Advertisement

Structure–Function Relations in the Coronary Vasculature

  • Benjamin Kaimovitz
  • Yunlong Huo
  • Yoram Lanir
  • Ghassan S. KassabEmail author

Abstract

The function of the coronary system is to deliver blood to the capillary network, to nourish the myocardium and to autoregulate coronary blood flow. The coronary vessels run through cyclically contracting, cardiac muscle. Consequently, intramyocardial pressures have a major influence on vascular transmural pressure and, therefore, on the flow. It is widely acknowledged that the distribution of coronary blood is spatially heterogeneous. Aside from the interaction between myocardial contraction and flow, causing impediment at the local level, the stochastic nature of the coronary tree geometry contributes to the inhomogeneity of the blood flow distribution. Additionally, variations of flow exist from epicardium to endocardium. Flow heterogeneity is further enhanced in pathologies, such as ischemia, which induces vulnerability of the subendocardium to ischemia. The coronary perfusion distribution as well as local coronary flow is difficult to measure, especially in the endocardium. Hence it is not yet fully understood as to what the specific effects cardiac contraction, local neurogenic controls, cardiac and vascular pathologies, and specific therapeutic modalities (e.g., drugs) have on the extent and distribution of coronary perfusion. For this reason, simulation is an attractive methodological alternative. Accordingly, realistic analysis of the flow distribution must be carried out within a framework of a realistic three-dimensional (3D) representation of the coronary geometry and its biological variability. Recent morphological studies facilitate realistic reconstructions of the coronary vasculature to serve as a foundation for simulation of the flow in the entire coronary system.

Keywords

Right Coronary Artery Coronary Vasculature Great Cardiac Vein Epicardial Vessel Venous Tree 
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.

