# PPG Signals-Based Blood-Pressure Estimation Using Grid Search in Hyperparameter Optimization of CNN–LSTM

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.2. Preprocessing

#### 2.3. Hyperparameters Tuning for the Proposed Model

#### Optimizer, Learning Rate, and Batch Size

- The stochastic gradient descent (SGD) optimizer updates the parameters iteratively by subtracting the gradient multiplied by the learning rate, as described in Equation (3):$${W}_{new}={W}_{old}-\alpha \nabla L\left({W}_{old},{x}_{i},{y}_{i}\right)$$

- b.
- Root mean square propagation (RMSprop): The RMSprop optimizer adapts the learning rate for each parameter based on the gradient changes in the previous iterations. RMSprop utilizes the average squared estimation of the previous gradients to adjust the learning rate at each parameter update step. The formula for RMSprop is described in Equations (4) and (5), where ρ represents the forgetting factor (set to 0.9) and t denotes the current time step:$${W}_{new}={W}_{old}-\frac{\alpha}{\sqrt{MeanSqure\left(W,t\right)}}\nabla L\left({W}_{old}\right)$$$$Meansquare\left(W,t\right)\rho MeanSquare\left(W,t-1\right)+\left(1-\rho \right){\left(\nabla L\left(W\right)\right)}^{2}$$

- c.
- Adaptive moment estimation (Adam): Adam is the most commonly used optimization algorithm in deep learning for training models. The Adam optimizer combines momentum optimization concepts and RMSprop to effectively update model parameters during the training process. The Adam optimizer is widely employed in training deep learning models on time series datasets because it accelerates convergence and achieves superior results. The formula for the Adam optimizer is shown in Equation (6):$${m}_{t}={\rho}_{1}{m}_{t-1}+\left(1-{\rho}_{1}\right){g}_{t}$$$${u}_{t}={\rho}_{1}{u}_{t-1}+\left(1-{\rho}_{2}\right){g}_{t}{}^{2}$$$$\widehat{{m}_{t}}=\frac{{m}_{t}}{1-{\rho}_{1}t}$$$$\widehat{{u}_{t}}=\frac{{u}_{t}}{1-{\rho}_{2}t}$$

- d.
- Adadelta is an extension from AdaGrad, which is calculated by using Equation (12), where RMS is root mean square error:$${W}_{i+1}={W}_{t}-\frac{RMS{\left[\Delta W\right]}_{i-1}}{RMS{\left[g\right]}_{t}}{g}_{t}$$

#### 2.4. Proposed Deep Learning Model for Estimating BP

#### 2.4.1. Long Short Term-Memory (LSTM) Architecture

#### 2.4.2. LSTM-Based Autoencoder

#### 2.4.3. CNN–LSTM Architecture

#### 2.5. Metrics and Evaluation

**The IEEE standard:**For analyzing the performance, the IEEE standard was proposed using the MAEs as the parameters, as used in the current standard [40]. As shown in Table 1, an A grade was attained when the mean absolute difference (MAD) ≤ 5 mmHg. The MAE was the average difference between the actual and predicted values, as shown in Equation (13). Here, $n$ is for the data size, ${p}_{i}$ is the test measurement and ${y}_{i}$ is the average of reference measurement.

**British Hypertension Society (BHS) standard:**The BHS is a standard used to assess BP measurement devices and methods. According to the BHS standard, the performance is determined by the absolute error, which is divided into three categories: A, B, and C. If the evaluation score was less than grade C, the study failed to meet the minimum requirements of the BHS standard. As per the standard, the absolute percentage error of prediction must be ≤5, 10, and 15 mmHg to achieve grades A, B, and C, respectively [41].

**Association for the Advancement of Medical Instrumentation (AAMI) standard:**The AAMI standard is used to evaluate SBP and DBP measurement devices and algorithms. This evaluation assesses the mean error (ME) and standard deviation (SD) [42]. As shown in Table 1, the ME should be ≤5 mmHg, and the SD should be ≤8 mmHg. The ME represents the average error between the predicted and actual values, as shown in Equation (14). The estimated values $\widehat{y}$ = [y1, y2, …, yn] and ${y}_{i}$ = [y1, y2, …, yn] are the ground truth values and N is the total sample size.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**One-dimensional wavelet decomposition. The PPG signals are passed into the LPF to produce an approximation component and are passed into HPF to produce the detail component. In one-dimensional wavelet decomposition, eight-level decomposition generated nine sub-bands, which consisted of one approximation component and eight detail component sub-bands.

**Figure 8.**Bland–Altman plots of the proposed LSTM model: (

**a**) systolic blood pressure and (

**b**) diastolic blood pressure. Error histogram predicted systolic blood pressure (

**c**) and diastolic blood pressure (

**d**).

**Figure 9.**Bland–Altman plots of the proposed LSTM–autoencoder model (

**a**) systolic blood pressure and (

**b**) diastolic blood pressure. Error histogram predicted systolic blood pressure (

**c**) and diastolic blood pressure (

**d**).

**Figure 10.**Bland–Altman plots of the proposed CNN–LSTM model (

**a**) systolic blood pressure and (

**b**) diastolic blood pressure. Error histogram predicted systolic blood pressure (

**c**) and diastolic blood pressure (

**d**).

**Table 1.**Performance requirements based on evaluations of three standards: the IEEE standard, the BHS standard, and the AAMI standard. MAE: mean absolute difference, CP: cumulative percentage, ME: mean error, SD: standard deviation.

