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Edited by: Ahsan H. Khandoker, Khalifa University, United Arab Emirates

Reviewed by: Ganesh R. Naik, Western Sydney University, Australia; Enrico Capobianco, University of Miami, United States

This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Electrocardiography is the gold standard for electrical heartbeat activity, but offers no direct measurement of mechanical activity. Mechanical cardiac activity can be assessed non-invasively using, e.g., ballistocardiography and recently, medical radar has emerged as a contactless alternative modality. However, all modalities for measuring the mechanical cardiac activity are affected by respiratory movements, requiring a signal separation step before higher-level analysis can be performed. This paper adapts a non-linear filter for separating the respiratory and cardiac signal components of radar recordings. In addition, we present an adaptive algorithm for estimating the parameters for the non-linear filter. The novelty of our method lies in the combination of the non-linear signal separation method with a novel, adaptive parameter estimation method specifically designed for the non-linear signal separation method, eliminating the need for manual intervention and resulting in a fully adaptive algorithm. Using the two benchmark applications of (i) cardiac template extraction from radar and (ii) peak timing analysis, we demonstrate that the non-linear filter combined with adaptive parameter estimation delivers superior results compared to linear filtering. The results show that using locally projective adaptive signal separation (LoPASS), we are able to reduce the mean standard deviation of the cardiac template by at least a factor of 2 across all subjects. In addition, using LoPASS, 9 out of 10 subjects show significant (at a confidence level of 2.5%) correlation between the R-T-interval and the R-radar-interval, while using linear filters this ratio drops to 6 out of 10. Our analysis suggests that the improvement is due to better preservation of the cardiac signal morphology by the non-linear signal separation method. Hence, we expect that the non-linear signal separation method introduced in this paper will mostly benefit analysis methods investigating the cardiac radar signal morphology on a beat-to-beat basis.

Electrocardiography (ECG) has become a universally accepted standard for measuring heart rate. However, since ECG is caused by depolarization and repolarization of the heart, it is difficult to directly asses the mechanical activity of the heart using ECG (

While these applications are undoubtedly of great importance, the original intention behind the development of BCG and related modalities was to non-invasively asses the mechanical cardiac and hemodynamic activity and derive covariates of measures such as cardiac output (

In this paper, we demonstrate that this non-linear signal separation method can be adapted to mechanical heartbeat signals obtained with radar. Medical radar for non-contact vital signs acquisition is a rapidly developing modality, which faces very similar challenges to BCG, including sensitivity to movement artifacts, high variability in signal morphology and spectral overlap between cardiac and respiratory components (

In addition, we also address the issue of parameter estimation, which was identified as a weakness of the original non-linear signal separation method, by improving an automated parameter estimation scheme developed for BCG signals (

Combining signal separation and parameter estimation, we obtain an adaptive algorithm for the extraction of the cardiac component from radar signals. Since the signal separation method from

The intended application of LoPASS is to extract and denoise the cardiac component from radar recordings during the preprocessing step prior to any analysis of mechanical cardiac activity that requires precise knowledge of the signal morphology. In order to demonstrate the advantage of LoPASS, we compare the results from preliminary analyses performed on a dataset of radar recordings which have been preprocessed with either LoPASS or linear filters. We chose linear filters for this comparison, since they are still used regularly for the extraction of the cardiac component, even by state-of-the-art beat detection algorithms (

Specifically, we perform two benchmark applications: First, we extract a heartbeat template from the radar signal via R-peak-synchronized averaging, showing that the LoPASS-preprocessed data exhibits much higher coherence and lower standard deviation. Then, we examine the relationship between the timing of the peaks in the radar signal and the R-T-interval. Since ventricular systole, the main cause for the deflections in the cardiac radar signal, takes place during the R-T-interval (

This article is structured as follows. In Section “Materials and Methods,” we describe the proposed LoPASS algorithm and investigate its robustness via sensitivity analysis. In addition, we also provide details on the data acquisition procedure. Section “Results” contains the results of the data analysis and the comparison between linear filters and LoPASS-based preprocessing. In Section “Discussion,” we will discuss our findings, and finally a conclusion.

