# Heart Rate Estimation from Incomplete Electrocardiography Signals

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## Abstract

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## 1. Introduction

## 2. Related Works

## 3. Methods

#### 3.1. Bidirectional Long Short-Term Memory Model (Bi-LSTM)

#### 3.2. Temporal Convolution Network

#### 3.3. Data Preparation for Short-Time Heart Rate Estimation

_{RRI}denotes the time duration of RRI, and HR was measured in beats per minute (bpm).

## 4. Evaluation Metrics and Result Analysis

_{e}was evaluated by its standard deviation (denoted as HR

_{SD}):

_{SD}indicates that the measuring values of HR

_{e}tend to be closer to the average value.

_{p}denotes the mean value of predicted HR, and M

_{gt}denotes the mean value of the ground truth values. $\mathsf{\gamma}\in [-1,1]$, where 1 indicates the total positive linear correlation and -1 indicates the total negative correlation.

#### 4.1. The Result with Different Input Lengths

_{e}of TCN and Bi-LSTM fell in a small range and do not show a significant regularity (see Table 1). However, three metrics (i.e., HR

_{MAPE}and HR

_{RMSE}) show a general trend of decreasing and then increasing, corresponding to a trend of increasing and then decreasing in performance, which indicates that the variations of the sequence length is distributed over an interzone with a higher accuracy. It should be noted that all γ were greater than 0.9, indicating that estimated HR has a strong linear correlation with real HR. TCN method performs best at the sampling frequency of 640 Hz and Bi-LSTM method performs best at the sampling frequency of 128 Hz. Apparently, both models show outstanding performance in time series with missing values, and the prediction result is not determined by the length of sequence.

#### 4.2. The Result at Different Input Duration Time

_{SD}, HR

_{MAPE}, and HR

_{RMSE}in previous experiment. RNN was stacked by LSTM layers (see Table 2) and CNN was stacked by residual blocks (see Table 3). Meanwhile, we have described further details about the networks, including the number of neurons, dropout rate, and so on.

_{e}climbed up initially, followed by a decline, and remained steady; lastly, 0.35 s and 0.25 s were two critical turning points in the curves. Meanwhile, HR

_{SD}, HR

_{MAPE}, and HR

_{RMSE}rose slowly with the decreasing percentage of input in the early stage. Three metrics rose rapidly after the input duration was reduced to 0.35 s. Continuing the reduction of the input duration to 0.25 s, HR

_{SD}, HR

_{MAPE}, and HR

_{RMSE}began to remain stable. In terms of the Pearson correlation coefficient γ, all results were greater than 0.8 until the input duration was below 0.35 s, proving a strong positive linear correlation between input and predicted output. Within the range of 0.3–0.25 s, the absolute value of γ is lower than 0.3, meaning that there was a weak linear correlation between input and estimated HR. The Pearson correlation coefficient also maintains steady in the later intervals. Therefore, the fastest HR estimation should be maintained input sequences of no less than 0.35 s duration. In order to implement normal resting HR quick estimation at an acceptable accuracy, the duration of input sequences should be no less than 0.35 s.

#### 4.3. The Result in Arrhythmia Cases

_{e}, HR

_{SD}, HR

_{MAPE}, and HR

_{RMSE}increased significantly compared with the normal heart rhythm database. It is easy to see why the approach performs more poorly. On the one hand, the blurring of details of signals caused by the denoising algorithm lead to the loss of information when removing the artifacts of arrhythmias, such as ST segment, QT interval, and so on, which could be regarded as biometric identification for the actual individuals and has been proven in [41]. On the other hand, even though a large number of the heart beat fragments were used for model training, the individual morphological features of ECGs varied among patients in the database. In the normal heart rhythm database, long-term ECG recordings (over 60,000 s) of every person have been utilized. There are many individual targets tested in the database, but only up to signals of 10 s of each patient can be exploited in this experiment. However, the γ were greater than 0.6, indicating that estimated HR from irregular heartbeat signal has a moderate linear correlation with real HR. Results show that HR recovered from incomplete ECGs with arrhythmias validly.

