# A Novel Cuffless Blood Pressure Prediction: Uncovering New Features and New Hybrid ML Models

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## Abstract

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^{2}, mean square error (MSE), and the mean absolute error (MAE). The obtained RMSE was 4.277 for systolic blood pressure (SBP) values using the Matérn 5/2 Gaussian process regression model. The obtained RMSE was 2.303 for diastolic blood pressure (DBP) values using the rational quadratic Gaussian process regression model. The results of this study have shown that the proposed feature extraction and regression models can predict cuffless blood pressure with reasonable accuracy. This study provides a novel approach for predicting cuffless blood pressure and can be used to develop more accurate models in the future.

## 1. Introduction

## 2. Material and Method

#### 2.1. Datasets

#### 2.2. Preprocessing Signals

#### 2.3. Feature Extraction

#### 2.4. Regression Models

#### 2.4.1. Linear Regression

#### 2.4.2. Robust Linear Regression

#### 2.4.3. Rational Quadratic Gaussian Process Regression

#### 2.4.4. Square Exponential Gaussian Process Regression

#### 2.4.5. Matérn 5/2 Gaussian Process Regression

#### 2.4.6. Linear Support Vector Machine

#### 2.4.7. Medium Gaussian Support Vector Machine

## 3. Evaluated of Results

^{2}, mean absolute percentage error (MAPE), box plots of the predicted values, and the Bland–Altman plot. The performance metric formulas are given below:

^{2}takes a value of between –∞ and 1. Negative values indicate worse predictions.

## 4. Discussion

^{2}, MSE, and MAE) as the evaluation metric. The MAE values obtained for systolic and diastolic blood pressure are 3.073 and 1.721, respectively. The MAE values obtained by the authors are comparable to those obtained in other studies using the same dataset. In addition, this paper provides a clear description of the preprocessing, feature extraction, and regression models used in the prediction process—a compelling case for the efficacy of our proposed method. Table 6 shows a performance comparison of the conducted works in the literature and our proposed method for predicting SBP and DBP concerning the obtained MAE values.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**The normalized PPG signals, the normalized ABP signals, and the negative graph between the PPG signals and ABP signals. (The correlation coefficient between normalized PPG signals and normalized ABP signals is −0.279).

**Figure 5.**Predicted SBP for the Matérn 5/2 Gaussian process regression method: (

**a**) the plot of the correlation and (

**b**) the Bland–Altman Plot.

**Figure 6.**Predicted DBP for the rational quadratic Gaussian process regression method: (

**a**) correlation plot and (

**b**) the Bland–Altman Plot.

**Figure 7.**The target and predicted values in the prediction of SBP values using the Matérn 5/2 Gaussian process regression method (blue mark: actual SBP values; orange mark: the predicted SBP values).

**Figure 8.**The target and predicted values in the prediction of DBP values using the rational quadratic Gaussian process regression method (blue mark: actual DBP values; orange mark: the predicted DBP values).

Category | Systolic Blood Pressure (mmHg) | Diastolic Blood Pressure (mmHg) |
---|---|---|

Blood pressure | ||

Optimal | <120 | <80 |

Normal | <130 | <85 |

High normal | 130–139 | 85–89 |

Hypertension | ||

Grade 1 (Mild) | 140–159 | 90–99 |

Grade 2 (Moderate) | 160–179 | 100–109 |

Grade 3 (Severe) | ≥180 | ≥110 |

Isolated systolic hypertension | ||

Grade 1 | 140–159 | <90 |

Grade 2 | ≥160 | <90 |

Number of Features | Domain Information | Name of the Feature in the Dataset | Explanation of the Feature |
---|---|---|---|

1 | Time | Enhanced Mean Absolute Value | $EMAV=\frac{1}{L}{\displaystyle {\displaystyle \sum}_{i=1}^{L}}\left|{\left({x}_{i}\right)}^{P}\right|$ |

2 | Time | Enhanced Wavelength | $EML={\displaystyle {\displaystyle \sum}_{i=2}^{L}}\left|{\left({x}_{i}-{x}_{\left(i-1\right)}\right)}^{P}\right|$ |

3 | Time | Mean Absolute Value | $MAV=\frac{1}{L}{\displaystyle {\displaystyle \sum}_{i=1}^{L}}\left|{x}_{i}\right|$ |

4 | Time | Wavelength | ${w}_{L}={\displaystyle {\displaystyle \sum}_{i=2}^{L}}\left|{x}_{i}-{x}_{\left(i-1\right)}\right|$ |

