Annals of Biomedical Engineering

, Volume 42, Issue 4, pp 797–811 | Cite as

Multi-Scale Parameterisation of a Myocardial Perfusion Model Using Whole-Organ Arterial Networks

  • Eoin R. HydeEmail author
  • Andrew N. Cookson
  • Jack Lee
  • Christian Michler
  • Ayush Goyal
  • Taha Sochi
  • Radomir Chabiniok
  • Matthew Sinclair
  • David A. Nordsletten
  • Jos Spaan
  • Jeroen P. H. M. van den Wijngaard
  • Maria Siebes
  • Nicolas P. Smith


A method to extract myocardial coronary permeabilities appropriate to parameterise a continuum porous perfusion model using the underlying anatomical vascular network is developed. Canine and porcine whole-heart discrete arterial models were extracted from high-resolution cryomicrotome vessel image stacks. Five parameterisation methods were considered that are primarily distinguished by the level of anatomical data used in the definition of the permeability and pressure-coupling fields. Continuum multi-compartment porous perfusion model pressure results derived using these parameterisation methods were compared quantitatively via a root-mean-square metric to the Poiseuille pressure solved on the discrete arterial vasculature. The use of anatomical detail to parameterise the porous medium significantly improved the continuum pressure results. The majority of this improvement was attributed to the use of anatomically-derived pressure-coupling fields. It was found that the best results were most reliably obtained by using porosity-scaled isotropic permeabilities and anatomically-derived pressure-coupling fields. This paper presents the first continuum perfusion model where all parameters were derived from the underlying anatomical vascular network.


Cryomicrotome Anatomical vascular model Multi-compartment Darcy Perfusion Permeability 



The authors would like to acknowledge funding from the Engineering and Physical Sciences Research Council (EP/G007527/2) European Community’s Seventh Framework Program FP7-ICT Grant No. 224495: euHeart, the Wellcome Trust Medical Engineering Centre at King’s College London, the National University of Ireland (ERH), the Netherlands Heart Foundation Grant 2006B226 (JAS and MS). JvdW was supported by a Veni grant from the Netherlands Organization for Scientific Research (NWO 91611171).

Supplementary material

10439_2013_951_MOESM1_ESM.pdf (6.8 mb)
PDF (6961 kB)


