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

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{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

- World Health Organization. Primary Health Care on the Road to Universal Health Coverage: 2019 Global Monitoring Report; World Health Organization: Geneva, Switzerland, 2021.
- Wu, C.Y.; Hu, H.Y.; Chou, Y.J.; Huang, N.; Chou, Y.C.; Li, C.P. High Blood Pressure and All-Cause and Cardiovascular Disease Mortalities in Community-Dwelling Older Adults. Medicine
**2015**, 94, e2160. [Google Scholar] [CrossRef] [PubMed] - Ferdinand, D.P.; Nedunchezhian, S.; Ferdinand, K.C. Hypertension in African Americans: Advances in community outreach and public health approaches. Prog. Cardiovasc. Dis.
**2020**, 63, 40–45. [Google Scholar] [CrossRef] [PubMed] - Guidelines Committee. 2003 European Society of HypertensionEuropean Society of Cardiology guidelines for the management of arterial hypertension. J. Hypertens.
**2003**, 21, 1011–1053. [Google Scholar] [CrossRef] [PubMed] - Guo, C.-Y.; Chang, H.-C.; Wang, K.-J.; Hsieh, T.-L. An Arterial Compliance Sensor for Cuffless Blood Pressure Estimation Based on Piezoelectric and Optical Signals. Micromachines
**2022**, 13, 1327. [Google Scholar] [CrossRef] [PubMed] - El-Hajj, C.; Kyriacou, P.A. Deep learning models for cuffless blood pressure monitoring from PPG signals using attention mechanism. Biomed. Signal Process. Control
**2021**, 65, 102301. [Google Scholar] [CrossRef] - Zhang, Q.; Shen, L.; Liu, P.; Xia, P.; Li, J.; Feng, H.; Liu, C.; Xing, K.; Song, A.; Li, M.; et al. Highly sensitive resistance-type flexible pressure sensor for cuffless blood-pressure monitoring by using neural network techniques. Compos. Part B Eng.
**2021**, 226, 109365. [Google Scholar] [CrossRef] - Senturk, U.; Polat, K.; Yucedag, I. A non-invasive continuous cuffless blood pressure estimation using dynamic Recurrent Neural Networks. Appl. Acoust.
**2020**, 170, 107534. [Google Scholar] [CrossRef] - Bradley, C.K.; Shimbo, D.; Colburn, D.A.; Pugliese, D.N.; Padwal, R.; Sia, S.K.; Anstey, D.E. Cuffless blood pressure devices. Am. J. Hypertens.
**2022**, 35, 380–387. [Google Scholar] [CrossRef] - Pandit, J.A.; Lores, E.; Batlle, D. Cuffless blood pressure monitoring: Promises and challenges. Clin. J. Am. Soc. Nephrol.
**2020**, 15, 1531–1538. [Google Scholar] [CrossRef] - Schutte, A.E.; Kollias, A.; Stergiou, G.S. Blood pressure and its variability: Classic and novel measurement techniques. Nat. Rev. Cardiol.
**2022**, 19, 643–654. [Google Scholar] [CrossRef] - Li, Y.-H.; Harfiya, L.N.; Purwandari, K.; Lin, Y.-D. Real-time cuffless continuous blood pressure estimation using deep learning model. Sensors
**2020**, 20, 5606. [Google Scholar] [CrossRef] - El-Hajj, C.; Kyriacou, P.A. Cuffless blood pressure estimation from PPG signals and its derivatives using deep learning models. Biomed. Signal Process. Control
**2021**, 70, 102984. [Google Scholar] [CrossRef] - Baek, S.; Jang, J.; Yoon, S. End-to-end blood pressure prediction via fully convolutional networks. IEEE Access
**2019**, 7, 185458–185468. [Google Scholar] [CrossRef] - Thambiraj, G.; Gandhi, U.; Mangalanathan, U.; Jose, V.J.M.; Anand, M. Investigation on the effect of Womersley number, ECG and PPG features for cuff less blood pressure estimation using machine learning. Biomed. Signal Process. Control
**2020**, 60, 101942. [Google Scholar] [CrossRef] - Keke, Q.; Wu, H.; Tao, Z. Multitask deep label distribution learning for blood pressure prediction. Inf. Fusion
**2023**, 95, 426–445. [Google Scholar] - Chowdhury, M.H.; Shuzan, M.N.I.; Chowdhury, M.E.H.; Mahbub, Z.B.; Uddin, M.M.; Khandakar, A.; Reaz, M.B.I. Estimating blood pressure from the photoplethysmogram signal and demographic features using machine learning techniques. Sensors
**2020**, 20, 3127. [Google Scholar] [CrossRef] - Ibrahim, B.; Jafari, R. Cuffless blood pressure monitoring from a wristband with calibration-free algorithms for sensing location based on bio-impedance sensor array and autoencoder. Sci. Rep.
**2022**, 12, 319. [Google Scholar] [CrossRef] - Ali, N.F.; Atef, M. An efficient hybrid LSTM-ANN joint classification-regression model for PPG based blood pressure monitoring, Biomed. Signal Process. Control
**2023**, 84, 104782. [Google Scholar] - Farki, A.; Kazemzadeh, R.B.; Noughabi, E.A. A Novel Clustering-Based Algorithm for Continuous and Non-invasive Cuff-Less Blood Pressure Estimation. J. Healthc. Eng.
