# A Heart Rate Variability-Based Paroxysmal Atrial Fibrillation Prediction System

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection

#### 2.2. Signal Preprocessing

#### 2.3. Feature Matrices Conversion

**x**

_{1},

**x**

_{2}, …,

**x**

_{m}], where

**x**

_{i}= [x

_{i,}

_{1}, x

_{i}

_{,2},…, x

_{i,n}]

^{T}in the unit of beats/min, i = 1, 2, …, m. The process of constructing a feature matrix

**A**∈ $\mathcal{R}$

^{s}

^{×t}from an HRV sequence $\mathrm{x}\in {\mathbb{R}}^{n}$ can be accomplished through a mapping function, Φ, such that

**A**= Φ(x). In this work, we chose the discretized Poincaré plot to perform such a conversion for its easy construction, modification, and interpretation. In addition, it has been related to HRV physiology [38,39] and adopted for HRV analysis on PAF prediction for decades [11,13,40,41,42]. However, most of the previous works used features that measure only a certain facet of the plot and thus the information carried in the plot is not fully utilized. In fact, according to the definition of various abnormal beats in [43], these beats can be found in different regions in the Poincaré plot of an HRV sequence, as illustrated in Figure 1. More importantly, the discretized Poincaré plot of a sequence is shift-invariant in that the plot is independent of the feature locations in the sequence.

_{i}versus x

_{i}

_{+}

_{1}of a sequence,

**x**= x

_{1}, x

_{2}, …, x

_{n}, where I = 1, 2, …, n − 1. This plot is used to capture the correlation between two consecutive data points. It can be extended to calculate the correlation between sequential data points that are τ points away (lag), where τ is a positive integer less than n. Therefore, an n-point sequence can be represented by an extended Poincaré plot by drawing the points (x

_{i}, x

_{i}

_{+}

_{τ}) where i = 1, 2, …, n−τ. However, the Poincaré plot is a 2-dimensional real-valued image with an infinite number of points in a data-dependent range of [l

**, u**

_{x}**] × [l**

_{x}**, u**

_{x}**], where l**

_{x}**= min(**

_{x}**x**) and u

**= max(**

_{x}**x**). To generate a fixed-size matrix

**A**∈ ${\mathbb{N}}^{s\times s}$ for each HRV sequence, the range of allowable heart rates is to be defined, and then the resultant plot needs to be discretized before it can be used in the subsequent analysis. Let l

_{p}and u

**represent accordingly the lower and the upper bounds of the heart rates to be included in the feature matrix**

_{p}**A**. The (i, j)-th component of the feature matrix,

**A**(i, j), 1 ≤ i, j ≤ s, denotes the number of points lying within the region in the Poincaré plot defined by [l

_{p}+ (i − 1)q, l

_{p}+ iq] × [l

_{p}+ (j − 1)q, l

_{p}+ jq], where q = (u

**− l**

_{p}_{p})/s is the quantization factor. The quantitation factor affects not only the heart rate range considered in our system, but also the level of noise tolerated by the system. In this design, the lower and the upper bounds of the Poincaré plot can be adjusted to reduce noise in an HRV sequence introduced by incorrect QRS detection. The missing and additional R waves due to incorrect QRS detection usually result in very low and very high heart rates accordingly that fall outside the normal resting heart rates (i.e., outliers), and thus can be removed by the bounds. On the other hand, the quantitation factor is useful in reducing noise caused by inaccurate QRS detection. This is because inaccurate QRS detection often leads to a small shift from its original value, which can be covered by a quantization window. The robustness of our system to the noise in the HRV sequences will be investigated in the discussion section.

**x**, from its original range to the feature matrix ranges.

#### 2.4. Feature Selection and Classification

#### 2.5. Parameter Determinations

**vt**

_{i}+ 1, where

**vt**

_{i}, i = 1, 2, 3, 4, were binary vectors of length 5, making each time lag drawn from integers in the range of [1, 32]. The first two time lags were for the two inter-person feature matrices, whereas the latter two were for the two intra-person feature matrices. An additional binary vector,

**vm**, of length 4 were used to control the usage (1 for use and 0 for not use) of the four feature matrices, resulting in a total of 24 binary numbers for feature conversion.

**vl**

_{i}, i = 1, 2, 3, 4, 5, were employed to regulate the usage of the convolution layer, batch normalization layer, ReLU layer, and max-pooling layer sequentially in each of the layer sets. Finally, the number of filters and the size of the filters in the convolution layer of each layer set were determined accordingly via

**vf**

_{i}+ 1 and

**vs**

_{i}+ 1, where

**vf**

_{i}and

**vs**

_{i}, i = 1, 2, 3, 4, 5, were binary vectors of length 4, making the number of filters and the size of filters all drawn from integers in the range of [1, 16].