BHS | Grade | CP$\mathbf{5}mmHg$ | CP$\mathbf{10}mmHg$ | CP$\mathbf{15}mmHg$ | IEEE | Grade | MAD (mmHg) | AAMI | Grade | ME (mmHg) | SD (mmHg) |

A | 60% | 85% | 95% | A | ≤5 | Pass | ≤5 | ≤8 | |||

B | 50% | 75% | 90% | B | 5–6 | ||||||

C | 40% | 65% | 85% | C | 6–7 | ||||||

D | Lower than C | D | Lower than C |

**Table 2.**Evaluation of the performances of the proposed method with the prior studies in estimating systolic blood pressure (SBP) and diastolic blood pressure (DBP) using mean absolute error (MAE) and standard evaluation (SD).

Author | Method | Input | Dataset | SBP | DBP | ||
---|---|---|---|---|---|---|---|

MAE | SD | MAE | SD | ||||

Proposed work | LSTM | PPG | MIMIC III | 14.2 | 20.7 | 7.53 | 10.01 |

Proposed work | LSTM– Autoencoder | PPG | MIMIC III | 13.45 | 19.01 | 5.71 | 7.67 |

Proposed work | CNN + LSTM | PPG | MIMIC III | 3.64 | 7.04 | 2.39 | 3.79 |

[44] | SVR | PPG | MIMIC II | 8.54 | - | 4.34 | - |

[7] | SVM | PPG | Queensland | 11.6 | 8.2 | 7.6 | 6.7 |

[10] | Spectro-temporal ResNet | PPG | MIMIC III | 9.43 | - | 6.88 | - |

[13] | ANN | PPG | MIMIC II | 9.74 | 12.40 | 4.65 | 6.29 |

[12] | RNN | PPG | MIMIC III | 12.08 | 15.67 | 5.56 | 7.32 |

[11] | U-Net | PPG | MIMIC III | 5.73 | - | 3.45 | - |

[45] | CNN | PPG | Private dataset | - | 14.03 | - | - |

[8] | AdaBoost | PPG | MIMIC II | 8.22 | 10.38 | 4.17 | 4.22 |

[16] | CNN–BiLSTM | PPG | UCI (MIMIC II) | 7.85 | 8.41 | 4.42 | 4.80 |

**Table 3.**Performance evaluation of the proposed model for the estimation of systolic blood pressure (SBP) and diastolic blood pressure (DBP) by using three evaluation standards: the IEEE standard, the BHS standard, and the AAMI standard. MAE: mean absolute error, MAPD: mean absolute percentage differences, CP: cumulative percentages, ME: mean differences, SD: standard deviations.

Assessment Evaluation | IEEE Standard | AAMI Standard | BHS Standards | ||||||
---|---|---|---|---|---|---|---|---|---|

MAD (≤4 mmHg) | MAPD (%) | Grade | ME (<5 mmHg) | SD (<8 mmHg) | CP_{5} (>60%) | CP_{10} (>85%) | CP_{15} (>95%) | Grade | |

LSTM proposed model | |||||||||

SBP | 14.281 | 0.12 | D | −0.49 | 20.7 | 30.92 | 53.07 | 67.37 | D |

DBP | 7.53 | 0.133 | C | −0.21 | 10.01 | 45.14 | 72.02 | 86 | C |

LSTM–autoencoder proposed model | |||||||||

SBP | 26.94 | 0.11 | D | −0.93 | 19.01 | 27 | 52.5 | 68.70 | D |

DBP | 5.71 | 0.01 | B | −0.56 | 7.67 | 56.67 | 83.8 | 92.98 | B |

CNN–LSTM proposed model | |||||||||

SBP | 5.34 | 0.04 | B | 0.13 | 7.04 | 63.4 | 85.9 | 92.78 | B |

DBP | 2.89 | 0.05 | A | 0.48 | 3.79 | 81.70 | 98.28 | 100 | A |

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## Share and Cite

**MDPI and ACS Style**

Mahardika T, N.Q.; Fuadah, Y.N.; Jeong, D.U.; Lim, K.M.
PPG Signals-Based Blood-Pressure Estimation Using Grid Search in Hyperparameter Optimization of CNN–LSTM. *Diagnostics* **2023**, *13*, 2566.
https://doi.org/10.3390/diagnostics13152566

**AMA Style**

Mahardika T NQ, Fuadah YN, Jeong DU, Lim KM.
PPG Signals-Based Blood-Pressure Estimation Using Grid Search in Hyperparameter Optimization of CNN–LSTM. *Diagnostics*. 2023; 13(15):2566.
https://doi.org/10.3390/diagnostics13152566

**Chicago/Turabian Style**

Mahardika T, Nurul Qashri, Yunendah Nur Fuadah, Da Un Jeong, and Ki Moo Lim.
2023. "PPG Signals-Based Blood-Pressure Estimation Using Grid Search in Hyperparameter Optimization of CNN–LSTM" *Diagnostics* 13, no. 15: 2566.
https://doi.org/10.3390/diagnostics13152566