# Application of the Permutation Entropy over the Heart Rate Variability for the Improvement of Electrocardiogram-based Sleep Breathing Pause Detection

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Database

#### 2.2. Extraction of RR Intervals and Post Processing

#### 2.3. Variables Obtained from Heart Rate Variability

#### 2.3.1. Permutation Entropy

#### 2.3.2. Cepstrum Analysis

#### 2.3.3. Power Measures from the Electrocardiogram Derived Respiratory Signal

#### 2.4. Classifiers

#### 2.4.1. Logistic Regression

_{i}

_{1}, …,X

_{ip}represents the input feature vector in the instant i and β

_{0}, …, β

_{p}, the model parameters. Based on this probability, a threshold-based diagnostic rule that optimizes the classifier performance is defined.

#### 2.4.2. Quadratic Discriminant Analysis

_{k}and ∑

_{k}are the mean vector and covariance matrix of each class k (apnea and no-apnea class). QDA defines a linear boundary between the classes as:

_{k}is the prior probability of class k.

#### 2.5. Experiment Definition

## 3. Results

## 4. Discussion

## Author Contributions

## Conflicts of Interest

## References

- Becker, H.F.; Jerrentrup, A.; Ploch, T.; Grote, L.; Penzel, T.; Sullivan, C.E.; Peter, J.H. Effect of nasal continuous positive airway pressure treatment on blood pressure in patients with obstructive sleep apnea. Circulation
**2003**, 107, 68–73. [Google Scholar] - Ravelo, A.; Travieso, C.; Lorenzo, F.; Navarro, J.; Martin, S.; Alonso, J.; Ferrer, M. Application of support vector machines and gaussian mixture models for the detection of obstructive sleep apnoea based on the RR series. WSEAS Trans. Comput.
**2006**, 5, 121–124. [Google Scholar] - Penzel, T.; Moody, G.B.; Mark, R.G.; Goldberger, A.L.; Peter, J.H. The apnea-ECG database. Proceedings of Computers in Cardiology 2000, Cambridge, MA, USA, 24–27 September 2000; pp. 255–258.
- Goldberger, A.L.; Amaral, L.A.N.; Glass, L.; Haussdorff, J.M.; Ivanov, P.C.; Mark, R.G.; Mietus, J.E.; Moody, G.B.; Peng, C.K.; Stanley, H.E.; Physiobank, PhysioToolkit. PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulatio
**2000**, 101, 215–220. [Google Scholar] - Zanin, M.; Zunino, L.; Rosso, O.A.; Papo, D. Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review. Entropy
**2012**, 14, 1553–1577. [Google Scholar] - Bian, C.; Qin, C.; Ma, Q.D.Y.; Shen, Q. Modified permutation-entropy analysis of heartbeat dynamics. Phys. Rev. E
**2012**, 85, 021906. [Google Scholar] - Penzel, T.; McNames, J.; Murray, A.; de Chazal, P.; Moody, G.; Raymond, B. Systematic comparison of different algorithms for apnoea detection based on electrocardiogram recordings. Med. Biol. Eng. Comput.
**2002**, 40, 402–407. [Google Scholar] - Ravelo-García, A.G.; Saavedra-Santana, P.; Juliá-Serdá, G.; Navarro-Mesa, J.L.; Navarro-Esteva, J.; Álvarez-López, X.; Gapelyuk, A.; Penzel, T.; Wessel, N. Symbolic dynamics marker of heart rate variability combined with clinical variables enhance obstructive sleep apnea screening. Chaos
**2014**, 24, 024404. [Google Scholar] - Wessel, N.; Voss, A.; Malberg, H.; Ziehmann, C.; Schirdewan, A.; Meyerfeldt, U.; Kurths, J. Nonlinear analysis of complex phenomena in cardiological data. Herzschrittmachertherapie und Elektrophysiologie
**2000**, 11, 159–173. [Google Scholar] - Kurths, J.; Voss, A.; Witt, A.; Saparin, P.; Kleiner, H.J.; Wessel, N. Quantitative analysis of heart rate variability. Chaos
**1995**, 5, 88–94. [Google Scholar] - Voss, A.; Kurths, J.; Kleiner, H.J.; Witt, A.; Wessel, N.; Saparin, P.; Osterziel, K.J.; Schumann, R.; Dietz, R. The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death. Cardiovasc. Res.
