Cardio-Vascular Interaction Determines Pressure and Flow

  • N. Westerhof

Abstract

The arterial system as part of the circulation has been a subject of study since Harvey’s monograph of 1628. In 1735 Stephen Hales was the first to measure arterial blood pressure and noticed the oscillatory aspects of it. He also suggested that reduction of the arterial pressure oscillations resulted from arterial compliance. By the end of the last century the Windkessel model was proposed by Frank as a lumped model of the systemic arterial tree (Frank, 1899). Although wave travel was neglected in this model, the importance of arterial compliance as part of the load on the heart was clearly brought forward. With modern techniques simultaneous high quality pressure and flow data became available. These data could be analyzed with the newly developed computers and led to the derivation of input impedance, a comprehensive description of the arterial system. Knowledge of the input impedance provided a great step forward in the understanding of arterial function.

Keywords

Input Impedance Arterial System Peripheral Resistance Characteristic Impedance Aortic Pressure 
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.

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References

  1. Allaart, C.P., Sipkema, P., and Westerhof, N., 1995, Effect of perfusion pressure on diastolic stress strain relations of isolated rat papillary muscle. Am. J. Physiol. 268:H945–H954.PubMedGoogle Scholar
  2. Anliker, M., Histand, M.B., and Ogden, E., 1968. Dispersion and attenuation of small artificial pressure waves in the canine aorta. Circ. Res. 23:539–551.PubMedCrossRefGoogle Scholar
  3. Avolio, A.P., O’Rourke, M.F., Mang, K., Bason, P.T., and Gow, B.S., 1976, A comparative study of pulsatile arterial hemodynamics in rabbits and guinea pigs. Am. J. Physiol. 230:868–875.PubMedGoogle Scholar
  4. Baan. J., Van der Velde, E.T., De Bruin, H.G., Smeenk, G.J., Koops, J., Van Dijk, A.D., Temmerman, D., Senden, P.J., and Buis, B., 1984, Continuous measurement of left ventricular volume in animals and humans by conductance catheter. Circulation 70:812–823.PubMedCrossRefGoogle Scholar
  5. Berger, D.S., Li, J. K.-J., and Noordergraaf, A., 1994, Differential effects of wave reflections and peripheral resistance on aortic blood pressure: a model based study. Am. J. Physiol. 266:H1626–H1642.PubMedGoogle Scholar
  6. Broemser, Ph., 1935, Über die optimalen Beziehungen zwischen Hertztätigkeit und physikalischen Konstantes des Gefäss-systems. Zeitschr. f. Biol. 96:1–10.CrossRefGoogle Scholar
  7. Burattini, R., and Campbell, K.B., 1989, Modified asymmetric T-tube model to infer arterial wave reflection at the aortic root. IEEE Trans. Biomed. Eng. 36:805–814.Google Scholar
  8. Burattini, R., Fogliardi, R., and Campbell, K.B., 1994, Lumped model of terminal aorta impedance in the dog. Ann. Biomed. Eng. 22:381–391.PubMedCrossRefGoogle Scholar
  9. Cope, F.W., 1960, An elastic reservoir theory of the human systemic arterial system using current data on aortic elasticity. Bull. Math. Biophys. 22:19–26.CrossRefGoogle Scholar
  10. Cope, F.W., 1961, 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. In: Circulatory Analog Computers. A. Noordergraaf, G.N. Jager, and N. Westerhof (eds.). Amsterdam, North Holland Publ. Company, pp. 44–55.Google Scholar
  11. Dick, D.E., Kendrick, J.E., Matsom, G.L., and Rideout, V.C., 1968, Measurement of nonlinearity in the arterial system of the dog by a new method. Circ. Res. 22:101–111.PubMedCrossRefGoogle Scholar
  12. Elzinga, G., and Westerhof, N., 1973, Pressure and flow generated by the left ventricle against different impedances. Circ. Res. 32:178–186.PubMedCrossRefGoogle Scholar
  13. Elzinga. G., and Westerhof, N., 1979, How to quantify pump function of the heart. The value of variables derived from measurements on isolated muscle. Circ. Res. 44:303–308.PubMedCrossRefGoogle Scholar
  14. Elzinga, G., and Westerhof, N., 1980, Pump function of the feline left heart: changes with heart rate and its bearing on the energy balance. Cardiovasc. Res. 14:81–92.PubMedCrossRefGoogle Scholar
