Heart sound validation

The feasibility of radar-based heart sound detection is investigated by comparison with ECG data as gold standard method for heartbeat detection and with PCG data as gold standard method for heart sound detection, in particular. Figure 1 shows the sensor signals for an exemplary measurement, in which the PUT was stationary with resting heart rate (60…80 bpm) and breathing at leisure (8…12 breaths per minute). The radar antenna was focused on the xiphoid process, while the PCG was positioned at the fourth intercostal space at the left side (4 L). Both ROIs are illustrated in Fig. 8(a). A 25-second window of the acquired radar distance data is shown in Fig. 1(a). Frequent occurrences of two subsequent, short vibrations with an amplitude of approximately 10 m are clearly visible. A cutout of 7 s is plotted enlarged in Fig. 1(b), in which correlation with the detected R-peaks and T-wave ends in the ECG signal can be observed. The hypothesis of this paper is that theses vibrations correspond to the heart sounds, which is proven in the following. In accordance to cardiovascular physiology, the first vibration (S1) immediately follows the R-peaks, while the second vibration (S2) occurs near the T-wave ends. The corresponding heart sound cutout of the synchronised PCG data is shown in Fig. 1(c). Both cutouts visually show high similarities regarding signal shapes, as well as time of occurrences of the detected vibrations. While the timing of occurrences is analysed in the following subsection, this paragraph deals with a morphology analysis of both heart sounds. The importance of a morphology analysis is discussed in Papadaniil et al.50. The highlighted heart sounds in Fig. 1(b and c) are depicted enlarged in Fig. 1(d–g). The morphological comparison is conducted by correlation. Since PCG are based on acceleration, whereas radar data represents the distance, one of the data has to be converted to fit the same domain for both sensing concepts for correlation. In principle, the radar data can be differentiated twice, but this will lead to an overweighting of the noise component artificially lowering the correlation result. Therefore, the PCG data is integrated twice to fit the data representation of the radar. The Pearson correlation coefficient is 91.41% for the shown S1 signals of radar and PCG, respectively, in Fig. 1(d and e) and 92.35% for the shown S2 signals in Fig. 1(f and g). The overall correlation of the heart sounds in Fig. 1 is 91.54 ± 3.19% for S1 and 80.98 ± 11.53% for S2. Evaluating the complete database by utilising all heart sounds with sufficient signal-to-noise ratio (SNR) results in similarly high values: The correlation between radar and PCG data is 82.97 ± 11.15% for 5274 used occurrences of S1 and 80.72 ± 12.16% for 5277 used occurrences of S2. The differences to a perfect correlation of 100% can be addressed to different sources: For the radar, the antenna characteristic has some influence as well as the integrating behaviour of the relatively large ROI compared to the PCG44. The morphology also varies in PCG-based measurements, since the pressure, which is used to push the PCG on the ROI, highly influence the measurement signal. Furthermore, to minimise any mutual influence between PCG and radar sensor due to micro-vibrations of the manually positioned PCG, the corresponding ROIs were chosen slightly different with no overlap, but close to each other for the radar and the PCG during the simultaneous measurements, which also results in different signal morphologies and is hard to compensate for. Also the sizes of both ROIs are different. Nevertheless, the measured radar-based heart sound signals show high correlation regarding timing and signal shape to the PCG signals.

Figure 1 (a) Exemplary filtered radar signal with the xiphoid process in focus. (b) Enlarged cutout with two highlighted heart sounds S1 and S2. (c) Synchronised PCG measurement data with corresponding heart sounds highlighted. (d) Enlarged versions of the highlighted S1 in radar and (e) PCG data. (f) Enlarged versions of the highlighted S2 in radar and (g) PCG data. Full size image

Timing analysis

PCG and radar data in Fig. 1(a) representing heart sounds show a high similarity provided both sensors are placed in close proximity. As phonocardiography constitutes touch-based measurement of high frequency vibrations on the surface of the body, PCG and radar detect the same physiological phenomenon, but in different domains (acceleration versus distance). In case of detection of heart sounds, surface vibrations are caused by mechanical action of the heart. To investigate the propagation velocity of these vibrations, signal timings at different ROIs have to be evaluated, which are depicted in Fig. 8(a). In Fig. 2 the exact timing of S1 and S2 occurrences in the radar signal is analysed for two ROIs in the same PUT. While the antenna was focused on 4 L in Fig. 2(a), CL was focused on in Fig. 2(b). Next to the radar signal, significant characteristics of the ECG signal are marked, as well. Since the T-peak represents a more explicit reference point than the T-wave end, the T-peaks are shown together with the R-peaks in these plots. Comparing the included timing labels, two findings are observed. First, intervals between R-peak and S1, as well as T-peak and S2 are larger in CL comparison to 4 L. Second, increase of interval is heightened between R-peak and S1 in comparison to T-peak and S2. This phenomenon is accounted for by the different points of origin of S1 and S2 in reference to the ROIs. ROI in CL is approximately 0.30 m further remote from S1 than ROI in 4 L, whereas only 0.15 m from S2. Based on these approximations for an average PUT, propagation velocities of 3.8 \(\frac{{\rm{m}}}{{\rm{s}}}\) and 4.0 \(\frac{{\rm{m}}}{{\rm{s}}}\), respectively are calculated from the radar data. While the measured propagation velocities vary between PUT, they are approximately equal for each single PUT. This implies that both heart sounds propagate in the same physical manner. The propagation velocity range for all PUT is about 4…9 \(\frac{{\rm{m}}}{{\rm{s}}}\), which corresponds to the values published in literature51,52,53. In addition, this value range corresponds to investigated pulse wave velocities, which implies transversal dispersion through tissue and along anatomic surfaces as equal kind of propagation51.

