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Modeling the Heart and the Circulatory System pp 51–96Cite as

Multiscale Modelling of Cardiac Perfusion

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Part of the book series: MS&A ((MS&A,volume 14))

Abstract

To elucidate the mechanisms governing coronary blood flow in health and disease requires an understanding of the structure—function relationship of the coronary system, which exhibits distinct characteristics over multiple scales. Given the complexities arising from the multiscale and distributed nature of the coronary system and myocardial mechanical coupling, computational modelling provides an indispensable tool for advancing our understanding. In this work, we describe our strategy for an integrative whole-organ perfusion model, and illustrate a series of examples which apply the framework within both basic science and clinical translation settings. In particular, the one-dimensional reduced approach common in vascular modelling is combined with a new poromechanical formulation of the myocardium that is capable of reproducing the full contractile cycle, to enable simulation of the dynamic coronary and myocardial blood flow. In addition, a methodology for estimating continuum porous medium parameters from discrete network geometry is presented. The benefit of this framework is first demonstrated via an application to coronary wave intensity analysis, a technique developed to study time-dependent aspects of pulse waves invasively measured in the vessels. It is shown that, given experimentally-acquired boundary conditions the 1D model is capable of reproducing a wave behaviour broadly consistent with that observed in vivo, however, its utility is limited to a phenomenological level. The integrated 1D-poromechanical model on the other hand enables a mechanistic investigation of wave generation thus allowing the influence of contractile function and distal hemodynamic states on coronary flow to be described. In addition, when coupled with the advection-diffusion-reaction equation, the integrated model can be used to study the transport of tracers through the vascular network, thus allowing the dependence of noninvasive imaging signal intensities on the diffusive properties of the contrast agent to be quantified. A systematic investigation of the commonly used clinical indices and whole-organ modelling results are illustrated. Taken together, the proposed model provides a comprehensive framework with which to apply quantitative analysis in whole organ coronary artery disease diagnosis using noninvasive perfusion imaging modalities. The added value of the model in clinical practice lies in its ability to combine comprehensive patient-specific information into therapy. In this regard, we close the chapter with a discussion on potential model-aided strategies of disease management.

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References

  1. Aguado-Sierra, J., Parker, K., Davies, J., Francis, D., Hughes, A., Mayer, J.: Arterial pulse wave velocity in coronary arteries. EMBS Annual International Conference, pp. 867–870 (2006)

    Google Scholar 

  2. Ambrosi, D., Quarteroni, A., Rozza, G.: Modeling of Physiological Flows, Springer, Milan (2012)

    Book  Google Scholar 

  3. Anrep, G.V., Saalfeld, E.V.: The effect of the cardiac contraction upon the coronary flow. J. Physiol. 79(3), 31–331 (1933)

    Article  Google Scholar 

  4. Aquaro, G.D., Todiere, G., Di Bella, G., Guiducci, L., Pingitore, A., Lionetti, V.: A fast and effective method of quantifying myocardial perfusion by magnetic resonance imaging. Int. J. Cardiovasc. Imaging. 29(6), 1313–1324 (2013)

    Article  Google Scholar 

  5. Barnard, A., Hunt, W., Timlake, W., Varley, E.: A theory of fluid flow in compliant tubes. Biophysical Journal 6(6) (1966)

    Google Scholar 

  6. J. Bear. Dynamics of Fluids in Porous Media. Number 2. Courier Dover Publications, (Aug. 1972)

    Google Scholar 

  7. Beaudoin, A., Dreuzy, J.-R., Erhel, J.: An efficient parallel particle tracker for advection-diffusion simulations in heterogeneous porous media, in: Kermarrec, A.-M., Bougé, L., Priol, T. (eds.): Euro-Par 2007 Parallel Processing, Lecture Notes in Computer Science 4641, pp. 717–726, Springer, Berlin Heidelberg (2007)

    Google Scholar 

  8. Beller, G.A., Zaret, B.L.: Contributions of nuclear cardiology to diagnosis and prognosis of patients with coronary artery disease, Circulation 101, 1465–1478 (2000)

