Skip to main content
Log in

The Effect of Heart Rate, Preload, and Afterload on the Viscoelastic Properties of the Swine Myocardium

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Experiments were performed to test the hypothesis that viscoelastic properties of the swine myocardium are independent of heart rate (HR), preload (PL), and afterload (AL). Left ventricular pressure and aortic flow (AoF) waveforms were recorded in 13 swine. At different paced heart rates, an inferior vena caval occlusion (IVC) was used to reduce PL, then the IVC was released and simultaneously the aorta was clamped to increase AL. Equivalent left ventricular pressure waveform pairs consisting of an ejecting waveform (denoted as LVP) and isovolumic waveform (denoted as hydromotive pressure, HMP) were selected according to specified criteria resulting in 371 equivalent waveform pairs. From the selected waveform pairs and corresponding aortic flow waveforms, the viscoelastic properties (k and ε1) were estimated by HMP = LVP + ε1 V EJ + k × LVP × AoF. Here ε1 is the parallel elastance, k is the myocardial friction, and V EJ is the integral of AoF over ejection. Next, using k, ε1, LVP, and AoF waveforms, HMP was estimated using the equation above. To validate the model, the measured HMP and model-calculated HMP were compared for 371 matched waveform pairs (R 2 = 0.97, SEE = 3.7 mmHg). The viscoelastic parameters (k and ε1) did not exhibit any clear or predictable dependence on HR, PL, and AL.

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

REFERENCES

  1. Berlew, B. S., and K. T. Weber. Connective tissue and the heart: Functional significance and regulatory mechanisms. Cardiol. Clin. 18(3):435–442, 2001.

    Google Scholar 

  2. Blix, M. Scand. Arch. Physiol. 4:399, 1893.

  3. Burden, R. L., J. D. Faires, and A. C. Reynolds. Numerical differentiation In: Numerical Analysis, 2nd ed., edited by Weber and Schmidt. Boston: Prindle, 1981, p. 130.

    Google Scholar 

  4. Campbell, K. B., R. D. Kirkpatrick, G. G. Knowlen, and J. A. Ringo. Late-systolic pumping properties of the left-ventricledeviation from elastance-resistance behavior. Circ. Res. 66:218–233, 1990.

    Google Scholar 

  5. Chang, K. C., and T. S. Kuo. Single-beat estimation of the ventricular pumping mechanics in terms of the systolic elastance and resistance. J. Theor. Biol. 189:89–95, 1997.

    Google Scholar 

  6. Chapman, R. E., and F. G. Spinale. Extracellular protease activation and unraveling of the myocardial interstitium: Critical steps toward clinical applications. Am. J. Physiol. Heart Circ. Physiol. 286(1):H1–H10, 2004.

    Google Scholar 

  7. Covell, J. W., R. R. Taylor, E. H. Sonnenblick, and J. Ross, Jr. Series elasticity in the intact heart. Evidence for the application of the Hill model for muscle to the intact left ventricle. Pflugers Arch. 357(3-4):225–236, 1975.

    Google Scholar 

  8. Drew, G. A., and S. C. Koenig. Biomedical patient monitoring, data acquisition, and playback with LabVIEW. In: LabVIEW for Automotive, Telecommunication, Semiconductor, Biomedical, and Other Application. J. B. Olansen and E. Roscow (ed.) Upper Saddle River: Prentice-Hall PTR, 2000, pp. 92–98.

    Google Scholar 

  9. Elliot, G. F., and C. R. Worthington. Muscle contraction: Viscous friction and the impulsive model. Int. J. Biol.Macromol. 27:327–332, 2000.

    Google Scholar 

  10. Elzinga, G., and N. Westerhof. The pumping ability of the left heart and the effect of coronary occlusion. Circ. Res. 38(4):297–302, 1976.

    Google Scholar 

  11. Ernst, E. Sliding friction contra sliding hypothesis. Acta Biochim. Biophy. Acad. Sci. Hung. 12(1):83–85, 1977.

    Google Scholar 

  12. Fenn, W. O. A quantitative comparison between the energy liberated and the work performed by the isolated sartorius muscle of the frog. J. Physiol. 58:175–203, 1923.

    Google Scholar 

  13. Ficke, A. 1882.Mech. ArbeitK.Wärmeentwickelung b.d. muskel thätigkeit, Leipzig: Brockhaus, p 67.

    Google Scholar 

  14. Fung, Y. C. Mathematical representation of the mechanical properties of the heart muscle. J. Biomech. 3(4):381–404, 1970.

    Google Scholar 

  15. Fung, Y. C. Comparison of different models of the heart muscle. J. Biomech. 4(4):289–295, 1971.

    Google Scholar 

  16. Glantz, S. A. A constitutive equation for the passive properties of muscle. J. Biomech. 7(2):137–145, 1974.

    Google Scholar 

  17. Glantz, S. A. A three-element model describes excised cat papillary muscle elasticity. Am. J. Physiol. 228(1):284–294, 1975.

