# A Continuous Cuffless Blood Pressure Estimation Using Tree-Based Pipeline Optimization Tool

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## Abstract

**:**

## 1. Introduction

## 2. Background and Related Works

^{−3}. This approach achieved a sufficient result, however, it is time-consuming and required an expert to understand the raw PPG data of the subjects. Likewise, the authors have developed a novel Spectro temporal deep neural network [STDNN] in [39], whereby the PPG signal and its first and second derivatives were taken as inputs. Authors in [39] have attempted to extract the PPG signal from BP using a deep neural network (DLN) and based on the MIMIC III database belonging to 510 subjects. Therefore, the study employed MAE to conduct cross-validation experiments, achieving 9.43 mmHg for SBP and 6.88 mmHg for DBP. Comparatively, the support vector machine (SVM) method for continuous blood pressure estimation from a PPG signal presented better precision in [49] than the linear regression [50,51] and ANN methods. The results in [49] show that the mean error was 11.6415 ± 8.2022 mmHg for systolic BP and 7.617 ± 6.7837 mmHg for diastolic BP based on a large sample data, while the results achieved using ANN were 11.8984 ± 10.180 mmHg for SBP and 13.94 ± 11.24 for DBP. In [51], the 2-Element Windkessel model was used to approximate the overall peripheral resistance and arterial compliance of an individual using PPG functions, followed by linear regression to simulate the arterial blood pressure. The experimental findings on a regular hospital dataset yielded absolute errors of 0.78 ± 13.01 and 0.59 ± 10.23 mmHg for systolic and diastolic blood pressure values, respectively. A similar approach was suggested in [50], where the findings of the experiments show that the average error in measuring BP is less than 10% of the currently available optical BP tracking system.

## 3. Methods

#### 3.1. Dataset

#### 3.2. Hybrid Pre-Processing Stage

#### 3.3. Features Selection Methods

#### 3.4. Automated Machine Learning

- Selection: At every generation, each solution is evaluated.
- Crossover: The most fit solution is selected, and crossover occurs to create a new population.
- Mutation: The children from the new population are mutated randomly, and the process is repeated once more to obtain the best solution.

^{N}, ∈the weight vector that maximizes a measure of w

^{T}X non-Gaussianity of the projection, with X ∈R

^{(N+M)}representing a pre-whitened data matrix as discussed in [68]. Note that w is a column vector. FastICA relies on a nonquadratic nonlinear function f(u), its first derivative g(u), and its second derivative g(u), to calculate non-Gaussianity. The steps taken in FastICA to extract the weight vector w for the SBP portion are as follows.

- ⯀
- Whiten data.
- ⯀
- Randomize the initial weight vector w.
- ⯀
- Select a non-quadratic function, for example:

_{1}u). According to $W\leftarrow E\left(xg\left({W}^{T}x\right)\right)W,$loops continually iterate until their convergence. The absolute value of E(xg(W

^{T}x)) would get smaller and smaller. Descendent Newton can be used to boost the stability and uniformity of the convergence. Furthermore, standard scalar standardizes data set characteristics by scaling to unit variance and eliminating the mean utilizing column summary statistics on the samples in the training set (optionally). This process is a pre-processing phase that is very popular. During the optimization process, standardization enhances the convergence rate. During model training, it also prevents characteristics with large variances from exerting a tremendous effect.

^{T}X be a rank r, square, symmetric m $\times $ m matrix. {$\widehat{{v}_{1}},\widehat{{v}_{2},}\widehat{{v}_{3}}\dots \dots \dots .\widehat{{v}_{r}}$} is an orthonormal set of m $\times $ l eigenvectors with associated eigenvalues for {λ

_{1}, λ

_{2}, λ

_{3}, ……… λ

_{r}} the symmetric matrix X

^{T}X.

_{i}are ordered such that σ

_{i}≥ σ

_{i+}

_{1}and X multiplied by an eigenvector of X

^{T}X is equal to a scalar time, another vector. The set of eigenvectors {$\widehat{{v}_{1}},\widehat{{v}_{2},}\widehat{{v}_{3}}\dots \dots \dots .\widehat{{v}_{r}}$} and the set of vectors are {$\widehat{{u}_{1}},\widehat{{u}_{2},}\widehat{{u}_{3}}\dots \dots \dots .\widehat{{u}_{r}}$} both orthonormal sets and bases in r dimensional space. Hence, the constructed accompanying orthogonal matrices are:

_{1}=

^{T}to arrive at the decomposition’s final form.

#### 3.5. Evaluation Metrics

- Mean absolute error (MAE): Absolute error is the sum of error expected. The mean absolute error is the mean for all absolute errors.$$MAE=\frac{1}{N}{\displaystyle \sum}_{i=1}^{N}\left|{X}_{p}-{\stackrel{\u02c7}{X}}_{p}\right|$$
- Mean squared error (MSE): MSE measures the squared number of errors. MSE is a risk function that corresponds to the estimated value of the squared error loss. MSE includes both the variance and bias of the estimator.$$MSE=\frac{1}{N}{\displaystyle \sum}_{i=1}^{N}{\left|{X}_{P}-{\stackrel{\u02c7}{X}}_{p}\right|}^{2}$$
- Correlation coefficient (R): A statistical technique that calculates how closely connected two variables are (predictors and the predictions). It also informs us how close the prediction is to the trend line.$$R=\sqrt{1-\frac{\mathit{MSE}\left(\mathit{model}\right)}{\mathit{MSE}\left(\mathit{baseline}\right)}}$$

_{p}is the actual value, ${\stackrel{\u02c7}{X}}_{p}$ is the predicted value, and N is the number of observations. The optimum value is 0 for MAE and MSE. R takes value –∞ and 1. Negative values are indicated as worse prediction. When utilizing the AutoML (TPOT) approach in python, the above criteria are automatically calculated by python, and these values were utilized to evaluate the performance of the algorithms that TPOT has chosen.

