Nonlinear Models of Coronary Flow Mechanics

  • Jos. A. E. Spaan


The coronary circulation is the vascular system that supplies the heart with blood and thereby with oxygen and substrates so it can performs its task. The task of the heart is elementary to life and cessation of its performance for only a few seconds will result in unconsciousness. Cessation of blood supply to the brain exceeding 2 to 3 minutes results in irreversible brain damage. The heart itself is also vulnerable to insufficient blood supply. The body is rather inconsiderate in its demand for perfusion and the circulatory control systems drive the heart to accommodate this demand. As a result there may be circumstances that coronary blood flow is not sufficient to deliver oxygen to the heart so it can perform its task. Mostly this is the case as a result of a disease process that either reduces the upper limit of blood supply as in atheroscleroses or increases the mass of the heart to an extent that the demands for oxygen can not sufficiently be met as in hypertrophy.


Coronary Flow Coronary Blood Flow Left Ventricular Pressure Cardiac Contraction Smooth Muscle Tone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Armour, J.A., and Randall, W.C. 1995, Canine left ventricular intramyocardial pressures. Am J Physiol 220: 1833–1839.Google Scholar
  2. 2.
    Armour, J.P., and Randall, W.C. 1971, Canine left ventricular intramyocardial pressure. Am J Physiol 220: 1833–1839.PubMedGoogle Scholar
  3. 3.
    Arts, T., and Reneman, R.S. 1985, Interaction between intramyocardial pressure (IMP) and myocarcial circulation. J Biomed Eng 107: 51–56.Google Scholar
  4. 4.
    Arts, T., Veenstra, P.C., and Reneman, R.S. 1982, Epicardial deformation and left ventricular wall mechanics during ejection in the dog. Am J Physiol 243: H379–H390.PubMedGoogle Scholar
  5. 5.
    Bache, R.J., and Cobb, F.R. 1977, Effect of maximal coronary vasodilation on transmural myocardial perfusion during tachycardia in the awake dog. Circ Res 41: 648–653.PubMedCrossRefGoogle Scholar
  6. 6.
    Baez, S., Feldman, S.M., and Gootman, P.M. 1977, Central neural influence on precapillary microvessels and sphincter. Am J Physiol 233: H141–H147.PubMedGoogle Scholar
  7. 7.
    Baird, R.J., Goldbach, M.M., and de la Rocha, A. 1972, Intramyocardial pressure: the persistence of its transmural gradient in the empty heart and its relationship to myocardial oxygen consumption. J Thorac Cardiovasc Surg 64: 635–646.PubMedGoogle Scholar
  8. 8.
    Bellamy, R.F. 1978, Diastolic coronary pressure-flow relations in the dog. Circ Res 43: 92–101.PubMedCrossRefGoogle Scholar
  9. 9.
    Borg, T.K., and Caulfield, J.B. 1981, The collagen matrix of the heart. Federation Proceedings 40: 2037–2041.PubMedGoogle Scholar
  10. 10.
    Bouma, P., Sipkema, P., and Westerhof, N. 1993, Coronary arterial inflow impediment during systole is little affected by capacitive effects. Am J Physiol Heart Circ Physiol 264: H715–H721.Google Scholar
  11. 11.
    Brace, R.A., and Guyton, A.C. 1979, Interstitial fluid pressure: capsule, free fluid, gel fluid, and gel absorption pressure in subcutaneous tissue. Microvasc Res 18: 217–228.PubMedCrossRefGoogle Scholar
  12. 12.
    Bruinsma, P., Arts, T., Dankelman, J., and Spaan, J.A.E. 1988, Model of the coronary circulation based on pressure dependence of coronary resistance and compliance. Basic Res Cardiol 83: 510–524.PubMedCrossRefGoogle Scholar
  13. 13.
    Canty, J.M.J., Klocke, F.J., and Mates, R.E. 1985, Characterization of capacitance-free pressure—flow relations during single diastoles in dogs using an RC model with pressure-dependent parameters Pressure and tone dependence of coronary diastolic input impedance and capacitance. Circ Res 248: H700–H711.Google Scholar
  14. 14.
    Canty, J.M.J., Klocke, F.J., and Mates, R.E. 1985, Pressure and tone dependence of coronary diastolic input impedance and capacitance. Am J Physiol 248: H700–H711.PubMedGoogle Scholar
  15. 15.
    Caulfield, J.B., and Borg, T.K. 1979, The Collagen Network of the Heart. Lab Invest 40, No.3: 364–372.PubMedGoogle Scholar
  16. 16.
    Chan, C, Wentzel, J., Spaan, J.A.E. 1995, Tissue thickness is a measure of coronary vascular volume in canine interventricular septa. Federation Proceedings A4910[Abstract].Google Scholar
  17. 17.
