Cuffless Blood Pressure Estimation Using AI Models: A Comparative Study of SVR, LSTM, and LightGBM

Blood pressure (BP) represents one of the key life-threatening illnesses, which necessitates an accurate and efficient diagnostic tool. A significant risk factor for cardiovascular disease, elevated blood pressure, or hypertension, is the cause of more than 9 million annual fatalities [1]. In fact, unusual changes in blood pressure can also put the kidney, liver, brain, heart, and other organs at significant risk for harm. Hypertension is characterized by systolic and diastolic blood pressures that are greater than 140 and 90 mmHg, respectively. If addressed, these unfavorable blood pressure levels might harm internal body organs. Hence, due to the large number of people affected by blood pressure issues, many researchers are attempting to make BP monitoring technologies more accurate and less inconvenient [2]. BP is often monitored using cuff-based devices, which are cumbersome and do not permit continuous measurement. Continuous blood pressure monitoring is extremely useful for learning about people's health issues [3]. On the other hand, for wearable technology and continuous monitoring, cuffless techniques are more practical. They are better suited for ambulatory and continuous monitoring because they do not need a cuff to be inflated and deflated. However, in specific medical situations or for clinical accuracy, cuffless approaches may face hurdles in terms of accuracy and may not be as dependable as cuff-based measures. It's crucial to remember that cuffless blood pressure monitoring is a field that is actively being researched and developed, and that these techniques' precision and dependability are continually being improved [4].

In this paper, ML and DL algorithms are used to improve the accuracy of the cuffless BP system. The following are the primary contributions of this paper:

• Comparing the effectiveness of the three ML algorithms, SVR, LSTM, and LightGBM, in terms of the accuracy of BP estimation.
• Application of the proposed system with the aid of IoT technology using an Amazon Web Server (AWS) to work anywhere, anytime.

The structure of the paper is as follows. Section 2 discusses prior research studies. Section 3 presents the key elements of the research. The suggested ML and DL methods are presented in Section 4. Section 5 presents the findings and the performance evaluation. In Section 6, the conclusion of the paper is illustrated.

The fundamentals of the study, such as SVR, Long Short-Term Memory LSTM, and LightGBM, are briefly described in this section, as well as the used dataset.

3.1 Support Vector Regression algorithm

SVR is related to SVM in that it is an extension of SVMs, except that the latter deal with regression problems. An SVR attempts to find a regression function that is as flat as possible, if the deviations of the estimated values from the actual ones do not exceed some tolerance, ρ, a departure from SVMs, where the main goal is to find a hyperplane separating data points for classification, as shown in Figure 1. This uses an ϵ-insensitive loss function in which errors smaller than ϵ are ignored, but bigger ones are penalized through a cost parameter C. 

Figure 1. SVR-based regression approach

When the data show some nonlinear relationships, the SVR method uses appropriate kernel functions (linear, polynomial, RBF) to treat them accordingly.

The essential mathematical expression of the SVR is demonstrated as follows.

To keep the model as flat as possible, SVR attempts to fit a function f(x) with a maximum deviation ρ from the actual targets [21].

$\min _{w, b, \delta_i, \delta_i^*} \frac{1}{2}\|w\|^2+C \sum_{l=1}^n\left(\delta_i+\delta_i^*\right)$           (1)

where, the weight vector, w, determines the regression hyperplane's orientation and slope. The bias term (intercept) that causes the hyperplane to move up or down is denoted by b. C is a parameter for regularization, $\delta_i, \delta_i^*$ represents the slack variables that manage errors by allowing specific points to fall outside the ϵ-insensitive tube. The SVR optimization problem is subject to: 

$\begin{aligned} & y_i-\left(w . x_i+b\right) \leq \rho+\delta_i \\ & \left(w . x_i+b\right)-y_i \leq \rho+\delta_i^* \\ & \delta_i, \delta_i^* \geq 0\end{aligned}$               (2)

Function of regression:

$f(x)=\sum_{i=1}^n\left(\beta_i-\beta_i^*\right) K\left(x_i, x\right)+b$             (3)

where, K(x_i,x) is the kernel function (such as RBF or linear), $\beta_i, \beta_i^*$ are used to quantify the degree to which the associated constraint is active.