References

  1. Ansari A. Anatomy and clinical significance of ventricular Thebesian veins. Clin Anat. 2001;14:102–10.PubMedCrossRefGoogle Scholar
  2. Bales GS. Great cardiac vein variations. Clin Anat. 2004;17:436–43.PubMedCrossRefGoogle Scholar
  3. Baroldi G, Scomazzoni, G. Coronary circulation in the normal and the pathologic heart. Washington, DC: Office of the surgeon general. Department of the army; 1967.Google Scholar
  4. Bassingthwaighte JB, Yipintsoi T, Harvey RB. Microvasculature of the dog left ventricular myocardium. Microvasc Res. 1974;7:229–49.PubMedPubMedCentralCrossRefGoogle Scholar
  5. Bassingthwaighte JB, King RB, Roger SA. Fractal nature of regional myocardial blood flow heterogeneity. Circ Res. 1989;65:578–90.PubMedPubMedCentralCrossRefGoogle Scholar
  6. Beard DA, Bassingthwaighte JB. The fractal nature of myocardial blood flow emerges from a whole-organ model of arterial network. J Vasc Res. 2000;37:282–96.PubMedCrossRefGoogle Scholar
  7. Berne R, Rubio R. Coronary circulation. In: Berne RM, editor. Handbook of physiology. Section2. The cardiovascular system, The heart, vol. 1. Baltimore: American Physiological Society; 1979.Google Scholar
  8. Bruinsma P, Arts T, Dankelman J, Spaan JA. Model of the coronary circulation based on pressure dependence of coronary resistance and compliance. Basic Res Cardiol. 1988;83:510–24.PubMedCrossRefGoogle Scholar
  9. Chadwick RS, Tedgui A, Michel JB, Ohayon J, Levy BI. Phasic regional myocardial inflow and outflow: comparison of theory and experiments. Am J Physiol. 1990;258:H1687–98.PubMedGoogle Scholar
  10. Chilian WM. Microvascular pressures and resistances in the left ventricular subepicardium and subendocardium. Circ Res. 1991;69:561–70.PubMedCrossRefGoogle Scholar
  11. Chilian WM, Marcus ML. Coronary venous outflow persists after cessation of coronary arterial inflow. Am J Physiol. 1984;247:H984–90.PubMedGoogle Scholar
  12. Chilian WM, Layne SM, Klausner EC, Eastham CL, Marcus ML. Redistribution of coronary microvascular resistance produced by dipyridamole. Am J Physiol. 1989;256:H383–90.PubMedGoogle Scholar
  13. Choy JS, Kassab GS. Wall thickness of coronary vessels varies transmurally in the LV but not the RV: implications for local stress distribution. Am J Physiol Heart Circ Physiol. 2009;297:H750–8.PubMedPubMedCentralCrossRefGoogle Scholar
  14. Crystal GJ, Downey HF, Bashour FA. Small vessel and total coronary blood volume during intracoronary adenosine. Am J Physiol. 1981;241:H194–201.PubMedGoogle Scholar
  15. Feigl EO. Coronary physiology. Physiol Rev. 1983;63:1–205.PubMedGoogle Scholar
  16. Fulton W. Morphometry of the myocardial circulation in microcirculation of the heart: theoretical and clinical problems. New York: Springer; 1982.Google Scholar
  17. Gray H, Williams PL, Bannister LH. Gray’s anatomy: the anatomical basis of medicine and surgery. New York: Churchill Livingstone; 1995.Google Scholar
  18. Grayson J. Functional morphology of the coronary circulation in the coronary artery. New York: Oxford University Press; 1982.Google Scholar
  19. Hester RL, Hammer LW. Venular-arteriolar communication in the regulation of blood flow. Am J Physiol Regul Integr Comp Physiol. 2002;282:R1280–5.PubMedCrossRefGoogle Scholar
  20. Hiramatsu O, Goto M, Yada T, Kimura A, Chiba Y, Tachibana H, Ogasawara Y, Tsujioka K, Kajiya F. In vivo observations of the intramural arterioles and venules in beating canine hearts. J Physiol. 1998;509(Pt 2):619–28.PubMedPubMedCentralCrossRefGoogle Scholar
  21. Hoffman JI, Spaan JA. Pressure-flow relations in coronary circulation. Physiol Rev. 1990;70:331–90.PubMedGoogle Scholar