**2022**, 2022, 3549238. [Google Scholar] [CrossRef] - Sannino, G.; De Falco, I.; De Pietro, G. Non-invasive risk stratification of hypertension: A systematic comparison of machine learning algorithms. J. Sens. Actuator Netw.
**2020**, 9, 34. [Google Scholar] [CrossRef] - Şentürk, Ü.; Polat, K.; Yücedağ, İ. Towards wearable blood pressure measurement systems from biosignals: A review. Turk. J. Electr. Eng. Comput. Sci.
**2019**, 27, 3259–3281. [Google Scholar] [CrossRef] - El-Hajj, C.; Kyriacou, P.A. A review of machine learning techniques in photoplethysmography for the non-invasive cuff-less measurement of blood pressure. Biomed. Signal Process. Control
**2020**, 58, 101870. [Google Scholar] [CrossRef] - Khalid, S.G.; Liu, H.; Zia, T.; Zhang, J.; Chen, F.; Zheng, D. Cuffless blood pressure estimation using single channel photoplethysmography: A two-step method. IEEE Access
**2020**, 8, 58146–58154. [Google Scholar] [CrossRef] - Hosanee, M.; Chan, G.; Welykholowa, K.; Cooper, R.; Kyriacou, P.A.; Zheng, D.; Allen, J.; Abbott, D.; Menon, C.; Lovell, N.H.; et al. Cuffless single-site photoplethysmography for blood pressure monitoring. J. Clin. Med.
**2020**, 9, 723. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hsu, Y.-C.; Li, Y.-H.; Chang, C.-C.; Harfiya, L.N. Generalized deep neural network model for cuffless blood pressure estimation with photoplethysmogram signal only. Sensors
**2020**, 20, 5668. [Google Scholar] [CrossRef] - Zurada, J.; Levitan, A.; Guan, J. A Comparison of Regression and Artificial Intelligence Methods in a Mass Appraisal Context. J. Real Estate Res.
**2011**, 33, 349–388. [Google Scholar] [CrossRef] - Yu, C.; Yao, W.; Bai, X. Robust Linear Regression: A Review and Comparison. Commun. Stat. -Simul. Comput.
**2014**, 46, 6261–6282. [Google Scholar] [CrossRef] - Rasmussen, C.E.; Williams, C.K.I. Gaussian Processes for Machine Learning; The MIT Press: Cambridge, MA, USA, 2006; ISBN 026218253X. [Google Scholar]
- Zhang, N.; Xiong, J.; Zhong, J.; Leatham, K. Gaussian Process Regression Method for Classification for High-Dimensional Data with Limited Samples. In Proceedings of the 2018 Eighth International Conference on Information Science and Technology (ICIST), Cordoba, Granada, and Seville, Spain, 30 June–6 July 2018; pp. 358–363. [Google Scholar] [CrossRef]
- Okwuashi, O.; Ndehedehe, C. Tide modelling using support vector machine regression. J. Spat. Sci.
**2017**, 62, 29–46. [Google Scholar] [CrossRef] - Nogueira, M.S.; Maryam, S.; Amissah, M.; Lu, H.; Lynch, N.; Killeen, S.; O’Riordain, M.; Andersson-Engels, S. Improving colorectal cancer detection by extending the near-infrared wavelength range and tissue probed depth of diffuse reflectance spectroscopy: A support vector machine approach. In Proceedings of the Optical Biopsy XX: Toward Real-Time Spectroscopic Imaging and Diagnosis, San Francisco, CA, USA, 25–27 January 2022; Volume 11954. [Google Scholar]
- Haque, C.A.; Kwon, T.H.; Kim, K.D. Cuffless blood pressure estimation based on Monte Carlo simulation using photoplethysmography signals. Sensors
**2022**, 22, 1175. [Google Scholar] [CrossRef] - Slapničar, G.; Mlakar, N.; Luštrek, M. Blood Pressure Estimation from Photoplethysmogram Using a Spectro-Temporal Deep Neural Network. Sensors
**2019**, 19, 3420. [Google Scholar] [CrossRef][Green Version] - Ibtehaz, N.; Mahmud, S.; Chowdhury, M.E.H.; Khandakar, A.; Salman Khan, M.; Ayari, M.A.; Tahir, A.M.; Rahman, M.S. PPG2ABP: Translating Photoplethysmogram (PPG) Signals to Arterial Blood Pressure (ABP) Waveforms. Bioengineering
**2022**, 9, 692. [Google Scholar] [CrossRef] - Han, W.; Wang, J.; Hou, S.; Bai, T.; Jeon, G.; Rodrigues, J.J. An PPG signal and body channel based encryption method for WBANs. Future Gener. Comput. Syst.
**2023**, 141, 704–712. [Google Scholar] [CrossRef] - Sharifi, I.; Goudarzi, S.; Khodabakhshi, M.B. A novel dynamical approach in continuous cuffless blood pressure estimation based on ECG and PPG signals. Artif. Intell. Med.
**2019**, 97, 143–151. [Google Scholar] [CrossRef] - Fati, S.M.; Muneer, A.; Akbar, N.A.; Taib, S.M. A continuous cuffless blood pressure estimation using tree-based pipeline optimization tool. Symmetry
**2021**, 13, 686. [Google Scholar] [CrossRef] - Esmaelpoor, J.; Moradi, M.H.; Kadkhodamohammadi, A. Cuffless blood pressure estimation methods: Physiological model parameters versus machine-learned features. Physiol. Meas.
**2021**, 42, 035006. [Google Scholar] [CrossRef]

**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 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## 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