# Deep-Learning-Based Estimation of the Spatial QRS-T Angle from Reduced-Lead ECGs

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## Abstract

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## 1. Introduction

## 2. Conventional Approach for QRS-T Angle Estimation

## 3. Deep-Learning-Based Approach for QRS-T Angle Estimation

#### 3.1. Deep Learning Model Architecture

#### 3.1.1. Feature Extraction Network

#### 3.1.2. Regression Network

#### 3.2. Loss Function

#### 3.3. Tuning of Hyperparameters

## 4. Data

#### 4.1. Data Preparation and Labeling

#### 4.1.1. Signal Preprocessing

#### 4.1.2. Data Labeling

#### 4.2. Exploratory Data Analysis

- Sex-related morphological differences in the ECG may influence the decision of the regression network (see Section 3.1.2); thus, the training set must be proportioned in terms of sex.
- Each of the morphological classes is characterized by distinctive morphological traits. Since contrastive ECG morphologies can still exhibit QRS-T angles of comparable range, the training set must include a diversity of morphologies to prevent the model from associating a specific range of QRS-T angles with just one subset of particular morphological traits.
- Randomly splitting the data without considering the uneven distribution of $\alpha $ within specific ranges could result in a disproportionate depiction of specific ranges in the training set, leading to higher errors in other ranges.

#### 4.3. Training and Validation Sets

## 5. Experiments and Performance Evaluation

^{®}Core

^{®}i7-8700k 3.70 GHz CPU with six cores (12-threads), 32 GB of RAM, and NVIDIA

^{®}GeForce

^{®}GTX 1080Ti.

#### 5.1. Selection of Subsets of ECG Leads

#### 5.2. Performance Metrics

## 6. Results

#### 6.1. Influence of Hyperparameter Tuning on the Model Performance

#### 6.2. Performance of the Best Configurations on Estimating the Spatial QRS-T Angle

## 7. Discussion

#### 7.1. Summary and Significance

#### 7.2. Considerations on the Model Architecture

#### 7.3. Considerations on the Attained Results

#### 7.4. Suitability for ECG Consumer Healthcare Devices

#### 7.5. Limitations and Future Directions

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CD | Conduction Disturbance |

CNN | Convolutional neural network |

CNN1D | 1D convolutional neural network |

ECG | Electrocardiogram |

HYP | Hypertrophy |

LOWM | Low magnitude (i.e., flat) T waves |

MI | Myocardial Infarction |

NORM | Normal |

SCD | Sudden Cardiac Death |

STTC | Change in ST-T segment |

TCRT | Total cosine R to T |

VCG | Vectocardiogram |

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**Figure 1.**Overview of the proposed deep learning model for estimation of QRS-T angle using reduced-lead ECGs. The model is composed of two parts: feature extraction and regression. The target vectors ${\overrightarrow{u}}_{QRS}$ and ${\overrightarrow{u}}_{T}$ and spatial QRS-T angle $\alpha $ are computed from VCGs.

**Figure 2.**Detailed representation of the three types of blocks employed in the feature extraction network: (

**a**) first block, (

**b**) the last block, and (

**c**) blocks with residual connections.

**Figure 3.**Case scenarios of: (

**a**) similar QRS-T angles $\alpha $ of two ${\overrightarrow{u}}_{QRS}$ and ${\overrightarrow{u}}_{T}$ located in two different planes; (

**b**) correct location of one vector (${\overrightarrow{u}}_{T}$) but not the other (${\overrightarrow{u}}_{QRS}$), yielding large errors in the estimated QRS-T angle $\widehat{\alpha}$; (

**c**) compromise between minor errors in the location of both ${\overrightarrow{u}}_{QRS}$ and ${\overrightarrow{u}}_{T}$ to achieve a more accurate QRS-T angle estimation.

**Figure 4.**Data preparation and labeling. Signals undergo preprocessing to generate the input signal-averaged beats.

**Figure 5.**Distribution of spatial QRS-T angles $\alpha $ of across the ranges of $\alpha $ = [0:5:180]° according to sex (overlapped) for all eligible recordings in the dataset (

**left**) and for each morphological class (

**right**). $\alpha $ is the angle between the VCG vectors ${\overrightarrow{u}}_{QRS}$ and ${\overrightarrow{u}}_{T}$. The dashed line is the median $\alpha $ for each class.

**Figure 6.**Distribution of spatial QRS-T angle $\alpha $ across the ranges of $\alpha $ = [0:5:180]° according to sex (overlapped) for all recordings suitable for analysis (

**left**) and for each morphological class (

**right**) in the (

**a**) training and (

**b**) validation sets. The dashed line is the median $\alpha $ for each class.

**Figure 7.**Performance of various model configurations tuned with different combinations of hyperparameters ${w}_{1}$ and ${w}_{2}$ in estimating the spatial QRS-T angle from leads XYZ in the validation dataset. (

**a**) Boxplot of the obtained absolute error $\u03f5$ (outliers not shown) for every combination of ${w}_{1}$ and ${w}_{2}$. ${w}_{1}$ increases to the left side, wheres ${w}_{2}$ to the right. The other hyperparameter value is obtained as $|1-w|$ on each side. (

**b**) Mean absolute error $\overline{\u03f5}$ and the respective 95% confidence interval across the ranges of $\alpha $ = [0:5:180]° for increasing ${w}_{1}$ (

**top row**) and ${w}_{2}$ (

**bottom row**). The last column displays the number of training samples for each range of $\alpha $.

**Figure 8.**Scatter plot diagrams of the deep-learning-estimated $\widehat{\alpha}$ vs. target $\alpha $ from various sets of leads for (

**top row**) all recordings, and ECGs with normal (

**middle row**) NORM and (

**bottom row**) cardiac disease in the validation dataset. The estimation error $\u03f5$ of every $\widehat{\alpha}$ in the first row is color-grouped based on the absolute median ($\tilde{\u03f5}$), mean ($\overline{\u03f5}$), and standard deviation (${\sigma}_{\u03f5}$) error.