  22. Howe BB, Winbury MM. Effect of pentrinitrol, nitroglycerin and propranolol on small vessel blood content of the canine myocardium. J Pharmacol Exp Ther. 1973;187:465–74.PubMedGoogle Scholar
  23. Huo Y, Kassab GS. A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree. Am J Physiol Heart Circ Physiol. 2007;292:H2623–33.PubMedCrossRefGoogle Scholar
  24. Huo Y, Kassab GS. The scaling of blood flow resistance: from a single vessel to the entire distal tree. Biophys J. 2009;96:339–46.PubMedPubMedCentralCrossRefGoogle Scholar
  25. Huo Y, Kassab GS. Intraspecific scaling laws of vascular trees. J R Soc Interface. 2012;9:190–200.PubMedPubMedCentralCrossRefGoogle Scholar
  26. Huo Y, Linares CO, Kassab GS. Capillary perfusion and wall shear stress are restored in the coronary circulation of hypertrophic right ventricle. Circ Res. 2007;100:273–83.PubMedCrossRefGoogle Scholar
  27. Huo Y, Kaimovitz B, Lanir Y, Wischgoll T, Hoffman JI, Kassab GS. Biophysical model of the spatial heterogeneity of myocardial flow. Biophys J. 2009;96:4035–43.PubMedPubMedCentralCrossRefGoogle Scholar
  28. Hutchins GM, Moore GW, Hatton EV. Arterial-venous relationships in the human left ventricular myocardium: anatomic basis for countercurrent regulation of blood flow. Circulation. 1986;74:1195–202.PubMedCrossRefGoogle Scholar
  29. Izumi T, Yamazoe M, Shibata A. Three-dimensional characteristics of the intramyocardial microvasculature of hypertrophied human hearts. J Mol Cell Cardiol. 1984;16:449–57.PubMedCrossRefGoogle Scholar
  30. Jain AK, Smith EJ, Rothman MT. the coronary venous system: an alternative route of access to the myocardium. J Invasive Cardiol. 2006;18:563–8.PubMedGoogle Scholar
  31. James TN. Anatomy of the coronary arteries. New York: P.B. Hoeber; 1961.Google Scholar
  32. James T. Anatomy and pathology of small coronary arteries in coronary circulation: from basic mechanisms to clinical implications. Leiden: Nijhoff; 1987.Google Scholar
  33. Jones CJ, Kuo L, Davis MJ, Chilian WM. Distribution and control of coronary microvascular resistance. Adv Exp Med Biol. 1993;346:181–8.PubMedCrossRefGoogle Scholar
  34. Kaimovitz B, Lanir Y, Kassab GS. Large-scale 3-D geometric reconstruction of the porcine coronary arterial vasculature based on detailed anatomical data. Ann Biomed Eng. 2005;33:1517–35.PubMedCrossRefGoogle Scholar
  35. Kaimovitz B, Huo Y, Lanir Y, Kassab GS. Diameter asymmetry of porcine coronary arterial trees: structural and functional implications. Am J Physiol Heart Circ Physiol. 2008;294:H714–23.PubMedCrossRefGoogle Scholar
  36. Kaimovitz B, Lanir Y, Kassab GS. A full 3-D reconstruction of the entire porcine coronary vasculature. Am J Physiol Heart Circ Physiol. 2010;299:H1064–76.PubMedPubMedCentralCrossRefGoogle Scholar
  37. Kajiya F, Goto M. Integrative physiology of coronary microcirculation. Jpn J Physiol. 1999;49:229–41.PubMedCrossRefGoogle Scholar
  38. Kalsho G, Kassab GS. Bifurcation asymmetry of the porcine coronary vasculature and its implications on coronary flow heterogeneity. Am J Physiol Heart Circ Physiol. 2004;287:H2493–500.PubMedCrossRefGoogle Scholar
  39. Kassab GS. Functional hierarchy of coronary circulation: direct evidence of a structure-function relation. Am J Physiol Heart Circ Physiol. 2005;289:H2559–65.PubMedCrossRefGoogle Scholar
  40. Kassab GS. Scaling laws of vascular trees: of form and function. Am J Physiol Heart Circ Physiol. 2006;290:H894–903.PubMedCrossRefGoogle Scholar
  41. Kassab G. Design of coronary circulation: a minimum energy hypothesis. Comput Methods Appl Mech Eng. 2007;196:3033–42.CrossRefGoogle Scholar
  42. Kassab GS, Fung YC. Topology and dimensions of pig coronary capillary network. Am J Physiol. 1994;267:H319–25.PubMedGoogle Scholar
