Structure and function of the coronary arterial tree

  • Jos A. E. Spaan
Part of the Developments in Cardiovascular Medicine book series (DICM, volume 124)


The Purpose of the coronary arterial tree, a branching network of vessels, is to distribute blood over the capillary bed and to regulate coronary flow. Regulation is exercised by the smooth muscle cells in the vessel walls, especially of the smaller arteries and arterioles. These smooth muscle cells are under the control of tissue metabolism and are able to adapt perfusion to local needs independently of the structure of the arterial tree. However, the architecture of the arterial tree determines the potential for the distribution of blood flow, which then is modulated by control. The magnitude by which vessels of certain diameter may contribute to the control of flow depends on their contribution to overall resistance. This can be inferred from the pressure distribution over the coronary arterial tree. If the drop of pressure over vessels with a certain diameter is negligible, their potential to alter flow significantly will also be very slight. Theoretically, the resistance of a vessel can readily be estimated from its length and diameter, applying Poiseuille’s law and neglecting entrance effects and peculiarities of rheology. However, the vessel’s contribution to the overall resistance and its potential to alter flow distribution depends strongly on the structure of the network and the position of the vessel in it. A good test of whether the relation between structure and function of the arterial tree is understood follows from the comparison between the experimentally determined pressure distribution and its prediction on the basis of the structure of the arterial tree.