**v**= [

**vt**

_{i},

**vm**,

**vl**

_{j},

**vf**

_{j},

**vs**

_{j}], i = 1, 2, 3, 4 and j = 1, 2, 3, 4, 5, selected by GA determined the parameters and the architecture of our PAF prediction system. Figure 2 shows the flowchart for the construction of the system. Let E

_{t}(

**v**) and E

_{v}(

**v**) denote accordingly the training error and the validation error of the system determined by a binary vector

**v**, then the design of our PAF prediction system can be formulated as the following optimization problem.

## 3. Results

#### 3.1. Data Split

#### 3.2. The Converted Feature Matrices

**vm**, obtained from GA were all 1s, all four matrices were retained for the inputs of the subsequent CNN. Figure 3 presents the images of the four matrices generated from a non-PAF subject in the upper panel, whereas those generated from a PAF patient are presented in the lower panel.

#### 3.3. Performance of the Developed PAF Prediction System

## 4. Discussion

#### 4.1. Comparison with Similar Systems

^{®}environment with an Intel

^{®}Core™ i7-9750H CPU at 2.60 GHz and 32 GB RAM. In addition, because our features can directly link back to the original HRV sequence, their medical implications can be traced easily. Some of the implications from the designed inter- and intra-features are discussed next.

#### 4.2. Medical Implications from the Features

#### 4.3. Robustness of the System

#### 4.4. Analysis of Misclassifications

#### 4.5. Future Works

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Heart rate distribution of the HRV sequences in the PAF Prediction Challenge Database (AFPDB). Upper Left: Boxplot of the heart rate values of all of the HRV sequences. Upper Right: Histogram of the heart rate values of all of the HRV sequences. Lower Left: Boxplot of the heart rate values in the range of [0, 200] beats/min. Lower Right: Histogram of the heart rate values in the range of [0, 200] beats/min, from which we determined to adopt the range of [30, 190] for HRV sequence filtering.

**Figure A2.**The nine PAF subgroups and the six non-PAF subgroups from hierarchical clustering. The nine PAF subgroups (

**a**) and the six non-PAF subgroups (

**b**) were obtained by using a cutting threshold of 3500.

No. | Name | Type | Activations | Learnables |
---|---|---|---|---|

1 | imageinput32 × 32 × 4 images with ‘zerocenter’ normalization | Image Input | 32 × 32 × 4 | - |

2 | conv_116 3 × 3 × 4 convolutions with stride [1 1] and padding ‘same’ | Convolution | 32 × 32 × 16 | Weights 3 × 3 × 4 × 16 Bias 1 × 1 × 16 |

3 | relu_1ReLU | ReLU | 32 × 32 × 16 | - |

4 | conv_216 15 × 15 × 16 convolutions with stride [1 1] and padding ‘same’ | Convolution | 32 × 32 × 16 | Weights 15 × 15 × 16 × 16 Bias 1 × 1 × 16 |

5 | batchnorm_1Batch normalization with 16 channels | Batch Normalization | 32 × 32 × 16 | Offset 1 × 1 × 16 Scale 1 × 1 × 16 |

6 | conv_316 13 × 13 × 16 convolutions with stride [1 1] and padding ‘same’ | Convolution | 32 × 32 × 16 | Weights 13 × 13 × 16 × 16 Bias 1 × 1 × 16 |

7 | conv_414 16 × 16 × 16 convolutions with stride [1 1] and padding ‘same’ | Convolution | 32 × 32 × 14 | Weights 16 × 16 × 16 × 14 Bias 1 × 1 × 14 |

8 | batchnorm_2Batch normalization with 14 channels | Batch Normalization | 32 × 32 × 14 | Offset 1 × 1 × 14 Scale 1 × 1 × 14 |

9 | relu_2ReLU | ReLU | 32 × 32 × 14 | - |

10 | conv_515 12 × 12 × 14 convolutions with stride [1 1] and padding ‘same’ | Convolution | 32 × 32 × 15 | Weights 12 × 12 × 14 × 15 Bias 1 × 1 × 15 |

11 | batchnorm_3Batch normalization with 15 channels | Batch Normalization | 32 × 32 × 15 | Offset 1 × 1 × 15 Scale 1 × 1 × 15 |

12 | relu_3ReLU | ReLU | 32 × 32 × 15 | - |

13 | fc2 fully connected layer | Fully Connected | 1 × 1 × 2 | Weights 2 × 15360 Bias 2 × 1 |

14 | dropout50% dropout | Dropout | 1 × 1 × 2 | - |

15 | softmaxsoftmax | Softmax | 1 × 1 × 2 | - |

16 | classoutputcrossentropyex with classes ‘0′ and ‘1′ | Classification Output | - |

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**Figure 1.**Regions related to different abnormal beats in an accumulated discretized Poincaré plot of PAF HRV sequences.

