Bispectral Analysis of Heart Rate Variability to Characterize and Help Diagnose Pediatric Sleep Apnea
Abstract
:1. Introduction
2. Subjects and Signals under Study
3. Methods
3.1. Bispectrum Estimation
3.2. Determination of Bispectral Regions
3.3. Feature Extraction Stage
3.3.1. Bispectral Region Amplitude Features
- Maximum amplitude (Bmax), measured as the maximum magnitude value inside each of the regions considered [46]:
- Minimum amplitude (Bmin), measured as the minimum magnitude value inside each of the regions considered [46]:
- Total bispectral power (Btotal), measured as the sum of all magnitudes inside each of the regions considered [46]:
3.3.2. Bispectral Entropy Features
- Normalized bispectral entropy (BE1), normalized squared bispectral entropy (BE2) and normalized cubed bispectral entropy (BE3). These parameters, based on Shannon’s entropy, quantify the irregularity of the bispectral distribution in each region and are computed as [29,34]
- Phase entropy (PE), which quantifies the phase regularity of the region [29]. PE, as with the bispectral entropies, is higher as the randomness of a process increases, meaning it would be zero for a harmonic, periodic and predictable process [34]. PE computation is performed applying Shannon’s entropy to the normalized distribution of the region phase angles [29,46]:
3.3.3. Bispectral Region Moment Features
- The sum of the logarithmic magnitude values of the region (H1), sum of the logarithmic magnitude values of the diagonal of the region (H2) and first- and second-order spectral moments of the magnitude values of the diagonal elements of the region (H3 and H4, respectively). These features were included as they allow characterizing the nonlinearity of the regions and are computed as follows [46]:
3.3.4. Bispectral WCOB Features
- WCOB allows reflecting the interaction of different frequency components through the assignment of a weight to each bispectral point of the region [46]. The weighted center of each region is composed of two vectors, f1m and f2m, which indicate the coupling focus of the region as a summary of the frequency interaction [46]. Those components of WCOB are computed as [46]
3.3.5. Relative Power of the Diagonal, a Novel Bispectral Feature
- The relative power of the diagonal (RPDiag), computed as the sum of the bispectral amplitudes of the diagonal elements of the region, after a normalization applied over the whole diagonal. This novel parameter evaluates the relative bispectral magnitude value inside the diagonal of the region with respect to the complete bispectral diagonal magnitude:
3.4. Feature Selection Stage