  15. Elzinga, G., and Westerhof. N., 1981, “Pressure-volume” relations in isolated cat trabeculae. Circ. Res. 49:388–394.PubMedCrossRefGoogle Scholar
  16. Elzinga, G., and Westerhof, N., 1982, Isolated cat trabeculae in a simulated feline heart and arterial system: contractile basis of cardiac pump function. Circ. Res. 51:430–438.PubMedCrossRefGoogle Scholar
  17. Elzinga, G., and Westerhof, N., 1984, Does the history of contraction affect the pressure-volume relationship? Fed. Proc. 43:2402–2407.PubMedGoogle Scholar
  18. Elzinga, G., and Westerhof, N., 1991, Matching between ventricle and arterial load follows from evolution. Circ. Res. 68:1495–1500.PubMedCrossRefGoogle Scholar
  19. Frank, O., 1895, Zur Dynamik des Herzmuskels. Zeitschr. f. Biol. 32:370–447.Google Scholar
  20. Frank, O., 1899, Die Grundform des Arteriellen Puls. Zeitschr. f. Biol. 37:483–526.Google Scholar
  21. Hunter, W.C., 1989, End-systolic pressure as a balance between opposing effects of ejection. Circ. Res. 64:265–275.PubMedCrossRefGoogle Scholar
  22. Jager, G.N., Westerhof, N., and Noordergraaf, A., 1965, Oscillatory flow impedance in electrical analog of arterial system. Circ. Res. 16:121–133.PubMedCrossRefGoogle Scholar
  23. Katz, L.A., Swain, J.A., Portman M.A., and Balaban, R.S., 1989, Relation between phosphate metabolites and oxygen consumption in heart in vivo. Am. J. Physiol. 256:H265–H274.PubMedGoogle Scholar
  24. Langendorff, O., 1899, Zur Kenntnisse des Blutlaufs in den Kranz-Gefässen des Herzens. Pflügers Arch. 78:423–440.CrossRefGoogle Scholar
  25. Laxminarayan, S., Sipkema, P., and Westerhof, N., 1978, Characterization of the arterial system in the time domain. IEEE Trans. BME 25:177–184.CrossRefGoogle Scholar
  26. Li, J.K.-J., (1986), Time resolution of forward and reflected waves in the aorta. IEEE Trans. BME 33:783–785.CrossRefGoogle Scholar
  27. Milnor, W.R., 1979, Aortic wave length as a determinant of the relation between heart rate and body size. Am. J. Physiol. 237:R3–R6.PubMedGoogle Scholar
  28. Milnor, W.R., 1989, Hemodynamics. Baltimore, Williams and Wilkins, pp. 282–284.Google Scholar
  29. Mitchell, G.F., Pfeffer, M.A., Westerhof, N., and Pfeffer, J.M., 1994, Measurement of aortic input impedance in rats. Am. J. Physiol. 267:H1907–H1915.PubMedGoogle Scholar
  30. Murgo, J.P., Westerhof, N., Giolma, J.P., and Altobelli, S.A., 1980, Aortic input impedance in normal man: relationship to pressure wave forms. Circulation 62:105–116.PubMedCrossRefGoogle Scholar
  31. Murgo, J.P., Westerhof, N., Giolma, J.P., and Altobelli, S.A., 1981. Manipulation of ascending aortic pressure and flow wave reflections with the Valsalva maneuver: relationship to input impedance. Circulation 63:122–132.PubMedCrossRefGoogle Scholar
  32. Newman, D.L., Sipkema, P., Greenwald, S.E., and Westerhof, N., 1986, High frequency characteristics of the arterial system. J. Biomech. 19:817–824.PubMedCrossRefGoogle Scholar
  33. O’Rourke, M.F., 1965, Pressure and flow in arteries. Ph.D. Dissertation. University of Sydney, Sydney, Australia.Google Scholar
  34. O’Rourke, M.F., and Cartmill, T.B., 1971, Influence of aortic coarctation on pulsatile hemodynamics in the proximal aorta. Circulation 44:281–292.PubMedCrossRefGoogle Scholar
  35. O’Rourke, M.F., and Avolio, A.P., 1980, Pulsatile flow and pressure in human systemic arteries: studies in man and in a multi-branched model of the human systemic arterial tree. Circ. Res. 46:363–372.PubMedCrossRefGoogle Scholar
  36. Patterson, S.W., and Starling, E.H., 1914, On the mechanical factors which determine the output of the ventricles. J. Physiol. (London) 48:357:379.Google Scholar
  37. Randall, O.S., van den Bos, G.C., and Westerhof, N., 1984, Systemic compliance: does it play a role in the genesis of essential hypertension? Cardiovasc. Res. 18:455–462.PubMedCrossRefGoogle Scholar
  38. Reuderink, P., Hoogstraten, H.W., Sipkema, P., Hillen, B., and Westerhof N., 1989, Linear and non-linear one-dimensional models of pulse wave transmission at high Womersley numbers. J. Biomech. 22:819–827.PubMedCrossRefGoogle Scholar