The overall algorithm steps can be illustrated as follows:

•     Select the kernel function K, such as linear or RBF.
•     Set $\rho$ and C as hyperparameters.
•     Determine $\beta_i, \beta_i^*$ by solving the convex optimization problem.
•     Determine bias b.
•     Predict with f(x).

3.2 Long Short-Term Memory

LSTM is a type of RNN that is designed to handle long-range dependencies while preventing the vanishing gradient problem. A memory cell is utilized here, with gates to control flows of information: forget, input, and output. The difference between LSTM and a regular RNN is that LSTM can choose to keep or forget certain information over obviously large time sequences, so they are effectively used for time-series prediction, speech recognition, and natural language processing. The mathematical expression of LSTM is shown in the following expressions [22, 23].

$l_t=\vartheta\left(S_f\left[H_{t-1}, F_t\right]+z_f\right)$               (4)

$k_t=\vartheta\left(S_i\left[H_{t-1}, F_t\right]+z_i\right)$               (5)

$\varphi=\tanh \left(S_c\left[H_{t-1}, F_t\right]+z_c\right)$            (6)

$\varphi_t=l_t * \varphi_{t-1}, k_t * \varphi$              (7)

$O_t=\vartheta\left(S_o\left[H_{t-1}, F_t\right]+z_o\right)$                 (8)

$H_t=O_t * \tanh \left(\varphi_t\right)$              (9)

$Out_{ {class }}=\vartheta\left(H_t * S_{ {out }}\right)$               (10)

where, $l_t$ is the forgetting layer's output; $k_t$ is a function that the input gate uses; $\varphi$ is the new candidate's values' vector; $\varphi_t$ is the cell's most recent state; $S_f, S_i, S_c, S_o, S_{ {out }}$ are the weights; $z_f, z_i, z_c, z_o$ are the biases; $H_t$ is the output at time $\mathrm{t}; F_t$ is the input features; Out ${ }_{ {class }}$ is the output of classification.

Figure 2. The architecture of the proposed LSTM model

Steps of the LSTM Algorithm are as follows:

Step 1: Set cell state $\varphi_0$ and hidden state $H_0$ to zero. 

Step 2: Every time step t.

a. Compute forget gate $l_t$ from $H_{t-1}$ and $F_t$.

b. Compute input gate $k_t$  and candidate cell state $\phi$.

c. Update cell state $φ_t=l_t.φ_{t-1}+ k_t.φ .$

d. Compute output gate $O_t$.

e. Update hidden state $H_t=O_t  .tanh(φ_t)$.

Step 3: For the last output layer, use the most recent hidden state (or series of hidden states).

The structure of the proposed LSTM model for blood pressure prediction is shown in Figure 2, and the hyperparameter values are listed in Table 2.

Table 2. Models hyperparameters

3.3 Light Gradient Boosting Machine

LightGBM is a speedy implementation of Gradient Boosting Decision Trees (GBDT). A series of decision trees is constructed sequentially, where each tree fits negative gradients of the loss function and thereby corrects the errors committed by the preceding tree. LightGBM differs from traditional GBDT in that it grows trees leaf-wise instead of level-wise based on whichever split gives the maximum information gain. It employs Histogram-based binning to provide faster computation and can handle large datasets with a smaller memory footprint. The mathematical description of LightGBM is illustrated as follows. The model is updated as follows at iteration j. In other words, Eq. (11) outlines the gradual improvement of the ensemble [24].

$f_j(x)=f_{j-1}(x)+\mu h_j(x)$             (11)

where, $f_j(x)$ represents the improved model following $j$ iterations, $f_{j-1}(x)$ is the model afterwards $j-1$ iterations, $h_j(x)$ At iteration $j$, a new decision tree (weak learner) is added, $\mu$ is the rate of learning $(0<\eta \leqslant 1), x$ is the input vector for features. Now, with regard to the split gain expression, which determines the optimal split, LightGBM employs a leaf-wise growth strategy based on histograms. When a node is divided into left and right child nodes, the gain (loss reduction). This means that Eq. (12) explains how LightGBM balances regularization and gradient information when choosing which feature and threshold to split at each node. 