  1. 1.
    Arts, M. A Mathematical Model of the Dynamics of the Left Ventricle and the Coronary Circulation. Ph.D. Thesis, Rijksuniversiteit Limburg, 1978.Google Scholar
  2. 2.
    Bear, J. Dynamics of Fluids in Porous Media. 2. New York: Courier Dover Publications, 1972.Google Scholar
  3. 3.
    Braakman, R., P. Sipkema, and N. Westerhof. A dynamic non-linear lumped parameter model for skeletal muscle circulation. Ann. Biomed. Eng. 17(6):593–616, 1989.PubMedCrossRefGoogle Scholar
  4. 4.
    Chapelle, D., J.-F. Gerbeau, J. Sainte-Marie, I. E. Vignon-Clementel. A poroelastic model valid in large strains with applications to perfusion in cardiac modeling. Comput. Mech. 46(1):91–101, 2009.CrossRefGoogle Scholar
  5. 5.
    Chapman, S. J., R. J. Shipley, and R. Jawad. Multiscale modeling of fluid transport in tumors. Bull. Math. Biol. 70(8):2334–2357, 2008.PubMedCrossRefGoogle Scholar
  6. 6.
    Chilian, W. M. W., C. L. Eastham, and M. L. Marcus. Microvascular distribution of coronary vascular resistance in beating left ventricle. Am. J. Physiol. Heart Circ. Physiol. 251:779–788, 1986.Google Scholar
  7. 7.
    Chilian, W. M. W., S. M. Layne, E. C. Klausner, C. L. Eastham, M. L. Marcus, C. Klausner, and C. Edward. Redistribution of coronary microvascular resistance produced by dipyridamole. J. Physiol. Heart Circ. Physiol. 256:383–390, 1989.Google Scholar
  8. 8.
    Cookson, A. N., J. Lee, C. Michler, R. Chabiniok, E. R. Hyde, D. A. Nordsletten, M. Sinclair, M. Siebes, and N. P. Smith. A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics. J. Biomech. 45(5):850–855, 2012.PubMedCentralPubMedCrossRefGoogle Scholar
  9. 9.
    Crick, S., M. Sheppard, S. Ho, L. Gebstein, and R. Anderson. Anatomy of the pig heart: comparisons with normal human cardiac structure. J. Anat. 193(Pt 1):105–119, 1998.Google Scholar
  10. 10.
    Dellsperger, K. C., D. L. Janzen, C. L. Eastham, and M. L. Marcus. Effects of acute coronary artery occlusion on the coronary microcirculation. Am. J. Physiol. Heart Circ. Physiol. 259:909–916, 1990.Google Scholar
  11. 11.
    Dijkstra, E. A note on two problems in connexion with graphs. Numer. Math. 1:269–271, 1959.Google Scholar
  12. 12.
    Fokkema, D. S., J. W. G. E. VanTeeffelen, S. Dekker, I. Vergroesen, J. B. Reitsma, and J. A. E. Spaan. Diastolic time fraction as a determinant of subendocardial perfusion. Am. J. Physiol. Heart Circ. Physiol. 288(5):H2450–H2456, 2005.PubMedCrossRefGoogle Scholar
  13. 13.
    Frangi, A., and W. Niessen. Multiscale vessel enhancement filtering. Med. Image Comput. Comput. Assist Interv. 1496:130–137, 1998.Google Scholar
  14. 14.
    Goyal, A., J. Lee, P. Lamata, V. Grau, J. P. H. M. van den Wijngaard, P. van Horssen, J. A. E. Spaan, M. Siebes, and N. P. Smith. Model-based vasculature extraction from optical fluorescence cryomicrotome images. IEEE TMI 32(1):56–72, 2013.Google Scholar
  15. 15.
    Horssen, P. V., J. P. H. M. van den Wijngaard, F. Nolte, I. Hoefer, R. Haverslag, J. A. E. Spaan, and M. Siebes. Extraction of coronary vascular tree and myocardial perfusion data from stacks of cryomicrotome images. In: FIMH, Vol. 5528, edited by N. Ayache, H. Delingette, and M. Sermesant. Berlin: Springer, 2009, pp. 486–494.Google Scholar
  16. 16.
    Huyghe, J. M., T. Arts, D. H. van Campen, R. S. Reneman. Porous medium finite element model of the beating left ventricle. Am. J. Physiol. Heart Circ. Physiol. 262(4):H1256–H1267, 1992.Google Scholar
  17. 17.