**1996**, 31, 419–433. [Google Scholar] - Riedl, M.; Müller, A.; Wessel, N. Practical considerations of permutation entropy. Eur. Phys. J. Spec. Top.
**2013**, 222, 249–26. [Google Scholar] - Zanin, M.; Zunino, L.; Rosso, O.A.; Papo, D. Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review. Entropy
**2012**, 14, 1553–1577. [Google Scholar] - Parlitz, U.; Berg, S.; Luther, S.; Schirdewan, A.; Kurths, J.; Wessel, N. Classifying cardiac biosignals using ordinal pattern statistics and symbolic dynamics. Comput. Biol. Med.
**2012**, 42, 319–327. [Google Scholar] - Frank, B.; Pompe, B.; Schneider, U.; Hoyer, D. Permutation entropy improves fetal behavioural state classification based on heart rate analysis from biomagnetic recordings in near term fetuses. Med. Biol. Eng. Comput.
**2006**, 44, 179–187. [Google Scholar] - Bandt, C.; Pompe, B. Permutation Entropy: A Natural Complexity Measure for Time Series. Phys. Rev. Lett.
**2002**, 88, 174102. [Google Scholar] - Ravelo-Garcia, A.; Navarro-Mesa, J.L.; Martin-González, S.; Hernández-Pérez, E.; Quintana-Morales, P.; Guerra-Moreno, I.; Navarro-Esteva, J.; Juliá-Serdá, G. Cepstrum Coefficients of the RR Series for the Detection of Obstructive Sleep Apnea Based on Different Classifiers. Proceedings of the 14th International Conference on Computer Aided Systems Theory, Las Palmas de Gran Canaria, Spain, 10–15 February 2013; pp. 266–271.
- Ravelo-Garcia, A.; Navarro-Mesa, J.; Hernádez-Pérez, E.; Martin-González, S.; Quintana-Morales, P.; Guerra-Moreno, I.; Juliá-Serdá, G. Cepstrum Feature Selection for the Classification of Sleep Apnea-Hypopnea Syndrome based on Heart Rate Variability. Proceedings of 2013 Computing in Cardiology Conference (CinC), Zaragoza, Spain, 22–25 September 2013; pp. 959–962.
- O’Brien, C.; Heneghan, C. A comparison of algorithms for estimation of a respiratory signal from the surface electrocardiogram. Comput. Biol. Med.
**2007**, 37, 305–314. [Google Scholar] - Hastie, T.J.; Tibshirani, R.J. Generalized Additive Models; Chapman & Hall: London, UK, 1986; pp. 297–310. [Google Scholar]
- Clarke, W.; Lachenbruch, P.; Broffitt, B. How non-normality affects the quadratic discriminant function. Commun. Stat.-theory Methods
**1979**, 8, 1285–1301. [Google Scholar] - Patuwo, E.; Michael, Y.H.; Ming, S. Two-Group Classification Using Neural Networks. Decis. Sci.
**1993**, 24, 825–845. [Google Scholar]

**Figure 1.**(

**a**) RR intervals in seconds; (

**b**) All possible symbols for n = 3; (

**c**) Relative frequencies of the sequences in the signal of (a).

**Figure 3.**(

**a**) 1 minute-EDR of a normal breathing; (

**b**) One minute-EDR of an apnea event; (

**c**) and (

**d**) Power spectral density estimates of (a) and (b) respectively.

**Figure 4.**Boxplot for the variables PEnt in apnea and normal segments for different values of order n and delay t. (

**a**) Order = 2; (

**b**) Order = 3.

**Figure 5.**Evaluation of misclassification error for variables obtained from EDR+Cepstrum+PE series with LR classifier (