3.5. Classification Stage
3.6. Statistical Analysis
4. Results
4.1. Feature Selection in the Training Set
4.2. Descriptive Analysis of the Features Selected
4.3. MLP Network Optimization and Training
4.4. Correlation Analysis in the Test Set
4.5. Diagnostic Ability Assessments
5. Discussion
5.1. Physiological Interpretation of the Features Selected
5.2. Diagnostic Performance of the Bispectral Models
5.3. Comparison with Previous Work
5.4. Limitations and Outlook
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Determination of HRV OSA-Specific Frequency Ranges and Averaged Bispectral Regions in the Training Set
Appendix B. Diagnostic Performance of Bispectral Region Models with a Linear Discriminant Analysis Classifier
Feature/Model | AHI Threshold = 1 e/h | AHI Threshold = 5 e/h | AHI Threshold = 10 e/h | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Se | Sp | Acc | AUC | Se | Sp | Acc | AUC | Se | Sp | Acc | AUC | ||
RPVLF | 68.9 | 31.6 | 56.3 | 0.518 | 33.0 | 65.0 | 60.2 | 0.456 | 40.6 | 64.2 | 62.1 | 0.495 | |
Previous work (frequency analysis approach) | RPLF | 43.5 | 62.9 | 50.1 | 0.557 | 52.7 | 58.4 | 57.6 | 0.590 | 59.4 | 58.4 | 58.5 | 0.666 |
RPHF | 35.5 | 71.9 | 47.8 | 0.523 | 39.3 | 68.1 | 63.8 | 0.540 | 43.5 | 76.7 | 73.7 | 0.605 | |
LF/HF | 37.7 | 70.3 | 48.7 | 0.540 | 45.5 | 66.8 | 63.7 | 0.567 | 49.3 | 70.8 | 68.8 | 0.643 | |
RPBW1 | 66.3 | 45.3 | 59.2 | 0.559 | 65.2 | 54.0 | 55.6 | 0.621 | 69.6 | 52.3 | 53.9 | 0.624 | |
RPBW2 | 32.7 | 78.1 | 48.1 | 0.591 | 45.5 | 82.0 | 76.6 | 0.670 | 58.0 | 78.2 | 76.4 | 0.751 | |
RPBWRes | 45.5 | 56.6 | 49.3 | 0.532 | 44.6 | 64.0 | 61.2 | 0.571 | 49.3 | 64.0 | 62.6 | 0.628 | |
LDA Classic Bands | 25.7 | 81.3 | 44.5 | 0.559 | 46.4 | 72.2 | 68.4 | 0.633 | 50.7 | 75.3 | 73.1 | 0.685 | |
LDA Bands of Interest | 42.5 | 72.3 | 52.6 | 0.592 | 50.0 | 80.9 | 76.4 | 0.688 | 63.8 | 84.7 | 82.8 | 0.796 | |
Present work (bispectral analysis approach) | LDAClassic | 30.1 | 81.3 | 47.4 | 0.601 | 53.6 | 85.3 | 80.6 | 0.779 | 66.7 | 89.7 | 87.6 | 0.847 |
LDASpecific | 37.9 | 77.3 | 51.3 | 0.615 | 63.4 | 82.8 | 79.9 | 0.792 | 71.0 | 85.9 | 84.5 | 0.842 |
Appendix C. Surrogate Data Approach
Appendix C.1. Testing for Nonlinearities
Appendix C.2. Bispectrum with Surrogate
References
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All | Training Set (UofC) | Test Set (CHAT) | |
---|---|---|---|
Subjects (n) | 1738 | 981 | 757 |
Age (years) | 6.4 [3.3] | 6.0 [6.0] | 7.0 [2.4] |
Males (n) | 962 (55.35%) | 602 (61.37%) | 360 (47.95%) |
BMI (kg/m2) | 17.63 [5.37] | 18.02 [5.86] | 17.28 [4.64] |
AHI (e/h) | 2.23 [5.27] | 3.8 [7.76] | 1.46 [2.07] |
