Abstract
In this chapter we attempt to relate the coronary vascular anatomy, a system of parallel paths with differing transit times, to regional flow distributions, to transit time distribution, and to measures of regional physiological functions. To do this we explore some approaches to algorithmic vascular growth. “Growth” from embryonic beginnings through development of the heart is not what we treat here; rather we try to capture the essence of the adult form of the vascular network in algorithmic form in order to see how well its behavior matches that of the real system. This first part of the exercise, instead of following the dimensional and physiological changes that occur from embryonic to adult life, is an attempt to determine whether or not forming a network model from a set of statistically defined vessels, and positioning them within the contours of the adult heart, produces a network which shows appropriate physiological behavior.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Austin R.E., Jr., Aldea G.S., Coggins D. L., Flynn A.E., and Hoffman J.I.E, Profound spatial heterogeneity of coronary reserve: Discordance between patterns of resting and maximal myocardial blood flow. Circ. Res. 67:319–331, 1990.
Bassingthwaighte J.B., Yipintsoi T., and Harvey R.B, Microvasculature of the dog left ventricular myocardium. Microvasc. Res. 7:229–249, 1974.
Bassingthwaighte J.B. Physiological heterogeneity: Fractals link determinism and randomness in structures and functions. News Physiol. Sci. 3:5–10, 1988.
Bassingthwaighte J.B., King R.B., and Roger S.A, Fractal nature of regional myocardial blood flow heterogeneity. Circ. Res. 65:578–590, 1989.
Bassingthwaighte J.B., and Beyer R.P. Fractal correlation in heterogeneous systems. Physica D 53:71–84, 1991.
Bassingthwaighte J.B., and Beard D.A, Fractal 15O-water washout from the heart. Circ. Res. 77:1212–1221, 1995.
Bassingthwaighte J.B., Beard D.A., and King R.B. Fractal regional myocardial blood flows: the anatomical basis. In: Fractals in Biology and Medicine, edited by Losa G., Weibel E., and Nonnenmacher T. Basel: Birkhauser, 1997, pp. 000–000.
Batra S., and Rakusan K. Capillary length, tortuosity, and spacing in rat myocardium during cardiac cycle. Am. J. Physiol. 263 (Heart Circ. Physiol. 32):H1369-H1376, 1992.
Beard D.A., and Bassingthwaighte J.B, Fractal nature of myocardial blood flow described by a whole-organ model of arterial network. Circ. Res. 1997.
Caldwell J.H., Martin G.V., Raymond G.M., and Bassingthwaighte J.B. Regional myocardial flow and capillary permeability-surface area products are nearly proportional. Am. J. Physiol. 267 (Heart Circ. Physiol. 36):H654-H666, 1994.
Chilian W.M. Microvascular pressures and resistances in the left ventricular subepicardium and subendocardium. Circ. Res. 69:561–570, 1991.
Hudlická O. Development of microcirculation: capillary growth and adaptation. In: Handbook of Physiology. Section 2: The Cardiovascular System Volume IV, edited by Renkin E.M. and Michel C.C. Bethesda, Maryland: American Physiological Society, 1984, pp. 165–216.
Kassab G.S., Rider C.A., Tang N.J., and Fung Y.B, Morphometry of pig coronary arterial trees. Am. J. Physiol. 265 (Heart Circ. Physiol. 34):H350-H365, 1993.
Kassab G.S., Berkley J., and Fung Y.C.B, Analysis of pig’s coronary arterial blood flow with detailed anatomical data. Ann. Biomed. Eng. 25:204–217, 1997a.
Kassab G.S., Pallencaoe E., and Fung Y C. The longitudinal position matrix of the pig coronary artery and its hemodynamic implications. Ann. Biomed. Eng. 25, 1997b.
King R.B., Bassingthwaighte J.B., Hales J.R.S., and Rowell L.B, Stability of heterogeneity of myocardial blood flow in normal awake baboons. Circ. Res. 57:285–295, 1985.
