Abstract
Based on morphometric data, we calculate the structural parameters of the coronary vasculature as an optimal branching bed. We show (i) significant correlations between the diameters of the larger daughter and the parent vessel and between the diameter of the smaller daughter vessel and the asymmetry coefficient; (ii) differences in the structural parameters for two types of artery that deliver and distribute blood in the cardiac muscle; and (iii) the length-diameter relationships for different arteries. The coronary vasculature is characterized by asymmetrical branching and thus should be modeled with self-similar asymmetrical tree-like systems.
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A. E. Flynn, D. L. Coggins, M. Goto, et al., Amer. Physiol. 262, 1759 (1992).
J. A. E. Spaan, P. W. Breuls, and J. D. Laird, Circ. Res. 49, 584 (1981).
Yi-Hui Sun, T. J. Anderson, K. H. Parker, and J. V. Tyberg, Amer. J. Physiol. 286, 1590 (2004).
G. S. Kassab, E. Pallencaoe, A. Schatz, and Y.C. Fung, Amer. J. Physiol. 273, 2832 (1997).
G. S. Kassab, J. Berkley, and Y. C. Fung, Ann. Biomed. Eng. 25, 204 (1997).
J. S. Parker, Ch. B. Cave, J. L. Adrell, et al., J. Appl. Physiol. 83, 1370 (1997).
D. A. Beard and J. B. Bassingthwaighte, J. Vasc. Res. 37, 282 (2000).
M. Marxen and R. M. Henkelman, Amer. J. Physiol. 284, 1848 (2003).
J. Meier, M. Kleen and K. Messmer, Bull. Math. Biol. 66, 1155 (2004).
W. Schreiner, F. Neumann, M. Neumann, et al., J. Gen. Physiol. 109, 129 (1997).
J. H. Van Beek, S. A. Roger, and Bassingthwaighte, Amer. J. Physiol. 257, 1670 (1989).
S. Aharinejad, W. Schreiner, and F. Neumann, Anat. Rec. 251, 50 (1998).
M. Zamir, S. Phipps, B. L. Langille, and T. H. Wonnacott, Can. J. Physiol. Pharmacol. 62, 1453 (1984).
M. Zamir and H. Chee, Canad. J. Physiol. Pharmacol. 64, 661 (1986).
M. Zamir and H. Chee, Blood Vessels. 24, 76 (1987).
M. Zamir, J. Gen. Physiol. 91, 725 (1988).
M. H. Friedman and Z. Ding, Biomech. 31, 273 (1998).
C. D. Murray, Proc. Natl. Acad. Sci. USA 12, 207 (1926).
M. La Barbera, Science 249, 992 (1990).
Y. Zhou, G. S. Kassab, and S. Molloi, Phys. Med. Biol. 44, 2929 (1999).
M. Zamir and M. D. Silver, Canad. J. Cardiol. 1, 363 (1985).
Y. Zhou, G. S. Kassab, and S. Molloi, Phys. Med. Biol. 21, 977 (2002).
M. H. Friedman, A. M. Brinkman, J. J. Qin, and W. A. Seed, Atherosclerosis 25, 193 (1993).
R. McKay, R. H. Anderson, and A. Smith, J. Thorac. Cardiovasc. Surg. 111, 988 (1996).
J. M. Downey and E. S. Kirk, Circ. Res. 36, 753 (1975).
R. Krams, P. Sipkema, and N. Westerhof, Amer. J. Physiol. 257, 1471 (1989).
M. Ye. Bondarenko and N. N. Kizilova, Russian J. Biomech. 4, 52 (2002).
N. N. Kizilova, in Proc. of II international conference on computational bioengineering, Eds. by H. Rodrigues, M. Cerrolaza, M. Doblare, J. Ambrosio, M. Viceconti (IST Press, Lisboa, 2005), pp. 412–421.
N. N. Kizilova, in Proc. of the 1-st Intern. Conf. on Complex Medical Engineering, (Japan, 2005), pp. 287–292.
R. Rosen, Optimality Principle in Biology (Mir, Moscow, 1969) [in Russian].
D. J. Brown, IEEE Trans. BME. 43, 715 (1996).
K. A. Shoshenko, Architectonics of the Blood Flow Bed (Nauka, Novosibirsk, 1982) [in Russian].
G. S. Kassab and Y. C. Fung, Ann. Biomed. Eng. 23, 13 (1995).
C. A. Dawson, G. S. Krenz, K. L. Karau, et al., J. Appl. Physiol. 86, 569 (1999).
N. N. Kizilova, Izv. RAN, Ser. MZhG No. 5, 127 (2003).
Y. Y. Wang, W. C. Lia, H. Hsiu, et al., IEEE Trans. BME 47, 313 (2000).
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Original Russian Text © O.K. Zenin, N.N. Kizilova, E.N. Filippova, 2007, published in Biofizika, 2007, Vol. 52, No. 5, pp. 924–930.
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Zenin, O.K., Kizilova, N.N. & Filippova, E.N. Studies on the structure of human coronary vasculature. BIOPHYSICS 52, 499–503 (2007). https://doi.org/10.1134/S0006350907050089
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DOI: https://doi.org/10.1134/S0006350907050089