_{e}, HR

_{SD}, HR

_{MAPE}, and HR

_{RMSE}will rise to over 40, indicating that estimated HR has a weak correlation with the ground truth. For a larger range and wider variety of HR, a longer inputting series (0.4 s and above) is needed for prediction.

#### 4.4. The Result in More General Cases

#### 4.5. Further Discussion

_{e}is reduced to 6.76 from 24.0, indicating that HR errors in the predictions are decreased significantly and more concentrated around the real values. In addition, M

_{e}is reduced to −1.59 and MAPE is reduced to 6.12%, which demonstrates that the accuracy of forecasting results has been improved. In general, introducing an appropriate skipped window cuts down the minimum duration required for the input sequence.

_{e}were less than 10 when input duration is reduced to 0.2 s or less. Although the amplitude of the predicted R wave is already very low in this case, the values of the metrics indicate that the proposed approach is still effective. Nevertheless, extremely short-time estimation has to be implemented under the premise that the HR diversity of the dataset is limited to a small range and starts at a constant position. Therefore, the proposed method is more applicable for estimating the resting HR (usually 60–100 bpm) or some personalized predictions.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The diagram of the proposed iHR estimation approach employing time-series forecasting with CNN and RNN, and its main three steps: data preprocessing, sequence forecasting, and HR estimation. Following ECG signal normalization, a pretrained neural network would be able to generate time series for a short period of time in the future. We calculate a complete RRI and estimate HR in advance by combining the restored and original signals.

**Figure 2.**System structure of the iHR estimation model using Bi-LSTM. The original signal as input for Bi-LSTM, and hidden units of LSTM capture temporal dependencies in time series. Dropout layer close to each Bi-LSTM layer to reduce overfitting. To generate HR estimation sequences, three layers of Bi-LSTM and dropout, an FC layer, and an output layer were stacked.

**Figure 3.**The system structure of the iHR estimation model using TCN in AlexNet style. Stacking residual blocks with dilation casual convolution layers using skip connection (simplified and visualized by the black dash boxed areas), a generic TCN model would be designed for sequence modeling. The bottom boxed areas show an example of a residual connection in a TCN. Two solid black lines indicate that the input of the Dilated Conv1 module in the top boxed area corresponds to the input layer in the bottom boxed area, and the input of Dilated Conv2 module in the top boxed area corresponds to the block output layer in the bottom boxed area. In this example, a dilated causal convolution with dilation factors d = 1,2 and filter size k = 3, the origin lines are filters in the residual function, and the blue lines are identity mappings. Across layers via identity mappings, skip connections effectively mitigate the gradient problem in deep models. To generate forecasting sequences, we also use an FC layer and output layer.

**Figure 4.**Examples of data segmenting of the recorded ECG. The time-leading parts are displayed in blue and the time-lagged part are displayed in orange. The elements between the time-leading parts and the time-lagged parts (grey) are deleted.

**Figure 5.**Prediction results of two sequences (

**a**,

**b**). Black lines denote the input sequence and green dash lines denote the ground truth ECG. The red imaginary lines denote the predicted ECG from the proposed method. The change in shape does not affect the determination of the extremum point.

**Figure 6.**Results comparison on inputs of different lengths. (

**a**) The absolute value of mean error; (

**b**) standard deviation; (

**c**) mean absolute percentage error; (

**d**) root mean square error; and (

**e**) Pearson correlation coefficient. The red line denotes the predicted results of CNN models and the blue line denotes the results of RNN models. As the time duration of input fell from 0.5 s to 0.2 s, a high, similar trend was demonstrated in Bi-LSTM and TCN.

**Figure 7.**The statistical histograms of real HR and estimated HR in the test set. The red bar represents the ground truth HR, and the blue bar represents the predicted values by TCN. We also plot the kernel density curves of real HR and estimated HR with the red line and blue line, respectively, in the upper right corner.

**Table 1.**iHR estimation performance comparisons on the MIT-BIH Normal Sinus Rhythm Database at various sampling frequencies (64–1024 Hz).