AHI ≥ 1 (e/h) | 1309 (75.31%) | 808 (82.36%) | 501 (66.18%) |
AHI ≥ 5 (e/h) | 519 (29.86%) | 407 (41.49%) | 112 (14.80%) |
AHI ≥ 10 (e/h) | 298 (17.15%) | 229 (23.34%) | 69 (9.11%) |
Classic Region Feature Set | OSA-Specific Region Feature Set | |||||
---|---|---|---|---|---|---|
Features | VLF | LF | HF | BW1 | BW2 | BWRes |
RPDiag | VLF_RPDiag | LF_RPDiag | HF_RPDiag | BW1_RPDiag | BW2_RPDiag | - |
Bmax | VLF_Bmax | LF_Bmax | HF_Bmax | BW1_Bmax | BW2_Bmax | BWRes_Bmax |
Bmin | VLF_Bmin | LF_Bmin | HF_Bmin | BW1_Bmin | BW2_Bmin | BWRes_Bmin |
BTotal | VLF_BTotal | LF_BTotal | HF_BTotal | BW1_BTotal | BW2_BTotal | BWRes_BTotal |
BE1 | VLF_BE1 | LF_BE1 | HF_BE1 | BW1_BE1 | BW2_BE1 | BWRes_BE1 |
BE2 | VLF_BE2 | LF_BE2 | HF_BE2 | BW1_BE2 | BW2_BE2 | BWRes_BE2 |
BE3 | VLF_BE3 | LF_BE3 | HF_BE3 | BW1_BE3 | BW2_BE3 | BWRes_BE3 |
PE | VLF_PE | LF_PE | HF_PE | BW1_PE | BW2_PE | BWRes_PE |
H1 | VLF_H1 | LF_H1 | HF_H1 | BW1_H1 | BW2_H1 | BWRes_H1 |
H2 | VLF_H2 | LF_H2 | HF_H2 | BW1_H2 | BW2_H2 | - |
H3 | VLF_H3 | LF_H3 | HF_H3 | BW1_H3 | BW2_H3 | - |
H4 | VLF_H4 | LF_H4 | HF_H4 | BW1_H4 | BW2_H4 | - |
f1m | VLF_f1m | LF_f1m | HF_f1m | BW1_f1m | BW2_f1m | BWRes_f1m |
f2m | VLF_f2m | LF_f2m | HF_f2m | BW1_f2m | BW2_f2m | BWRes_f2m |
BISPClassic Features | ||||||||
PSG Index | VLF_f2m | LF_BE2 | HF_PE | |||||
ρS | p-Value | ρS | p-Value | ρS | p-Value | |||
AHI | 0.274 | <<0.01 | −0.185 | <<0.01 | −0.112 | 0.002 * | ||
OAHI | 0.261 | <<0.01 | −0.149 | <<0.01 | −0.097 | 0.008 | ||
OAI | 0.167 | <<0.01 | −0.105 | 0.004 * | −0.064 | 0.079 | ||
ODI | 0.215 | <<0.01 | −0.123 | 0.001 * | −0.054 | 0.138 | ||
#Awakenings | −0.075 | 0.039 | −0.027 | 0.461 | −0.020 | 0.586 | ||
WASO | −0.003 | 0.929 | 0.065 | 0.076 | −0.022 | 0.538 | ||
%N1 | 0.089 | 0.014 | −0.071 | 0.052 | −0.030 | 0.404 | ||
%N2 | −0.034 | 0.357 | 0.099 | 0.007 * | 0.013 | 0.715 | ||
%N3 | 0.034 | 0.355 | −0.025 | 0.497 | −0.044 | 0.23 | ||
%REM | −0.125 | 0.001 | −0.052 | 0.154 | 0.059 | 0.108 | ||
TAI | 0.213 | <<0.01 | −0.158 | <<0.01 | −0.115 | 0.002 * | ||
BISPSpecific Features | ||||||||
PSG Index | BW2_RPDiag | BW2_BE1 | BWRes_Bmin | BWRes_BE3 | ||||
ρS | p-Value | ρS | p-Value | ρS | p-Value | ρS | p-Value | |
AHI | 0.308 | <<0.01 | −0.180 | <<0.01 | 0.054 | 0.136 | 0.045 | 0.214 |
OAHI | 0.261 | <<0.01 | −0.180 | <<0.01 | 0.098 | 0.007 * | 0.028 | 0.435 |
OAI | 0.177 | <<0.01 | −0.173 | <<0.01 | 0.071 | 0.051 | 0.058 | 0.112 |
ODI | 0.247 | <<0.01 | −0.139 | 0.001 | 0.019 | 0.61 | 0.072 | 0.047 |
#Awakenings | −0.033 | 0.372 | −0.001 | 0.994 | −0.006 | 0.876 | 0.035 | 0.331 |
WASO | 0.071 | 0.05 | 0.078 | 0.031 | −0.018 | 0.622 | 0.056 | 0.126 |