    Article  Google Scholar 

  9. Bertoglio, C., Barber, D., Gaddum, N., Valverde, I., Rutten, M., Beerbaum, P., Moireau, P., Hose, R., Gerbeau, J.-F.: Identification of artery wall stiffness: in vitro validation and in vivo results of a data assimilation procedure applied to a 3D fluid-structure interaction model. J. Biomech. 47(5), 1027–1034 (2014)

    Article  Google Scholar 

  10. Bertoglio, C., Moireau, P., Gerbeau, J.-F.: Sequential parameter estimation in fluid-structure problems. Application to hemodynamics. Int. J. Num. Meth. Biomed. Eng. 28, 434–455 (2012)

    Article  MathSciNet  Google Scholar 

  11. Bessems, D., Giannopapa, C.G., Rutten, M.C.M., van de Vosse, F.N.: Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels. J. Biomech. 41(2), 284–291 (2008)

    Article  Google Scholar 

  12. Bishop, A.H., Samady, H.: Fractional flow reserve: Critical review of an important physiologic adjunct to angiography, American Heart Journal 147(5), 792–802 (2004)

    Article  Google Scholar 

  13. Bruinsma, P., Arts, T., Dankelman, J., Spaan, J.: Model of the coronary circulation based on pressure dependence of coronary resistance and compliance. Basic Research in Cardiology 83(5), 510–524 (1988)

    Article  Google Scholar 

  14. Caruel, M., Chabiniok, R., Moireau, P., Lecarpentier, Y., Chapelle, D.: Dimensional reductions of a cardiac model for effective validation and calibration, Biomechanics and Modeling in Mechanobiology (2013), in press

    Google Scholar 

  15. Chabiniok, R., Moireau, P., Lesault, P.-F., Rahmouni, A., Deux, J.-F., Chapelle, D.: Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model, Biomechanics and modeling in mechanobiology 11(5), 609–30 (2012)

    Article  Google Scholar 

  16. Chapelle, D., Fragu, M., Mallet, V., Moireau, P.: Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart, Medical & Biological Engineering & Computing (2013)

    Google Scholar 

  17. Chapelle, D., Gerbeau, J.-F., Sainte-Marie, J., Vignon-Clementel, I.: A poroelastic model valid in large strains with applications to perfusion in cardiac modeling, Computational Mechanics 46(1), 91–101 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  18. Chilian, W.M., Layne, S.M., Klausner, E.C., Eastham, C.L., Marcus, M.L.: Redistribution of coronary microvascular resistance produced by dipyridamole. American Journal of Physiology — Heart and Circulatory Physiology 256, H383–H390 (1989)

    Google Scholar 

  19. Chiribiri, A., Schuster, A., Ishida, M., Hautvast, G., Zarinabad, N., Morton, G., Otton, J., Plein, S., Breeuwer, M., Batchelor, P., Schaeffter, T., Nagel, E.: Perfusion phantom: An efficient and reproducible method to simulate myocardial first-pass perfusion measurements with cardiovascular magnetic resonance, Magnetic Resonance in Medicine 69(3), 698–707 (2013)

    Article  Google Scholar 

  20. Cookson, A.N., Lee, J., Michler, C., Chabiniok, R., Hyde, E., Nordsletten, D., Smith, N.P.: A spatially-distributed computational model to quantify behaviour of contrast agents in MR perfusion imaging. Medical Image Analysis, (in review) (2013)

    Google Scholar 

  21. Cookson, A.N., Lee, J., Michler, C., Chabiniok, R., Hyde, E.R., Nordsletten, D.A., Sinclair, M., Siebes, M., Smith, N.P.: A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics, J. Biomech. 45(5), 850–855 (2012)

    Article  Google Scholar 

  22. Corrado, C., Gerbeau, J., Moireau, P.: Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiology, J. Computational Physics (in review) (2014)

    Google Scholar 

  23. Coussy, O.: Mechanics of porous continua. Wiley (1995)

    Google Scholar 

  24. Coussy, O.: Poromechanics. Wiley (2004)

    Google Scholar 

  25. Davies, J.E., Whinnett, Z.I., Francis, D.P., Manisty, C.H., Aguado-Sierra, J., Willson, K., Foale, R., Malik, I.S., Hughes, A.D., Parker, K.H., Mayet, J.: Evidence of a dominant backward-propagating “suction” wave responsible for diastolic coronary filling in humans, attenuated in left ventricular hypertrophy, Circulation, 113(14), 1768–78 (2006)

