Digital Computer Simulation of Arterial Blood Flow

  • B. T. Fairchild
  • L. J. Krovetz
  • C. E. Huckaba


The advent of high speed electronic computers has relaxed the necessity for restrictive assumptions demanded by classical mathematical methods, and numerical solution techniques now provide a means for investigation of complex mathematical systems. Thus, it is desirable to re-evaluate physiological models in terms not limited by traditional techniques; to search for new areas of application; and to show how these models may be used in clinical and research studies.


Arterial Blood Flow Dimensionless Pressure Elastic Tube Digital Computer Simulation Pressure Step 
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.

Literature Cited

  1. ATTINGER, E. O. and ANNE, A. (1966). Simulation of the Cardiovascular System. Ann. N. Y. Acad. Sci., 128, 810–29.CrossRefGoogle Scholar
  2. BIRD, R. B., STEWART, W. E., and LIGHTFOOT, E. N. (1960). Transport Phenomena. New York, London: John Wiley & Sons.Google Scholar
  3. BURTON, A. C. (1960). Hemodynamics and the Physics of the Circulation. In: Medical Physiology and Biophysics, Ruch, T. C., and Fulton, J. F. (eds.), pp. 643–66. Philadelphia: Saunders.Google Scholar
  4. CHANG, C. C. and ATABEK, H. B. (1961). The Inlet Length for Oscillatory Flow and its Effects on the Determination of the Rate of Flow in Arteries. Phys. Med. Biol., 6, 303–317.CrossRefGoogle Scholar
  5. DEFARES, J. G., HARA, H. H., OSBORN, J. J. AND McLEOD, J. (1963). Theoretical Analysis and Computer Simulation of the Circulation with Special Reference to the Starting Properties of the Ventricles. In: Circulatory Analog Computers, Noordergraaf, A., Jager, G. N. and Westerhof, N. (eds.), pp. 91–122. Amsterdam: North-Holland Publishing Company.Google Scholar
  6. FAIRCHILD, B. T., WENGROW, H. R. and MAY, F. P. (1965). AMOS: Numerical Integration of Differential Equations with the Adams-Moulton-Shell Method. Report from the Department of Chemical Engineering, University of Florida, Gainesville, Florida.Google Scholar
  7. FOX, E. A. AND SAIBEL, E. (1963). Attempts in the Mathematical Analysis of Blood Flow. Trans. Soc. Rheology, 7, 25–31.CrossRefGoogle Scholar
  8. FRY, D. L. (1959). The Measurement of Pulsatile Blood Flow by the Computed Pressure Gradient Technique. IRE Trans. on Med. Electronics, 6, 259–64.CrossRefGoogle Scholar
  9. FRY, D. L. AND GREENFIELD, J. C. JR. (1964). The Mathematical Approach to Hemodynamics, with Particular Reference to Womersley’s Theory. In: Pulsatile Blood Flow, Attinger, E. D. (ed.), pp. 85–99. New York: McGraw-Hill.Google Scholar
  10. GESSNER, U. AND BERGEL, D. H. (1964). Frequency Response of Electromagnetic Flowmeters. J. Appl. Physiol., 19, 1209–11.Google Scholar
  11. GREENFIELD, J. C. JR. AND FRY, D. L. (1962). Measurement Errors in Estimating Aortic Blood Velocity by Pressure Gradient. J. Appl. Physiol., 17, 1013–19.Google Scholar
  12. KARREMAN, G. (1952). Some contributions to the Mathematical Biology of Blood Circulation. Reflections of Pressure Waves in the Arterial System. Bull. Math. Biophys., 14, 327–50.CrossRefGoogle Scholar
  13. KROVETZ, L. J. (1965). The Effect of Vessel Branching on Haemodynamic Stability. Phys. Med. Biol., 10, 417–27.CrossRefGoogle Scholar
  14. KROVETZ, L. J. AND BENSON, R. W. (1965). Mixing of Dye and Blood in the Canine Aorta. J. Appl. Physiol., 20, 922–926.Google Scholar
  15. LAMBERT, J. W. (1956). Fluid Flow in a Nonrigid Tube. Ph. D. Thesis, Purdue University.Google Scholar
  16. LAMBERT, J. W. (1958). On the Nonlinearities of Fluid Flow in Nonrigid Tubes. J. Franklin Inst., 266, 83–102.CrossRefGoogle Scholar
