Medical literature shows that acoustic signals, physiologically called heart tones, are associated with mechanical events related to the haemo-dynamics of the heart valves during the various phases of the cardiac cycle. With the onset of diseases related to valve dysfunction, heart murmurs are generated, mostly due to the development of turbulent haemo-dynamics. The investigative approach used in this study is that of Computational Aero Acoustics (CAA) within the Computational Thermo-Haemo-Dynamics (CTHD) in order to simulate turbulent flow, CTHD, to derive the haemo-dynamic quantities of interest and the acoustic signals related to heart murmurs. Stenosis and aortic valve insufficiency are taken into consideration. A brief introduction is made, either physiological or pathophysiological, on the state of the art of the literature in terms of models, boundary conditions, numerical methods and algorithms used. A two-dimensional model, 2D, for severe and mild stenosis, which reproduces the pathological aortic valve, is created, on which a study domain is applied with the finite volume approach. The approach for the solution of turbulent flow (RANS) with a fluid dynamics simulation software is used. For the 2D geometries, steady-state simulations are conducted with three differently refined calculation grids in order to choose the one that represents the right compromise between result accuracy and smaller computational cost. Transient regime simulations are also conducted. The fields of velocity, pressure, viscosity, vorticity, shear stress and derived wall quantities are evaluated. The acoustic field is then studied by employing the model of Ffowcs-Williams and Hawkings (FW-H), modified by Brentner and Farassat (B-F), related to signals generated by heart murmurs. The spectrum of acoustic waves is evaluated on different receivers, positioned around the heart valve. Heart murmurs turn out to be low-frequency signals, in accordance with medical literature, with a cut-off at about 300 Hz. The spectra of the acoustic waves present some peaks for specific harmonics. The spectra found in the two 2D models show a first harmonic at a frequency around 60 Hz and a second at about 165 Hz, with higher intensity for mild stenosis compared to severe. The signals obtained from the numerical simulations are used to reproduce the typical trends recorded in pathological phonograms, that is, in cases of stenosis and aortic insufficiency, obtaining the so-called diamond signal and the damped signal, in which different oscillations, in amplitude and frequency, are noted relative to the different geometries studied. In cases where the jet has a larger section, a greater amount of fluid is set in motion, thus generating greater oscillations. This study constitutes a first approach to the numerical simulation of computational acoustics in the cardiac CTHD field, with two 2D models of pathological aortic valves, which, although limited by the size of the grids and calculation times, can provide interesting indications on the acoustics of heart murmurs.

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Acoustics in Cardiac Thermo-Haemo-Dynamics

  • Alex Colucci,
  • Fabio Gori Ammannati

摘要

Medical literature shows that acoustic signals, physiologically called heart tones, are associated with mechanical events related to the haemo-dynamics of the heart valves during the various phases of the cardiac cycle. With the onset of diseases related to valve dysfunction, heart murmurs are generated, mostly due to the development of turbulent haemo-dynamics. The investigative approach used in this study is that of Computational Aero Acoustics (CAA) within the Computational Thermo-Haemo-Dynamics (CTHD) in order to simulate turbulent flow, CTHD, to derive the haemo-dynamic quantities of interest and the acoustic signals related to heart murmurs. Stenosis and aortic valve insufficiency are taken into consideration. A brief introduction is made, either physiological or pathophysiological, on the state of the art of the literature in terms of models, boundary conditions, numerical methods and algorithms used. A two-dimensional model, 2D, for severe and mild stenosis, which reproduces the pathological aortic valve, is created, on which a study domain is applied with the finite volume approach. The approach for the solution of turbulent flow (RANS) with a fluid dynamics simulation software is used. For the 2D geometries, steady-state simulations are conducted with three differently refined calculation grids in order to choose the one that represents the right compromise between result accuracy and smaller computational cost. Transient regime simulations are also conducted. The fields of velocity, pressure, viscosity, vorticity, shear stress and derived wall quantities are evaluated. The acoustic field is then studied by employing the model of Ffowcs-Williams and Hawkings (FW-H), modified by Brentner and Farassat (B-F), related to signals generated by heart murmurs. The spectrum of acoustic waves is evaluated on different receivers, positioned around the heart valve. Heart murmurs turn out to be low-frequency signals, in accordance with medical literature, with a cut-off at about 300 Hz. The spectra of the acoustic waves present some peaks for specific harmonics. The spectra found in the two 2D models show a first harmonic at a frequency around 60 Hz and a second at about 165 Hz, with higher intensity for mild stenosis compared to severe. The signals obtained from the numerical simulations are used to reproduce the typical trends recorded in pathological phonograms, that is, in cases of stenosis and aortic insufficiency, obtaining the so-called diamond signal and the damped signal, in which different oscillations, in amplitude and frequency, are noted relative to the different geometries studied. In cases where the jet has a larger section, a greater amount of fluid is set in motion, thus generating greater oscillations. This study constitutes a first approach to the numerical simulation of computational acoustics in the cardiac CTHD field, with two 2D models of pathological aortic valves, which, although limited by the size of the grids and calculation times, can provide interesting indications on the acoustics of heart murmurs.