Assessment of the Mitral Valve Mechanical Properties using the Damped Harmonic Oscillator Model

The standard echocardiographic mitral valve (MV) EAE/ASE recommendations are based on the evaluation its planimetry, anatomy, & Doppler flow velocities while the leaflets` properties are estimated subjectively. Our objective was to study a novel model for the MV leaflets` viscoelastic behavior quantification normal valves & diseased mitral valves.

Methods:
using image processing techniques the centerline of the leaflet was extracted & tracked over a few cardiac cycles and the the leaflet`s opening angle was calculated. The physical model considers the valve tissue, the Chordea & the papillary muscles as one elastic string operating in an environment with friction. As such, it is hypothesized that during ventricular diastole valve angle behaves like a step response of a damped harmonic oscillator, which can be mathematically described by two parameters - W₀ & ξ . W₀ being the natural frequency, representing elasticity & ξ being the damping coefficient, representing the friction forces. To evaluate these coefficients an optimization algorithm searches for the best fit for extracted valve angle during the cardiac cycle.

Retrospective evaluation of parasternal long axis echo images of 35 healthy subjects, ages 34±11 y.o. & of 17 subjects with mitral stenosis, mean gradient of 8 mmHg & above, ages 48±14 y.o. was conducted. For each study the MV anterior leaflet median line was constructed and analyzed.

Results:
The calculated parameters were ξ of 0.34±0.14 & W₀ of 0.55±0.15 in healthy leaflets & ξ of 0.86±0.23 & W₀ of 1.06±0.30 in diseased stenotic leaflets. Logistic regression used to build a discrimination model in which the patient status was the dependent when W₀ & ξ were the independent variables showed statistical significance, p<0.0001.

Discussion:
Using novel image processing methodologies it is possible to track the MV & quantify its properties, allowing objective numerical long term assessment & follow up.