  39. Sagawa, K., 1978, The ventricular pressure-volume diagram revisited. Circ. Res. 43:677–687.PubMedCrossRefGoogle Scholar
  40. Sagawa, K., and Eisner, A., 1975, Static pressure-flow relation in the total systemic vascular bed of the dog and its modification by the baroreceptor reflex. Circ. Res. 36:406–413.PubMedCrossRefGoogle Scholar
  41. Sagawa, K., Maughan L., Suga, H., and Sunagawa, K., 1988, Cardiac contraction and the pressure-volume relationship. New York, Oxford University Press.Google Scholar
  42. Schouten. V.J.A., Allaart, C.P., and Westerhof, N., 1992, Effect of perfusion pressure on force of contraction in thin papillary muscles and trabeculae from rat hart. J. Physiol. 451:585–604.PubMedCentralPubMedGoogle Scholar
  43. Sipkema, P., and Westerhof, N., 1975, Effective length of the arterial system. Ann. Biomed. Engng. 3:296–307.CrossRefGoogle Scholar
  44. Sipkema, P., Westerhof, N., and Randall, O.S., 1980. The arterial system characterised in the time domain. Cardiovasc. Res. 14:270–279.PubMedCrossRefGoogle Scholar
  45. Sipkema, P., Latham, R.D., Westerhof, N., Rubal, B.J., and Slife, D.M., 1990, Isolated aorta set up for hemodynamic studies. Ann. Biomed. Engng. 18:491–503.CrossRefGoogle Scholar
  46. Stergiopulos, N., Young, D.F., and Rogge, T.R., 1992, Computer simulation of arterial flow with applications to arterial and aortic stenosis. J. Biomech. 25:1477–1488.PubMedCrossRefGoogle Scholar
  47. Stergiopulos, N., Tardy, Y., and Meister, J.-J., 1993, Nonlinear seperation of forward and backward running waves in arteries. J. Biomech. 26:201–209.PubMedCrossRefGoogle Scholar
  48. Stergiopulos, N., Meister, J.-J., and N. Westerhof, N., 1994, Simple and accurate way for estimating total and segmental arterial compliance: The pulse pressure method. Ann. Biom. Engng. 22:392–397.CrossRefGoogle Scholar
  49. Stergiopulos, N., Meister, J.-J., and Westerhof, N., 1995a, Evaluation of methods for estimation of total arterial compliance. Am. J. Physiol. 268: H1540–H1548.PubMedGoogle Scholar
  50. Stergiopulos, N., Meister, J.-J., and Westerhof, N., 1995b, Scottes in input inpedance. Am. J. Physiol. 269: H1490–H1495.PubMedGoogle Scholar
  51. Suga, H., Sagawa, K., and Shoukas, A.A., 1973, Load dependence of the instantaneous pressure-volume relation of the canine left ventricle and the effect of epinephrine and heart rate on the ratio. Circ. Res. 32:314–322.PubMedCrossRefGoogle Scholar
  52. Suga, H., 1979, Total mechanical energy of a ventricle model and cardiac oxygen consumption. Am. J. Physiol. 236:H499–H505.Google Scholar
  53. Suga, H., Hisano, R., Goto, Y., Yamada, O., and Ogarshi, Y., 1983, Effect of positive inotropic agents on the relation between oxygen consumption and systolic pressure volume area in the canine left ventricle. Circ. Res. 53:306–318.PubMedCrossRefGoogle Scholar
  54. Suga, H., 1990, Ventricular energetics. Physiol. Reviev 70:247–275.Google Scholar
  55. Sunagawa, K., Maughan, W.L., Burkhoff, D., and Sagawa, K., 1983, Left ventricular interaction with arterial load, studied in isolated canine ventricle. Am. J. Physiol. 245:H773–H780.PubMedGoogle Scholar
  56. Taylor, M.G., 1966a, The input impedance of an assembly of randomly branching tubes. Biophys. J. 6:29–51.PubMedCentralPubMedCrossRefGoogle Scholar
  57. Taylor, M.G., 1966b, Wave transmission through an assembly of randomly branching tubes. Biophys. J. 6:697–716.PubMedCentralPubMedCrossRefGoogle Scholar
  58. Ten Velden, G.H.M., Elzinga, G., and Westerhof, N., 1982, Left ventricular energetics: heat loss and temperature distribution of canine myocardium. Circ. Res. 50:63–73.PubMedCrossRefGoogle Scholar
  59. Toorop, G.P., Westerhof, N., and Elzinga, G., 1987, Beat-to-beat estimation of peripheral resistance and total arterial compliance during pressure transients. Am. J. Physiol. 252:H1275–H1283.PubMedGoogle Scholar
  60. Toorop, G.P., Van den Horn, G.J., Elzinga, G., and Westerhof, N., 1988, Matching between feline left ventricle and arterial load: optimal external power or efficiency. Am. J. Physiol. 254:H279–H285.PubMedGoogle Scholar