    Chilian, W.M., and Marcus, M.L. 1982, Phasic coronary flow velocity in intramural and epicardial coronary arteries. Circ Res 50: 775–781.PubMedCrossRefGoogle Scholar
  18. 18.
    Chilian, W.M., and Marcus, M.L. 1984, Coronary venous outflow persists after cessation of coronary arterial inflow. Am J Physiol 247: H984–H990.PubMedGoogle Scholar
  19. 19.
    Cornelissen, J.M., Chan, C., Wentzel, J., et al. 1995, Pressure dependence of transfer functions between coronary vascular pressure, flow and volume. Federation Proceedings A4914[Abstract].Google Scholar
  20. 20.
    Dole, W.P., and Bishop, V.S. 1982, Influence of autoregulation and capacitance on diastolic coronary artery pressure-flow relationships in the dog. Circ Res 51: 261–270.PubMedCrossRefGoogle Scholar
  21. 21.
    Domenech, R.J. 1978, Regional diastolic coronary blood flow during diastolic ventricular hypertension. Cardiovasc Res 12: 639–645.PubMedCrossRefGoogle Scholar
  22. 22.
    Doucette, J.W., Goto, M., Flynn, A.E., Austin, R.E., Jr., Husseini, W.K., and Hoffman, J.I.E. 1993, Effects of cardiac contraction and cavity pressure on myocardial blood flow. Am J Physiol Heart Circ Physiol 265:H1342–H1352.Google Scholar
  23. 23.
    Downey, J.M., and Kirk, E.S. 1975, Inhibition of coronary blood flow by a vascular waterfall mechanism. Circ Res 36: 753–760.PubMedCrossRefGoogle Scholar
  24. 24.
    Eng, C, Jentzer, J.H., and Kirk, E.S. 1981, Coronary capacitive effects on estimates of diastolic critical closing pressures. Basic Res Cardiol 76: 559–563.PubMedCrossRefGoogle Scholar
  25. 25.
    Feigl, E.O. 1983, Coronary physiology. Circ 63: 1–205.Google Scholar
  26. 26.
    Gregg, D.E., and Green, H.D. 1940, Registration and interpretation of normal phasic inflow into a left coronary artery by an improved differential manometric method. Am J Physiol 130: 114–125.Google Scholar
  27. 27.
    Han, Y., Vergroesen, I., Goto, M., Dankelman, J., van der Ploeg, C.P.B., and Spaan, J.A.E. 1993, Left ventricular pressure transmission to myocardial lymph vessels is different during systole and diastole. Pflügers Arch 423: 448–454.PubMedCrossRefGoogle Scholar
  28. 28.
    Han, Y., Vergroesen, I., and Spaan, J.A.E. 1993, Stopped flow epicardial lymph pressure is affected by left ventricular pressure in anesthetized goats. Am J Physiol (Heart Circ Physiol) 264: H1624–H1628.Google Scholar
  29. 29.
    Hanley, F.L., Messina, L.M., Grattan, M.T., and Hoffman, J.I.E. 1984, The effect of coronary inflow pressure on coronary vascular resistance in the isolated dog heart. Circ Res 760-772.Google Scholar
  30. 30.
    Heineman, F.W., and Grayson, J. 1985, Transmural distribution of intramyocardial pressure measured by micropipette technique. Am J Physiol 249: H1216–H1223.PubMedGoogle Scholar
  31. 31.
    Hiramatsu, O., Goto, M., Yada, T., Kimura, A., Tachibana, H., Ogasawara, Y., Tsujioka, K., and Kajiya, F. 1994, Diameters of subendocardial arterioles and venules during prolonged diastole in canine left ventricles. Circ Res 75: 393–399.PubMedCrossRefGoogle Scholar
  32. 32.
    Hoffman, J.I.E. 1984, Maximal coronary flow and the concept of coronary vascular reserve. Circ 70: 153–159.CrossRefGoogle Scholar
  33. 33.
    Hoffman, J.I.E. 1987, A critical view of coronary reserve. Circ 75 Suppl I: 6–11.Google Scholar
  34. 34.
    Hoffman, J.I.E., and Spaan, J.A.E. 1990, Pressure-flow relations in coronary circulation. Physiol Rev 70: 331–389.PubMedGoogle Scholar
  35. 35.
    Judd, R.M., Resar, J.R., and Yin, F.C.P. 1993, Rapid measurements of diastolic intramyocardial vascular volume. Am J Physiol 265: H1038–H1047.PubMedGoogle Scholar
  36. 36.
