Abstract
An approach to quantitative work on optimal systems is considered. Desired optimal principles are utilized in constructing a hypothetical system similar to the organ system considered. A comparison of this constructed system with the anatomical system then gives an indication of the importance of the optimal principles in the form or function of the organ system considered.
These ideas are applied to the mammalian vascular system, and limiting values are obtained for some of its important component parts. The constructed system gives good agreement with anatomical data for vessel radii, lengths, and hydrodynamic resistance to flow.
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Literature
Clark, W. E. and P. B. Medawar. 1945.Essays on Growth and Form. Presented to D'Arcy Wentworth Thompson. Oxford: The Clarendon Press.
Coulter, N. A. and J. R. Pappenheimer. 1949. “Development of Turbulence in Flowing Blood.”Am. Jour. Physiol.,159, 401–08.
Green, Harold D. 1950. “Circulatory System: Physical Principles.”Medical Physics,11, 228–51. Ed. O. Glasser. Chicago: The Year Book Publishers, Inc.
Höber, R. 1945.Physical Chemistry of Cells and Tissues. Philadelphia: The Blakiston Company.
Krogh, A. 1929.The Anatomy and Physiology of Capillaries. New Haven: Yale University Press.
Rashevsky, N. 1948.Mathematical Biophysics. Rev. Ed. Chicago: University of Chicago Press.
Rubner, M. 1883. “Ueber den Einfluss der Körpergrösse auf Stoffund Kraftwechsel.”Zeit. f. Biol.,19, 535–62.
Thompson, D. W. 1917.On Growth and Form. Cambridge: The University Press.
Zuckerman, S. 1950. “A Discussion on the Measurement of Growth and Form.”Proc. Roy Soc. Lond.,B 137, 433–523.
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Cohn, D.L. Optimal systems: I. The vascular system. Bulletin of Mathematical Biophysics 16, 59–74 (1954). https://doi.org/10.1007/BF02481813
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DOI: https://doi.org/10.1007/BF02481813