Skip to main content
Log in

The principle of adequate design and the cardiovascular system

  • Published:
The bulletin of mathematical biophysics Aims and scope Submit manuscript

Abstract

The principle of adequate design (N. Rashevsky,Mathematical Biophysics, 3rd Ed., Vol. II, Dover Publications, Inc., New York, 1960) is applied to some parts of the cardiovascular system, extending the work of David Cohn (Bull. Math. Biophysics,16, 59–74, 1954;ibid.,17, 219–227, 1955). In addition to the diameterr a of the aorta and the peripheral resistanceR, calculated by Cohn, other quantities are estimated as to their order of magnitude. It is shown that the specifications of the average metabolic rate lead, from considerations of design, to the possibility of evaluating the orders of magnitude of the average blood pressure, the systolic and diastolic pressures, stroke volume of the heart, duration of the cardiac period and the volume elasticity of the aorta. The calculated values are of the correct orders of magnitude. The purpose of the paper is to illustrate how the application of the principle of adequate design can lead to the evaluation of the above parameters from purely theoretical considerations, rather than from indirect measurements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Aperia, A. 1940. “Hemodynamical Studies.”Skand. Arch. f. Physiologie,83, Supplement 16, 1–230.

    Google Scholar 

  • Carlson, A. J., and V. Johnson. 1953.The Machinery of the Body. Chicago: The University of Chicago Press.

    Google Scholar 

  • Cohn, David L. 1954. “Optimal Systems: I. The Vascular System.”Bull. Math. Biophysics,16, 59–74.

    Article  Google Scholar 

  • — 1955. “Optimal Systems: II. The Vascular System.”Ibid.,17, 219–227.

    Article  Google Scholar 

  • Cope, Freeman W. 1960. “An Elastic Reservoir Theory of the Human Systemic Arterial System Using Current Data on Aortic Elasticity.”Bull. Math. Biophysics,22, 19–40.

    Google Scholar 

  • — 1961. “A Method for the Computation of Aortic Distensibility in the Living Human Patient and Its Use for the Determination of the Aortic Effects of Aging, Drugs, and Exercise.”Ibid.,23, 337–353.

    Article  Google Scholar 

  • — 1962. “A Method for Calculation of Human Systolic and Diastolic Blood Pressures Using an Elastic Reservoir Theory of the Systemic Arterial System, and Some Clinical and Physiological Applications.”Ibid.,24, 137–157.

    Google Scholar 

  • Eddington, A. S. 1949.Fundamental Theory. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Euler, Leonard. 1862.Opera Postuma. II. Principia Pro Motu Sanguinis Per Arterias Determinando. St. Petersburg (Russia).

  • Frank, O. 1899. “Die Grundform des Arteriellen Pulses.”Z. f. Biol.,37, 483–526.

    Google Scholar 

  • — 1905. “Der Puls in den Arterien.”Ibid.,46, 441–553.

    Google Scholar 

  • — 1920. “Die Elasticität der Blutgefässe.”Ibid.,71, 255–272.

    Google Scholar 

  • — 1927. “Die Theorie der Pulswellen.”Ibid.,85, 91–130.

    Google Scholar 

  • — 1928. “Der Ablauf der Strömungsgeschwindigkeit in den Gefässen.”Ibid.,88, 249–263.

    Google Scholar 

  • King, A. L. 1946. “Pressure-Volume Relation for Cylindrical Tubes With Elastomeric Walls: The Human Aorta.”J. Appl. Physics,17, 501–505.

    Article  Google Scholar 

  • McDonald, D. A. 1960.Blood Flow in Arteries. Baltimore: Williams & Wilkins.

    Google Scholar 

  • Rashevsky, N. 1943. “Outline of a New Mathematical Approach to General Biology: I.”Bull. Math. Biophysics,5, 33–47.

    Article  Google Scholar 

  • — 1944. “Studies in the Physicomathematical Theory of Organic Form.”Ibid. 6, 1–59.

    Article  MathSciNet  Google Scholar 

  • — 1960.Mathematical Biophysics, 3rd and Rev. Ed. New York: Dover Publications, Inc.

    MATH  Google Scholar 

  • — 1961.Mathematical Principles in Biology and Their Applications. Springfield: Charles C. Thomas, Publisher.

    MATH  Google Scholar 

  • Remington, J. W., C. R. Noback, W. F. Hamilton, and J. J. Gold. 1948. “Volume Elasticity Characteristics of the Human Aorta and the Prediction of the Stroke Volume from the Pressure Pulse.”Am. J. Physiol.,153, 298–308.

    Google Scholar 

  • Roston, S. 1959. “Mathematical Formulation of Cardiovascular Dynamics by Use of the Laplace Transform.”Bull. Math. Biophysics,21, 1–11.

    Article  Google Scholar 

  • Weber, E. H. 1831. InHildebrands Handbuch der Anatomie, Vol. 3, p. 70.

  • Wetzler, K., and A. Böger. 1939. “Die Dynamik des Arteriellen Systems.”Ergeb. d. Physiol.,41, 292–606.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rashevsky, N. The principle of adequate design and the cardiovascular system. Bulletin of Mathematical Biophysics 25, 59–74 (1963). https://doi.org/10.1007/BF02477771

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02477771

Keywords

Navigation