    Article  Google Scholar 

  26. De Silva, K., Foster, P., Guilcher, A., Bandara, A., Jogiya, R., Lockie, T., Chowiencyzk, P., Nagel, E., Marber, M., Redwood, S., Plein, S., Perera, D.: Coronary Wave Energy: A Novel Predictor of Functional Recovery After Myocardial Infarction, Circulation. Cardiovascular interventions (March 2013)

    Google Scholar 

  27. Dormieux, L., Kondo, D., Ulm, F.-J.: Microporomechanics, Wiley (2004)

    Google Scholar 

  28. Escaned, J.: Imaging: Can FFRCT replace old indices of coronary stenosis severity? Nature Reviews Cardiology (2014)

    Google Scholar 

  29. Factor, S.M., Okun, E.M., Minase, T., Kirk, E.S.: The microcirculation of the human heart: end-capillary loops with discrete perfusion fields, Circulation, 66(6), 1241–1248 (1982)

    Article  Google Scholar 

  30. Federico, S., Grillo, A.: Elasticity and permeability of porous fibre-reinforced materials under large deformations, Mechanics of Materials 44, 58–71 (2012)

    Article  Google Scholar 

  31. Fischer, J.J., Samady, H., McPherson, J.A., Sarembock, I.J., Powers, E.R., Gimple, L.W., Ragosta, M.: Comparison between visual assessment and quantitative angiography versus fractional flow reserve for native coronary narrowings of moderate severity, The American Journal of Cardiology 90, 210–215 (2002)

    Article  Google Scholar 

  32. Fiss, D.M.: Normal coronary anatomy and anatomic variations, Supplement to Applied Radiology, pp. 14–26 (2007)

    Google Scholar 

  33. Formaggia, L., Lamponi, D., Quarteroni, A.: One-dimensional models for blood flow in arteries, Journal of Engineering Mathematics (2002)

    Google Scholar 

  34. Formaggia, L., Nobile, F., Quarteroni, A., Veneziani, A.: Multiscale modelling of the circulatory system: a preliminary analysis, Computing and visualization in science 2(2–3), 75–83 (1999)

    Article  MATH  Google Scholar 

  35. Formaggia, L., Quarteroni, A., Veneziani, A.: Cardiovascular Mathematics: Modeling and simulation of the circulatory system, Springer, Milan (2009)

    Book  Google Scholar 

  36. Fulton, W.F.M.: Arterial anastomoses in the coronary circulation. i. anatomical features in normal and diseased hearts demonstrated by stereoarteriography, Scottish Med. J. 8, 420–434 (1963)

    Google Scholar 

  37. Gould, K.L., Kirkeeide, R.L., Buchi, M.: Coronary flow reserve as a physiologic measure of stenosis severity, JACC 15(2), 459–474 (1990)

    Article  Google Scholar 

  38. Gregg, D.E., Green, H.D.: Registration and interpretation of normal phasic inflow into the left coronary artery by an improved differential manometric method, Am. J. Physiol. 130, 114–125 (1940)

    Google Scholar 

  39. Hautvast, G.L.T.F., Chiribiri, A., Lockie, T., Breeuwer, M., Nagel, E., Plein, S.: Quantitative analysis of transmural gradients in myocardial perfusion magnetic resonance images. Magnetic Resonance in Medicine 66, 1477–1487 (2011)

    Article  Google Scholar 

  40. Helfant, R.H., Vokonas, P.S., Gorlin, R.: Functional importance of the human coronary collateral circulation, New England Journal of Medicine 284(23), 1277–1281 (1971)

    Article  Google Scholar 

  41. Holzapfel, G.A., Ogden, R.W.: Constitutive modelling of passive myocardium: a structurally based framework for material characterization, Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 367(1902), 3445–75 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  42. Hsu, L.-Y., Kellman, P., Arai, A.E.: Nonlinear myocardial signal intensity correction improves quantification of contrast-enhanced first-pass MR perfusion in humans, J. Magn. Reson. Imaging 27(4), 793–801 (2008)