    Kajiya, F., Tsujioka, K., Goto, M., Wada, Y., Chen, X.L., Nakai, M., Tadaoka, S., Hiramatsu, O., Ogasawara, Y., Mito, K., et al. 1986, Functional characteristics of intramyocardial capacitance vessels during diastole in the dog. Circ Res 58: 476–485.PubMedCrossRefGoogle Scholar
  37. 37.
    Kajiya, F., Yada, T., Kimura, A., Hiramatsu, O., Goto, M., Ogasawara, Y., and Tsujioka, K. 1993, Endocardial coronary microcirculation of the beating heart. Adv Exp Med Biol 346: 173–180.PubMedCrossRefGoogle Scholar
  38. 38.
    Katz, S.A., and Feigl, E.O. 1988, Systole has little effect on diastolic coronary blood flow. Circ Res 62: 443–451.PubMedCrossRefGoogle Scholar
  39. 39.
    Klocke, F.J., Mates, R.E., Canty, J.M.J., and Edit, A.K. 1985, Response to the article by Spaan on ‘Coronary diastolic pressure-flow relation and zero flow pressure explained on the basis of intramyocardial compliance’ (Circ. Res. 56: 293-309,1985). Circ Res 56: 791–792.Google Scholar
  40. 40.
    Klocke, F.J., Mates, R.E., Canty, J.M.J., and Eclit, A.K. 1985, Coronary pressure-flow relationships. Controversial issues and probable implications. Circ Res 56: 310–323.PubMedCrossRefGoogle Scholar
  41. 41.
    Kouwenhoven, E., Vergroesen, I., Han, Y, and Spaan, J.A.E. 1992, Retrograde coronary flow is limited by time-varying elastance. Am J Physiol 263: H484–H490.PubMedGoogle Scholar
  42. 42.
    Krams, R., Sipkema, P., and Westerhof, N. 1989, Can coronary systolic-diastolic flow difference be predicted by left ventricular pressure of time varying intramyocardial elastance? Basic Res Cardiol 84: 149–159.PubMedCrossRefGoogle Scholar
  43. 43.
    Krams, R., Sipkema, P., and Westerhof, N. 1989, The varying elastance concept may explain coronary systolic flow impediment. Am J Physiol 257: H1471–H1479.PubMedGoogle Scholar
  44. 44.
    Krams, R., Sipkema, P., and Westerhof, N. 1990, Coronary oscillatory flow amplitude is more affected by perfusion pressure than ventricular pressure. Am J Physiol 258: H1889–H1898.PubMedGoogle Scholar
  45. 45.
    Krams, R., Sipkema, P., Zegers, J., and Westerhof, N. 1989, Contractility is the main determinant of coronary systolic flow impediment. Am J Physiol 257: H1936–1944.PubMedGoogle Scholar
  46. 46.
    Lee, J., Chambers, D.E., Akizuki, S., and Downey, J.M. 1984, The role of vascular capacitance in the coronary arteries. Circ Res 55: 751–762.PubMedCrossRefGoogle Scholar
  47. 47.
    Meer, J. J. v., Reneman, R.S., Schneider, H., and Wieberdink, J. 1970, A technique for estimation of intramyocardial pressure in acute and chronic experiment. Cardiovasc Res IV: 132–140.CrossRefGoogle Scholar
  48. 48.
    Permuti, S., and Riley, R.L. 1963, Hemodynamics of collapsible vessels with tone: the vascular waterfall. J Appl Physiol 18:924–932.Google Scholar
  49. 49.
    Rabbany, S.Y., Kresh, J.Y., and Noordergraaf, A. 1989, Intramyocardial pressure interaction of myocardial fluid pressure and fiber stress. Am J Physiol 257: H357–H364.PubMedGoogle Scholar
  50. 50.
    Sabiston, D. C. j., and Gregg, D.E. 1957, Effect of cardiac contraction on coronary blood flow. Circ 15: 14–20.CrossRefGoogle Scholar
  51. 51.
    Salisbury, P.F., Cross, C.E., and Rieben, P.A. 1962, Intramyocardial pressure and strength of left ventricular contraction. Circ Res 10: 608–623.PubMedCrossRefGoogle Scholar
  52. 52.
    Scaramucci, J. 1695, De motu cordis, theorema sextum. in: Theoremata familiaria de physico-medicus lucubrationibus Iucta leges mecanicas, Anonymous.Google Scholar
  53. 53.
    Scharf, S.M., Bromberger-Barnea, B., and Permuti, S. 1971, Distribution of coronary venous flow. J Appl Physiol 30: 657–662.PubMedGoogle Scholar
  54. 54.
    Spaan, J.A.E. 1985, Coronary diastolic pressure-flow relation and zero flow pressure explained on the basis of intramyocardial compliance. Circ Res 56: 293–309.PubMedCrossRefGoogle Scholar
  55. 55.