    Google Scholar 

  18. Goldsmith, E. C., and T. K. Borg. The dynamic interaction of the extracellular matrix in cardiac remodeling. J. Card. Fail. 8(6, Suppl.):S314–S318, 2002.

    Google Scholar 

  19. Granzier, H. L., and S. Labeit. The giant protein titin: A major player in myocardial mechanics, signaling, and disease. Circ. Res. 94(3):284–295, 2004.

    Google Scholar 

  20. Harris, T.S., C. F. Baicu, C. H. Conrad, M. Koide, J.M. Buckley, M. Barnes, G. Cooper IV, and M. R. Zile. Constitutive properties of hypertrophied myocardium: Cellular contribution to changes in myocardial stiffness. Am. J. Physiol. Heart Circ. Physiol. 282:H2173–H2182, 2002.

    Google Scholar 

  21. Hein, S., S. Kostin, A. Heling, Y. Maeno, and J. Schaper. The role of the cytoskeleton in heart failure. Cardiovasc. Res. 45:273–278, 2000.

    Google Scholar 

  22. Hein, S., D. Scholz, N. Fujitani, H. Rennollet, T. Brand, A. Friedl, and J. Schaper. Altered expression of titin and contractile proteins in failing human myocardium. J. Mol. Cell. Cardiol. 26:1291–1306, 1994.

    Google Scholar 

  23. Hess, O. M., J. Grimm, and H. P. Krayenbuehl. Diastolic simple elastic and viscoelastic properties of the left ventricle in man. Circulation 59(6):1178–1187, 1979.

    Google Scholar 

  24. Hill, A. The maximum work and mechanical efficiency of human muscles, and their most economical speed. J. Physiol. 56:19–41, 1922.

    Google Scholar 

  25. Hill, A. Myothermic Experiments on the frog's gastrocnemius. Proc. R. Soc. Ser. B 109:267–303, 1931.

    Google Scholar 

  26. Hill, A. V. The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. Ser. B 126:136–195, 1938.

    Google Scholar 

  27. Hunter, P. J., A. D. McCulloch, and H. E. D. J. ter Keurs. Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol. 69(2-3):289–331, 1998. Review.

    Google Scholar 

  28. Hunter, W. C., J. S. Janicki, and K. T. Weber. Mechanical properties of the ventricle during systole. Fed. Proc. 39:169–174, 1980.

    Google Scholar 

  29. Hunter, W. C., J. S. Janicki, K. T. Weber, and A. Noordergraaf. Flow-pulse response: New method for the characterization of ventricular mechanics. Am. J. Physiol. Heart Circ. Physiol. 237:H282–H292, 1979.

    Google Scholar 

  30. Hunter, W. C., J. S. Janicki, K. T. Weber, and A. Noordergraaf. Systolic mechanical properties of the left ventricle: Effects of volume and contractile state. Circ. Res. 52:319–327, 1983.

    Google Scholar 

  31. Huxley, A. F. Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7:255–318, 1957.

    Google Scholar 

  32. Huxley, A. F., and R. Niedergerke. Structural changes in muscle during contraction; interference microscopy of living muscle fibres. Nature 173:971–973, 1954.

    Google Scholar 

  33. Huxley, H. E., and E. J. Hanson. Changes in the cross-striations of muscle during contraction and stretch and their structural interpretation. Nature 173:973–976, 1954.

    Google Scholar 

  34. Kulke, M., S. Fukita-Becker, E. Rostkova, C. Neagoe, K. Labeit, D. J. Manstein, M. Gautel, and W. A. Linke. Interaction between PEVK-Titan and actine filament: Origin of a viscous force component in cardiac myofibrils. Circ. Res. 89:874–881, 2001.

    Google Scholar 

  35. Landesberg, A., Y. Landesberg, S. Sideman, and H. E. Ter Kers. Molecular motion and cardiac muscle motor dynamics. Ann. N. Y. Acad. Sci. 972:119–126, 2002.

    Google Scholar 

  36. Landesberg, A., L. Livshitz, and H. E. ter Keurs. The effect of sarcomere shortening velocity on force generation, analysis, and verification of models for crossbridge dynamics. Ann. Biomed. Eng. 28(8):968–978, 2000.

    Google Scholar 

  37. Linke, W. A., and J. M. Fernandez. Cardiac titan: Molecular basis of elasticity and cellular contribution to elastic and viscous stiffness components in myocardium. J. Muscle Res. Cell Motil. 23:483–497, 2002.

    Google Scholar 

  38. Morano, I., K. Hadicke, S. Grom, A. Koch, R. H. Schwinger, M. Bohm, S. Bartel, E. Erdmann, and E. G. Krause. Titin, myosin light chains and C-protein in the developing and failing human heart. J. Mol. Cell Cardiol. 26:361–368, 1994.