**Figure 9.**Variation of the mean absolute error $\overline{\u03f5}$ and the respective the 95% confidence interval across the ranges of $\alpha $ = [0:5:180]° for ECGs with normal (NORM) and diseased cardiac function. The right axis indicates the number of training samples in each range of $\alpha $. Since the number of NORM subjects with $\alpha $ > 120° is almost negligible, $\overline{\u03f5}$ is not shown for these ranges of $\alpha $.

**Figure 10.**Bland-Altman diagrams of deep-learning-based estimation of $\widehat{\alpha}$ from various sets of leads of ECGs with (

**top**) normal (NORM) and (

**bottom**) diseased cardiac function.

**Figure 11.**Distribution of the Euclidean distance ${\mathcal{L}}_{d}\left(\overrightarrow{u},\widehat{\overrightarrow{u}}\right)$ between ${\overrightarrow{u}}_{QRS}$ and ${\widehat{\overrightarrow{u}}}_{QRS}$, and ${\overrightarrow{u}}_{T}$ and ${\widehat{\overrightarrow{u}}}_{T}$ in each of the three planes: $XY$ (frontal), $XZ$ (transverse), and $YZ$ (sagittal).

**Table 1.**Performance deep-learning-based estimation of the spatial QRS-T angle $\alpha $ from various sets of leads in whole the validation dataset, and in ECGs with healthy and diseased cardiac function.

Subset of Leads | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

XYZ | {I, aVF, V2, V6} | {I, II, aVF, V2} | {I, II, aVL, aVR} | ||||||||||

Recordings | Ranges of $\mathbf{\alpha}$ | RMSE | $\overline{\mathbf{\u03f5}}$ | $\tilde{\mathbf{\u03f5}}$ | RMSE | $\overline{\mathbf{\u03f5}}$ | $\tilde{\mathbf{\u03f5}}$ | RMSE | $\overline{\mathbf{\u03f5}}$ | $\tilde{\mathbf{\u03f5}}$ | RMSE | $\overline{\mathbf{\u03f5}}$ | $\tilde{\mathbf{\u03f5}}$ |

All val. dataset | $0\xb0\le \alpha \le 180\xb0$ | 12.2° | 5.8° | 3.3° | 17.2° | 10.3° | 6.4° | 18.4° | 11.4° | 7.3° | 25.4° | 17.9° | 12.7° |

$5\xb0\le \alpha <115\xb0$ ${}^{1}$ | 9.2° | 4.7° | 2.9° | 15.4° | 9.8° | 6.3° | 16.0° | 10.5° | 7.1° | 22.8° | 16.6° | 12.2° | |

NORM | $0\xb0\le \alpha \le 180\xb0$ | 6.1° | 3.4° | 2.5° | 13.5° | 8.3° | 5.5° | 14.1° | 9.0° | 6.1° | 21.0° | 14.9° | 11.1° |

$5\xb0\le \alpha <70\xb0$ ${}^{1}$ | 4.6° | 3.0° | 2.4° | 11.0° | 7.2° | 5.1° | 11.1° | 7.6° | 5.7° | 15.2° | 11.7° | 9.8° | |

Cardiac disease | $0\xb0\le \alpha \le 180\xb0$ | 16.8° | 8.7° | 4.9° | 20.5° | 12.2° | 7.3° | 21.8° | 13.7° | 8.7° | 29.1° | 20.7° | 14.3° |

$15\xb0\le \alpha <115\xb0$ ${}^{1}$ | 12.8° | 7.2° | 4.2° | 18.4° | 12.1° | 8.1° | 19.6° | 13.3° | 9.5° | 27.7° | 20.6° | 15.0° |

^{1}Ranges of α adequately represented in the training dataset (>200 samples).

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**MDPI and ACS Style**

Santos Rodrigues, A.; Augustauskas, R.; Lukoševičius, M.; Laguna, P.; Marozas, V.
Deep-Learning-Based Estimation of the Spatial QRS-T Angle from Reduced-Lead ECGs. *Sensors* **2022**, *22*, 5414.
https://doi.org/10.3390/s22145414

**AMA Style**

Santos Rodrigues A, Augustauskas R, Lukoševičius M, Laguna P, Marozas V.
Deep-Learning-Based Estimation of the Spatial QRS-T Angle from Reduced-Lead ECGs. *Sensors*. 2022; 22(14):5414.
https://doi.org/10.3390/s22145414

**Chicago/Turabian Style**

Santos Rodrigues, Ana, Rytis Augustauskas, Mantas Lukoševičius, Pablo Laguna, and Vaidotas Marozas.
2022. "Deep-Learning-Based Estimation of the Spatial QRS-T Angle from Reduced-Lead ECGs" *Sensors* 22, no. 14: 5414.
https://doi.org/10.3390/s22145414