    Huyghe, J. M., and D. H. van Campen. Finite deformation theory of hierarchically arranged porous solids. II: constitutive behaviour. Int. J. Eng. Sci. 33(13):1873–1886, 1995.CrossRefGoogle Scholar
  18. 18.
    Hyde, E. R., C. Michler, J. Lee, A. N. Cookson, R. Chabiniok, D. A. Nordsletten, and N. P. Smith. Parameterisation of multi-scale continuum perfusion models from discrete vascular networks. Med. Biol. Eng. Comput. 51(5):557–570, 2013.PubMedCentralPubMedCrossRefGoogle Scholar
  19. 19.
    Kanatsuka, H., K. G. Lamping, C. L. Eastham, and M. L. Marcus. Heterogeneous changes in epimyocardial microvascular size during graded coronary stenosis. Evidence of the microvascular site for autoregulation. Circ. Res. 66(2):389–396, 1990.PubMedCrossRefGoogle Scholar
  20. 20.
    Kassab, G. S., J. Berkley, and Y. C. Fung. Analysis of pig’s coronary arterial blood flow with detailed anatomical data. Ann. Biomed. Eng. 25(1):204–217, 1997.PubMedCrossRefGoogle Scholar
  21. 21.
    Kassab, G. S., and Y. C. Fung. Topology and dimensions of pig coronary capillary network. Am. J. Physiol Heart Circ. Physiol. 267(6):H319–H25, 1994.Google Scholar
  22. 22.
    Kassab, G. S., D. H. Lin, and Y. C. Fung. Morphometry of pig coronary venous system. Am. J. Physiol. Heart Circ. Physiol. 267(6):H2100–H2113, 1994.Google Scholar
  23. 23.
    Lamata, P., S. Niederer, D. Nordsletten, D. C. Barber, I. Roy, D. R. Hose, and N. P. Smith. An accurate, fast and robust method to generate patient-specific cubic Hermite meshes. Med. Image Anal. 15(6):801–813, 2011.PubMedCrossRefGoogle Scholar
  24. 24.
    Lee, J., P. E. Beighley, E. L. Ritman, and N. P. Smith. Automatic segmentation of 3D micro-CT coronary vascular images. Med. Image Anal. 11(6):630–647, 2007.PubMedCrossRefGoogle Scholar
  25. 25.
    Lee, J., and N. P. Smith. Development and application of a one-dimensional blood flow model for microvascular networks. Proc. Inst. Mech. Eng., H J. Eng. Med. 222(4):487–512, 2008.CrossRefGoogle Scholar
  26. 26.
    Lee, J., and N. P. Smith. The multi-scale modelling of coronary blood flow. Ann. Biomed. Eng. 40(11):2399–2413, 2012.PubMedCentralPubMedCrossRefGoogle Scholar
  27. 27.
    Linninger, A., I. G. Gould, T. Marinnan, C.-Y. Hsu, M. Chojecki, and A. Alaraj. Cerebral microcirculation and oxygen tension in the human secondary cortex. Ann. Biomed. Eng. 41(11):2264–2284, 2013.Google Scholar
  28. 28.
    Maxwell, M. P., D. J. Hearse, and D. M. Yellon. Species variation in the coronary collateral circulation during regional myocardial ischaemia: a critical determinant of the rate of evolution and extent of myocardial infarction. Cardiovasc. Res. 21(10):737–746, 1987.PubMedCrossRefGoogle Scholar
  29. 29.
    Michler, C., A. N. Cookson, R. Chabiniok, E. R. Hyde, J. Lee, M. Sinclair, T. Sochi, A. Goyal, G. Vigueras, D. A. Nordsletten, and N. P. Smith. A computationally efficient framework for the simulation of cardiac perfusion using a multi-compartment Darcy porous-media flow model. Int. J. Numer. Methods Biomed. Eng. 29(2):217–232, 2013.CrossRefGoogle Scholar
  30. 30.
    Muehling, O., M. Jerosch-Herold, P. Panse, A. Zenovich, B. Wilson, R. Wilson, and N. Wilke. Regional heterogeneity of myocardial perfusion in healthy human myocardium: assessment with magnetic resonance perfusion imaging. J. Cardiovasc. Magn. Reson. 6(2):499–507, 2004.PubMedCrossRefGoogle Scholar
  31. 31.
    Otsu, N. A threshold selection method from gray-level histograms. Automatica 20(1):62–66, 1975.Google Scholar
  32. 32.
    Pries, A. R., T. W. Secomb, and P. Gaehtgens. Biophysical aspects of blood flow in the microvasculature. Cardiovasc. Res. 32(4):654–667, 1996.PubMedCrossRefGoogle Scholar