The non-linear signal separation used in this paper was previously applied to the problem of extracting fetal ECG signals (

Deterministic signals tend to occupy a low dimensional manifold when embedded into delay space using delay embedding techniques, while noise generally spreads into all dimensions of the delay space. This property of deterministic signals, which is formally described in Takens’ delay embedding theorem (

Here, _{t}

Linearizing the function _{0}, to the manifold in delay space occupied by the deterministic signal:

Since the manifold is restricted to a lower-dimensional subspace, matrix _{0}. Hence, projecting onto the subspace spanned by the columns of

The principle outlined above was formalized by _{t}_{t}:

In

This uncommon method of specifying the noise characteristic, combined with the fact that LPNR operates in delay space as opposed to frequency domain, enables this method to perform noise reduction even if the noise process has a similar spectrum as the signal (_{1} and _{2} with overlapping spectra, one simply applies LPNR to remove one of the components, say _{1} (usually, the faster and smaller component), in order to obtain an estimate of the other component _{2}. This is achieved by setting ε equal to the peak-to-peak amplitude of _{1}, which is typically obtained by visual inspection. Subtracting the estimate of _{2} from the raw input signal then yields an estimate of the first component _{1} (_{1} corresponds to the heartbeat and _{2} to the respiration signal.

Signal separation using LPNR. The input signal (here radar) containing respiration, heartbeat and noise is filtered using LPNR with parameter settings such that heartbeat and noise are removed (specifically, ε approximately equals the heartbeat amplitude). Subtracting respiration from the input and applying LPNR again, with parameter settings such that noise is removed, extracts the heartbeat component.

By design, LPNR operates on the entirety of the input data, meaning it is technically not a filter but a smoother. However, fast online approximations to the LPNR algorithm have also been developed (

One of the main weaknesses of LPNR-based methods is the choice of the parameters, and specifically the choice of ε. The general approach is to choose this parameter via visual inspection (

We have previously introduced an algorithm for estimating a suitable value for ε for the separation of BCG component (

Similar to our approach in _{t}_{t} of the high-pass-filtered signal _{0},…, _{t}_{T}

Next, we calculate the median _{a}

The median of a set _{n}

The estimate for ε is then taken as 1.5 times the median:

For parameter estimation the raw signal (upper left) is high-pass-filtered and the maximum altitude difference in slices of 1.5 s are collected throughout the signal. One such slice is shown in the lower left plot. The median of these amplitude differences is multiplied with 1.5 and used as the estimate (green and red lines, right plot).

In practice, we apply parameter estimation to epochs of 1 min. The estimate of ε is then used for LPNR-based signal separation on the given epoch and the whole procedure of estimation and separation is repeated for each epoch. Combining the adaptive parameter estimation method with LPNR-based signal separation eliminates the need to manually choose the parameter ε and results in an algorithm that can adapt itself to signals with non-stationary amplitudes. Hence, we call this algorithm locally projective adaptive signal separation (LoPASS).

Previously, we have shown that LPNR-based signal separation is relatively robust against small misspecifications of the ε parameter (_{sc}_{sc}_{sc}

Here, _{x}_{sc}_{sc}_{sc}

_{sc} by up to ±50% results in a relative change of the output _{rel} (blue circles) by around 5% on average. Error bars indicate one standard deviation.

In this paper, we demonstrate that LPNR-based signal separation can be applied to recordings obtained from medical radar. Medical radar has been proposed as contactless vital signs estimation method for use in infection screening systems (

Similar to BCG, radar can be used in a bed-mounted configuration as shown in

In this paper, we perform a preliminary analysis on recordings from medical radar obtained in a controlled laboratory experiment. The main goal of this analysis is to assess the ability of LoPASS to extract the cardiac components from radar recordings.