## 4. Results and Analysis

#### Comparison with Literature

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Automated search of machine learning (ML) model using the tree-based pipeline optimization tool. A machine learning operator corresponds to each circle, and the arrows indicate the direction of the flow of data: (

**a**) Feature preprocessing pipeline; (

**b**) feature construction pipeline; (

**c**) the best pipeline chosen by TPOT for systolic blood pressure (SBP), and (

**d**) the best pipeline chosen by TPOT for diastolic blood pressure (DBP). The following subsections will discuss the steps in detail.

**Figure 3.**BP, photoplethysmogram (PPG), and electrocardiogram (ECG) signal plots from the collected PhysioNet dataset in this study.

**Figure 4.**Key points of PPG pulse; (

**a**) The location of the key points; (

**b**) division of PPG into ascending and descending components; (

**c**) first derivative waveform; (

**d**) second derivative waveform [60].

**Figure 5.**PPG key features, where X and Y are the amplitudes of systolic peak and inflection points, respectively, and ∆T

_{DVP}is the interval of time between the two [60].

**Figure 9.**The heatmap of the seven features selected automatically by the TPOT approach shows how these features are correlated.

**Figure 10.**Results of (

**a**) systolic pressure signal produced using the random forest (RF) regression. Blue—predicted values; red—true values and (

**b**) diastolic pressure signal produced using the k-nearest neighbor (k-NN) regression. Blue—predicted values; red—true value.

**Figure 11.**Results of SBP signal produced using the RF regression. Blue means the predicted values, and orange presented the true values.

**Figure 12.**Diastolic pressure signal produced through the use of k-NN regression. Blue presented the predicted values and orange the true values.

Parameters | PPG Systolic Pressure | PPG Diastolic Pressure | PPG Foot Pressure |
PPG Notch Pressure | BP Systolic Pressure | BP Diastolic Pressure | BP Notch Pressure |
---|---|---|---|---|---|---|---|

count | 64,121.000 | 64,121.000 | 64,121.000 | 64,121.000 | 64,115.000 | 64,115.000 | 64,115.000 |

mean | 2.2417 | 1.1376 | 1.0870 | 1.5180 | 119.9480 | 76.3792 | 92.0488 |

std | 0.5049 | 0.2259 | 0.2125 | 0.3397 | 21.9371 | 16.0327 | 18.3158 |

min | 0.4017 | 0.1766 | 0.15109 | 0.2873 | 59.7634 | 50.5536 | 56.0053 |

25 | 1.9758 | 1.0685 | 1.0360 | 1.3684 | 104.7578 | 64.9357 | 77.7494 |

50 | 2.2089 | 1.1306 | 1.0804 | 1.4968 | 116.7934 | 72.6420 | 87.9682 |

75 | 2.6065 | 1.2331 | 1.1671 | 1.7008 | 133.4375 | 83.5564 | 105.1952 |

Max | 3.5698 | 2.3116 | 2.3096 | 2.8044 | 197.5693 | 190.8637 | 191.5196 |

BP Classification | MAE (mmHg) | MSE (mmHg) |
---|---|---|

Systolic Validation (mmHg) | 6.52 | 7.48 |

Diastolic Validation (mmHg) | 4.19 | 5.13 |

**Table 3.**Comparison between the results obtained in this study and the literature in terms of SBP and DBP.

Study | Evaluation Metrics | Results Obtained | Method |
---|---|---|---|

Miao et al. [58] | SBP (7.10) DBP (4.61) | Res-LSTM | |

Kachuee et al. [50] | MAE | SBP (11.17) DBP (5.35) | Adaboosting |

Slapnicar, Mlakar, and Luštrek [39] | MAE | SBP (9.43) DBP (6.88) | DNN |

Kurylyak, Lamonaca, Grimaldi [55] | MAE | 3.80 ± 3.46 for SBP 2.21 ± 2.09 for DBP | ANN |

Our study | MAE | SBP (6.52) DBP (4.19) | AutoML (TPOT) |

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/sym13040686

**AMA Style**

Fati SM, Muneer A, Akbar NA, Taib SM. A Continuous Cuffless Blood Pressure Estimation Using Tree-Based Pipeline Optimization Tool. *Symmetry*. 2021; 13(4):686.
https://doi.org/10.3390/sym13040686

**Chicago/Turabian Style**

Fati, Suliman Mohamed, Amgad Muneer, Nur Arifin Akbar, and Shakirah Mohd Taib. 2021. "A Continuous Cuffless Blood Pressure Estimation Using Tree-Based Pipeline Optimization Tool" *Symmetry* 13, no. 4: 686.
https://doi.org/10.3390/sym13040686