Assessment of Left Ventricular Viscoelastic Components Based on Ventricular Harmonic Behavior

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Abstract
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.