# Characterization of Complex Fractionated Atrial Electrograms by Sample Entropy: An International Multi-Center Study

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

**Figure 1.**Block diagram of the new methodology proposed, from the raw atrial electrograms (A-EGM) input signal preprocessing stage, up to the classification results.

#### 2.1. Sample Entropy

#### SampEn m and r Parameter Optimization

#### 2.2. Validation

#### 2.3. Experimental Dataset

- C0: Non-fractionated A-EGM.
- C1: Fractionated A-EGM with periodic activity.
- C2: A mixture of periodic fractionated and periodic non-fractionated A-EGM.
- C3: High frequency A-EGM with continuous activity. No regular activation can be seen.

#### 2.3.1. German Database

**Figure 2.**One signal from each fractionation level, ranging from C0 (top) to C3 (bottom). Original raw signals after baseline wander removal. (

**A**) German (GE) database and (

**B**) Czech (CZ) database.

#### 2.3.2. Czech Database

#### 2.3.3. Mixed Database

## 3. Experiments and Results

**Table 1.**Selection criteria value (SCV), AUC and sample entropy (SampEn) parameters $(m,r)$ obtained for the training subset using the optimization scheme described. Sensitivity (Se) and specificity (Sp) values are shown for the corresponding $(m,r)$ parameters in each row. The K-fold column refers to each of the folds considered from 1–10.

K-fold | SCV | AUC (%) | m | r | Sp (%) | Se (%) |
---|---|---|---|---|---|---|

1 | 1.278 | 88.6 | 4 | 0.65 | 85.1 | 76.4 |

2 | 1.299 | 90.9 | 8 | 0.65 | 80.6 | 78.7 |

3 | 1.331 | 89.2 | 4 | 0.65 | 88.1 | 76.4 |

4 | 1.380 | 90.9 | 4 | 0.65 | 91.0 | 77.5 |

5 | 1.195 | 89.1 | 4 | 0.65 | 86.6 | 78.7 |

6 | 1.161 | 91.2 | 8 | 0.65 | 88.1 | 76.4 |

7 | 1.140 | 88.3 | 4 | 0.65 | 88.1 | 75.3 |

8 | 1.266 | 84.7 | 2 | 0.65 | 89.6 | 77.5 |

9 | 1.238 | 90.0 | 4 | 0.65 | 83.6 | 79.8 |

10 | 1.295 | 88.5 | 4 | 0.65 | 85.7 | 77.8 |

**Table 2.**SampEn statistics for the fractionated/non-fractionated (F/NF) A-EGM for $m=4,r=0.65$. DB stands for database. Results are summarized using mean and median SampEn values, standard deviation (SD), confidence intervals (CI), AUC, sensitivity (Se), specificity (Sp) and the p-value of the Mann–Whitney statistical test.

DB | class | mean | median | SD | 95% CI | AUC (%) | Se (%) | Sp (%) | p |
---|---|---|---|---|---|---|---|---|---|

BT | NF | 0.054 | 0.049 | 0.003 | [0.047,0.061] | 89.3 | 86.9 | 77.5 | 0.001 |

F | 0.115 | 0.108 | 0.005 | [0.105,0.125] | 89.3 | 86.9 | 77.5 | 0.001 | |

CZ | NF | 0.050 | 0.050 | 0.003 | [0.044,0.055] | 88.7 | 79.5 | 89.1 | 0.001 |

F | 0.090 | 0.086 | 0.003 | [0.083,0.097] | 88.7 | 79.5 | 89.1 | 0.001 | |

GE | NF | 0.043 | 0.023 | 0.003 | [0.038,0.048] | 93.4 | 94.5 | 82.9 | 0.001 |

F | 0.137 | 0.134 | 0.003 | [0.130,0.143] | 93.4 | 94.5 | 82.9 | 0.001 |

**Table 3.**SampEn statistics for the F/NF A-EGM for individual parameters $(m,r)$ optimized individually on the CZ and GE databases. DB stands for database and params for parameters $(m,r)$. Results are summarized using mean and median values, standard deviation (SD), confidence intervals (CI), area under ROC (AUC), sensitivity (Se), specificity (Sp) and the Mann–Whitney statistical probability (p).