${gain}=\left(\frac{Q_L^2}{D_L+\lambda}+\frac{Q_R^2}{D_R+\lambda}-\frac{\left(Q_L+Q_R\right)^2}{D_L+D_R+\lambda}\right)-\phi$              (12)

where, gain is the objective function's improvement (better split equal to larger gain), $Q_L, Q_R$ are the sum of the left and right child nodes' first-order gradients, or residuals, of the loss, $D_L, D_R$ denote the sum of the loss's second-order gradients (Hessian) for the left and right child nodes, $Q_L+Q_R$ refer tothe parent node's total gradient prior to splitting, $D_L+D_R$ are the parent node's total hessian prior to splitting, $\lambda$ is the regularization on leaf weights, $\phi$ is the cost of complexity, or the penalty for taking a different leaf. Now, the steps that describe the LightGBM algorithm can be demonstrated as follows: 

Step 1: Set the average target value (for regression) as the initial value for predictions.

Step 2: For every iteration of boosting:

a. Using the current predictions, calculate the gradients $Q_j$ and hessians $D_j$.

b. Use $Q_j$ and hessians $D_j$ to determine the split with the highest gain for each leaf. 

c. Expand the tree leaf by leaf until the maximum depth or minimum leaf data is attained.

d. Use Eq. (11) to update predictions. 

Step 3: Provide the final model, which is the ensemble of trees.

Figure 3. A sample from the applied dataset

3.4 Cuffless dataset description

The dataset illustrated in Table 3 is used in this study, namely the UCI ML Repository Cuffless Blood Pressure Estimation Dataset [25]. The applied dataset consists of a sample, which is depicted in Figure 3. It has 12000 samples in total. The signals ECG, PPG, and ABP are the only ones present in each sample, with a sampling rate of 125 Hz. First, the Electrocardiogram (ECG) represents a recording of the electrical activity of the heart muscle over time. The heart's electrical impulses are responsible for coordinating its contractions and making it possible for blood to flow through the body. Secondly, Photoplethysmography (PPG) is a non-invasive technique that uses light to measure blood flow in the capillaries of the skin. PPG provides important insights into the cardiovascular system; moreover, it is a non-invasive, portable, and cost-effective method. The third signal, arterial blood pressure (ABP), refers to the pressure that the blood exerts on the walls of the arteries. Blood pressure is interlinked to the heart cycle, which has two alternating phases: systole, when the heart contracts and propels the blood through the arteries, and diastole, when the heart relaxes after the contraction. 

Table 3. UCI Cuffless Blood Pressure Dataset description

3.5 Wearable cuffless for blood pressure hypertension 

Cuffless, wearable blood pressure measurement devices offer a very convenient way to monitor hypertension and hypotension while increasing the opportunity for long-term management of blood pressure [26]. It makes use of biophysiological signals such as photoplethysmograms (PPG) and electrocardiograms (ECGs). However, some of its limitations are: first, calibration is necessary for accuracy when using cuff-based devices. Second, reliability may be lowered by signal noise, which includes skin tone, motion artifacts, and ambient light. Additionally, clinical-grade accuracy is still being validated. Several medical, technological, and practical requirements drive the decision to employ AI for Blood Pressure (BP) prediction or forecasting rather than more conventional techniques [27, 28], including 

(1) motivation in healthcare

- Early and ongoing monitoring is necessary to identify abnormal blood pressure trends before complications like stroke, heart attack, or kidney failure arise because hypertension is a silent killer.

- Traditional cuff-based devices are unable to record the dynamic fluctuations in blood pressure caused by stress, activity, or sleep. These temporal variations can be modeled by AI.

- Personalized healthcare: Unlike one-size-fits-all cuff methods, AI models can adjust to the physiology of each patient.

(2) Technical inspiration

- Nonlinear physiological relationships: Heart rate variability, PPG, ECG, and other signals are intricate and interconnected. Traditional statistical techniques are unable to reveal hidden nonlinear patterns; AI can.

- Automation of feature extraction: AI (such as deep learning) eliminates the need for manually created features by automatically extracting significant features from unprocessed signals.

- Predicting future blood pressure trends: AI can predict future risks (such as the onset of hypertension) in addition to current blood pressure, something that traditional methods are unable to do.