    Article  Google Scholar 

  43. Hughes, T.J., Lubliner, J.: On the one-dimensional theory of blood flow in the larger vessels (1973)

    Google Scholar 

  44. Huyghe, J.M., Arts, T., van Campen, D.H., Reneman, R.S.: Porous medium finite element model of the beating left ventricle, American Journal of Physiology-Heart and Circulatory Physiology 262(4), H1256–H1267 (1992)

    Google Scholar 

  45. Huyghe, J.M., Van Campen, D.H.: Finite deformation theory of hierarchically arranged porous solids. I: Balance of mass and momentum, International J. Engineering Science 33(13), 1861–1871 (1995)

    Article  MATH  Google Scholar 

  46. Hyde, E.R., Cookson, A.N., Lee, J., Michler, C., Goyal, A., Sochi, T., Chabiniok, R., Sinclair, M., Nordsletten, D.A., Spaan, J., van den Wijngaard, J.P.H.M., Siebes, M., Smith, N.P.: Multi-Scale Parameterisation of a Myocardial Perfusion Model Using Whole-Organ Arterial Networks, Annals of biomedical engineering (Dec. 2013)

    Google Scholar 

  47. Hyde, E.R., Michler, C., Lee, J., Cookson, A.N., Chabiniok, R., Nordsletten, D.A., Smith, N.P.: Parameterisation of multi-scale continuum perfusion models from discrete vascular networks, Med. Biol. Eng. Comput. 51(5), 557–570 (2013)

    Article  Google Scholar 

  48. Imperiale, A., Chabiniok, R., Moireau, P., Chapelle, D.: Constitutive Parameter Estimation Using Tagged-MRI Data. In D.N. Metaxas and L. Axel, editors, FIMH’11 — Sixth International Conference on Functional Imaging and Modeling of the Heart, vol. 6666, pp. 409–417, Springer, New York (2011)

    Google Scholar 

  49. Ishida, M., Sakuma, H., Murashima, S., Nishida, J., Senga, M., Kobayasi, S., Takeda, K., Kato, N.: Absolute blood contrast concentration and blood signal saturation on myocardial perfusion MRI: Estimation from CT data, J. Magnetic Resonance Imaging 29(1), 205–210 (2009)

    Article  Google Scholar 

  50. Jogiya, R., Kozerke, S., Morton, G., De Silva, K., Redwood, S., Perera, D., Nagel, E., Plein, S.: Validation of dynamic 3-dimensional whole heart magnetic resonance myocardial perfusion imaging against fractional flow reserve for the detection of significant coronary artery disease, JACC 60(5), 756–765 (2012)

    Article  Google Scholar 

  51. Johnson, N.P., Kirkeeide, R.L., Gould, K.L.: Is discordance of coronary flow reserve and fractional flow reserve due to methodology or clinically relevant coronary pathophysiology? JACC Cardiovasc Imaging 5(2), 193–202 (2012)

    Article  Google Scholar 

  52. Judd, R.M., Levy, B.I.: Effects of barium-induced cardiac contraction on large- and small-vessel intramyocardial blood volume, Circulation Research 56(3), 293–309 (1985)

    Article  Google Scholar 

  53. Kajiya, F., Tomonaga, G., Tsujioka, K., Ogasawara, Y., Nishihara, H.: Evaluation of local blood flow velocity in proximal and distal coronary arteries by laser Doppler method, Journal of biomechanical engineering 107, 10–15 (1985)

    Article  Google Scholar 

  54. Kassab, G.S.: Scaling laws of vascular trees: of form and function, Am J Physiol., (2006) 290:H894–903

    Google Scholar 

  55. Kassab, G.S., Rider, C.A., Tang, N.J., Fung, Y.: Morphometry of pig coronary arterial trees. Am. J. Physiol. 265, 350–365 (1993)