**a**) and with QDA classifier (

**b**).

PE | F | P |
---|---|---|

PE32 | 59.65 | 1.43×10^{−13} |

PE42 | 77.36 | 8.60×10^{−17} |

PE52 | 94.30 | 9.84×10^{−20} |

PE62 | 96.69 | 3.87×10^{−20} |

PE72 | 67.70 | 4.70×10^{−15} |

PE33 | 138.06 | 8.57×10^{−27} |

PE43 | 162.14 | 2.16×10^{−30} |

PE53 | 176.24 | 2.05×10^{−32} |

PE63 | 156.99 | 1.22×10^{−29} |

PE73 | 79.98 | 2.96×10^{−17} |

**Table 2.**Classifier performance in terms of the feature types, classifier and the number of features.

Features | Classifier | N | Acc (%) | Se (%) | Sp (%) | AUC |
---|---|---|---|---|---|---|

EDR | LR | 20 | 79.3 | 65.6 | 87.7 | 85.0 |

EDR + PE | LR | 21 | 84.1 | 75.3 | 89.5 | 90.3 |

Cepstrum | LR | 20 | 79.7 | 63.8 | 89.2 | 86.0 |

Cepstrum + PE | LR | 21 | 82.3 | 69.4 | 90.3 | 87.7 |

EDR + Cepstrum | LR | 40 | 82.7 | 68.9 | 91.3 | 89.4 |

EDR + Cepstrum + PE | LR | 41 | 84.4 | 71.9 | 92.1 | 90.3 |

EDR | QDA | 12 | 78.5 | 59.4 | 90.3 | 83.9 |

EDR + PE | QDA | 9 | 83.1 | 74.9 | 88.2 | 89.0 |

Cepstrum | QDA | 16 | 79.3 | 67.2 | 86.8 | 86.9 |

Cepstrum + PE | QDA | 17 | 82.7 | 68.2 | 91.7 | 89.1 |

EDR + Cepstrum | QDA | 40 | 83.3 | 73.5 | 89.5 | 91.0 |

EDR + Cepstrum + PE | QDA | 41 | 84.6 | 75.1 | 90.5 | 91.7 |

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**MDPI and ACS Style**

Ravelo-García, A.G.; Navarro-Mesa, J.L.; Casanova-Blancas, U.; Martin-Gonzalez, S.; Quintana-Morales, P.; Guerra-Moreno, I.; Canino-Rodríguez, J.M.; Hernández-Pérez, E.
Application of the Permutation Entropy over the Heart Rate Variability for the Improvement of Electrocardiogram-based Sleep Breathing Pause Detection. *Entropy* **2015**, *17*, 914-927.
https://doi.org/10.3390/e17030914

**AMA Style**

Ravelo-García AG, Navarro-Mesa JL, Casanova-Blancas U, Martin-Gonzalez S, Quintana-Morales P, Guerra-Moreno I, Canino-Rodríguez JM, Hernández-Pérez E.
Application of the Permutation Entropy over the Heart Rate Variability for the Improvement of Electrocardiogram-based Sleep Breathing Pause Detection. *Entropy*. 2015; 17(3):914-927.
https://doi.org/10.3390/e17030914

**Chicago/Turabian Style**

Ravelo-García, Antonio G., Juan L. Navarro-Mesa, Ubay Casanova-Blancas, Sofia Martin-Gonzalez, Pedro Quintana-Morales, Iván Guerra-Moreno, José M. Canino-Rodríguez, and Eduardo Hernández-Pérez.
2015. "Application of the Permutation Entropy over the Heart Rate Variability for the Improvement of Electrocardiogram-based Sleep Breathing Pause Detection" *Entropy* 17, no. 3: 914-927.
https://doi.org/10.3390/e17030914