Background: Assessment of left ventricular (LV) function with an emphasis on contractility has been a challenge in cardiac mechanics during the recent decades. The LV function is usually described by the LV pressure-volume (P-V) relationship. Based on this relationship, the ratio of instantaneous pressure to instantaneous volume is an index for LV chamber stiffness. The standard P-V diagrams are easy to interpret but difficult to obtain and require invasive instrumentation for measuring the corresponding volume and pressure data. In the present study, we introduce a technique that can estimate viscoelastic properties, not only the elastic component but also the viscous properties of the LV based on oscillatory behavior of the ventricular chamber and it can be applied non-invasively as well. Materials and Methods: The estimation technique is based on modeling the actual long axis displacement of the mitral annulus plane toward the cardiac base as a linear damped oscillator with time-varying coefficients. Elastic deformations resulting from the changes in the ventricular mechanical properties of myocardium are represented as a time-varying spring while the viscous components of the model include a time-varying viscous damper, representing relaxation and the frictional energy loss. To measure the left ventricular axial displacement ten healthy sheep underwent left thoracotomy and sonomicrometry transducers were implanted at the apex and base of the LV. The time-varying parameters of the model were estimated by a standard Recursive Linear Least Squares (RLLS) technique. Results: LV stiffness at end-systole and end-diastole was in the range of 61.86–136 dyne/g.cm and 1.25–21.02 dyne/g.cm, respectively. Univariate linear regression was performed to verify the agreement between the estimated parameters, and the measured values of stiffness. The averaged magnitude of the stiffness and damping coefficients during a complete cardiac cycle were estimated as 58.63±12.8 dyne/g.cm and 0 dyne.s/g.cm, respectively. Conclusion: The results for the estimated elastic coefficients are consistent with the ones obtained from force-displacement diagram. The trend of change in the estimated parameters is also in harmony with the previous studies done using P-V diagram. The only input used in this model is the long axis displacement of the annulus plane, which can also be obtained non-invasively using tissue Doppler or MR imaging.
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REFERENCES
Applegate RJ, Cheng CP, and Little WC. Simultaneous conductance catheter and dimension assessment of left ventricular volume in the intact animal. Circulation 81: 638–648, 1990.
Bland JM, and Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet xx: 307–310, 1986.
Brecher GA. Experimental evidence of ventricular diastolic suction. Circ Res 4: 513–518, 1956.
Burkhoff D, de Tombe PP, and Hunter WC. Impact of ejection on the magnitude and time course of ventricular pressure generating capacity. Am J Physiol Heart Circ Physiol 265: H899–H909, 1993.
Burkhoff D, Mirsky I, and Suga H. Assessment of systolic and diastolic ventricular properties via pressure-volume analysis: A guide for clinical, translational, and basic researchers. Am J Physiol Heart Circ Physiol 289: 501–512, 2005.
Burkhoff D, and Sagawa K. Ventricular efficiency predicted by an analytical model. Am J Physiol Regul Integr Comp Physiol 250: R1021–R1027, 1986.
Campbell KB, Kirkpatrick RD, Knowlen GG, and Ringo JA. Late systolic mechanical properties of the left ventricle: Deviation from elastance-resistance behavior. Circ Res 66: 218–233, 1990.
Campbell KB, Shroff SG, and Kirkpatrick RD. Short time-scale LV systolic dynamics: Evidence for a common mechanism in both LV chamber and heart-muscle mechanics. Circ Res 68: 1532–1548, 1991.
Campbell KB, Wu Y, Simpson AM, Kirkpatrick RD, Shroff SG, Granzier HL, and Slinker BK. Dynamic myocardial contractile parameters from left ventricular pressure volume measurements. Am J Physiol Heart Circ Physiol. 289: H114–H130, 2005.
Cazorla O, Wu Y, Irving TC, and Granzier H. Titin-based modulation of calcium sensitivity of active tension in mouse skinned cardiac myocytes. Circ Res 88: 1028–1035, 2001.
Chiu YL, Ballou EW, and Ford LE. Internal viscoelastic loading in cat papillary muscle. Biophys J 40: 109–120, 1982a.
Chiu YL, Ballou EW, and Ford LE. Velocity transients and viscoelastic resistance to active shortening in cat papillary muscle. Biophys J 40: 121–128, 1982b.
Chen CH, Fetics B, Nevo E, Rochitte CE, Chiou KR, et al. Noninvasive Single-Beat Determination of Left Ventricular End-Systolic Elastance in Humans. J Am Coll Cardiol 38: 2028–2034, 2001.
Firstenberg MS, Smedira NG, Greenberg NL, Prior DL, et al. Relationship between early diastolic intraventricular pressure gradients, an index of elastic recoil, and improvements in systolic and diastolic function. Circulation 104(12 Suppl l): I330–I335, 18 Sep 2001.
