# Early Ventricular Fibrillation Prediction Based on Topological Data Analysis of ECG Signal

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Pre-Processing

#### 2.2. TDA Features Extraction

#### 2.2.1. Phase Space Reconstruction

**Takens’ theorem**$M$ is a $d$-dimensional manifold, the map $\phi :M\to M$ is a smooth differential homogeneous embryo, and the map $y:M\to R$ has continuous second-order derivatives $\Phi \left(\phi ,y\right):M\to {R}^{2d+1}$, which are described as Formula (1).

#### 2.2.2. Topological Data Analysis

- Obtain the barcode from the point cloud;
- Calculate the PH duration length (PHDL) of each complex during the filtration process, which is defined as the difference between the radius when the complex disappears and the radius when the complex appears:$${\mathrm{PHDL}}_{b}\left(i\right)={\epsilon}_{\mathrm{disappear}}-{\epsilon}_{\mathrm{appear}}\left(i=1,2,3,4,\dots ,\mathrm{N}\right),$$
- Finally, the three statistical features of PHDL in the barcodes with Betti number b are calculated as follows:

#### 2.3. Other Features Extraction

#### 2.3.1. Box-Counting Features

#### 2.3.2. HRV Features

#### 2.4. VF Prediction

## 3. Results

#### 3.1. Reconstruction Parameter Determination

#### 3.2. Split Frame Length Selection

#### 3.3. Prediction Performance Comparison

#### 3.4. Features Ranking

## 4. Discussion

#### 4.1. Effect of Reconstruction Parameters and Split Frame Length

#### 4.2. Evaluation of TDA Features

#### 4.3. Comparison with Previous Prediction Methods

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Results of pre-processing. (

**a**) The original ECG signal; (

**b**) The pre-processed ECG signal. By comparison, the baseline drift in the original ECG signal is eliminated by moving average filtering and its amplitude is adjusted to the 0–1 range by normalization.

**Figure 3.**Phase space trajectories of VF and nVF split frames. (

**a**) VF split frame; (

**b**) nVF split frame.

**Figure 4.**Barcode diagram of VF and nVF split frames. (

**a**) VF split frame with Betti number 0 to 2; (

**b**) nVF split frame with Betti number 0 to 2.

**Figure 5.**Box plots for four different split frame lengths. (

**a**) 5s-length split frame: the median of the first local minimum of the MI function is obtained as 12; (

**b**) 8s-length split frame: the median of the first local minimum is 10.5; (

**c**) 10s-length split frame: the median of the first local minimum is 12.5; (

**d**) 15s-length split frame: the median of the first local minimum is 11. And the “+” represents the outlier.

Database | Data | Sampling Rate |
---|---|---|

CUDB | ‘cu10′; ‘cu11′;‘cu13′;‘cu24′;‘cu17′;‘cu22′;‘cu23′; ‘cu05′;‘cu15′;‘cu19′;‘cu32′;‘cu33′;‘cu03′;‘cu14′;‘cu18 | 250 Hz |

SDDB | 31;32;33;34;35;36;37;38;44;45;46;47;48;50;51 | 250 Hz |

PTBDB | ‘s0552_re’;‘s0551_re’;‘s0543_re’;‘s0534_re’;‘s0533_re’;‘s0532_re’;‘s0531_re’;‘s0527_re’;‘s0526_re’;‘s0506_re’;‘s0504_re’;‘s0503_re’;’s0502_re’;’s0500_re’;’s0499_re’;’s0496_re’;’s0491_re’;‘s0487_re’;‘s0486_re’;‘s0481_re’;‘s0480_re’;‘s0479_re’;‘s0478_re’;‘s0474_re’;‘s0473_re’;‘s0472_re’;‘s0471_re’;‘s0470_re’;‘s0469_re’;‘s0468_re’ | 1000 Hz |

Features | TDA 0 | TDA 1 | TDA 2 |
---|---|---|---|

Sum | sum 0 | sum 1 | sum 2 |

Variance | var 0 | var 1 | var 2 |

Mean | mean 0 | mean 1 | mean 2 |

Features | Equation |
---|---|

$MNN$ | $\sum _{i=1}^{\mathrm{N}}}\mathrm{Y}\left(i\right)/\mathrm{N$ |

$SDNN$ | $\sqrt{{\displaystyle \sum _{i=1}^{\mathrm{N}}}{\left(\mathrm{Y}\left(i\right)-MNN\right)}^{2}/\mathrm{N}}$ |

$RMSSD$ | $\sqrt{{\displaystyle \sum _{i=1}^{\mathrm{N}}}{\left(\mathrm{Y}\left(i+1\right)-\mathrm{Y}\left(i\right)\right)}^{2}/\left(\mathrm{N}-1\right)}$ |

$NN50$ | The number of RRI sequences where the difference between adjacent terms is greater than 50 ms |

$PNN50$ | The ratio of the number of adjacent terms in RRI sequence whose difference is greater than 50 ms to the sequence length |

$skewness$ | ${\mathrm{M}}_{3}\sqrt{{({\mathrm{M}}_{2})}^{3}}$ |

$kurtosis$ | $\frac{{\mathrm{M}}_{4}}{{({\mathrm{M}}_{2})}^{2}}-3$ |

$\mathit{\tau}$ | 5 s Split Frame | 8 s Split Frame | 10 s Split Frame | 15 s Split Frame |
---|---|---|---|---|

