The bulletin of mathematical biophysics

, Volume 27, Supplement 1, pp 71–83 | Cite as

On the theory of the cardiovascular system

  • J. G. Defares
  • J. J. Osborn
  • H. H. Hara


Most theoretical studies of the circulation have focussed on the transmission line properties of arteries. Only a small number of papers have dealt with the circulation as a closed (lumped) system with two pumps connected by the lesser and greater circulation (Beneken, inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Defares,et al., inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Grodins,Quart. Rev. of Biology,34, 93, 1959; Guyton,Cardiac Output and its Regulation, Saunders Publ. Co., New York, 1963). F. W. Cope's recent studies in this journal (Bull. Math. Biophysics,22, 19, 1960;23, 337, 1961;24, 137, 1962) deal with essentially the same questions, although here the circuit is not “closed”. We have attempted to extend the analysis of the areflex (closed) circulation. The complete study is reported elsewhere (Defares,et al., Acta Physiol, et Parmac. Neerl., 1963).


Stroke Volume Systemic Arterial Pressure Holland Publ Complete Paper Aortic Elasticity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Beneken, J. E. W. 1963. “Investigation on the Regulatory System of the Blood Circulation”. InCirculatory Analog Computers, A. Noordergraaf, Ed. Amsterdam: North Holland Publ. Co.Google Scholar
  2. Borst, H. G., M. McGregor, J. L. Whittenburger, and E. Berglund. 1956. “Influence of Pulmonary Arterial and Left Pressures on Pulmonary Vascular Resistance”.Circ. Res.,4, 393.Google Scholar
  3. Cope, F. W. 1960. “An Elastic Reservoir Theory of the Human Systemic Arterial System Using Current Data on Aortic Elasticity”.Bull. Math. Biophysics,22, 19.CrossRefGoogle Scholar
  4. —. 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.CrossRefGoogle Scholar
  5. — 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.CrossRefGoogle Scholar
  6. — 1963. “A Modified Windkessel (Elastic Reservoir) Theory of the Human Systemic Arterial System Using Modern Data on Aortic Elasticity so as to Yield Computational Accuracy Sufficient for Clinical Usefulness”. InCirculatory Analog Computers, A. Noordergraaf, Ed., Amsterdam: North Holland Publ. Co.Google Scholar
  7. Defares, J. G., H. H. Hara, J. J. Osborn, and J. McLeod. 1963. “Theoretical Analysis and Computer Simulation of the Circulation with Special Reference to the Starling Properties of the Ventricles”. InCirculatory Analog Computers, A. Noordergraaf, Ed., Amsterdam: North Holland Publ. Co.Google Scholar
  8. Defares, J. G., J. J. Osborn, and H. H. Hara. 1963. “Theoretical Synthesis of the Cardiovascular System”.Acta Physiol. et Parmac. Néerl.,12, 189.Google Scholar
  9. Franklin, D. L., R. L. Van Citters and R. F. Rushmer. 1962. “Balance Between Right and Left Ventricular Output”.Circ. Res.,10, 17.Google Scholar
  10. Gebhardt, W. 1961. “Die Druck-Volumen Beziehungen des Warmbluter Herzens”.Arch. f. Kreislaufforschung,34, 201.CrossRefGoogle Scholar
  11. Green, H. D. 1950. “Circulation: Physical Principles”. InMedical Physics, O. Glasser, Ed. Chicago: Year Book Publ.1.Google Scholar
  12. Grodins, F.S. 1959. “Integrative Cardiovascular Physiology: A Mathematical Synthesis of Cardiac and Blood Vessel Hemodynamics”.Quart. Review of Biology,34, 93.CrossRefGoogle Scholar
  13. Guyton, A. C. 1963.Cardiac Output and its Regulation. New York: Saunders Publ. Co.Google Scholar
  14. Macey, R. 1955. “Studies on the Relations Between Pressures and Flow in the Circulation”.Bull. Math. Biophysics,17, 169.CrossRefGoogle Scholar
  15. Mitchell, J. H., A. G. Wallace, and N. Skinner Sheldon, Jr. 1963. “Intrinsic Effect of Heart Rate on Left Ventricular Performance”.Amer. Jour. Physiol.,205, 41.Google Scholar
  16. Monroe, G. and G. N. French. 1961. “Left Ventricular Pressure-Volume Relationships and Myocardial Oxygen Consumption in the Isolated Heart”.Circ. Res.,9, 362.Google Scholar
  17. Rosenblueth, A. 1962. “The Intrinsic Adaptation of the Work of Ventricular Muscle”.Proc. Intern. Union Physiological Sciences,1, 144 XXXII Intern. Congress).Google Scholar
  18. Sarnoff, S. J., J. H. Mitchell, J. P. Gilmore, and J. P. Remensnijder. 1960. “Homeometric Autoregulation in the Heart”.Circ. Res.,8, 1077.Google Scholar
  19. Sarnoff, S. J. and J. H. Mitchell. 1962. “The Control of the Function of the Heart”. InHandbook of Physiology, Sec. Vol. I Circulation, W. F. Hamilton, Ed. Washington: Amer. Physiol. Soc.Google Scholar
  20. Starling, E. H. 1918.The Linacre Lecture on the Law of the Heart. London: Longmans, Green.Google Scholar

Copyright information

© N. Rashevsky 1965

Authors and Affiliations

  • J. G. Defares
    • 1
    • 2
  • J. J. Osborn
    • 1
    • 2
  • H. H. Hara
    • 1
    • 2
  1. 1.Department of PhysiologyUniversity of Leydenthe Netherlands
  2. 2.The Institute of Medical SciencesUniversity of the Pacific at the Presbyterian Medical CenterSan Francisco

Personalised recommendations