    Google Scholar 

  56. Kerckhoffs, R., Bovendeerd, P., Prinzen, F., Smits, K., Arts, T.: Intra-and interventricular asynchrony of electromechanics in the ventricularly paced heart, J. Engineering Mathematics 47(3–4), 201–216 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  57. Kim, H.J., Vignon-Clementel, I.E., Coogan, J.S., Figueroa, C.A., Jansen, K.E., Taylor, C.A.: Patient-specific modeling of blood flow and pressure in human coronary arteries, Annals of Biomedical Engineering 38(10), 3195–209 (2010)

    Article  Google Scholar 

  58. Lee, J., Cookson, A., Roy, I., Kerfoot, E., Asner, L., Vigueras, G., Sochi, T.: C. Michler, N. Smith, and D. Nordsletten. Cheart: A multi-physics parallel computing engine, in prep.

    Google Scholar 

  59. Lee, J., Nordsletten, D., Cookson, A., Rivolo, S., Smith, N.: In silico coronary wave intensity analysis: cardiac function to wave generating mechanisms, J. Physiology, in review

    Google Scholar 

  60. Lee, J., Smith, N.: Development and application of a one-dimensional blood flow model for microvascular networks. Proceedings of the Institution of Mechanical Engineers, Part H, J. Engineering in Medicine 222, 487–511 (2008)

    Article  Google Scholar 

  61. Lee, J., Smith, N.P.: The Multi-Scale Modelling of Coronary Blood Flow, Annals of biomedical engineering (May 2012)

    Google Scholar 

  62. Zamir, H.C.M.: Branching characteristics of human coronary arteries, Can. J. Physiol. Pharmacol. 64, 661–668 (1986)

    Article  Google Scholar 

  63. Makowski, M.R., Henningsson, M., Spuentrup, E., Kim, W.Y., Maintz, D., Manning, W., Botnar, R.: Characterization of coronary atherosclerosis by magnetic resonance imaging, Circulation 128, 1244–1255 (2013)

    Google Scholar 

  64. Matthys, K.S., Alastruey, J., Peiró, J., Khir, A.W., Segers, P., Verdonck, P.R., Parker, K.H., Sherwin, S.J.: Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements, J. biomechanics 40(15), 3476–86 (2007)

    Article  Google Scholar 

  65. Meier, P., Gloekler, S., Zbinden, R., Beckh, S., de Marchi, S.F., Zbinden, S., Wustmann, K., Billinger, M., Vogel, R., Cook, S., Wenaweser, P., Togni, M., Windecker, S., Meier, B., Seiler, C.: Beneficial effect of recruitable collaterals a 10-year follow-up study in patients with stable coronary artery disease undergoing quantitative collateral measurements, Circulation 116(9), 975–983 (2007)

    Article  Google Scholar 

  66. Moireau, P., Bertoglio, C., Xiao, N., Figueroa, C.A., Taylor, C., Chapelle, D., Gerbeau, J.-F.: Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data, Biomechanics and Modeling in Mechanobiology 12(3), 475–496 (2012)

    Article  Google Scholar 

  67. Murray, S.W., Rathore, S., Stables, R.H., Palmer, N.D.: Contemporary coronary imaging from patient to plaque — part 1: IVUS-derived virtual histology, British J. Cardiology 17(3), 129–132 (2010)

    Google Scholar 

  68. Mynard, J.P., Nithiarasu, P.: A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method, Communications In Numerical Methods In Engineering, 367–417 (March 2008)

    Google Scholar 

  69. Mynard, J.P., Penny, D.J., Smolich, J.J.: Scalability and in-vivo validation of a multiscale numerical model of the left coronary circulation, American J. Physiology — Heart and Circulatory Physiology (2013)

    Google Scholar 

  70. Nagler, A., Bertoglio, C., Gee, M., Wall, W.: Personalization of cardiac fiber orientations from image data using the unscented kalman filter. In S. Ourselin, D. Rueckert, and N. Smith, editors, 7th International Conference on Functional Imaging and Modeling of the Heart, FIMH 2013, Lecture Notes in Computer Science 7945, pp. 132–140. Springer-Verlag, Berlin Heidelberg (2013)

