Blood flow and optimal vascular topography: role of the endothelium

  • T. M. Griffith
  • D. H. Edwards
  • M. D. Randall


We have used x-ray microangiography to investigate the influence of EDRF and endothelin-1 on arterial diameters (70–800 μm) at bifurcations in the isolated rabbit ear and the “optimality” of its branching geometry. The median value of the junction exponent x (which is given by d 0 x =d 1 x +d 2 x , where d 0 d 1 and d 2 are parent and daughter artery diameters respectively) was close to 3 at different flow rates in unconstricted preparations. When x = 3, branching geometry is optimal in that i) power losses and intravascular volume are both minimised, and ii) fractal considerations suggest that the total surface area for metabolic exchange is maximised. Under conditions of vasoconstriction (by 5HT/histamine) the junction exponent deviated from its control value but was restored towards 3, both by basal and by acetylcholine-stimulated EDRF activity. In contrast, endothelin-1 caused a dose-dependent reduction in the junction exponent from its optimal value 3. This suggests that the endothelium helps to optimise microvascular function through EDRF but not endothelin-1 release.

Key words

Endothelium EDRF endothelin-1 optimality rabbit ear microvascular function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bittner HR, Wlczek P, Sernetz M (1989) Characterization of fractal biological objects by image analysis. Acta Stereol 8:31–40Google Scholar
  2. 2.
    Edwards DH, Griffith TM, Ryley HC, Henderson AH (1986) Haptoglobin-haemoglobin complex in human plasma inhibits endothelium-dependent relaxation: evidence that endotheliumderived relaxing factor acts as a local autacoid. Cardiovasc Res 20:549–556PubMedCrossRefGoogle Scholar
  3. 3.
    Griffith TM, Edwards DH, Davies RLl, Harrison TJ, Evans KT (1987) EDRF coordinates the behaviour of vascular resistance vessels. Nature 329:442–445PubMedCrossRefGoogle Scholar
  4. 4.
    Griffith TM, Edwards DH, Davies RLl, Harrison TJ, Evans KT (1988) Endothelium-derived relaxing factor (EDRF) and resistance vessels in an intact vascular bed: a microangiographic study of the rabbit isolated ear. Br J Pharmacol 93:654–662PubMedGoogle Scholar
  5. 5.
    Griffith TM, Edwards DH, Davies RLl, Henderson AH (1989) The role of EDRF in flow distribution: a microangiographic study of the rabbit isolated ear. Microvascular Res 37:162–177CrossRefGoogle Scholar
  6. 6.
    Griffith TM, Edwards DH (1990) Basal EDRF activity helps to keep the geometrical configuration of arterial bifurcations close to the Murray optimum. J Theor Biol 146:545–573PubMedCrossRefGoogle Scholar
  7. 7.
    Harris P (1983) Evolution and the cardiac patient: Origins of the blood pressure. Cardiovascular Res 17:373–378CrossRefGoogle Scholar
  8. 8.
    Hirata Y, Takagi Y, Fukuda Y, Marumo F (1989) Endothelin is a potent mitogen for rat vascular smooth muscle cells. Atherosclerosis 78:225–228PubMedCrossRefGoogle Scholar
  9. 9.
    Langille L, O’Donnell F (1986) Reductions in arterial diameter produced by chronic decreases in blood flow are endothelium-dependent. Science 231:405–407PubMedCrossRefGoogle Scholar
  10. 10.
    Mandelbrot BB (1982) The fractal geometry of nature. Freeman, N.Y. pp 158Google Scholar
  11. 11.
    Mayrovitz HN, Roy J (1982) Microvascular blood flow: evidence indicating a cubic dependence on arteriolar diameter. Am J Physiol 245:H1031–H1038Google Scholar
  12. 12.
    Miller VM, Vanhoutte PM (1988) Enhanced release of endothelium-derived factor(s) by chronic increases in blood flow. Am J Physiol 255:H446–H451PubMedGoogle Scholar
  13. 13.
    Murray CD (1926) The physiological principle of minimum work applied to the angle of branching of arteries. J Gen Physiol 9:835–841PubMedCrossRefGoogle Scholar
  14. 14.
    Pohl U, Busse R, Kuon E, Bassenge E (1986) Pulsatile perfusion stimulates the release of endothelial autacoids. J Appl Cardiol 1:215–235Google Scholar
  15. 15.
    Rubanyi GM, Romero JC, Vanhoutte PM (1986) Flow-induced release of endothelium-derived relaxing factor. Am J Physiol 250:H1145–H1149PubMedGoogle Scholar
  16. 16.
    Sherman TF, Popel AS, Koller A, Johnson PC (1989) The cost of departure from optimal radii in microvascular networks. J Theor Biol 136:245–265PubMedCrossRefGoogle Scholar
  17. 17.
    Speden RN, Warren DM (1986) Myogenic adaptation of rabbit ear arteries to pulsatile internal pressure. J Physiol (Lond) 391:313–323Google Scholar
  18. 18.
    Woldenberg MJ, Horsfield K (1983) Finding the optimal lengths for three branches as a junction. J Theor Biol 104:301–318PubMedCrossRefGoogle Scholar
  19. 19.
    Woldenberg MJ, Horsfield K (1986) Relation of branching angles to optimality for four cost principles. J Theor Biol 122:187–204PubMedCrossRefGoogle Scholar
  20. 20.
    Yosizumi M, Kurihara H, Sugiyama T, Takaku F, Yanagisawa M, Masaki T, Yazaki Y (1989) Haemodynamic shear stress stimulates endothelin production by cultured endothelial cells. Biochem Biophys Res Comm 161:859–864CrossRefGoogle Scholar
  21. 21.
    Zamir M (1976) Optimality principles in arterial branching. J Theor Biol 62:227–251PubMedCrossRefGoogle Scholar
  22. 22.
    Zamir M, Wrigley SM, Langille BL (1983) Arterial bifurcations in the cardiovascular system of a rat. J Gen Physiol 81:325–335PubMedCrossRefGoogle Scholar
  23. 23.
    Zamir M, Bigelow DC (1984) Cost of departure from optimality in arterial branching. J Theor Biol 109:401–409PubMedCrossRefGoogle Scholar

Copyright information

© Dr. Dietrich Steinkopff Verlag GmbH & Co. KG, Darmstadt 1991

Authors and Affiliations

  • T. M. Griffith
    • 1
  • D. H. Edwards
    • 1
  • M. D. Randall
    • 1
  1. 1.Department of Cardiology and RadiologyUniversity of Wales College of MedicineGB-CardiffUK

Personalised recommendations