    Spaan, J.A.E. 1985, Response to the article by Klocke et al. on “Coronary pressure-flow relationships: controversial issues and probable implications” (Circ.Res. 56: 310-323, 1985). Circ Res 56: 789–792.PubMedCrossRefGoogle Scholar
  56. 56.
    Spaan, J.A.E. 1991, Interaction between contraction and coronary flow: Theory. 6, in: Coronary blood flow; Mechanics, Distribution, and Control.; Spaan JAE. editors.Dordrecht/Boston/London: Kluwer Academic Publishers, p. 131–62.CrossRefGoogle Scholar
  57. 57.
    Spaan, J.A.E. 1991, Interaction between contraction and coronary flow: Experiment. 7, in: Coronary blood flow; Mechanics, Distribution, and Control.; Spaan JAE. editors.Dordrecht/Boston/London: Kluwer Academic Publishers, p. 163–92.CrossRefGoogle Scholar
  58. 58.
    Spaan, J.A.E. 1995, Mechanical determinants of myocardial perfusion. Basic Res Cardiol 90: 89–102.PubMedCrossRefGoogle Scholar
  59. 59.
    Spaan, J.A.E., Breuls, N.P.W., and Laird, J.D. 1981, Forward coronary flow normally seen in systole is the result of both forward and concealed back flow. Basic Res Cardiol 76: 582–586.PubMedCrossRefGoogle Scholar
  60. 60.
    Spaan, J.A.E., Breuls, N.P.W., and Laird, J.D. 1981, Diastolic-systolic coronary flow differences are caused by intramyocardial pump action in the anesthetized dog. Circ Res 49: 584–593.PubMedCrossRefGoogle Scholar
  61. 61.
    Suga, H., Sagawa, K., and Shoukas, A.A. 1973, Load independence of the instanteneous pressure-volume ratio of the canine left ventricle and effects of epiniphrine and heart rate on the ratio. Circ Res 32:314–322.PubMedCrossRefGoogle Scholar
  62. 62.
    Tomonaga, G., Tsujioka, K., Ogasawara, Y., et al. 1984, Dynamic Characteristics of diastolic pressure-flow relation in the canine coronary artery. in: The Coronary Sinus.; Mohl W. Wolner E, and Glogar D, editors. Darmstadt: Steinkopff Verlag, p. 79–85.CrossRefGoogle Scholar
  63. 63.
    Uhlig, P.N., Baer, R.W., Vlahakes, G.J., Hanley, F.L., Messina, L.M., and Hoffman, J.I.E. 1984, Arterial and venous coronary pressure-flow relations in anesthetized dogs. Evidence for a vascular waterfall in epicardial coronary veins. Circ Res 55: 238–248.PubMedCrossRefGoogle Scholar
  64. 64.
    Van Winkle, D.M., Swafford, A.N., and Downey, J.M. 1991, Subendocardial coronary compression in beating dog hearts is independent of pressure in the ventricular lumen. Am J Physiol 261: H500–H505.PubMedGoogle Scholar
  65. 65.
    Vergroesen, I., Han, Y., Goto, M., and Spaan, J.A.E. 1994, Cardiac contraction and intramyocardial venous pressure generation in the anaesthetized dog. J Physiol London 480: 343–353.PubMedCentralPubMedGoogle Scholar
  66. 66.
    Vergroesen, I., Noble, M.I.M., and Spaan, J.A.E. 1987, Intramyocardial blood volume change in first moments of cardiac arrest in anesthetized goats. Am J Physiol 253: H307–H316.PubMedGoogle Scholar
  67. 67.
    Watanabe, J., Levine, M.J., Bellotto, F., Johnson, R.G., and Grossman, W. 1990, Effects of coronary venous pressure on left ventricular diastolic distensibility. Circ Res 67: 923–932.PubMedCrossRefGoogle Scholar
  68. 68.
    Watanabe, J., Maruyama, Y, Satoh, S., Keitoku, M., and Takashima, T. 1987, Effects of the pericardium on the diastolic left coronary pressure-flow relationship in the isolated dog heart. Circ 75: 670–675.CrossRefGoogle Scholar
  69. 69.
    Westerhof, N. 1990, Physiological hypotheses-Intramyocardial pressure. A new concept, suggestions for measurement. Basic Res Cardiol 85: 105–119.PubMedCrossRefGoogle Scholar
  70. 70.
    Wüsten, B., Buss, D.D., Deist, H., and Schaper, W. 1977, Dilatory capacity of the coronary circulation and its correlation to the arterial vasculature in the canine left ventricle. Basic Res Cardiol 72: 636–650.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Jos. A. E. Spaan
    • 1
  1. 1.Deparment of Medical Physics Academic Medical CenterUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations