Estimating Respiratory and Heart Rates from the Correntropy Spectral Density of the Photoplethysmogram

The photoplethysmogram (PPG) obtained from pulse oximetry measures local variations of blood volume in tissues, reflecting the peripheral pulse modulated by heart activity, respiration and other physiological effects. We propose an algorithm based on the correntropy spectral density (CSD) as a novel way to estimate respiratory rate (RR) and heart rate (HR) from the PPG. Time-varying CSD, a technique particularly well-suited for modulated signal patterns, is applied to the PPG. The respiratory and cardiac frequency peaks detected at extended respiratory (8 to 60 breaths/min) and cardiac (30 to 180 beats/min) frequency bands provide RR and HR estimations. The CSD-based algorithm was tested against the Capnobase benchmark dataset, a dataset from 42 subjects containing PPG and capnometric signals and expert labeled reference RR and HR. The RR and HR estimation accuracy was assessed using the unnormalized root mean square (RMS) error. We investigated two window sizes (60 and 120 s) on the Capnobase calibration dataset to explore the time resolution of the CSD-based algorithm. A longer window decreases the RR error, for 120-s windows, the median RMS error (quartiles) obtained for RR was 0.95 (0.27, 6.20) breaths/min and for HR was 0.76 (0.34, 1.45) beats/min. Our experiments show that in addition to a high degree of accuracy and robustness, the CSD facilitates simultaneous and efficient estimation of RR and HR. Providing RR every minute, expands the functionality of pulse oximeters and provides additional diagnostic power to this non-invasive monitoring tool.