  61. Van den Bos, G.C., Westerhof, N., and Randall, O.S., 1982, Pulse wave reflection: can it explain the differences between systemic and pulmonary pressure and flow waves? Circ. Res. 51:479–485.PubMedCrossRefGoogle Scholar
  62. Van den Bos, G.C., Westerhof, N., and Randall, O.S., 1982, Pulse wave reflection: can it explain the differences between systemic and pulmonary pressure and flow waves? A study in dogs. Circ. Res. 51:479–485.PubMedCrossRefGoogle Scholar
  63. Van den Horn, G.J., Westerhof, N., and Elzinga, G., 1984, Interaction of heart and arterial system. Ann. Biomed. Eng. 12:151–162.PubMedCrossRefGoogle Scholar
  64. Van den Horn, G.J., Westerhof, N., and Elzinga, G., 1985, Optimal power generation by the left ventricle: a study in the anesthetized open-thorax cat. Circ. Res. 56:252–261.PubMedCrossRefGoogle Scholar
  65. Van Huis, G.A., Sipkema. P., and Westerhof, N., 1987, Coronary input impedance during the cardiac cycle as determined by impulse response method. Am. J. Physiol. 253:H317–H324.PubMedGoogle Scholar
  66. Vrettos, A.M., and Gross, D.R., 1994, Instantaneous changes in arterial compliance reduce energetic load on left ventricle during systole. Am. J. Physiol. 267:H24–H32.PubMedGoogle Scholar
  67. Westerhof, N., 1968, Analog studies of human systemic arterial hemodynamics. Ph.D. Dissertation. University of Pennsylvania, Philadelphia, Pa.Google Scholar
  68. Westerhof, N., Bosman, F., de Vries G.J., and Noordergraaf, A., 1969, Analog studies of the human systemic arterial tree. J. Biomechanics 2:121–143.CrossRefGoogle Scholar
  69. Westerhof, N., Elzinga, G., and Sipkema, P., 1971, An artificial arterial system for pumping hearts. J. Appl. Physiol. 31:776–781.PubMedGoogle Scholar
  70. Westerhof, N.P., Sipkema, P., van den Bos, G.C., and Elzinga, G., 1972, Forward and backward waves in the arterial system. Cardiovasc. Res. 6:648–656.PubMedCrossRefGoogle Scholar
  71. Westerhof, N., and Elzinga, G., 1978, The apparent source resistance of heart and muscle. Ann. Biomed. Engng. 6:16–32.CrossRefGoogle Scholar
  72. Westerhof, N., Murgo, J.P., Sipkema, P., Giolma, J.P., and Elzinga, G., 1979, Arterial impedance. In: Quantitative Cardiovascular Studies. N.H.C. Hwang, D.R. Gross, and D.J. Patel (eds.). University Park Press, Baltimore, pp. 111–150.Google Scholar
  73. Westerhof, N., and Elzinga, G., 1988, Hemodynamics. In: Encyclopedia of Medical Devices and Instruments. J.G. Webster (ed.). John Wiley and Sons, pp. 1493-1509.Google Scholar
  74. Westerhof, N., and Elzinga, G., 1991, Normalized input impedance and arterial decay time over heart period are independent of body size. Am. J. Physiol. 261:R126–R133.PubMedGoogle Scholar
  75. Westerhof, N., and Elzinga, G. 1993, Why Smaller Animals have Higher Heart Rates. In: Interaction Phenomena in the Cardiovascular System. Advances Exp. Med. and Biol. S. Sideman and R. Beyar (eds.), 346:319-329.Google Scholar
  76. Westerhof, N., 1993, Arterial Hemodynamics. In: The Physics of Heart and Circulation. J. Strackee, and N. Westerhof (eds.). IOP Press, pp. 355-382.Google Scholar
  77. Westerhof, N., 1994a, Heart period is related to time constant of arterial system and not to minimum of impedance modulus. In: Recent Progress in Cardiovascular Mechanics. S. Hosoda, T. Yaginuma, M. Sugawara, M.F. Taylor, and C.G. Caro (eds.). Harwood Acad. Publ., Chur Switzerland, pp. 115–127.Google Scholar
  78. Westerhof, N., 1994b, Heart period is proportional to body length. Cardioscience 5: 283–285.PubMedGoogle Scholar
  79. Wiggers, G.J., and Katz, L.N., 1921, Contour of ventricular volume curves under different conditions. Am. J. Physiol. 58:439–475.Google Scholar
  80. Wilcken, D.E.L., Charlier, A.A., Hoffman. J.I.E., and Guz, A., 1964, Effects of alterations in aortic impedance on the performance of the ventricles. Circ. Res. 14:283–293.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • N. Westerhof
    • 1
  1. 1.Laboratory for Physiology Institute for Cardiovascular Research (ICaR-VU)Free University of AmsterdamAmsterdamThe Netherlands

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