5 | Time | Zero Crossing | $zC={\displaystyle {\displaystyle \sum}_{i=1}^{L-1}}f\left({x}_{i}\right)$ |

6 | Time | Slope Sign Change | $SSC={\displaystyle {\displaystyle \sum}_{i=2}^{L-1}}f\left({x}_{i}\right)$ |

7 | Time | Root Mean Square | $RMS=\sqrt{\frac{1}{L}{\displaystyle {\displaystyle \sum}_{i=1}^{L}}{\left({x}_{i}\right)}^{2}}$ |

8 | Time | Average Amplitude Change | $AAC=\frac{1}{L}{\displaystyle {\displaystyle \sum}_{i=1}^{L-1}}\left|{x}_{i+1}-{x}_{i}\right|$ |

9 | Time | Difference Absolute Standard Deviation Value | $DASDV=\sqrt{\frac{{{\displaystyle \sum}}_{i=1}^{L-1}{\left({x}_{i+1}-{x}_{i}\right)}^{2}}{L-1}}$ |

10 | Time | Log Detector | $LD=\mathrm{exp}\left(\frac{1}{L}{\displaystyle {\displaystyle \sum}_{i=1}^{L}}\mathrm{log}\left(\left|{x}_{i}\right|\right)\right)$ |

11 | Time | Modified Mean Absolute Value 1 | $MMAV=\frac{1}{L}{\displaystyle {\displaystyle \sum}_{i=1}^{L}}{w}_{i}\left|{x}_{i}\right|$ |

12 | Time | Modified Mean Absolute Value 2 | $MMAV2=\frac{1}{L}{\displaystyle {\displaystyle \sum}_{i=1}^{L}}{w}_{i}\left|{x}_{i}\right|$ |

13 | Time | Myopulse Percentage Rate | $MYOP=\frac{1}{L}{\displaystyle {\displaystyle \sum}_{i=1}^{L}}f\left({x}_{i}\right)$ |

14 | Time | Simple Square Integral | $SSI={\displaystyle {\displaystyle \sum}_{i=1}^{L}}{\left({x}_{i}\right)}^{2}$ |

15 | Time | Variance of Signal | $VAR=\frac{1}{L-1}{\displaystyle {\displaystyle \sum}_{i=1}^{L}}{\left({x}_{i}\right)}^{2}$ |

16 | Time | Willison Amplitude | $WA={\displaystyle {\displaystyle \sum}_{i=1}^{L-1}}f\left({x}_{i}\right)$ |

17 | Time | Maximum Fractal Length | $MFL={\mathrm{log}}_{10}\left(\sqrt{{\displaystyle {\displaystyle \sum}_{i=1}^{L-1}}{\left({x}_{i+1}-{x}_{i}\right)}^{2}}\right)$ |

18 | Chaotic | Sample Entropy | $SampEn\left(m,r,N\right)=-\mathrm{log}\left({\displaystyle {\displaystyle \sum}_{i=1}^{N-m}}{A}_{i}/{\displaystyle {\displaystyle \sum}_{i=1}^{N-m}}{B}_{i}\right)$ |

19 | Chaotic | Approximate Entropy | $ApEn\left(m,r,N\right)=-\frac{1}{N-m}{\displaystyle {\displaystyle \sum}_{i=1}^{N-m}}\mathrm{log}\left(\frac{Ai}{{B}_{i}}\right)$ |

20 | Chaotic | Fuzzy Entropy | $\mathrm{E}\left(\mathrm{A}\right)=-\mathrm{k}\left\{\mathrm{mA}\left(\mathrm{xi}\right)\mathrm{logmA}\left(\mathrm{xi}\right)+\left(1-\mathrm{mA}\left(\mathrm{xi}\right)\right)\mathrm{log}\left(1-\mathrm{mA}\left(\mathrm{xi}\right)\right)\right\}$ |

21 | Chaotic | Shannon Entropy | $H\left(\alpha \right)=-{\displaystyle {\displaystyle \sum}_{1}}{P}_{i}\ast \mathrm{log}{p}_{i}$ |

22 | Chaotic | Permutation Entropy | $H\left(n\right)=-{\displaystyle {\displaystyle \sum}_{i}^{n!}}p\left({\pi}_{i}\right)\mathrm{log}p\left({\pi}_{i}\right)$ |

23 | Chaotic | Higuchi Fractal Dimension | $l\left(k\right)=\frac{\left({{\displaystyle \sum}}_{i=1}^{\left[N-m/k\right]}\left|x\left(m+{i}_{k}\right)-x\left(m+{\left(i-1\right)}_{k}\right)\right|\left(N-1\right)\right)}{\left(\frac{N-m}{k}\right)k}$ |