Figure 2 Timing analysis of S1 and S2 at (a) 4 L and (b) CL. Full size image

Respiratory influence

In this section, the respiratory influence on the heart sounds is analysed utilising the database. The heart sound signal extracted from the radar data is compared with the synchronous RS signal confirming two physiological aspects, peak envelope variation of heart sounds, as well as S2 split during inspiration.

Peak envelope variation

To investigate the respiratory induced peak envelope variation, S1 and S2 each have to be extracted individually from the heart sound signal. Here, an HSMM-based heart sound segmentation49 was optimised for radar measurements and used to segment the heart sound signal in four distinct partitions: S1, systole (without S1), S2, and diastole (without S2). The resulting analysis is illustrated in Fig. 3. While Fig. 3(a) only contains the extracted S1 segments, the S2 segments are shown in Fig. 3(b). Additionally, the upper and lower peak envelopes are depicted in both sub-plots. The peak-peak envelope (PPE) of each heart sound (S1 PPE and S2 PPE ) is defined as the difference between upper and lower peak envelope. The distance-based breathing part of the detected distance variation (Δx Breath ) due to thorax movements was extracted from the radar signal by a fourth order Butterworth filter with a passband of 0.1…0.5 Hz. The RS signal and S1 PPE were filtered likewise. A comparison between these filtered signals, the RS signal, the S1 PPE , and the radar distance-based breathing signal Δx Breath is shown in Fig. 3(c). The PUT was breathing normally for the first 13 s, followed by 10 s of breath-holding, and breathing at leisure for the remaining time under observation. Breath-holding is observable in all signals of Fig. 3(c), since amplitude changes decrease considerably with breath-holding. Furthermore, the radar distance-based respiratory signal is highly similar to the signal from the RS, while PUT breathes at leisure: The correlation between both respiration signals is 94.44% for the presented measurement data and 89.14 ± 10.53% for the complete database. The S1 PPE , in contrast, shows a contradictory behaviour. While after breath-holding this signal equals both other signals, too, the curve is reversed before breath-holding. In general, the heart sound PPE, both for S1 and S2, are linearly dependent on breathing, either positively or invertedly. Evaluating the database, the sign of each PPE curve discloses a random behaviour, since comparing measurements does not show any regularity. While in some measurements the PPE curves of both heart sounds are equal, they are opposed in other ones. Neither can any regularity be found for an individual PUT, nor for a specific ROI. Reversal of PPE after breath-holding was observed in each PUT, but not consistently. These peculiar observations regarding the heart sound PPE are not caused by erroneous radar data, but confirm a known phenomenon in literature54,55,56.

Figure 3 (a) Peak envelope variation of S1 and (b) S2. (c) Breathing influence on the S1 peak envelopes by comparing its PPE to the RS, as well as to the extracted breathing data from the radar signal. Full size image

S2 split

Next to the peak envelope variation, a split of the second heart sound is occasionally measured, which is illustrated in Fig. 4. This non-pathological S2 split only occurs during inspiration and, according to literature57,58, is observed mostly for younger persons. Here, S2 is split into its two components, the aortic (A2) and pulmonary (P2) parts. While the stroke volume of the right ventricle increases during inspiration, the stroke volume of the left ventricle decreases, which leads to an extended systole of the right heart (pulmonary circulation) and a shortened systole of the left heart (body circulation), respectively. Hence, the aortic valve closes earlier and the pulmonary valve later, which results in a dispersed second heart sound. In Fig. 4, the physiological timing of radar-based data on heart sounds is substantiated by the R-peaks and end of T-waves of the ECG signal, while the RS signal after application of the bandpass filter with a passband of 0.1…0.5 Hz is used as reference. The S2 split is visible in the PCG signal measured at the second intercostal space at the left side (2 L), as well as in the heart sound signal extracted from the radar data measured at the second intercostal space at the right side (2 R). Both ROIs are illustrated in Fig. 8(a). While the gap between A2 and P2 is normally around 35.0 ms in the PCG data, the gap increases to approximately 62.5 ms during inspiration, which conforms to57. For the radar data, the gap increases from approximately 38.5 ms to about 66.0 ms. The slightly higher values are based on the lateral integrating behaviour of the radar system over a larger measurement spot44.