    Google Scholar 

  71. Niederer, S.A., Plank, G., Chinchapatnam, P., Ginks, M., Lamata, P., Rhode, K.S., Rinaldi, C.A., Razavi, R., Smith, N.P.: Length-dependent tension in the failing heart and the efficacy of cardiac resynchronization therapy, Cardiovascular Research 89(2), 336–343 (2011)

    Article  Google Scholar 

  72. Nolte, F., Hyde, E.R., Rolandi, C., Lee, J., van Horssen, P., Asrress, K., van den Wijngaard, J.P.H.M., Cookson, A.N., van de Hoef, T., Chabiniok, R., Razavi, R., Michler, C., Hautvast, G.L.T.F., Piek, J.J., Breeuwer, M., Siebes, M., Nagel, E., Smith, N.P., Spaan, J.A.E.: Myocardial perfusion distribution and coronary arterial pressure and flow signals: clinical relevance in relation to multiscale modeling, a review, Med. Biol. Eng. Comput. 51(11), 1271–1286 (2013)

    Article  Google Scholar 

  73. Nørgaard, B.L., Leipsic, J., Gaur, S., Seneviratne, S., Ko, B.S., Ito, H., Jensen, J.M., Mauri, L., De Bruyne, B., Bezerra, H., et al.: Diagnostic performance of non-invasive fractional flow reserve derived from coronary ct angiography in suspected coronary artery disease: The NXT trial, J. American College of Cardiology (2014)

    Google Scholar 

  74. Obaid, D.R., Murray, S.W., Palmer, N.D., Rudd, J.H.F.: Contemporary coronary imaging from patient to plaque — part 3: cardiac computed tomography, British J. Cardiology 17(5), 235–239 (2010)

    Google Scholar 

  75. Olufsen, M.: Structured tree outflow condition for blood flow in larger systemic arteries, American J. Physiology — Heart and Circulatory Physiology (1999)

    Google Scholar 

  76. Parker, K.H.: An introduction to wave intensity analysis, Medical & biological engineering & computing 47(2), 175–88 (2009)

    Article  Google Scholar 

  77. Pedley, T.J.: The Fluid Mechanics of Large Blood Vessels (1980)

    Google Scholar 

  78. Pijls, N.H., van Son, J.A., Kirkeeide, R.L., De Bruyne,Gould, K.L.: Experimental basis of determining maximum coronary, B., myocardial, and collateral blood flow by pressure measurements for assessing functional stenosis severity before and after percutaneous transluminal coronary angioplasty, Circulation 87, 1354–1367 (1993)

    Article  Google Scholar 

  79. Pindera, M.Z., Ding, H., Athavale, M.M., Chen, Z.: Accuracy of 1D microvascular flow models in the limit of low Reynolds numbers, Microvascular research 77(3), 273–280 (2009)

    Article  Google Scholar 

  80. Prinzen Bassingthwaighte, J.B.: Blood flow distributions by microsphere deposition methods, F.W., Cardiovascular Research 45, 13–21 (2000)

    Article  Google Scholar 

  81. Radjenovic, A., Biglands, J.D., Larghat, A., Ridgway, J.P., Ball, S.G., Greenwood, J.P., Jerosch-Herold, M., Plein, S.: Estimates of systolic and diastolic myocardial blood flow by dynamic contrast-enhanced MRI, Magnetic Resonance in Medicine 64, 1696–1703 (2010)

    Article  Google Scholar 

  82. Rathore, S., Murray, S., Stables, R., Palmer, N.: From patient to plaque. contemporary coronary imaging, part 2: optical coherence tomography, British J. Cardiology 17(4), 190–193 (2010)

    Google Scholar 

  83. Reymond, P., Merenda, F., Perren, F., Rüfenacht, D., Stergiopulos, N.: Validation of a one-dimensional model of the systemic arterial tree, American J. Physiology, Heart and circulatory physiology 297(1), H208–222 (2009)

    Article  Google Scholar 

  84. Schuster, A., Grünwald, I., Chiribiri, A., Southworth, R., Ishida, M., Hay, G., Neumann, N., Morton,Perera, D., G., Schaeffter, T., Nagel, E.: An isolated perfused pig heart model for the development, validation and translation of novel cardiovascular magnetic resonance techniques, J. Cardiovascular Magnetic Resonance 12(53) (2010)

