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Heart and Diabetes Center NRW, Ruhr University Bochum, Bad Oeynhausen, 32545 Germany
(Email: dfritzsche{at}hdz-nrw.de).
We read the letter by Bagno and associates [1] with interest. They reflected on several issues that evolved from studying our work [2]. Here is our rebuttal (and agreement) to their questions and concerns:
There is little doubt that continuous wavelet transform (CWT) could potentially be an adequate algorithm for the analysis of sound produced by mechanical heart valve prostheses. It is true that in broadband sound signals, CWT can offer an enhanced frequency resolution in the low-frequency domain, as well as an enhanced time resolution in the high-frequency domain. Short-time Fourier transform (FFT), in contrast, offers constant resolution of time and frequency over the entire frequency range of the sound signal.
Should FFT be replaced by CWT to analyze the sound spectra of the heart valve prosthesis, as implied by Bagno and coworkers [1]? This question can be answered with a "yes" and a "no" for several reasons. From an academic point of view, CWT may be more accurate than FFT in reflecting the sound spectra produced, so the answer is "yes." From an economic and simplistic standpoint, however, FFT suffices to accurately reflect the sound spectra and to reliably distinguish between normal and abnormal heart valve closing sounds. A great deal of our experimental work was devoted to the valve sound phenomena, and we found that the frequency band between 8 and 22 kHz is crucial for the analysis of the integrity of the valve prostheses. Considering the typical signal length of 20 ms, the resolution obtained is at 0.06%, which by far exceeds the needs for distinguishing between normal and abnormal closing sounds. Without being less scientific in replying to the question, if CWT must replace FFT, the answer can be "no."
What criteria are used in the evaluation of the integrity of valve prostheses by the analyses of their sound? We typically analyze the sound spectra in the time domain, based on experience gained in research and clinic. Bi-leaflet valve prostheses are generally used nowadays, and missing "double-clicks" are clear indicators of malfunction. Accordingly, a (near-) complete loss of a frequency band compared with baseline calibration indicates the impingement of one leaflet, as depicted in Figure 2 [2]. Bagno and coworkers [1] are correct that Figures 2a and 2b [2] represent examples of the time domain FFT, whereas Figure 2c is in the frequency domain.
The authors [1] go on to suggest using the frequency range below 10 kHz and above 20 kHz for analyzing the sound of the valve prostheses. As a matter of fact, the low-frequency band is perhaps useful to analyze valve associated pathologies, including sounds produced by the blood stream in response to leakage or calcification of bioprostheses. Our preliminary studies indicate that this can possibly be used, yet specific microphones and transducers are necessary, which in turn may preclude economic manufacturing. In addition, the low-frequency range is very susceptible to noise; the patient's valve sound recording can be interfered even by a motorcycle passing by.
The high-frequency range has not yet been studied, but we may address this shortcoming in the future as the requirements dictate.
We agree with Bagno and coworkers [1] that a cogent discussion of physics of the heart valve sounds vis-à-vis; its clinical implication will benefit its introduction into the routine, postoperative care of patients. Thank you for commenting on our work.
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