DL Models | Sampling Rate (f_{s}) | M_{e} (bpm) | HR_{SD} (bpm) | HR_{MAPE} | HR_{RMSE} (bpm) | γ |
---|---|---|---|---|---|---|

Bi-LSTM (RNN) | 0.5 | 1.98 | 6.19 | 5.82% | 6.51 | 0.91 |

1 | −0.25 | 5.91 | 5.22% | 5.91 | 0.92 | |

2 | 0.70 | 6.03 | 5.39% | 6.07 | 0.92 | |

3 | −0.14 | 5.97 | 5.28% | 5.97 | 0.92 | |

4 | 0.32 | 6.29 | 5.47% | 6.30 | 0.91 | |

5 | −0.34 | 6.04 | 5.26% | 6.05 | 0.91 | |

6 | 0.43 | 6.24 | 4.98% | 6.25 | 0.91 | |

7 | 0.71 | 6.26 | 5.58% | 6.30 | 0.91 | |

8 | 0.50 | 6.03 | 5.31% | 6.05 | 0.91 | |

TCN (CNN) | 0.5 | 1.01 | 6.18 | 5.43% | 6.27 | 0.91 |

1 | 0.03 | 5.90 | 5.18% | 5.90 | 0.92 | |

2 | −0.37 | 5.74 | 5.10% | 5.75 | 0.93 | |

3 | −0.58 | 5.67 | 5.07% | 5.70 | 0.93 | |

4 | −0.73 | 5.79 | 5.17% | 5.83 | 0.92 | |

5 | −0.53 | 5.62 | 4.96% | 5.64 | 0.93 | |

6 | −0.61 | 5.78 | 5.17% | 5.81 | 0.92 | |

7 | −0.98 | 5.66 | 5.06% | 5.75 | 0.93 | |

8 | −0.76 | 5.79 | 5.17% | 5.84 | 0.92 |

Layers | No. of Neurons | Dropout Rate |
---|---|---|

LSTM1 | 60 | 0.6 |

LSTM2 | 30 | 0.4 |

LSTM3 | 20 | 0.3 |

Modules | Filter Length/Dropout Rate | Dilation Factors |
---|---|---|

ResBlock1 | 128/0.2 | 1 |

ResBlock2 | 128/0.2 | 2 |

ResBlock3 | 64/0.2 | 4 |

ResBlock4 | 64/0.2 | 8 |

ResBlock5 | 32/0.2 | 16 |

ResBlock6 | 32/0.2 | 32 |

ResBlock7 | 16/0.2 | 64 |

ResBlock8 | 16/0.2 | 128 |

ResBlock9 | 8/0.2 | 256 |

ResBlock10 | 8/0.2 | 320 |

**Table 4.**Inputting a 0.4 s ECG segment and forecasting following 1.6 s, the iHR estimation performance comparisons on the A Large Scale 12-lead Electrocardiogram Database at different models (CNN and RNN) are shown. All the ECGs were filtered by the NLM method, and signals of CNN and RNN were set at a sampling rate of 640 Hz and 128 Hz.

DL Models | M_{e} (bpm) | HR_{SD} (bpm) | HR_{MAPE} | HR_{RMSE} (bpm) | γ |
---|---|---|---|---|---|

Bi-LSTM | −2.66 | 25.24 | 21.77% | 25.38 | 0.68 |

TCN | −4.01 | 26.22 | 23.37% | 26.52 | 0.65 |

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**MDPI and ACS Style**

Song, Y.; Chen, J.; Zhang, R.
Heart Rate Estimation from Incomplete Electrocardiography Signals. *Sensors* **2023**, *23*, 597.
https://doi.org/10.3390/s23020597

**AMA Style**

Song Y, Chen J, Zhang R.
Heart Rate Estimation from Incomplete Electrocardiography Signals. *Sensors*. 2023; 23(2):597.
https://doi.org/10.3390/s23020597

**Chicago/Turabian Style**

Song, Yawei, Jia Chen, and Rongxin Zhang.
2023. "Heart Rate Estimation from Incomplete Electrocardiography Signals" *Sensors* 23, no. 2: 597.
https://doi.org/10.3390/s23020597