    Google Scholar 

  85. Sherwin, S., Formaggia, L., Peiro, J.: Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system, International J. Numerical Methods in Fluids 43, 673–700 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  86. Sherwin, S.J., Alastruey, J., Parker, K.H., Peir, J.: Lumped Parameter Outflow Models for 1-D Blood Flow Simulations: Effect on Pulse Waves and Parameter Estimation, Communications in Computational Physics 4(2), 317–336 (2008)

    MathSciNet  Google Scholar 

  87. Sherwin, S.J., Franke, V., Peir, J., Parker, K.H.: One-dimensional modelling of a vascular network in space-time variables, J. Engineering Mathematics 47, 217–250 (2003)

    Article  MATH  Google Scholar 

  88. R. Shipley and S. Chapman. Multiscale modelling of fluid and drug transport in vascular tumours, Bulletin of Mathematical Biology 72(6), 1464–1491 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  89. Smith, N.P., Pullan, A.J., Hunter, P.J.: An Anatomically Based Model of Transient Coronary Blood Flow in the Heart, SIAM J. Applied Mathematics 62(3), 990 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  90. Spaan, J.A.E.: Coronary diastolic pressure-flow relation and zero flow pressure explained on the basis of intramyocardial compliance, Circulation Research 56(3), 293–309 (1985)

    Article  Google Scholar 

  91. Spaan, J.A.E., Kolyva, C., van den Wijngaard, J.P.H.M., ter Wee, R., van Horssen, P., Piek, J.J., Siebes, M.: Coronary structure and perfusion in health and disease. Philosophical transactions, Series A, Mathematical, physical, and engineering sciences 366(1878), 3137–53 (2008)

    Article  Google Scholar 

  92. Spaan, J.A.E., Siebes, M., Wee, R., Kolyva, C., Vink, H., Fokkema, D.S., Streekstra, G., Vanbavel, E.: Visualisation of intramural coronary vasculature by an imaging cryomicrotome suggests compartmentalisation of myocardial perfusion areas, Med. Biol. Eng. Comput. 43, 43–435 (2005)

    Article  Google Scholar 

  93. Steele, B.N., Wan, J., Ku, J.P., Hughes, T.J.R., Taylor, C.A.: In vivo validation of a one-dimensional finite-element method for predicting blood flow in cardiovascular bypass grafts, IEEE Trans. Biomed. Eng. 50(6), 649–656 (2003)

    Article  Google Scholar 

  94. Stettler, J., Niederer, P., Anliker, M.: Theoretical analysis of arterial hemodynamics including the influence of bifurcations, Annals of Biomedical Engineering 9(2), 145–164 (1981)

    Article  Google Scholar 

  95. Taylor, C.A., Steinman, D.A.: Image-based modeling of blood flow and vessel wall dynamics: applications, methods and future directions, Annals of Biomedical Engineering 38(3), 1188–1203 (2010)

    Article  Google Scholar 

  96. Topol, J.E., Nissen, S.E.: Our preoccupation with coronary luminology, Circulation 92, 2333–2342 (1995)

    Article  Google Scholar 

  97. Toyota, E., Ogasawara, Y., Hiramatsu, O., Tachibana, H., Kajiya, F., Yamamori, S., Chilian, W.M.: Dynamics of flow velocities in endocardial and epicardial coronary arterioles, American Journal of Physiology-Heart and Circulatory Physiology 57(4), H1598 (2005)

    Google Scholar 

  98. Traupe, T., Gloekler, S., de Marchi, S.F., Werner, G.S., Seiler, C.: Assessment of the human coronary collateral circulation, Circulation 122(12), 1210–1220 (2010)

    Article  Google Scholar 

  99. van de Vosse, F.N., Stergiopulos, N.: Pulse Wave Propagation in the Arterial Tree, Annual Review of Fluid Mechanics 43(1), 467–499 (2011)

    Article  Google Scholar 

  100. van den Wijngaard, J.P.H.M., van Horssen, P., ter Wee, R., Coronel, R., de Bakker, J.M., de Jonge, N., Siebes, M., Spaan, J.A.E.: Organization and collateralization of a subendocardial plexus in end-stage human heart failure, American J. Physiology — Heart and circulatory physiology 298(1), H158–62 (2010)