    Google Scholar 

  39. Palladino, J. L., and A. Noordergraaf. Muscle contraction mechanics from ultrastructural dynamics. In: Analysis and Assessment of Cardiovascular Function, edited by G. Drzewiecki and J. K. J. Li. New York: Springer-Verlag, 1998, pp. 33–57.

    Google Scholar 

  40. Piene, H. Impedance matching between ventricle and load. Ann. Biomed. Eng. 12(2):191–207, 1984.

    Google Scholar 

  41. Rankin, J. S., C. E. Arentzen, P. A. McHale, D. Ling, and R.W. Anderson. Viscoelastic properties of the diastolic left ventricle in the conscious dog. Circ. Res. 41(1):37–45, 1977.

    Google Scholar 

  42. Regen, D. M., P. Denton, W. Howe, L. Taylor, and D. Hansen. Characteristics of left-ventricular isovolumic pressure waves in isolated dog hearts. Heart Vessels 9:155–166, 1994.

    Google Scholar 

  43. Schroeder, M. J., B. Perrault, D. L. Ewert, and S. C. Koenig. HEART: An automated beat-to-beat cardiovascular analysis package using Matlab. Comp. Biol. Med. 34:371–388, 2003.

    Google Scholar 

  44. Schroff, S. G., J. S. Janicki, and K. T. Weber. Evidence and quantitation of left ventricular systolic resistance. Am. J. Physiol. Heart Circ. Physiol. 249:H358–H370, 1985.

    Google Scholar 

  45. Sonneblick, E. H. Implications of muscle mechanics in the heart. Fed. Proc. 21:975–990, 1962.

    Google Scholar 

  46. Sonneblick, E. H. Force velocity relations in mammalian muscle. Am. J. Physiol. 202:932–939, 1962.

    Google Scholar 

  47. F. G. Spinale, and M. R. Zile. Viscoelastic properties of pressure overload hypertrophied myocardium: Effect of serine protease treatment. Am. J. Physiol. Heart Circ. Physiol. 282:H2324–H2335, 2002.

    Google Scholar 

  48. Suga, H. Time course of left ventricular pressure-volume relationship under various end-diastolic volumes. Japan Heart J. 10:509–515, 1969.

    Google Scholar 

  49. Suga, H. Time course of left ventricular pressure-volume relationship under various extents of aortic occlusion. Japan Heart J. 11:373–378, 1970.

    Google Scholar 

  50. Suga, H. Left ventricular time-varying pressure-volume ratio in systole as index of myocardial inotropism. Japan Heart J. 12:153–160, 1971.

    Google Scholar 

  51. Sunagawa, K., A. Yamad, Y. Senda, Y. Kikuchi, M. Nakamura, T. Shibahara, and Y.Nose. Estimation of the hydromotive source pressure from ejecting beats of the left ventricle. IEEE Trans. Biomed. Eng. 27:299–305, 1980.

    Google Scholar 

  52. Takeda, K., R. Kadot, S. Yagi. Time-varying myocardial elastance of canine left ventricle. Am. J. Physiol. Heart Circ. Physiol. 261:H1554–H1562, 1991.

    Google Scholar 

  53. Takeuchi, M., Y. Igarashi, S. Tomimoto, M. Odake, T. Hayashi, T. Tsukamoto, K. Hata, H. Takaoka, and H. Fukuzaki. Singlebeat estimation of the slope of the end-systolic pressure-volume relation in the human left ventricle. Circ. 83:202–212, 1991.

    Google Scholar 

  54. Thevenin, M. L. Rendus hebdomadaires de seances de L'Academie des sciences, XCVII, 159, 1883.

    Google Scholar 

  55. Tskhovrebova, L., and J. Trinick. Role of titan in vertebrate striated muscle. Philos. Trans. R. Soc. Lond. B Biol. Sci. 357:199–206, 2002.

    Google Scholar 

  56. Wang, X., F. Li, S. E. Campbell, and A. M. Gerdes. Chronic pressure overload cardiac hypertrophy and failure in guinea pigs: II. Cytoskeletal remodeling. J. Mol. Cell Cardiol. 31(2):319–331, 1999.

    Google Scholar 

  57. Yamamoto, S., H. Tsutsui, M. Takahashi, Y. Ishibashi, H. Tagawa, K. Imanaka-Yoshida, Y. Saeki, and A. Takeshita. Role of microtubules in the viscoelastic properties of isolated cardiac muscle. J. Mol. Cell Cardiol. 30(9):1841–1853,1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dan Ewert.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ewert, D., Wheeler, B., Doetkott, C. et al. The Effect of Heart Rate, Preload, and Afterload on the Viscoelastic Properties of the Swine Myocardium. Annals of Biomedical Engineering 32, 1211–1222 (2004). https://doi.org/10.1114/B:ABME.0000039355.53117.6f

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1114/B:ABME.0000039355.53117.6f

Navigation