedCrossRefGoogle Scholar
  49. 49.
    Westerhof, N., J. W. Lankhaar, and B. E. Westerhof. The arterial windkessel. Med. Biol. Eng. Comput. 47:131–141, 2009.PubMedCrossRefGoogle Scholar
  50. 50.
    Wieseotte, C., M. Wagner, P. Schiel, and L. M. Schreiber. An estimate of Gd-DOTA diffusivity in human blood plasma based on the direct diffusion measurement of its hydrodynamic analogue Ga-DOTA. Magn. Reson. Med., 2013 (under review).Google Scholar
  51. 51.
    Wilke, N. M., M. Jerosch-Herold, A. Zenovich, and A. E. Stillman. Magnetic resonance first-pass myocardial perfusion imaging: clinical validation and future applications. J. Magn. Reson. Imaging 10:676–685, 1999.PubMedCrossRefGoogle Scholar
  52. 52.
    Yada, T., O. Hiramatsu, H. Tachibana, E. Toyota, and F. Kajiya. Role of NO and channels in adenosine-induced vasodilation on in vivo canine subendocardial arterioles. Am. J. Physiol. Heart C 277:1931–1939, 1999.Google Scholar

Copyright information

© Biomedical Engineering Society 2013

Authors and Affiliations

  • Karsten Sommer
    • 1
    Email author
  • Regine Schmidt
    • 1
  • Dirk Graafen
    • 1
  • Hanns-Christian Breit
    • 1
  • Laura M. Schreiber
    • 1
  1. 1.Section of Medical Physics, Department of RadiologyJohannes Gutenberg University Medical CenterMainzGermany

Personalised recommendations