Since the 24-GHz radar system (SHARP, DC6M4JN3000, Japan) used in the experiments was a prototype, which lacked automatic gain control, the amplification of the system was manually adjusted for each recording, with signal amplitudes differing by more than one order of magnitude across recordings (see

The experiment was approved by the ethics committee of the University of Electro-Communications, Tokyo, Japan. All participants were fully informed of the purposes and experimental procedures before they gave their written consent to participate.

Since the objective of the analysis is to assess the extraction of the cardiac component, we visually inspected all recordings and selected one representative, artifact free segment per subject. By excluding movement artifacts from the analysis, we focus on the ability of the separation algorithm to distinguish between respiration and heartbeat and minimize the possibility that our result might be biased by potential differences in resistance against artifacts between linear and non-linear preprocessing methods. Following this approach, we do not assess the resilience of LoPASS to movement artifacts. However, since it is known that movement artifacts assert a strong influence on mechanical heartbeat signal (

In this section, we present the results of our preliminary analysis. The main goal of this analysis is to compare LoPASS-based preprocessing to conventional linear filter-based preprocessing. Therefore, all analysis steps are carried out on two sets of data: (i) the artifact free radar recordings which were preprocessed using LoPASS and (ii) the same recordings preprocessed with linear filters. A secondary goal of this analysis is to assess the viability of radar as an unobtrusive and non-invasive modality for investigating medical questions of interest involving the mechanical heartbeat activity. For these reasons, we performed two benchmark applications: template construction and peak timing analysis. The following sections describe the analysis performed and the result.

The raw data used in the analysis presented in this section is released in the

Additional data not included in the

In the first benchmark application, we use the R-peaks of a simultaneously recorded ECG signal to construct a template of the cardiac radar component. Template construction is an important step in the analysis of mechanical heartbeat signals in both classical (

A sample segment from the radar recording (first row) with cardiac components extracted via the LoPASS algorithm (second row) and conventinal bandpass filtering (third row). The simultaneously recorded ECG reference is also shown (fourth row).

In order to quantify the resistance of LoPASS to these kinds of high frequency respiratory interference and its advantage compared to bandpass filtering, we extract the cardiac component from artifact free segments of the radar signal with both LoPASS and linear filters. The linear filters consisted of a finite impulse response (FIR) low-pass filter with order 128 and a cutoff frequency of 10 Hz, which was used to remove high frequency noise components. In addition, an FIR high-pass filter with order 256 and cutoff frequency of 0.75 Hz was used to remove the respiratory component. Using separate filters for these two tasks allowed us to adapt the filter steepness to each task separately. Furthermore, since the exact heart rate is not known in advance, we chose conservative cutoff frequencies resulting in a relatively wide bandwidth, in order to account for changes in heart rate.

For both separation methods, the resulting cardiac component was segmented using the R-peaks detected in the simultaneously recorded ECG reference, and a template of the mechanical heartbeat signal was calculated by resampling and averaging. In addition, we also calculated the standard deviation, which quantifies the deviation from the template. This procedure was performed for each subject individually. The resulting templates for subject 1 are shown in

Top row: Template of mechanical heartbeat calculated from the cardiac radar signal extracted with LoPASS

Average standard deviations across the templates calculated based on LoPASS and linear filter-extracted cardiac signal and their ratio.