  33. 33.
    Pudney, C. Distance-ordered homotopic thinning: a skeletonization algorithm for 3D digital images. Comput. Vis. Image Underst. 72(3):404–413, 1998.CrossRefGoogle Scholar
  34. 34.
    Sands, G. B., D. A. Gerneke, D. A. Hooks, C. R. Green, B. H. Smaill, and I. J. Legrice. Automated imaging of extended tissue volumes using confocal microscopy. Microsc. Res. Tech. 67(5):227–239, 2005.PubMedCrossRefGoogle Scholar
  35. 35.
    Sauvola, J., and M. Pietikäinen. Adaptive document image binarization. Pattern Recogn. 33:225–236, 2000.CrossRefGoogle Scholar
  36. 36.
    Sellke, F. W., P. R. Myers, J. N. Bates, and G. Harrison. Influence of vessel size on the sensitivity of porcine coronary microvessels to nitroglycerin. Am. J. Physiol. Heart Circ. Physiol. 258:H515–H520, 1990.Google Scholar
  37. 37.
    Sherwin, S., V. Franke, J. Peiró, K. Parker. One-dimensional modelling of a vascular network in space–time variables. J. Eng. Math. 47(3/4):217–250, 2003.CrossRefGoogle Scholar
  38. 38.
    Shipley, R. J., and S. J. Chapman. Multiscale modelling of fluid and drug transport in vascular tumours. Bull. Math. Biol. 72(6):1464–1491, 2010.PubMedCrossRefGoogle Scholar
  39. 39.
    Smith, N. P., A. J. Pullan, and P. J. Hunter. An anatomically based model of transient coronary blood flow in the heart. SIAM J. Appl. Math. 62(3):990–1018, 2001.CrossRefGoogle Scholar
  40. 40.
    Spaan, J. A. E., M. Siebes, R. Wee, C. Kolyva, H. Vink, D. S. Fokkema, G. Streekstra, 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
  41. 41.
    Taylor, C. A., and C. A. Figueroa. Patient-specific modeling of cardiovascular mechanics. Annu. Rev. Biomed. Eng. 11:109–134, 2009.PubMedCrossRefGoogle Scholar
  42. 42.
    van den Wijngaard, J. P. H. M., H. Schulten, P. van Horssen, R. D. Ter Wee, M. Siebes, M. J. Post, and J. A. E. Spaan. Porcine coronary collateral formation in the absence of a pressure gradient remote of the ischemic border zone. Am. J. Physiol. Heart Circ. Physiol. 300(5):H1930–H1977, 2011.PubMedCrossRefGoogle Scholar
  43. 43.
    Vankan, W. J., J. M. Huyghe, J. D. Janssen, A. Huson, and W. Schreiner. Finite element blood flow through biological tissue. Int. J. Eng. Sci. 35(4):375–385, 1997.CrossRefGoogle Scholar
  44. 44.
    Westerhof, N., C. Boer, R. R. Lamberts, and P. Sipkema. Cross-talk between cardiac muscle and coronary vasculature. Physiol. Rev. 86(4):1263–1308, 2006.PubMedCrossRefGoogle Scholar
  45. 45.
    Wüsten, B., D. D. Buss, H. Deist, and W. Schaper. Dilatory capacity of the coronary circulation and its correlation to the arterial vasculature in the canine left ventricle. Basic Res. Cardiol. 72(6):636–650, 1977.PubMedCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2013

Authors and Affiliations

  • Eoin R. Hyde
    • 1
    Email author
  • Andrew N. Cookson
    • 2
  • Jack Lee
    • 2
  • Christian Michler
    • 2
  • Ayush Goyal
    • 2
  • Taha Sochi
    • 2
  • Radomir Chabiniok
    • 2
  • Matthew Sinclair
    • 2
  • David A. Nordsletten
    • 2
  • Jos Spaan
    • 3
  • Jeroen P. H. M. van den Wijngaard
    • 3
  • Maria Siebes
    • 3
  • Nicolas P. Smith
    • 2
  1. 1.Department of Computer ScienceUniversity of OxfordOxfordUK
  2. 2.Imaging Sciences & Biomedical Engineering Division, St Thomas’ HospitalKing’s College LondonLondonUK
  3. 3.Department of Biomedical Engineering and Physics, Academic Medical CentreUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations