Cross Time-Frequency Analysis for Combining Information of Several Sources: Application to Estimation of Spontaneous Respiratory Rate from Photoplethysmography

A methodology that combines information from several nonstationary biological signals is presented. This methodology is based on time-frequency coherence, that quantifies the similarity of two signals in the time-frequency domain. A cross time-frequency analysis method, based on quadratic time-frequency distribution, has been used for combining information of several nonstationary biomedical signals. In order to evaluate this methodology, the respiratory rate from the photoplethysmographic (PPG) signal is estimated. The respiration provokes simultaneous changes in the pulse interval, amplitude, and width of the PPG signal. This suggests that the combination of information from these sources will improve the accuracy of the estimation of the respiratory rate. Another target of this paper is to implement an algorithm which provides a robust estimation. Therefore, respiratory rate was estimated only in those intervals where the features extracted from the PPG signals are linearly coupled. In 38 spontaneous breathing subjects, among which 7 were characterized by a respiratory rate lower than 0.15 Hz, this methodology provided accurate estimates, with the median error 0.00; 0.98 ？mHz ( 0.00; 0.31 %) and the interquartile range error 4.88; 6.59 ？mHz ( 1.60; 1.92 %). The estimation error of the presented methodology was largely lower than the estimation error obtained without combining different PPG features related to respiration. 1. Introduction Biomedical signals convey information about biological systems and can be recorded from different sources. For the study of a functional system or facing a clinical problem different biomedical signals and processing methods may be of interest. For instance, cardiovascular system activity is reflected in signals of such varied origins as electrical (ECG), optical (photoplethysmographic signal), or mechanical (blood pressure). Biomedical signals processing tools are typically applied on only one signal at a time and with limited knowledge of the interrelationships with other signals influenced by the same system. However, an analysis which takes into account multiple signals could significantly improve the results. Combining information from different physiological interactions increases the accuracy and offers more robust estimates [1]. Spectral coherence-based methods quantify the similarity of the frequency content of two signals. A peak in the coherence magnitude means that a common frequency is present in two signals, without specifying whether this common oscillation appears in both signals at the same time.