Assessment of Left Ventricular Viscoelastic Components Based on Ventricular Harmonic Behavior
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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.
Key wordsleft ventricle diastole systole cardiac modeling contractility viscoelasticity
This work is partially supported by NIH grants HL-63954, HL-71137, HL-73021 and HL-76560.
- Bland JM, and Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet xx: 307–310, 1986.Google Scholar
- 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.Google Scholar
- Burkhoff D, and Sagawa K. Ventricular efficiency predicted by an analytical model. Am J Physiol Regul Integr Comp Physiol 250: R1021–R1027, 1986.Google Scholar
- 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.Google Scholar
- Haberman R. Mathematical models: Mechanical vibrations, population dynamics and traffic flow. SIAM, 1998.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- Ljung L. System identification—Theory for the user, Prentice-Hall, Englewood Cliffs, NJ, 1987.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar