Hemodynamics-driven mathematical model of first and second heart sound generation

Abstract

We propose a novel, two-degree of freedom mathematical model of mechanical vibrations of the heart that generates heart sounds in CircAdapt, a complete real-time model of the cardiovascular system. Heart sounds during rest, exercise, biventricular (BiVHF), left ventricular (LVHF) and right ventricular heart failure (RVHF) were simulated to examine model functionality in various conditions. Simulated and experimental heart sound components showed both qualitative and quantitative agreements in terms of heart sound morphology, frequency, and timing. Rate of left ventricular pressure (LV dp/dtmax) and first heart sound (S1) amplitude were proportional with exercise level. The relation of the second heart sound (S2) amplitude with exercise level was less significant. BiVHF resulted in amplitude reduction of S1. LVHF resulted in reverse splitting of S2 and an amplitude reduction of only the left-sided heart sound components, whereas RVHF resulted in a prolonged splitting of S2 and only a mild amplitude reduction of the right-sided heart sound components. In conclusion, our hemodynamics-driven mathematical model provides fast and realistic simulations of heart sounds under various conditions and may be helpful to find new indicators for diagnosis and prognosis of cardiac diseases. New & noteworthy To the best of our knowledge, this is the first hemodynamic-based heart sound generation model embedded in a complete real-time computational model of the cardiovascular system. Simulated heart sounds are similar to experimental and clinical measurements, both quantitatively and qualitatively. Our model can be used to investigate the relationships between heart sound acoustic features and hemodynamic factors/anatomical parameters.

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“…While early studies hypothesized that sudden tensing of ventricular muscles or cardiac valves gives rise to heart sounds, later studies tended to support the idea of vibrations of the whole cardiohemic system including valves, myocardia, blood mass and adjacent tissues as origin of heart sounds [4][5][6][7]. The recent simulation study in our group, based on the cardiohemic hypothesis, appeared quite consistent with previous observations of heart sounds in normal condition, heart failure and exercise [8]. Chapter 4 showed a higher frequency of heart sounds in patients with elevated LV filling pressure.…”

“…Moreover, computer simulation studies in our group showed that S2 splitting is a promising tool for evaluation of type and evolution of heart failure. S2 splitting interval is prolonged as LV function worsens at constant RV function, while shortened or even reversed as only RV function worsens [8]. Therefore, S2 splitting interval, used alone or combined with other heart sound components such as third heart sound, may be helpful for titration of drugs such as diuretics and beta-blocker, as well as optimization of pacemaker therapy in heart failure patients.…”

Hemodynamics-driven mathematical model of third heart sound generation

“…The phonocardiogram is from a healthy subject with S3 in PhysioNet dataset ( Liu et al, 2016 ). The simulation is composed of simulated first and second heart sounds from a previous study ( Shahmohammadi et al, 2021 ) superposed to the simulated S3 in normal condition at rest (5 L/min)). Note the close agreement between the phonocardiogram and the simulation.…”

“…In addition to a blood impact model, proper expressions are needed for at each time snapshot before the S3 sound can be simulated. Because CircAdapt ( Figure 1A ) proved to be a reliable software for simulation of cardiovascular mechanics and hemodynamics in various conditions ( Walmsley et al, 2015 ; Shahmohammadi et al, 2021 ), we used this software to identify the most appropriate values for our model parameters. Details about the used parameters of CircAdapt are extensively described in ( Walmsley et al, 2015 ; van Loon et al, 2020 ).…”

“…CircAdapt can simulate cardiac strain patterns, blood pressures, flows and volumes in both normal and pathophysiological conditions ( Walmsley et al, 2015 ). In a previous study we extended CircAdapt with an S1/S2 module ( Shahmohammadi et al, 2021 ), now we want to add an S3 module. The simulated hemodynamics of normal and pathophysiological conditions in CircAdapt were used to generate initial conditions for a one-degree-of-freedom mass-dashpot-spring model which mimics the visco-elastic mechanics of cardiohemic structures.…”