Fukuda N, Sasaki D, Ishiwata S, and Kurihara S. Length dependence of tension generation in rat skinned cardiac muscle: Role of titin in the Frank-Starling mechanism of the heart. Circulation 104: 1639–1645, 2001.
Granzier HL, and Labeit S. The Giant Protein Titin: A Major Player in Myocardial Mechanics, Signaling, and Disease. Circ Res 94: 284–295, 2004.
Haberman R. Mathematical models: Mechanical vibrations, population dynamics and traffic flow. SIAM, 1998.
Hunter WC, Janicki JS, Weber KT, and Noordergraaf A. Systolic mechanical properties of the left ventricle. Effects of volume and contractile state. Circ Res 52: 319–327, 1983.
Kass DA, and Maughan WL. From “Emax” to pressure-volume relations: A broader view. Circulation 77: 1203–1212, 1988.
Kovacs SJ, Barzilai B, and Perez JE. Evaluation of diastolic function with Doppler echocardiography: The PDF formalism. Am J Physiol Heart Circ Physiol 252(1): H178–H187, Part 2, 1987.
Kulke M, Fujita-Becker S, Rostkova E, Neagoe C, Labeit D, Manstein DJ, Gautel M, and Linke WA. Interaction between PEVK-titin and actin filaments: Origin of a viscous force component in cardiac myofibrils. Ore Res 89: 874–881, 2001.
Ling D, Rankin JS, Edwards CH II, et al. Regional diastolic mechanics of the left ventricle in the conscious dog. Am J Physiol 236: H323–H330, 1979.
Ljung L. System identification—Theory for the user, Prentice-Hall, Englewood Cliffs, NJ, 1987.
McQueen DM, and Peskin CS. A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. Computer Graphics-US 34(1): 56–60, Feb 2000.
Nikolic SD, Feneley MP, Pajaro OE, et al. Origin of regional pressure gradients in the left ventricle during early diastole. Am J Physiol 268: H550–H557, 1995.
Opitz CA, Kulke M, Leake MC, Neagoe C, Hinssen H, Hajjar RJ, and Linke WA. Damped elastic recoil of the titin spring in myofibrils of human myocardium. Proc Natl Acad Sci USA 100: 12688–12693, 2003.
Rich MW, Stitziel NO, and Kovacs SJ. Prognostic value of diastolic filling parameters derived using a novel image processing technique in patients ≥70 years of age with congestive heart failure. Am J Cardiol 84(1): 82–86, 1999.
Schmiel FK, Lorenzen N, Fischer G, Harding P, and Kramer HH. Diastolic left ventricular function Experimental study of the early filling period using the Voigt model. Basic Res Cardiol 100(l): 64–74, Jan 2005.
Shroff SG, Campbell KB, and Kirkpatrick RD. Short time-scale LV systolic dynamics: Pressure vs. flow clamps and effects of activation. Am J Physiol Heart Circ Physiol 264: H946–H959, 1993.
Söderström T, Fan H, Carlsson B, and Bigi S. Least Squares Parameter Estimation of Continuous-Time ARX models from Discrete-Time Data. IEEE Trans. On Automatic Control 42(5): 659–673, 1997.
Suga H, and Sagawa K. Instantaneous pressure-volume relationships and their ratio in the excised, supported canine left ventricle. Ore Res 35: 117–126, 1974.
Takaoka H, Takeuchi M, Odake M, and Yokoyama M. Assessment of myocardial oxygen consumption (V∼O2) and systolic pressure-volume area (PVA) in human hearts. Eur Heart J 13: 85–90, 1992.
Templeton GH, and Nardizzi LR. Elastic and viscous stiffness of the canine left ventricle. J Appl Physiol 36(1): 123–127, 1974.
Weiss JL, Frederiksen JW, and Weisfeldt ML. Hemodynamic determinants of time-course of fall in canine left-ventricular pressure. J Clin Invest 58(3): 751–760 1976.
Yellin EL, Hori M, Yoran C, Sonnenblick EH, et al. Left-ventricular relaxation in the filling and nonfilling intact canine heart. Am J Cardiol: Part 2 250(4): H620–H629, 1986.
Yellin EL, Nikolic S, and Prater RWM. Left-ventricular filling dynamics and diastolic function. Progress in Cardiovascular Diseases 32(4): 247–271, 1990.
ACKNOWLEDGMENTS
This work is partially supported by NIH grants HL-63954, HL-71137, HL-73021 and HL-76560.
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Kheradvar, A., Milano, M., Gorman, R.C. et al. Assessment of Left Ventricular Viscoelastic Components Based on Ventricular Harmonic Behavior. Cardiovasc Eng 6, 30–39 (2006). https://doi.org/10.1007/s10558-006-9001-9
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DOI: https://doi.org/10.1007/s10558-006-9001-9