  43. Kassab GS, Rider CA, Tang NJ, Fung YC. Morphometry of pig coronary arterial trees. Am J Physiol. 1993;265:H350–65.PubMedGoogle Scholar
  44. Kassab GS, Lin DH, Fung YC. Morphometry of pig coronary venous system. Am J Physiol. 1994;267:H2100–13.PubMedGoogle Scholar
  45. Kassab GS, Pallencaoe E, Schatz A, Fung YC. Longitudinal position matrix of the pig coronary vasculature and its hemodynamic implications. Am J Physiol. 1997;273:H2832–42.PubMedGoogle Scholar
  46. Kassab GS, Navia JA, March K, Choy JS. Coronary venous retroperfusion: an old concept, a new approach. J Appl Physiol. 2008;104:1266–72.PubMedCrossRefGoogle Scholar
  47. Kaul S, Ito H. Microvasculature in acute myocardial ischemia: part I: evolving concepts in pathophysiology, diagnosis, and treatment. Circulation. 2004;109:146–9.PubMedCrossRefGoogle Scholar
  48. Klocke FJ, Mates RE, Canty Jr JM, Ellis AK. Coronary pressure-flow relationships. Controversial issues and probable implications. Circ Res. 1985;56:310–23.PubMedCrossRefGoogle Scholar
  49. Kresh JY, Fox M, Brockman SK, Noordergraaf A. Model-based analysis of transmural vessel impedance and myocardial circulation dynamics. Am J Physiol. 1990;258:H262–76.PubMedGoogle Scholar
  50. Kuo L, Arko F, Chilian WM, Davis MJ. Coronary venular responses to flow and pressure. Circ Res. 1993;72:607–15.PubMedCrossRefGoogle Scholar
  51. Loukas M, Bilinsky S, Bilinsky E, el-Sedfy A, Anderson RH. Cardiac veins: a review of the literature. Clin Anat. 2009;22:129–45.PubMedCrossRefGoogle Scholar
  52. McAlpine W. Heart and coronary arteries: an anatomical atlas for clinical diagnosis, radiological investigation, and surgical treatment. New York: Springer; 1975.CrossRefGoogle Scholar
  53. Miller DS. Internal flow systems. Cranfield: BHRA; 1990.Google Scholar
  54. Mittal N, Zhou Y, Ung S, Linares C, Molloi S, Kassab GS. A computer reconstruction of the entire coronary arterial tree based on detailed morphometric data. Ann Biomed Eng. 2005a;33(8):1015–26.PubMedCrossRefGoogle Scholar
  55. Mittal N, Zhou Y, Linares C, Ung S, Kaimovitz B, Molloi S, Kassab GS. Analysis of blood flow in the entire coronary arterial tree. Am J Physiol Heart Circ Physiol. 2005b;289:H439–46.PubMedCrossRefGoogle Scholar
  56. Mohl W, Wolner E, Glogar D. The coronary sinus: proceedings of the 1st international symposium on myocardial protection via the coronary sinus. Darmstadt: Steinkopff; 1984.CrossRefGoogle Scholar
  57. Murray CD. The physiological principle of minimum work applied to the angle of branching of arteries. J Gen Physiol. 1926;9:835–41.PubMedPubMedCentralCrossRefGoogle Scholar
  58. Myers WW, Honig CR. Number and distribution of capillaries as determinants of myocardial oxygen tension. Am J Physiol. 1964;207:653–60.PubMedGoogle Scholar
  59. Nielsen PM, Le Grice IJ, Smaill BH, Hunter PJ. Mathematical model of geometry and fibrous structure of the heart. Am J Physiol. 1991;260:H1365–78.PubMedGoogle Scholar
  60. Olsson RAB, Bugni WJ. Coronary circulation. In: Fozzard HA, editor. The heart and cardiovascular system: scientific foundations. New York: Raven; 1986. p. 2 v. (1694p.).Google Scholar
  61. Reneman RS, Arts T. Dynamic capacitance of epicardial coronary arteries in vivo. J Biomech Eng. 1985;107:29–33.PubMedCrossRefGoogle Scholar
  62. Rossitti S, Lofgren J. Vascular dimensions of the cerebral arteries follow the principle of minimum work. Stroke. 1993;24:371–7.PubMedCrossRefGoogle Scholar
  63. Sherman TF. On connecting large vessels to small. The meaning of Murray’s law. J Gen Physiol. 1981;78:431–53.PubMedCrossRefGoogle Scholar
  64. Smith NP, Pullan AJ, Hunter PJ. Generation of an anatomically based geometric coronary model. Ann Biomed Eng. 2000;28:14–25.PubMedCrossRefGoogle Scholar