  17. McDonald, D. A. (1952). The Occurrence of Turbulent Flow in the Rabbit Aorta. J. Physiol., 118, 340–47.Google Scholar
  18. McDonald, D. A. (1960). Blood Flow in Arteries. London: Edward Arnold, also Baltimore: Williams and Wilkins.Google Scholar
  19. MORGAN, G. W., AND KIELY, J. P. (1954). Wave Propagation in a Viscous Liquid Contained in a Flexible Tube. J. Acoust. Soc. Amer., 27, 715–25.CrossRefGoogle Scholar
  20. NOORDERGRAAF, A. (1963). Development of an Analog Computer for the Human Systemic Circulatory System. In: Circulatory Analog Computers, Noordergraaf, A., Jager, G. N. and Westerhof, N. (eds.), pp. 29–44. Amsterdam: North-Holland Publishing Company.Google Scholar
  21. OLMSTED, F. (1959). Measurement of Cardiac Output in Unrestrained Dogs by an Implanted Electromagnetic Meter. IRE Trans. on Med. Electronics, 6, 210–213.CrossRefGoogle Scholar
  22. OLMSTED, F. (1962). Phase Detection Electromagnetic Flowmeter-Design and Use. IRE Trans. on Bio-Med. Electronics, 9, 88–92.Google Scholar
  23. OLMSTED, F. AND ALDRICH, F. D. (1961). Improved Electromagnetic Flowmeter; Phase Detection, a New Principle. J. Appl. Physiol., 16, 197–201.Google Scholar
  24. REPETTI, R. W. AND LEONARD, E. F. (1965). Physical Basis for the Axial Accumulation of Red Cells. Paper presented at the 56th National Meeting AICHE, San Francisco, California.Google Scholar
  25. REYNOLDS., O. (1883). An Experimental Investigation of the Circumstances which Determine whether the Motion ofGoogle Scholar
  26. Water shall be Direct or Sinuous, and of the Laws of Resistance in Parallel Channels. Philos. Trans., 174, 935–82.Google Scholar
  27. SCHULTZ-GRUNOW, F. (1940). Pulsierender Durchflug durch Rohre. Forschg. Ing. - Wesen, 11, 170.CrossRefGoogle Scholar
  28. SEXL, TH. (1930). her den von E. G. Richardson entdeckten,,Annlareffekt“. Z. Phys. 61, 349.Google Scholar
  29. SHAPIRO, A. H. (1954). The Dynamics and Thermodynamics of Compressible Fluid Flow. New York: Ronald Press.Google Scholar
  30. SPENCER, M. P. AND DENISON, A. B. (1959). The Square-Wave Electromagnetic Flowmeter: Theory of Operation and Design of Magnetic Probes for Clinical and Experimental Application. IRE Trans. on Med. Electronics, 6, 220–28.CrossRefGoogle Scholar
  31. STREETER, V. L., KEITZER, W. F. AND BOHR, D. F. (1963). Pulsatile Pressure and Flow Through Distensible Vessels. Circulation Res., 13, 3–20.CrossRefGoogle Scholar
  32. UCHIDA, S. (1956). The Pulsating Viscous Flow Superposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe. ZAMP VII, 403–22.Google Scholar
  33. WARNER, H. R. (1959). The Use of an Analog Computer for Analysis of Control Mechanisms in the Circulation. Proc. IRE, 47, 1913–16.CrossRefGoogle Scholar
  34. WITZIG, K. (1914). Über erzwungene Wellenbewegungen zäher, incompressibler Flüssigkeiten in elastischen RBhren. Inaug. Diss. Bern. Bern: Wyss.Google Scholar
  35. WOMERSLEY, J. R. (1955). Method for the Calculation of Velocity, Rate of Flow and Viscous Drag in Arteries when the Pressure Gradient is Known. J. Physiol. 127, 553–63.Google Scholar
  36. WOMERSLEY, J. R. (1957). An Elastic Tube Theory of Pulse Transmission and Oscillatory Flow in Mammalian Arteries. Wright Air Development Center, Technical Report WADC-TR 56–614.Google Scholar

Copyright information

© Springer Science+Business Media New York 1967

Authors and Affiliations

  • B. T. Fairchild
    • 1
  • L. J. Krovetz
    • 2
  • C. E. Huckaba
    • 3
  1. 1.Central Research DepartmentMonsanto CompanySt. LouisUSA
  2. 2.Department of PediatricsUniversity of FloridaGainesvilleUSA
  3. 3.Department of Chemical EngineeringDrexel Institute of TechnologyPhiladelphiaUSA

Personalised recommendations