Analysis of the Impact of Interpolation Methods of Missing RR-intervals Caused by Motion Artifacts on HRV Features Estimations
1.1. Paper Contribution
1.2. Related Work
2. Materials and Methods
2.2. Missing Values Interpolation
- No interpolation: this approach does not create interpolated values of missing RR-intervals. Differently to the Deletion method that remove missing values merging non-consecutive beats that induce in missing interpretation of HRV features, the no-interpolation method maintains the missing values into the RR-intervals time series.
- Nearest neighbor: the nearest neighbor or proximate interpolation is the easiest interpolation method . This interpolation assigns the value of the closest known (existing) neighbor to the missing- value as shows in Equation (6).
- Linear: this method fits a straight line passing through points and . Interpolated data by the linear model are bound between and as showed in Equation (7).
- Spline cubic: fitting datapoints using polynomials of degree higher than one leads to problems of oscillation outside the fitted points, known as Runge’s phenomenon . This problem can be avoided by using a spline, a function defined piecewise by polynomials, using datapoints as control points instead of forcing the fitted function to pass through the data points. Cubic spline is a spline composed of piecewise third-order polynomials. By using third degree polynomials is possible to ensure that the resulting curve is smooth , avoiding the problem of the straight polynomial interpolation that tends to induce distortions on the edges of the polynomials, given by the fact that, in general, the first and second derivative of the function defined by piecewise polynomials will not be continuous at the edges of polynomials. With cubic spline, it is possible to force the first and second derivatives of consecutive polynomials to be equal, ensuring smoothness of the resulting curve.
2.3. Feature Engineering
- Time domain:
- HR mean: mean values of heart rate (HR) computed as showed in Equation (9).
- RMSSD: root mean square of the successive RR-intervals differences (Equation (10)) represents the strength of the autonomic nervous system (specifically the parasympathetic branch) at a given time.
- SDNN: standard deviation of RR-intervals (Equation (11)). It reflects the cyclic components responsible for variability in the RR-intervals time series. The SDNN is the “gold standard” for medical stratification of both morbidity and mortality .
- PNN50: the ratio between NN50 (i.e., number of pairs of successive RR intervals that differ by more than 50 ms) and the total number of RR-intervals (Equation (12)).
- Frequency domain:
- Power spectral density (PSD): describes the distribution of power into frequency components composing that signal. The Lomb–Scargle periodogram for PSD estimation was found to be the most appropriate method to analyze RR-interval data [5,6]. VLF (power in very-low-frequency ranges, i.e., ≤0.04 Hz), LF (power in low-frequency ranges, i.e., 0.04–0.15 Hz), HF (Power in high-frequency ranges, i.e., 0.15, 0.4 Hz), LF/HF ratio (ratio between LF and HF expressed as ms), and total power (Power in all the frequency ranges, i.e., ≤0.4) were obtained by the sum of the power in the relevant frequency range in the spectrum.
- Non-linear HRV features:
- Poincaré plot: it is a type of recurrence plot used to quantify self-similarity in processes. A Poincaré plot is a graph of RR interval () against the previous one (). From this scatter plot, it is possible to quantitatively analyze the variance of two consecutive RR-intervals by fitting an ellipse to the plotted shape. is the standard deviation of Poincaré plot perpendicular to the line-of-identity, while is the standard deviation of the Poincaré plot along the line-of-identity.
2.4. Success Metrics
3. Results and Discussions
3.1. Results Summary
3.2. HRV Features
3.2.1. Time Domain
3.2.2. Frequency Domain
3.2.3. Non-Linear Domain
Conflicts of Interest
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|Window Time (s)||RMSE (s)||RE (%)|
|HRV Features||Mean||95% CI|
|IBI (s)||0.78||[0.54, 1.11]|
|PNN50 (n)||8||[4, 16]|
|RMSSD (s)||0.039||[0.017, 0.36]|
|SD1 (s)||0.027||[0.012, 0.26]|
|SD2 (s)||0.077||[0.040, 0.25]|
|SDNN (s)||0.059||[0.017, 0.25]|
|VLF (s)||0.87||[0.22, 4.15]|
|LF (s)||0.477||[0.12, 5.57]|
|HF (s)||0.28||[0.050, 3.024]|
|total power (s)||1.91||[0.53, 21.44]|
|LF/HF (s)||2.9||[1.2, 10.2]|
|Missing Values (%)||HRV||How||Method||RE (%)||RMSE|
|total power (s)||Time||quadratic||17.16||6.26|
|total power (s)||Time||quadratic||27.59||3.96|
|total power (s)||Time||quadratic||72.07||5.27|
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Morelli, D.; Rossi, A.; Cairo, M.; Clifton, D.A. Analysis of the Impact of Interpolation Methods of Missing RR-intervals Caused by Motion Artifacts on HRV Features Estimations. Sensors 2019, 19, 3163. https://doi.org/10.3390/s19143163
Morelli D, Rossi A, Cairo M, Clifton DA. Analysis of the Impact of Interpolation Methods of Missing RR-intervals Caused by Motion Artifacts on HRV Features Estimations. Sensors. 2019; 19(14):3163. https://doi.org/10.3390/s19143163Chicago/Turabian Style
Morelli, Davide, Alessio Rossi, Massimo Cairo, and David A. Clifton. 2019. "Analysis of the Impact of Interpolation Methods of Missing RR-intervals Caused by Motion Artifacts on HRV Features Estimations" Sensors 19, no. 14: 3163. https://doi.org/10.3390/s19143163