  65. Smith N, Pillan AJ, Hunter PJ. Ana anatomically based model of transient coronary blood flow in the heart. SIAM J Appl Math. 2002;62:990–1018.CrossRefGoogle Scholar
  66. Spaan JA. Coronary diastolic pressure-flow relation and zero flow pressure explained on the basis of intramyocardial compliance. Circ Res. 1985;56:293–309.PubMedCrossRefGoogle Scholar
  67. Spaan JAE. Coronary blood flow: mechanics, distribution, and control. Dordrecht: Kluwer Academic Publishers; 1991.CrossRefGoogle Scholar
  68. Streeter DJ. Gross morphometry and fiber geometry of the heart. In: Berne RM, Sperelakis N, Geiger SR, editors. Handbook of physiology. Section 2. The cardiovascular system, The heart, vol. 1. Baltimore: American Physiological Society; 1979.Google Scholar
  69. Tanaka A, Mori H, Tanaka E, Mohammed MU, Tanaka Y, Sekka T, Ito K, Shinozaki Y, Hyodo K, Ando M, Umetani K, Tanioka K, Kubota M, Abe S, Handa S, Nakazawa H. Branching patterns of intramural coronary vessels determined by microangiography using synchrotron radiation. Am J Physiol. 1999;276:H2262–7.PubMedGoogle Scholar
  70. Toyota E, Koshida R, Hattan N, Chilian WM. Regulation of the coronary vasomotor tone: what we know and where we need to go. J Nucl Cardiol. 2001;8:599–605.PubMedCrossRefGoogle Scholar
  71. Uylings H. Optimization of diameter and bifurcation angles in lung and vascular tree structures. Bull Math Biol. 1977;39:509–19.PubMedCrossRefGoogle Scholar
  72. Van Bavel E. Metabolic and myogenic control of blood flow studied on isolated small arteries. Ph.D., University of Amsterdam; 1989.Google Scholar
  73. VanBavel E, Spaan JA. Branching patterns in the porcine coronary arterial tree. Estimation of flow heterogeneity. Circ Res. 1992;71:1200–12.PubMedCrossRefGoogle Scholar
  74. Vankan WJ, Huyghe JM, Slaaf DW, van Donkelaar CC, Drost MR, Janssen JD, Huson A. Finite-element simulation of blood perfusion in muscle tissue during compression and sustained contraction. Am J Physiol. 1997;273:H1587–94.PubMedGoogle Scholar
  75. von Lüdinghausen M. The venous drainage of the human myocardium. New York: Springer; 2003.CrossRefGoogle Scholar
  76. von Ludinghausen M. Anatomy of the coronary arteries and veins. In: Mohl W, Wolner E, Glogar D, editors. The coronary sinus: proceedings of the 1st international symposium on myocardial protection via the coronary sinus. Darmstadt: Steinkopff; 1984. p. 5–7.Google Scholar
  77. Weiss HR, Winbury MM. Nitroglycerin and chromonar on small-vessel blood content of the ventricular walls. Am J Physiol. 1974;226:838–43.PubMedGoogle Scholar
  78. Zamir M. Nonsymmetrical bifurcations in arterial branching. J Gen Physiol. 1978;72:837–45.PubMedCrossRefGoogle Scholar
  79. Zamir M. On fractal properties of arterial trees. J Theor Biol. 1999;197:517–26.PubMedCrossRefGoogle Scholar
  80. Zamir M. Arterial branching within the confines of fractal L-system formalism. J Gen Physiol. 2001;118:267–76.PubMedPubMedCentralCrossRefGoogle Scholar
  81. Zamir M, Brown N. Arterial branching in various parts of the cardiovascular system. Am J Anat. 1982;163:295–307.PubMedCrossRefGoogle Scholar
  82. Zamir M, Wrigley SM, Langille BL. Arterial bifurcations in the cardiovascular system of a rat. JGen Physiol. 1983;81:325–35.PubMedCrossRefGoogle Scholar
  83. Zamir M, Phipps S, Langille BL, Wonnacott TH. Branching characteristics of coronary arteries in rats. Can J Physiol Pharmacol. 1984;62:1453–9.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2016

Authors and Affiliations

  • Benjamin Kaimovitz
    • 1
  • Yunlong Huo
    • 2
  • Yoram Lanir
    • 1
  • Ghassan S. Kassab
    • 1
    Email author
  1. 1.IUPUIIndianapolisUSA
  2. 2.Peking UniversityBeijingChina

Personalised recommendations