Figure 4 A split of S2 in its aortic and pulmonary parts during inspiration can be observed both in the PCG signal measured at 2 L and in the radar signal measured at 2 R. The timing of the heart sounds is verified by the R-peaks and T-wave ends of the ECG signal. Full size image

Performance analysis

Performance of the HSMM-based heart sound segmentation is analysed regarding two criteria. First, the usability of radar systems is compared to PCG evaluating the correctness of the heart sound segmentation by means of the F-score (F 1 ). Second, the timing accuracy of this novel radar-based heartbeat detection method derived from heart sounds is compared to a pulse wave evaluating algorithm as state-of-the-art method regarding the obtained IBI values.

F-score

The F-score is a common measure for test accuracy, which considers both the precision p and the recall r59:

$${F}_{{\rm{1}}}=2\cdot \frac{p\cdot r}{p+r}\mathrm{.}$$ (1)

A cross-validation is applied on the complete measurement database with 9930 seconds of synchronised sensor data to calculate the F-scores, which each consist of a mean value and the standard deviation. While the data of six PUT are used to train the model, subsequently, residual data of five PUT are used for testing. All 462 possible combinations were evaluated to calculate the F-scores for PCG, as well as radar-based heart sound detection. In Table 1, the F-scores are compared for two HSMM variants, the model presented by Springer et al.49 (variant A) and the adjusted variant proposed in this paper (variant B). The F-scores for each individual heart sound are presented (F 1,S1 and F 1,S2 ), as well as the joint F-scores (F 1,AVG ). The upper lines in both variants show the training results in italic, while the test results are shown in the lines below. The adjustments of the algorithm parameters in variant B slightly decrease the performance of the PCG, but strongly increase the performance of the radar system. Since the F-scores for radar systems with adjusted parameters almost equal the values of the gold standard method, PCG with variant A, the feasibility of radar-based heart sound detection is confirmed. The lower mean values of the radar system F-scores, as well as the higher standard deviations are based on the radar’s lower heart sound SNR values. By Schmidt et al.60, these SNR values were defined as the ratio of the heart sound segment amplitudes and the amplitudes of the subsequent systole segment and diastole segment, respectively. The lower SNR values of 7.11 dB for S1 and 3.29 dB for S2, in comparison to 7.81 dB (S1) and 5.69 dB (S2) for the PCG data, are due to the limited dynamic range of the used radar system.

Table 1 Comparison of the F-scores in training (italic values) and test (standard typeface) between PCG and radar-based heart sound detection for two algorithm variants. Full size table

Root-mean-square error

The root-mean-square error (RMSE) of the IBI values is a further performance analysis measure, which represents the timing accuracy of detecting single heartbeats. In general, the RMSE describes the deviation of a measurand from a reference value. Before calculating the RMSE, all individual heartbeats have to be detected in the ECG signal as gold standard reference, as well as in the comparing measurement signals. The R-peaks in the ECG signal are defined as reference instants of time of heartbeat occurrence, and therefore, the distance between two R-peaks is used for IBI calculation. Regarding heart sound-based heartbeat detection, the starts of the S1-segments are used for the PCG data, as well as the radar data. The radar data are additionally bandpass filtered in a range of 0.75…3.0 Hz to obtain the pulse wave component, which is utilised by a state-of-the-art heartbeat detection algorithm for radar systems43. This advanced template matching (ATM) algorithm uses the detected pulse wave peaks to determine single heartbeat occurrences. For all measurement signals, the final IBI values are calculated once per second by averaging the five latest determined heartbeat intervals with a median filter. These IBI values are used to determine the RMSE:

$${\rm{RMSE}}=\sqrt{\frac{{\sum }_{t=1}^{n}{({I}_{t,{\rm{ECG}}}-{I}_{t})}^{2}}{n}}\mathrm{.}$$ (2)

Here, I t,ECG is the IBI value obtained from the ECG signal as reference at time instance t, I t is the simultaneously determined IBI value of the system to be compared to the reference, and n represents the number of time instances. An exemplary IBI curve comparison between all measurement systems is plotted in Fig. 5. Both curves belonging to heart sound-based heartbeat detection systems, radar (HSMM) and PCG, almost equal the IBI curve of the ECG as reference. While the IBI curve of the pulse wave detection-based variant, radar (ATM), is permanently within the ECG bounds of ±0.1 s for the complete time window of 50 s, its deviation from the ECG curve is considerably larger. In contrast to the mean RMSE value of 144.9 ms for the ATM variant, considering all IBI values of the complete database, the RMSE of 44.2 ms for radar-based heart sound detection is considerably smaller. The RMSE for PCG-based heart sound detection is larger with a value of 59.4 ms, despite the PCG’s higher F-scores. While the deviation of I t from I t,ECG is maximally 400 ms for radar measurements, few outliers for PCG measurements with values up to 1000 ms result in a worse RMSE. Here, the individually superior HSMM variant was chosen to calculate the RMSE values, variant A for the PCG data and variant B for the radar data, respectively.