Abstract
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).
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Literature
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.
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.
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.
—. 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.
— 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.
— 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.
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.
Defares, J. G., J. J. Osborn, and H. H. Hara. 1963. “Theoretical Synthesis of the Cardiovascular System”.Acta Physiol. et Parmac. Néerl.,12, 189.
Franklin, D. L., R. L. Van Citters and R. F. Rushmer. 1962. “Balance Between Right and Left Ventricular Output”.Circ. Res.,10, 17.
Gebhardt, W. 1961. “Die Druck-Volumen Beziehungen des Warmbluter Herzens”.Arch. f. Kreislaufforschung,34, 201.
Green, H. D. 1950. “Circulation: Physical Principles”. InMedical Physics, O. Glasser, Ed. Chicago: Year Book Publ.1.
Grodins, F.S. 1959. “Integrative Cardiovascular Physiology: A Mathematical Synthesis of Cardiac and Blood Vessel Hemodynamics”.Quart. Review of Biology,34, 93.
Guyton, A. C. 1963.Cardiac Output and its Regulation. New York: Saunders Publ. Co.
Macey, R. 1955. “Studies on the Relations Between Pressures and Flow in the Circulation”.Bull. Math. Biophysics,17, 169.
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.
Monroe, G. and G. N. French. 1961. “Left Ventricular Pressure-Volume Relationships and Myocardial Oxygen Consumption in the Isolated Heart”.Circ. Res.,9, 362.
Rosenblueth, A. 1962. “The Intrinsic Adaptation of the Work of Ventricular Muscle”.Proc. Intern. Union Physiological Sciences,1, 144 XXXII Intern. Congress).
Sarnoff, S. J., J. H. Mitchell, J. P. Gilmore, and J. P. Remensnijder. 1960. “Homeometric Autoregulation in the Heart”.Circ. Res.,8, 1077.
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.
Starling, E. H. 1918.The Linacre Lecture on the Law of the Heart. London: Longmans, Green.
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Defares, J.G., Osborn, J.J. & Hara, H.H. On the theory of the cardiovascular system. Bulletin of Mathematical Biophysics 27 (Suppl 1), 71–83 (1965). https://doi.org/10.1007/BF02477263
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DOI: https://doi.org/10.1007/BF02477263