11 | 90.0% RF | 86.7% RF | 88.3% DT | 83.3% DT |

12 | 91.7% RF | 93.3% RF | 88.3% RF | 83.3% RF |

ML Classifiers | Box-Counting Features | HRV Features | TDA Features | Fusion Features |
---|---|---|---|---|

Decision Trees | 70.0% | 61.7% | 86.7% | 91.7% |

Logistic Regression | 65.0% | 56.7% | 53.3% | 55.0% |

SVM | 71.7% | 71.7% | 55.0% | 55.0% |

KNN | 63.3% | 66.7% | 55.0% | 53.3% |

Radom Forest | 61.7% | 65.0% | 91.7% | 95.0% |

Features | MI | Chi−Square | MRMR | Out-of-Bag | ReliefF |
---|---|---|---|---|---|

$\mathrm{TDA}0\_\mathrm{sum}0$ | −0.06973 | 8.52156 | 0.14073 | 0.35355 | 0.22132 |

$\mathrm{TDA}1\_\mathrm{sum}1$ | −0.05626 | 9.05480 | 0.16236 | 0.38521 | 0.26416 |

$\mathrm{TDA}2\_\mathrm{sum}2$ | −0.26306 | 1.10083 | 0.05174 | 0.06355 | −0.04202 |

$\mathrm{TDA}0\_\mathrm{var}0$ | −0.02478 | 12.90666 | 0.36806 | 0.70518 | 0.58501 |

$\mathrm{TDA}1\_\mathrm{var}1$ | −0.08660 | 4.96328 | 0.13049 | 0.29902 | 0.20516 |

$\mathrm{TDA}2\_\mathrm{var}2$ | −0.05625 | 10.68233 | 0.26268 | 0.48215 | 0.26509 |

$\mathrm{TDA}1\_\mathrm{mean}1$ | −0.03002 | 11.78756 | 0.29908 | 0.62190 | 0.40754 |

$\mathrm{TDA}2\_\mathrm{mean}2$ | −0.12454 | 1.84986 | 0.12685 | 0.17107 | 0.12099 |

$MNN$ | −0.13324 | 1.77568 | 0.10477 | 0.14286 | 0.08333 |

$SDNN$ | −0.39715 | 0.18215 | 0.00018 | −0.14286 | −0.14500 |

$RMSSD$ | −0.83429 | 0.06164 | 3.49049 × 10^{−15} | −0.14286 | −0.15243 |

$NN50$ | −0.31335 | 0.76527 | 0.00076 | −0.10643 | −0.12677 |

$PNN50$ | −0.27056 | 1.06271 | 0.04106 | 0.00000 | −0.07877 |

$kurtosis$ | −0.31891 | 0.39783 | 0.00071 | −0.14286 | −0.13620 |

$skewness$ | −0.09189 | 2.35361 | 0.13049 | 0.24026 | 0.13275 |

$CV$ | −0.27523 | 1.03846 | 0.02133 | −0.03349 | −0.09768 |

$\kappa $ | −0.13934 | 1.15556 | 0.05641 | 0.09654 | 0.07217 |

Reference Index | Forecast Time | Database | Split Frame Length | ECG Features | Prediction Performance |
---|---|---|---|---|---|

[4] | 15 min | NSRDB 9 VFDB 9 | 60 s | 12 morphological features | Sensitivity 95% Specificity 90% |

[5] | 13 min | SDDB 23 NSRDB 18 | 60 s | 23 HRV features | Accuracy 84.28% |

[6] | 30 s | CUDB 27 PAFDB 22 NSRDB 6 | 120 s | 4 QRS features | Accuracy 98.6% |

[7] | 10 s | MVTDB 78 | 5 min | 11 HRV features | Accuracy 92.2% |

[8] | 5 min | SDDB 20 NSRDB 18 | 60 s | 13 HRV features | Accuracy 95% |

[9] | 4 min 31 s | CUDB 32 PTBDB 32 | 10 heart beats | 2 box-counting features | Accuracy 98.44% |

[12] | 0 s | CUDB 29 MVTDB 30 +29 PAFDB 12 NSRDB 18 | 20 s | 5 HRV features | Accuracy 88.64% |

Our work | 5 min | CUDB 15SDDB 15PTBDB 30 | 5 s,8 s,10 s,15 s | 2 box-counting features9 TDA features7 HRV features | Accuracy95% |

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## Share and Cite

**MDPI and ACS Style**

Ling, T.; Zhu, Z.; Zhang, Y.; Jiang, F. Early Ventricular Fibrillation Prediction Based on Topological Data Analysis of ECG Signal. *Appl. Sci.* **2022**, *12*, 10370.
https://doi.org/10.3390/app122010370

**AMA Style**

Ling T, Zhu Z, Zhang Y, Jiang F. Early Ventricular Fibrillation Prediction Based on Topological Data Analysis of ECG Signal. *Applied Sciences*. 2022; 12(20):10370.
https://doi.org/10.3390/app122010370

**Chicago/Turabian Style**

Ling, Tianyi, Ziyu Zhu, Yanbing Zhang, and Fangfang Jiang. 2022. "Early Ventricular Fibrillation Prediction Based on Topological Data Analysis of ECG Signal" *Applied Sciences* 12, no. 20: 10370.
https://doi.org/10.3390/app122010370