DB | Class | params | mean | median | SD | 95% CI | AUC (%) | Se (%) | Sp (%) | p |
---|---|---|---|---|---|---|---|---|---|---|

CZ | NF | (5,0.15) | 0.120 | 0.131 | 0.007 | [0.106,0.133] | 90.9 | 82.0 | 79.2 | 0.001 |

F | 0.224 | 0.227 | 0.008 | [0.208,0.240] | 90.9 | 82.0 | 79.2 | 0.001 | ||

GE | NF | (4,0.15) | 0.202 | 0.162 | 0.011 | [0.180,0.225] | 88.5 | 87.8 | 78.5 | 0.001 |

F | 0.452 | 0.454 | 0.008 | [0.437,0.468] | 88.5 | 87.8 | 78.5 | 0.001 |

**Figure 3.**Boxplot distribution of the SampEn values computed to the initially-optimized parameters for individual levels of fractionation, $(m,r)=$(4,0.65). (

**A**) The BT database. (

**B**) The GE database. (

**C**) The CZ database.

**Figure 4.**Boxplot distribution of the SampEn values computed with the individual optimized parameters for each of the levels of fractionation present in each database. (

**A**) The GE database (4,0.15). (

**B**) The CZ database (5,0.15).

DB | Class | mean | median | 95% CI |
---|---|---|---|---|

BT | C0 | 0.032 | 0.021 | [0.020, 0.045] |

C1 | 0.065 | 0.061 | [0.058, 0.072] | |

C2 | 0.102 | 0.097 | [0.093, 0.111] | |

C3 | 0.149 | 0.138 | [0.127, 0.172] | |

CZ | C0 | 0.029 | 0.028 | [0.024, 0.035] |

C1 | 0.061 | 0.058 | [0.055, 0.066] | |

C2 | 0.082 | 0.083 | [0.075, 0.088] | |

C3 | 0.113 | 0.114 | [0.100, 0.125] | |

GE | C0 | 0.030 | 0.014 | [0.024, 0.036] |

C1 | 0.070 | 0.064 | [0.062, 0.077] | |

C2 | 0.119 | 0.115 | [0.113, 0.125] | |

C3 | 0.186 | 0.187 | [0.176, 0.196] |

**Figure 5.**Comparison between both algorithms used for a specific patient undergoing radio frequency ablation (RFA) of atrial fibrillation (AF). SampEn with optimized parameters ($m=4,r=0.65$) (bottom) and CFEMean (St. Jude Medical) measurements mapped on a 3D model of heart tissue. The blue color in both measures reveals areas with a higher level of complexity of complex fractionated atrial electrograms (CFAEs). (

**A**) 3D atrial topographical map, whole mapped area, frontal view. (

**B**) A detail of the area around the pulmonary vein.

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Cirugeda–Roldán, E.; Novak, D.; Kremen, V.; Cuesta–Frau, D.; Keller, M.; Luik, A.; Srutova, M. Characterization of Complex Fractionated Atrial Electrograms by Sample Entropy: An International Multi-Center Study. *Entropy* **2015**, *17*, 7493-7509.
https://doi.org/10.3390/e17117493

**AMA Style**

Cirugeda–Roldán E, Novak D, Kremen V, Cuesta–Frau D, Keller M, Luik A, Srutova M. Characterization of Complex Fractionated Atrial Electrograms by Sample Entropy: An International Multi-Center Study. *Entropy*. 2015; 17(11):7493-7509.
https://doi.org/10.3390/e17117493

**Chicago/Turabian Style**

Cirugeda–Roldán, Eva, Daniel Novak, Vaclav Kremen, David Cuesta–Frau, Matthias Keller, Armin Luik, and Martina Srutova. 2015. "Characterization of Complex Fractionated Atrial Electrograms by Sample Entropy: An International Multi-Center Study" *Entropy* 17, no. 11: 7493-7509.
https://doi.org/10.3390/e17117493