The thermodynamics of diastole: Kinematic modeling-based derivation of the P-V loop to transmitral flow energy relation with in vivo validation

Pressure-volume (P-V) loop-based analysis facilitates thermodynamic assessment of left ventricular function in terms of work and energy. Typically these quantities are calculated for a cardiac cycle using the entire P-V loop, although thermodynamic analysis may be applied to a selected phase of the cardiac cycle, specifically, diastole. Diastolic function is routinely quantified by analysis of transmitral Doppler E-wave contours. The first law of thermodynamics requires that energy (ε) computed from the Doppler E-wave (ε_E-wave) and the same portion of the P-V loop (ε _{P-V E-wave}) be equivalent. These energies have not been previously derived nor have their predicted equivalence been experimentally validated. To test the hypothesis that ε_{P-V E-wave} and ε_E-wave are equivalent, we used a validated kinematic model of filling to derive ε_E-wave in terms of chamber stiffness, relaxation/ viscoelasticity, and load. For validation, simultaneous (conductance catheter) P-V and echocadiographic data from 12 subjects (205 total cardiac cycles) having a range of diastolic function were analyzed. For each E-wave, ε_E-wave was compared with ε_{P-V E-wave} calculated from simultaneous P-V data. Linear regression yielded the following: ε_{P-V E-wave} = αε_E-wave + b (R² = 0.67), where α = 0.95 and b = 6e^-5. We conclude that E-wave-derived energy for suction-initiated early rapid filling ε_E-wave, quantitated via kinematic modeling, is equivalent to invasive P-V-defined filling energy. Hence, the thermodynamics of diastole via ε_E-wave generate a novel mechanism-based index of diastolic function suitable for in vivo phenotypic characterization.