(3) Realistic motivation

- Constant monitoring and comfort: Although wearable cuffless devices are comfortable, their unprocessed signals are noisy. By removing noise and identifying reliable patterns, AI increases accuracy.

- Use of big data: AI can enhance population-level generalization by utilizing sizable medical datasets (from wearables, EHRs, and IoT systems).

- Integration with telemedicine: AI-powered cuffless blood pressure monitors can give physicians real-time decision support, early warnings, and remote monitoring.

Therefore, the goal of AI in blood pressure prediction is to overcome the drawbacks of conventional cuff-based systems and allow for continuous, personalized, and predictive hypertension management.

The performance evaluation in this work is divided into three scenarios based on different combinations of selected datasets, which are the ABP, PPG, and ECG. Where the ABP is used as a ground truth for prediction. Regarding the evaluation metrics, the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), as illustrated in Eqs. (13) and (14), are used to testify the accuracy of the proposed three models (SVR, LSTM, and LightGBM). The RMSE can be determined as follows:

$R M S E=\sqrt{\frac{1}{n} \sum_{i=1}^n\left(y_{i-} \hat{y}_i\right)^2}$              (13)

where, $n$ is the number of samples, $y_i$ is the i-th sample's actual (true) value, $\hat{y}_i$ The expected amount of the i -th sample.

Then the value of the Mean Absolute Error (MAE) can be calculated as follows:

$M A E=\sqrt{\frac{1}{n} \sum_{i=1}^n\left|y_{i-} \hat{y}_i\right|}$                 (14)

The reason behind using both the RMSE and the MAE is that the MAE directly measures the average amount of error (absolute error), while the RMSE gives greater weight to large errors (due to the squared).

Additionally, for statistical analysis measurement for the proposed models, the confidence interval (CI) metric is considered as follows.

$\mathrm{CI}=\delta \pm \vartheta \sqrt{\frac{\rho(1-\rho)}{\epsilon}}$                     (15)

where, $\delta$ is the model's accuracy, $\vartheta$ is the z -score level, and $\rho$ is the percentage of successes within the samples.

Now, in the first scenario, the PPG and ABP data are used to predict the blood pressure as depicted in Figure 6. It can be noted in Table 4 that the LSTM outperforms both the SVR and LightGBM in terms of prediction error.

Figure 6. Evaluation process of the models for scenario A

Table 4. Results of scenario A (PPG+ABP)

In the second scenario, the combination of the ECG and ABP is selected as input for predicting the BP, as shown in Figure 7. The evaluation results are shown in Table 5.

Figure 7. Evaluation process of the models for scenario B

Table 5. Results of scenario B (ECG+ABP)

Likewise, the LSTM is the best model compared to other approaches in terms of the prediction error.

Finally, the third scenario combines PPG, ABP, and ECG, which are used for BP forecasting as illustrated in Figure 8.

Figure 8. Evaluation process of the models for scenario C

Based on the results of scenario C, that shown in Table 6, it is worth stating that the LSTM also has the highest performance in terms of BP prediction.

Table 6. Results of scenario C (PPG+ECG+ABP)

Here, combining the (PPG, ECG, and ABP) achieved the best results compared to the first and the second scenarios due to BP correlates with Pulse Transit Time (PTT) / Pulse Arrival Time (PAT), measured between the ECG R-wave and PPG foot/peak; this timing is a strong surrogate for arterial stiffness/BP.

Furthermore, the experiments indicate that attempting to estimate BP with a PPG alone is an ambiguous and noise-sensitive task; combining the ECG+PPG signals increases the robustness and accuracy of the estimation.

Though it is difficult to make direct numerical comparisons among studies because of the various factors such as datasets, signal acquisition protocols, and evaluation strategies, the proposed LSTM model (RMSE = 12.36 mmHg, MAE = 10.36 mmHg for SBP) is still able to show performance that is on par with the latest PPG-based deep learning methods. Our approach, in contrast to attention-based or CNN-BiLSTM models such as the studies [9, 18], achieves similar accuracy with a less complex architecture and a different dataset. Meanwhile, multimodal systems, as in the study [5], report fewer errors, but they also require more sensing hardware. The proposed approach can work with just PPG signals, thus illustrating a favorable trade-off between accuracy and system complexity.