**Figure 3.**Feature matrices input to the CNN. (

**a**) Two inter-person feature matrices generated from the extended Poincaré plot of a non-PAF subject with τ = 2, q = 4 and τ = 1, q = 5. (

**b**) Two Intra-person feature matrices generated from the extended Poincaré plot of a non-PAF subject with τ = 4, q = 4 and τ = 5, q = 5. (

**c**) Two inter-person feature matrices generated from the extended Poincaré plot of a PAF patient with τ = 2, q = 4 and τ = 1, q = 5. (

**d**) Two intra-person feature matrices generated from the extended Poincaré plot of a PAF subject with τ = 4, q = 4 and τ = 5, q = 5. All the matrix values were log-transformed for better visualization. The symbol τ denotes time lag and q denotes the quantization factor.

**Figure 5.**Feature differences between PAF and non-PAF HRV sequences. The reddish pixels represent heart rate changes in a 400 HRV sequence that appear more frequently in PAF than in non-PAF subjects. Upper panel: (

**a**) Inter-person features with τ = 2 and q = 4 and (

**b**) with τ = 1 and q = 5; Lower panel: (

**c**) Intra-person features with τ = 4 and q = 4 and (

**d**) with τ = 5 and q = 5. The symbol τ denotes the time lag and q denotes the quantization factor.

**Figure 6.**Exemplar non-PAF and PAF HRV sequences. The non-PAF HRV sequences (

**a**) often exhibit larger variation than the PAF ones (

**b**). However, the PAF HRV sequences occasionally show large heart rate changes.

**Figure 7.**Prediction accuracy (Acc.), true positive percentage (TPP), and true negative percentage (TNP) in the (

**a**) training, (

**b**) validation, and (

**c**) testing datasets after different percentages of noise were added to the HRV sequences therein.

**Figure 8.**Clustering result of 4414 non-PAF and 1671 PAF HRV sequences using their converted features. The symbols of TP, TN, FP, and FN denote the true positive, true negative, false positive, and false negative, respectively. The number behind each group represents the group index, whereas the number in parentheses indicates the number of sequences in the corresponding subgroup.

**Table 1.**The number of non-PAF and PAF 400-point HRV sequences and the number of corresponding persons in our training, validation, and testing datasets.

Dataset | Non-PAF Sequences (Persons) | PAF Sequences (Persons) |
---|---|---|

Training | 444 (37) | 516 (46) |

Validation | 120 (10) | 120 (10) |

Testing | 3850 (18) | 1035 (21) |

Literature | Databases | Data Length (min) | Features | Cross-Validation | Results (%) | ||
---|---|---|---|---|---|---|---|

SEN | SPE | ACC | |||||

Hickey and Henegham [44] | AFPDB | 5 | HRV power spectral density and PACs | 5-fold | 51.0 | 79.0 | 68.0 |

Chazal and Henegham [45] | AFPDB | 5 | P-wave power spectral density | 5-fold | 81.0 | 69.0 | 75.6 |

Boon et al. [9] | AFPDB | 5 | Combination of 9 HRV features in time and frequency domains | 10-fold | 86.8 | 88.7 | 87.7 |

Narin et al. [10] | AFPDB | 5 | Combination of 26 HRV features in time and frequency domains | 10-fold | 92.0 | 88.0 | 90.0 |

Mendez et al. (This study) | AFPDB * NSRDB * AFDB * | ~5 (400 points) | 32 × 32 × 4 images from extended and discretized Poincaré plot | Single-fold | 80.4 | 89.0 | 87.2 |

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## Share and Cite

**MDPI and ACS Style**

Mendez, M.M.; Hsu, M.-C.; Yuan, J.-T.; Lynn, K.-S.
A Heart Rate Variability-Based Paroxysmal Atrial Fibrillation Prediction System. *Appl. Sci.* **2022**, *12*, 2387.
https://doi.org/10.3390/app12052387

**AMA Style**

Mendez MM, Hsu M-C, Yuan J-T, Lynn K-S.
A Heart Rate Variability-Based Paroxysmal Atrial Fibrillation Prediction System. *Applied Sciences*. 2022; 12(5):2387.
https://doi.org/10.3390/app12052387

**Chicago/Turabian Style**

Mendez, Milna Maria, Min-Chia Hsu, Jenq-Tay Yuan, and Ke-Shiuan Lynn.
2022. "A Heart Rate Variability-Based Paroxysmal Atrial Fibrillation Prediction System" *Applied Sciences* 12, no. 5: 2387.
https://doi.org/10.3390/app12052387