    Article  Google Scholar 

  101. Vankan, W., Huyghe, J., Janssen, J.: Poroelasticity of saturated solids with an application to blood perfusion, Int. J. Eng. Sci. 34(9), 1019–1031 (1996)

    Article  MATH  Google Scholar 

  102. Vankan, W.J., Huyghe, J.M., Janssen, J.D., Huson, A., Schreiner, W.: Finite element blood flow through biological tissue, Int. J. Engng. Sci. 35(4), 375–385 (1997)

    Article  MATH  Google Scholar 

  103. Vignon, I., Taylor, C.: Outflow boundary conditions for one-dimensional finite element modeling of blood flow and pressure waves in arteries, Wave Motion 39(4), 361–374 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  104. Werner, G.S., Ferrari, M., Heinke, S., Kuethe, F., Surber, R., Richartz, B.M., Figulla, H.R.: Angiographic assessment of collateral connections in comparison with invasively determined collateral function in chronic coronary occlusions, Circulation 107(15), 1972–1977 (2003)

    Article  Google Scholar 

  105. Westerhof, N., Boer, C., Lamberts, R., Sipkema, P.: Cross-talk between cardiac muscle and coronary vasculature, Physiol. Rev. 86, 1263–1308 (2006)

    Article  Google Scholar 

  106. Westerhof, N., Lankhaar, J.-W., Westerhof, B.: The arterial windkessel, Medical & Biological Engineering & Computing 47(2), 131–141 (2009)

    Article  Google Scholar 

  107. Willemet, M., Lacroix, V., Marchandise, E.: Inlet boundary conditions for blood flow simulations in truncated arterial networks, J. Biomechanics 44(5), 897–903 (2011)

    Article  Google Scholar 

  108. Xi, J., Lamata, P., Lee, J., Moireau, P., Chapelle, D., Smith, N.: Myocardial transversely isotropic material parameter estimation from in-silico measurements based on reduced-order unscented Kalman filter, J. mechanical behavior of biomedical materials 4(7), 1090–1102 (2011)

    Article  Google Scholar 

  109. Xi, J., Lamata, P., Shi, W., Niederer, S., Land, S., Rueckert, D., Duckett, S.G., Shetty, A.K., Rinaldi, C.A., Razavi, R., Smith, N.: An Automatic Data Assimilation Framework for Patient-Specific Myocardial Mechanical Parameter Estimation, in: Metaxas, D.N., Axel, L. (eds.), FIMH’11 — Sixth International Conference on Functional Imaging and Modeling of the Heart, vol. 6666, pp. 392–400, Springer, New York (2011)

    Google Scholar 

  110. Zamir, M.: Cost analysis of arterial branching in the cardiovascular systems of man and animals, J. Theor. Biol. 120, 111–23 (1986)

    Article  Google Scholar 

  111. Zarinabad, N., Chiribiri, A., Breeuwer, M.: Myocardial blood flow quantification from MRI — an image analysis perspective, Current Cardiovascular Imaging Reports 7(1), 1–9 (2014)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King’s College London, King’s Health Partners, St. Thomas’ Hospital, London, SE1 7EH, UK

    Jack Lee, Andrew Cookson, Radomir Chabiniok, Simone Rivolo, Eoin Hyde, Matthew Sinclair, Christian Michler & Taha Sochi

  2. Faculty of Engineering, The University of Auckland, Auckland, New Zealand

    Nicolas Smith

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  1. Jack Lee
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  2. Andrew Cookson
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  3. Radomir Chabiniok
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  4. Simone Rivolo
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  5. Eoin Hyde
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  6. Matthew Sinclair
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  7. Christian Michler
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  8. Taha Sochi
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  9. Nicolas Smith
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Correspondence to Nicolas Smith .

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  1. École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Alfio Quarteroni

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Lee, J. et al. (2015). Multiscale Modelling of Cardiac Perfusion. In: Quarteroni, A. (eds) Modeling the Heart and the Circulatory System. MS&A, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-05230-4_3

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