Pressure Drop Pressure Distribution Large Artery Small Artery Arterial Tree 
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  1. [1]
    Arts MGJ (1978) A mathematical model of the dynamics of the left ventricle and the coronary circulation. PhD Thesis. University of Limburg, Maastricht, The Netherlands.Google Scholar
  2. [2]
    Arts T, Kruger RTI, VanGerven W, Lambregts JAc , Reneman RS (1979) Propagation velocity and reflection of pressure waves in the canine coronary artery. Am. J. Physiol. 237 (Heart Circ. Physiol. 6): H469–H474.PubMedGoogle Scholar
  3. [3]
    Bassingthwaighte JB (1988) Physiological heterogeneity: fractals link determinism and randomness in structure and function. New Physiol. Sci. 3: 5–10.Google Scholar
  4. [4]
    Bassingthwaighte JB, King RB, Roger, SA (1989) Fractal nature of regional myocardial blood flow heterogeneity. Circ. Res. 65: 578–590.PubMedCrossRefGoogle Scholar
  5. [5]
    Bassingthwaighte JB, VanBeek JHGM (1988) Lightning and the heart: fractal behavior in cardiac function. Proc. IEEE 76: 693–699.CrossRefGoogle Scholar
  6. [6]
    Bassingthwaighte JB, Malone MA, Moffett TC, King RB, Little SE, Link JM, Krohn KA (1987) Validity of microsphere depositions for regional myocardial flows. Am. J. Physiol. 253 (Heart Circ. Physiol. 22): H184–H193.PubMedGoogle Scholar
  7. [7]
    Bassingthwaighte JB, Malone MA, Moffett TC, King RB, Chan IS, Link JM, Krohn KA (1990) Molecular and particulate depositions for regional myocardial flows in sheep. Circ. Res. 66: 1328–1344.PubMedCrossRefGoogle Scholar
  8. [8]
    Becker BF, Bardenheuer H, Oveehage de Reyes I, Gerlach E (1985) Effects of theophylline on dipyridamole-induced coronary venous adenosine release and coronary dilation. In: Adenosine: Receptors and modulation of cell function. Eds. Stevanovich V, Rudolphi K, Schubert K. IRL Oxford: 441–449.Google Scholar
  9. [9]
    Brown RE (1965) The pattern of the microcirculatory bed in the ventricular myocardium of domestic mammals. Am. J. Anat. 116: 335–374.CrossRefGoogle Scholar
  10. [10]
    Chien G, Dormandy J, Ernst E, Matrai A (1987) Clinical hemorheology. Martinus Nijhoff, Dordrecht, The Netherlands.Google Scholar
  11. [11]
    Chilian WM, Layne SM, Klausner EC, Eastham CL, Marcus ML (1989) Redistribution of coronary microvascular resistance produced by dipyridamole. Am. J. Physiol. 256 (Heart Circ. Physiol. 25): H383–H390.PubMedGoogle Scholar
  12. [12]
    Chilian WM, Eastham CL, Marcus ML (1986) Microvascular distribution of coronary vascular resistance in beating left ventricle. Am. J. Physiol. 251 (Heart Circ. Physiol. 20): H779–H788.PubMedGoogle Scholar
  13. [13]
    Davis MJ, Ferrer PN, Gore RW (1986) Vascular anatomy and hydrostatic pressure profile in the hamster cheek pouch. Am. J. Physiol. 250 (Heart Circ. Physiol. 19): H291–H303.PubMedGoogle Scholar
  14. [14]
    Douglas JE, Greenfield JC Jr (1970) Epicardial coronary artery compliance in the dog. Circ. Res. 27: 921–929.PubMedCrossRefGoogle Scholar
  15. [15]
    Eng C, Cho S, Factor SM, Sonnenblick EM, Kirk ES (1984) Myocardial micronecrosis produced by microsphere embolization. Role of α-adrenergic tonic influence on the coronary microcirculation. Circ. Res. 54: 74–82.PubMedCrossRefGoogle Scholar
  16. [16]
    Fam WM, McGregor M (1969) Pressure-flow relationships in the coronary circulation. Circ. Res. 25: 293–301.PubMedCrossRefGoogle Scholar
  17. [17]
    Fronek K, Zweifach BW (1975) Microvascular pressure distribution in skeletal muscle and the effect of vasodilation. Am. J. Physiol. 228: 791–796.PubMedGoogle Scholar
  18. [18]
    Fulton WFM (1965) The coronary arteries. Charles C. Thomas, Springfield III.Google Scholar
  19. [19]
    Goldberger AL, Rigney DR, West BJ (1990) Chaos and fractals in Human Physiology. Scientific Am. 262(2): 34–41.CrossRefGoogle Scholar
  20. [20]
    Gregg DE, Fisher LC (1963) Blood supply to the heart. Handbook of Physiology. Circulation. 2. Sect. 2. Am. Physiol. Soc., Washington D.C.Google Scholar
  21. [21]
    Hausdorff F (1919) Dimension und aüszeres Mass. Math. Analen 79: 157–197.CrossRefGoogle Scholar
  22. [22]
    Kendall MG, Stuart A (1958) The advanced theory of statistics. vol.1 Distribution Theory. Charles Griffin & Company Limited, London.Google Scholar
  23. [23]
    LaBarbera M (1990) Principles of design of fluid transport systems in zoology. Science 249: 992–1000.PubMedCrossRefGoogle Scholar
  24. [24]
    Mandelbrot B (1977) Fractals: From chance, and dimensions. Freeman, San Francisco.Google Scholar
  25. [25]
    McDonald N (1983) Trees and networks in biological models. John Wiley & Sons, New York.Google Scholar
  26. [26]
    Meininger GA, Fehr KL, Yates MB (1987) Anatomic and hemodynamic characteristics of the blood vessels feeding the cremaster skeletal muscle in the rat. Microvasc. Res. 33: 81–97.PubMedCrossRefGoogle Scholar
  27. [27]
    Murray CD (1926) The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc. Nat. Acad. Sci. 12: 207–214.PubMedCrossRefGoogle Scholar
  28. [28]
    Nellis SH, Liedtke AJ, Whitesell L (1981) Small coronary vessel pressure and diameter in an intact beating rabbit heart using fixed-position and free-motion techniques. Circ. Res. 49: 342–353.PubMedCrossRefGoogle Scholar
  29. [29]
    Pelosi G, Saviozzi G, Trivella MG, L’Abbate A (1987) Small artery occlusion: A theoretical approach to the definition of coronary architecture and resistance by a branching tree model. Microvasc. Res. 34: 318–355.PubMedCrossRefGoogle Scholar
  30. [30]
    Popel AS (1980) A model of the pressure and flow distribution in branching networks. Trans. ASME. J. Appl. Mechan. 102: 247–253.CrossRefGoogle Scholar
  31. [31]
    Schaper W (1971) The collateral circulation of the heart: volume I, Clinical Studies. Ed. Black Dak North Holland Co., Amsterdam, London.Google Scholar
  32. [32]
    Schoenmackers J (1958) Zur Anatomie und Pathologie der Coronarge-fasse. Bad Oeynhausener Gespräche II: 133.Google Scholar
  33. [33]
    Shapiro HM, Stromberg DD, Lee DR, Wiederhelm CA (1971) Dynamic pressures in the pial arterial microcirculation. Am. J. Physiol. 221: 279–283.PubMedGoogle Scholar
  34. [34]
    Suwa N, Niwa T, Fukasawa H, Sasaki Y (1963) Estimation of intravascular blood pressure gradient by mathematical analysis of arterial casts. Tohoku J. Exp. Med. 79: 168–198.PubMedCrossRefGoogle Scholar
  35. [35]
    Suwa N, Takahashi T (1971) Morphological and Morphometrical Analysis of Circulation in Hypertension and Ischemic Kidney. Eds. Urban & Schwarzenberg. Heidelberg, FRG.Google Scholar
  36. [36]
    Tillmanns H, Steinhausen M, Leinberger H, Thederan H, Kübler W (1981) Pressure measurements in the terminal vascular bed of the epimyocardium of rats and cats. Circ. Res. 49: 1202–1211.PubMedCrossRefGoogle Scholar
  37. [37]
    Tomanek RJ (1987) Microanatomy of the coronary circulation. In: Coronary circulation, from basic mechanisms to clinical implications. Eds. Spaan JAE, Bruschke AVG, Gittenberger-deGroot AC. Martinus Nijhoff, Dordrecht, The Netherlands.Google Scholar
  38. [38]
    VanBavel E (1989) Metabolic and myogenic control of blood flow studied on isolated small arteries. PhD Thesis. University of Amsterdam, The Netherlands.Google Scholar
  39. [39]
    VanBavel E, Spaan JAE (1990) Branching characteristics of the coronary circulation. FASEB J. 4(4): A850.Google Scholar
  40. [40]
    VanBeek JHGM, Roger SA, Bassingthwaighte JB (1989) Regional myocardial flow heterogeneity explained with fractal networks. Am. J. Physiol. 257 (Heart Circ. Physiol. 26): H1670–H1680.Google Scholar
  41. [41]
    Wieringa PA, Stassen HG, Laird JD, Spaan JAE (1988) Quantification of arteriolar density and embolization in rat myocardium. Am. J. Physiol. 254 (Heart Circ. Physiol. 23): H636–H650.PubMedGoogle Scholar
  42. [42]
    Wüsten B, Buss DD, Deist H, 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
  43. [43]
    Zamir M, Chee H (1987) Segment analysis of human coronary arteries. Blood vessels 24: 76–84.PubMedGoogle Scholar
  44. [44]
    Zweifach BW, Lipowsky HH (1977) Quantitative studies of microcirculatory structure and function III. Microvascular hemodynamics of cat mesentery and rabbit omentum. Circ. Res. 41: 380–390.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Jos A. E. Spaan
    • 1
  1. 1.Cardiovascular Research Institute Amsterdam (CRIA)AmsterdamThe Netherlands

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