Subject no. | Mean standard deviation LoPASS | Mean standard deviation BP | Ratio std BP/std LoPASS |
---|---|---|---|

1 | 0.0235 | 0.0758 | 3.22 |

2 | 0.0327 | 0.0743 | 2.27 |

3 | 0.1104 | 0.2645 | 2.40 |

4 | 0.0253 | 0.0677 | 2.68 |

5 | 0.0939 | 0.1988 | 2.12 |

6 | 0.0392 | 0.0810 | 2.07 |

7 | 0.2198 | 0.5436 | 2.47 |

8 | 0.0206 | 0.0569 | 2.76 |

9 | 0.0243 | 0.0617 | 2.53 |

10 | 0.0735 | 0.2575 | 3.50 |

Average ratio std BP/std LoPASS across all subjects: | 2.6 | ||

This result demonstrates that LoPASS-based cardiac component extraction leads to both visually and quantitatively more consistent templates as opposed to linear filter-based cardiac signal extraction. Judging from the samples shown in the lower row of

In the second benchmark application, we look at the relationship between the timing of the major peaks in the cardiac radar signal measured with respect to the R-peak of the simultaneously recorded ECG and the R-T-interval. The R-peak in the ECG signal marks the depolarization of the ventricle, while the T-wave marks the repolarization (

To confirm our conjecture, we detect the main peak in the cardiac radar signal for each cardiac cycle and calculate the correlation coefficient between the R-T-interval and the interval between R-peak and main peak of the radar signal (see

Relevant time points for the second benchmark application illustrated for one cardiac cycle. First vertical bar indicates the ECG R-peak (beginning of the cardiac cylce). Second bar marks the main peak in the radar signal (maximum mechanical activity). Third bar marks the T-peak (repolarization). In the benchmark application, we compare the interval between first and second bar to the interval between first and third bar. Note that these two intervals relate to different events in the cardiac cylce and hence, are not identical but are presumed to be correlated with each other. See

Subject no. | ||
---|---|---|

1 | 3.7 × 10^{-10} |
1.2 × 10^{-5} |

2 | 1.9 × 10^{-5} |
8.7 × 10^{-4} |

3 | 1.1 × 10^{-10} |
5.8 × 10^{-2} |

4 | 1.2 × 10^{-11} |
1.5 × 10^{-2} |

5 | 6.4 × 10^{-5} |
5.6 × 10^{-2} |

6 | 2.0 × 10^{-7} |
2.9 × 10^{-4} |

7 | 4.9 × 10^{-3} |
8.6 × 10^{-3} |

8 | 6.5 × 10^{-1} |
7.4 × 10^{-1} |

9 | 2.6 × 10^{-6} |
3.9 × 10^{-7} |

10 | 2.2 × 10^{-2} |
2.6 × 10^{-1} |

Significance level: 2.5% | 9 out of 10 significant | 6 out of 10 significant |

Mean and standard deviation of R-T-interval and R-radar-interval and correlation between the two intervals for all subject separated by preprocessing method (LoPASS vs. linear filtering).

Subject no. | R-T-interval: mean (SD) [ms] | R-radar-interval for LoPASS: mean (SD) [ms] | Correlation between intervals for LoPASS | R-radar-interval for linear filter: mean (SD) [ms] | Correlation between intervals for linear filter |
---|---|---|---|---|---|

1 | 233 (4.5) | 75 (5.9) | 37% | 184 (7.5) | 21% |

2 | 256 (4.9) | 109 (4.7) | 47% | 298 (5.7) | 35% |

3 | 212 (4.2) | 86 (6.3) | 34% | 277 (9.2) | 9% |

4 | 247 (9.2) | 94 (7.5) | 40% | 275 (6.1) | 12% |

5 | 236 (4.9) | 280 (7.1) | 45% | 282 (7.2) | 27% |

6 | 299 (4.3) | 274 (5.8) | 27% | 100 (7.5) | 18% |

7 | 241 (6.6) | 180 (6.7) | 23% | 195 (12.7) | 21% |

8 | 267 (7.5) | 539 (26) | -8.4% | 551 (38.5) | -15% |

9 | 271 (8.0) | 174 (6.0) | 51% | 182 (7.5) | 55% |

10 | 233 (5.4) | 173 (8.4) | 17% | 171 (9.9) | 6% |

Overall | 248 (30.0) | 157 (91.6) | 31.3% (average) | 208 (77.0) | 18.9% (average) |

In summary, using LoPASS-based preprocessing, we observe consistent results across almost all subjects (i.e., highly significant correlation between R-T-interval and R-radar-interval). However, using linear filter-based preprocessing, the results are inconsistent with only about half of all subjects exhibiting significant correlation.

