Relationship of the third heart sound to transmitral flow velocity deceleration

The third heart sound (S3) occurs shortly after the early (E-wave) peak of the transmitral diastolic Doppler velocity profile (DVP). It is thought to be due to cardiohemic vibrations powered by rapid deceleration of transmitral blood flow. Although the presence, timing, and clinical correlates of the S3 have been extensively characterized, derivation and validation of a causal, mathematical relation between transmitral flow velocity and the S3 are lacking.

To characterize the kinematics and physiological mechanisms of S3 production, we modeled the cardiohemic system as a forced, damped, nonlinear harmonic oscillator. The forcing term used a closed-form mathematical expression for the deceleration portion of the DVP. We tested the hypothesis that our model's predictions for amplitude, timing, and frequency of S3 accurately predict the transthoracic phonocardiogram, using the simultaneously recorded transmitral Doppler E wave as input, in three subject groups: those with audible pathological S3, those with audible physiological S3, and those with inaudible S3.

We found excellent agreement between model prediction and the observed data for all three subject groups. We conclude that, in the presence of a normal mitral valve, the kinematics of filling requires that all hearts have oscillations of the cardiohemic system during E-wave deceleration. However, the oscillations may not have high enough amplitude or frequency to be heard as an S3 unless there is sufficiently rapid fluid deceleration (of the Doppler E-wave contour) with sufficient cardiohemic coupling.