%N1 | 0.107 | 0.003 * | −0.061 | 0.093 | 0.023 | 0.527 | 0.028 | 0.441 |
%N2 | −0.061 | 0.091 | 0.008 | 0.837 | 0.048 | 0.184 | 0.059 | 0.104 |
%N3 | 0.053 | 0.147 | 0.008 | 0.817 | −0.075 | 0.04 | −0.092 | 0.011 |
%REM | −0.139 | 0.001 | 0.048 | 0.192 | −0.007 | 0.855 | 0.013 | 0.722 |
TAI | 0.225 | <<0.01 | −0.144 | <<0.01 | 0.068 | 0.062 | 0.068 | 0.06 |
Threshold: AHI = 1 e/h | ||||
Feature/Model | Se | Sp | Acc | AUC |
VLF_f2m | 44.5 | 72.3 | 53.9 | 0.605 |
LF_BE2 | 42.1 | 72.7 | 52.4 | 0.581 |
HF_PE | 42.9 | 63.3 | 49.8 | 0.550 |
BW2_RPDiag | 50.9 | 64.8 | 55.6 | 0.629 |
BW2_BE1 | 47.1 | 59.4 | 51.3 | 0.559 |
BWRes_Bmin | 40.5 | 57.4 | 46.2 | 0.482 |
BWRes_BE3 | 41.5 | 57.4 | 46.9 | 0.513 |
MLP1Classic | 52.3 | 59.4 | 54.7 | 0.600 |
MLP1Specific | 76.3 | 38.3 | 63.4 | 0.627 |
Threshold: AHI = 5 e/h | ||||
Feature/Model | Se | Sp | Acc | AUC |
VLF_f2m | 62.5 | 72.2 | 70.8 | 0.749 |
LF_BE2 | 56.3 | 74.4 | 71.7 | 0.670 |
HF_PE | 45.5 | 72.1 | 68.2 | 0.628 |
BW2_RPDiag | 60.7 | 77.7 | 75.2 | 0.747 |
BW2_BE1 | 56.3 | 70.1 | 68.0 | 0.671 |
BWRes_Bmin | 58.9 | 45.3 | 47.3 | 0.567 |
BWRes_BE3 | 47.3 | 58.4 | 56.8 | 0.569 |
MLP5Classic | 50.9 | 86.2 | 81.0 | 0.774 |
MLP5Specific | 62.5 | 84.2 | 81.0 | 0.791 |
Threshold: AHI = 10 e/h | ||||
Feature/Model | Se | Sp | Acc | AUC |
VLF_f2m | 63.8 | 76.7 | 75.6 | 0.784 |
LF_BE2 | 58.0 | 81.5 | 79.4 | 0.740 |
HF_PE | 53.6 | 72.1 | 70.4 | 0.663 |
BW2_RPDiag | 68.1 | 76.0 | 75.3 | 0.789 |
BW2_BE1 | 47.8 | 76.0 | 73.4 | 0.692 |
BWRes_Bmin | 56.5 | 50.6 | 51.1 | 0.557 |
BWRes_BE3 | 55.1 | 59.4 | 59.0 | 0.614 |
MLP10Classic | 43.5 | 96.5 | 91.7 | 0.847 |
MLP10Specific | 66.7 | 91.6 | 89.3 | 0.841 |
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Martín-Montero, A.; Gutiérrez-Tobal, G.C.; Gozal, D.; Barroso-García, V.; Álvarez, D.; del Campo, F.; Kheirandish-Gozal, L.; Hornero, R. Bispectral Analysis of Heart Rate Variability to Characterize and Help Diagnose Pediatric Sleep Apnea. Entropy 2021, 23, 1016. https://doi.org/10.3390/e23081016
Martín-Montero A, Gutiérrez-Tobal GC, Gozal D, Barroso-García V, Álvarez D, del Campo F, Kheirandish-Gozal L, Hornero R. Bispectral Analysis of Heart Rate Variability to Characterize and Help Diagnose Pediatric Sleep Apnea. Entropy. 2021; 23(8):1016. https://doi.org/10.3390/e23081016
Chicago/Turabian StyleMartín-Montero, Adrián, Gonzalo C. Gutiérrez-Tobal, David Gozal, Verónica Barroso-García, Daniel Álvarez, Félix del Campo, Leila Kheirandish-Gozal, and Roberto Hornero. 2021. "Bispectral Analysis of Heart Rate Variability to Characterize and Help Diagnose Pediatric Sleep Apnea" Entropy 23, no. 8: 1016. https://doi.org/10.3390/e23081016