King R.B., and Bassingthwaighte J.B, Temporal fluctuations in regional myocardial flows. Pflügers Arch. (Eur. J. Physiol.) 413/4:336–342, 1989.
Lefèvre J. Teleonomical optimization of a fractal model of the pulmonary arterial bed. J. Theor. Biol. 102:225–248, 1983.
Li Z., Yipintsoi T., and Bassingthwaighte J.B. Nonlinear model for capillary-tissue oxygen transport and metabolism. Ann. Biomed. Eng. 25:604–619, 1997.
Mandelbrot B.B. The Fractal Geometry of Nature. San Francisco: W.H. Freeman and Co., 1983, 468 pp.
Matsumoto T., Goto M., Tachibana H., Ogasawara Y., Tsujioka K., and Kajiya F. Microheterogeneity of myocardial blood flow in rabbit hearts during normoxic and hypoxic states. Am J. Physiol. 270:H435–441, 1996.
Meinhardt H. Models of Biological Pattern Formation. New York: Academic Press, 1982.
Murray C.D. The physiological principle of minimum work applied to the angle of branching of arteries. J. Gen. Physiol. 9:835–841, 1926.
Nellis S.H., Liedtke A.J., and Whitesell L. Small coronary vessel pressure and diameter in an intact beating rabbit heart using fixed-position and free-motion techniques. Circ. Res. 49:342–353, 1981.
Pries A.R., Secomb T.W., Gaehtgens P., and Gross J.F. Blood flow in microvascular networks. Experiments and simulation. Circ. Res. 67:826–834, 1990.
Remington J.W., and Wood E H, Formation of peripheral pulse contour in man. J. Appl. Physiol. 9:433–442, 1956.
Tillmanns H., Steinhausen M., Leinberger H., Thederan H., and Kübler W. Pressure measurements in the terminal vascular bed of the epimyocardium of rats and cats. Circ. Res. 49:1202–1211, 1981.
van Bavel E., and Spaan J.A, Branching patterns in the porcine coronary arterial tree. Estimation of flow heterogeneity. Circ. Res. 71:1200–1212, 1992.
van Beek J.H.G.M., Bassingthwaighte J.B., and Roger S.A. Fractal networks explain regional myocardial flow heterogeneity. In: Oxygen Transport to Tissue XI. Adv. Exp. Med. Biol. 248, edited by Rakusan K. New York: Plenum Press, 1989, pp. 249–257.
West G.B., Brown J.H., and Enquist B.J. A general model for the origin of allometric scaling laws in biology. Science 276:122–126, 1997.
Meinhardt H. Models for the formation of netlike structures. In: Vascular Morphogenesis: In Vivo, In Vitro, In Mente, edited by Little C.D., Mironov V., and Sage E.H. Boston: Birkhauser, 1997 pp. 147–172.
Sage E.H. Introduction to Part II. In: Vascular Morphogenesis: In Vivo, In Vitro, In Mente, edited by Little C.D., Mironov V., and Sage E.H. Boston: Birkhauser, 1997 pp. 73–77.
Murray J.A., Manoussaki D., Lubkin S.R., and Vernon R. A mechanical theory of in vitro vascular network formation. In: Vascular Morphogenesis: In Vivo, In Vitro, In Mente, edited by Little C.D., Mironov V., and Sage E.H. Boston: Birkhauser, 1997 pp. 173–188.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Birkhäuser
About this chapter
Cite this chapter
Bassingthwaighte, J.B., Beard, D.A., Li, Z., Yipintsoi, T. (1996). Is the Fractal Nature of Intraorgan Spatial Flow Distributions Based on Vascular Network Growth or on Local Metabolic Needs?. In: Little, C.D., Mironov, V., Sage, E.H. (eds) Vascular Morphogenesis: In Vivo, In Vitro, In Mente. Cardiovascular Molecular Morphogenesis. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4156-0_16
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4156-0_16
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8678-3
Online ISBN: 978-1-4612-4156-0
eBook Packages: Springer Book Archive