The results presented in the previous section demonstrate that extracting the cardiac component of the radar signal using LoPASS offers improved coherence as compared to using conventional linear filtering. Specifically, we have shown that using LoPASS leads to more coherent templates, which could benefit, for example beat detection algorithms relying on template matching techniques. Additionally, in our second benchmark application, we discovered a significant correlation between the R-T-interval in the ECG and the R-radar-interval. This suggests that the major deflections of the cardiac radar signal might indeed be closely related to the mechanical oscillations caused by ventricular ejection. Traditionally, the gold standard for measuring ventricular ejection timing is to detect the first and second heart sound using phonocardiography (

Note that here, we do not claim to have established a connection between the radar signal and ventricular ejection. Instead, we have shown that using LoPASS as a non-linear preprocessing technique uncovered an interesting correlation between medical radar and ECG, which points toward promising avenues for future studies. Importantly, a consistent result across all subjects was only observed for the LoPASS-extracted cardiac radar component, suggesting that a faithful extraction of the signal morphology is necessary for such an approach to succeed.

One important limitation of this study is the small size of the dataset and the lack of heterogeneity in the cohort. Hence, it is difficult to draw any medically relevant conclusions from these results which generalize to the entire population. However, drawing medical conclusions is not the intention of this paper. Instead, this paper aims to introduce LoPASS, and to demonstrate that (i) it can be applied to medical radar recordings and that (ii) it outperforms linear filters on the benchmark applications reported here. Solving these questions for the dataset at hand provided valuable insight which, in addition to demonstrating the performance of LoPASS, will help to design future studies that overcome the limitations of the current dataset.

The improvements due to using LoPASS come at the cost of an increase in computational complexity as LPNR is significantly slower than linear filters (

One further consideration is given by applications involving average signal characteristics, like, for example the calculation of mean heart rate or mean respiration rate. For these applications, we do not expect a significant improvement from the use of LoPASS, since they do not make use of the exact morphology of the signal. However, for applications relying on the signal morphology and especially for analysis methods investigating the signal on a beat-to-beat basis, applying LoPASS for cardiac component extraction can lead to significantly improved results as demonstrated in the Section “Peak Timing and R-T-Interval.”

Finally, it is worth pointing out that since the amplification of the system was manually adjusted for each recording and since the position of the radar differed between recordings, the amplitudes of the cardiac and respiratory components of the radar signals differed by more than one order of magnitude between recordings (as indicated in

In this paper, we have adapted a non-linear signal separation algorithm to extracting the cardiac component from medical radar recordings. Additionally, we have augmented this separation scheme with an adaptive parameter estimation method, which addresses the weakness of having to estimate the parameter for LPNR via visual inspection. The resulting locally projective adaptive signal separation (LoPASS) algorithm is best suited as a preprocessing step for analysis methods where preserving signal morphology is critical. Using two benchmark applications for radar recordings, we have demonstrated the superiority of LoPASS as compared to linear filters. In future projects, we will perform more detailed analyses of the cardiac radar signal. These will include comparisons of the cardiac radar signal to phonocardiograms, with the prospect of establishing radar as an unobtrusive and non-invasive estimator for ventricular ejection timing.

The experiment was approved by the ethics committee of the University of Electro-Communications. All participants were fully informed of the purposes and experimental procedures before they gave their written consent to participate.

YY, GS, TK, and MS conceptualized and designed the study. GS contributed to the acquisition of data. YY and GS analyzed and interpreted the data. YY, GS, and MS drafted the manuscript. All authors have approved the final version to be published.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The Supplementary Material for this article can be found online at:

Raw data from 10 subjects used for the benchmark applications presented in “Results” Section.