24 | Chaotic | Katz Fractal Dimension | $F{D}_{katz-norm}=\frac{{\mathrm{log}}_{10}\left(L\u2215a\right)}{{\mathrm{log}}_{10}\left(d\u2215a\right)}=\frac{{\mathrm{log}}_{10}\left(n\right)}{{\mathrm{log}}_{10}\left(\frac{d}{L}\right)+{\mathrm{log}}_{10}\left(n\right)}$ |

No | Model Name |
---|---|

1 | Linear regression |

2 | Robust linear regression |

3 | Rational quadratic Gaussian process regression |

4 | Square exponential Gaussian process regression |

5 | Matérn 5/2 Gaussian process regression |

6 | Linear support vector machine |

7 | Medium Gaussian support vector machine |

**Table 4.**The obtained SBP prediction metric rates in our study using three different machine learning methods.

Regression Methods | RMSE | R^{2} | MSE | MAE |
---|---|---|---|---|

Linear regression | 4.893 | 0.470 | 20.195 | 3.272 |

Robust linear regression | 4.557 | 0.450 | 20.767 | 3.227 |

Rational quadratic Gaussian process regression | 4.279 | 0.520 | 18.318 | 3.069 |

Square exponential Gaussian process regression | 4.305 | 0.510 | 18.318 | 3.090 |

Matérn 5/2 Gaussian Process Regression | 4.277 | 0.52 | 18.297 | 3.073 |

Linear support vector machine | 4.527 | 0.46 | 20.494 | 3.267 |

Medium Gaussian support vector machine | 4.399 | 0.490 | 19.353 | 3.107 |

**Table 5.**The obtained DBP prediction metric rates in our study using three different machine learning methods.

Regression Methods | RMSE | R^{2} | MSE | MAE |
---|---|---|---|---|

Linear regression | 2.463 | 0.228 | 6.071 | 1.872 |

Robust linear regression | 2.244 | 0.386 | 5.035 | 1.861 |

Rational quadratic Gaussian process regression | 2.303 | 0.330 | 5.306 | 1.721 |

Square exponential Gaussian process regression | 2.325 | 0.310 | 5.409 | 1.736 |

Matérn 5/2 Gaussian process regression | 2.309 | 0.320 | 5.335 | 1.724 |

Linear support vector machine | 2.514 | 0.200 | 6.321 | 1.857 |

Medium Gaussian support vector machine | 2.328 | 0.310 | 5.420 | 1.732 |

**Table 6.**The performance comparison of the conducted works in the literature and our proposed method in predicting SBP and DBP concerning the obtained MAE values.

Compared Methods | Systolic MAE (mmHg) | Diastolic MAE (mmHg) | Ref. |
---|---|---|---|

Generalized deep neural network model | 3.21 | 2.23 | [33] |

Spectro-temporal deep neural network | 9.43 | 6.88 | [34] |

Fully convolutional neural networks | 5.73 | 3.45 | [35] |

Machine learning model | 9.54 | 5.48 | [36] |

Deep learning model | 4.51 | 2.6 | [13] |

Regression by MARS (dynamical approach) | 7.83 | 4.86 | [37] |

Tree-based pipeline optimization tool | 6.52 | 4.19 | [38] |

CNN representations of PPG | 4.48 | 2.19 | [39] |

Matérn 5/2 Gaussian process regression and feature extraction | 3.073 | 1.724 | Proposed Methods |

Rational quadratic Gaussian process regression and feature extraction | 3.069 | 1.721 |

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## Share and Cite

**MDPI and ACS Style**

Nour, M.; Polat, K.; Şentürk, Ü.; Arıcan, M.
A Novel Cuffless Blood Pressure Prediction: Uncovering New Features and New Hybrid ML Models. *Diagnostics* **2023**, *13*, 1278.
https://doi.org/10.3390/diagnostics13071278

**AMA Style**

Nour M, Polat K, Şentürk Ü, Arıcan M.
A Novel Cuffless Blood Pressure Prediction: Uncovering New Features and New Hybrid ML Models. *Diagnostics*. 2023; 13(7):1278.
https://doi.org/10.3390/diagnostics13071278

**Chicago/Turabian Style**

Nour, Majid, Kemal Polat, Ümit Şentürk, and Murat Arıcan.
2023. "A Novel Cuffless Blood Pressure Prediction: Uncovering New Features and New Hybrid ML Models" *Diagnostics* 13, no. 7: 1278.
https://doi.org/10.3390/diagnostics13071278