1. Introduction

The continuous blood pressure monitoring is crucial to keep our healthy daily lives. Blood pressure denotes the force exerted by the blood flowing through blood vessels against their walls ^[1]. Actively utilized for the patients of the hypertension and cardiovascular diseases, the blood pressure provides vital information for health management ^[2]. High blood pressure stands out as a condition carrying a heightened risk of severe complications, including heart disease, stroke, and kidney disease. Statistics revealed that approximately 1.3 billion adults aged 30 to 79 worldwide are affected by the condition of the high blood pressure ^[3]. In this context, estimating blood pressure in appropriate settings serves as a fundamental element for the effective early diagnosis and treatment of the hypertension. Traditional methods of measuring the blood pressure involve invasive techniques, such as inserting a cannula needle into a blood vessel, or temporary approaches using a cuff wrapped around the arm ^[4]. While these methods excel in accuracy, their drawback lies in their bulky size, rendering them unsuitable for continuous monitoring in daily situations.

To address these limitations, there exists a method for blood pressure estimation utilizing physiological signals acquired through wearable devices. This approach estimates the blood pressure by analyzing the physiological signals like photoplethysmogram (PPG) and electrocardiogram (ECG), employing both feature extraction-based models and deep learning-based models ^{[5, 6]}. The blood pressure prediction based on the feature extraction involves metrics such as the pulse transit time (PTT), which is directly proportional to pulse wave velocity (PWV) — a factor associated with the blood pressure ^[7]. However, this method has the drawback of low accuracy compared with the traditional cuff-based blood pressure monitoring, as it tends to be deulated from the true value owing to changing measurement conditions ^[8]. Recently, deep learning models exhibit high accuracy for the blood pressure prediction. Nevertheless, their extensive computational requirements pose challenges for practical implementation, particularly in edge devices such as wearable gadgets.

Recent research has delved into the estimation of blood pressure utilizing signals measured from physiological sensors such as ECG and PPG. Among the previous studies, a real-time blood pressure estimation model was developed through the long short-term memory (LSTM) network, which analyze the temporal information in the ECG and PPG time-series data. Additionally, investigations into the blood pressure estimation have employed ResNet, a large-sized convolutional network model ^{[6, 9]}. However, these models exhibit the drawback of necessitating the training process with extensive datasets. Moreover, in the data analytics employing multi-channel signals, it becomes imperative to define the temporal and spatial relationships among the multiple signals ^[10]. Therefore, the relationship among the multi-channel physiological data should be considered to design these relationships on the outcomes of the blood pressure estimation model.

This study concentrates on enhancing the blood pressure estimation model with extracting and utilizing the relationship among the multi-channel physiological data for the deep learning architecture. We introduce a graph-based algorithm for blood pressure estimation, analyzing ECG, PPG, and 2-channel ballistocardiogram (BCG) signal recorded through a multi-channel sensor system. The blood pressure estimation model is designed based on a graph-based network architecture, aiming to boost the performance of blood pressure estimation by leveraging the strength of the relationships among the signals.

2. Methods

In this study, a total of 16 subjects were actively participated in the experiment. Signals were recorded for a duration of 30 minutes while the subjects sat on a chair equipped with a polyvinylidene fluoride (PVDF) sensor.

Fig. 1. Examples of the recorded ECG, PPG and 2-channel BCG signals.

Alongside the standard measurement of ECG recorded in a Lead II signal in the standard 12 leads, PPG signals were acquired using the BIOPAC module (Biopac MP36, BIOPAC Systems Inc., Goleta, CA, USA). PPG signals were measured from the subjects’ index finger. Additionally, two-channel ballistocardiogram (BCG) signals were recorded from the back and buttocks through the PVDF film attached to the chair ^[11]. Each signal was simultaneously sampled at a frequency of 1 kHz. To temporarily elevate blood pressure for the diagnosis of potential health risks. Blood pressure measurements were conducted under these conditions at regular intervals throughout the session. Examples of the recorded ECG, PPG and 2-channel BCG signals are displayed visualized in Fig. 1 ^[12]. This experiment was approved by the Institutional Review Board of Kwangwoon University (IRB 7001546-202300131-HR(SB)-001-03).

To mitigate noise in the collected signals, a preprocessing step was conducted utilizing a bandpass filter. For the ECG signals, the high-pass and low-frequency filters were applied to extract the components between 0.5 and 35 Hz, while those for the PPG signals were set between 0.5 and 8 Hz, and the 2-channel BCG signals were filtered between 4 and 15 Hz. Blood pressure was measured using a Finometer Pro (FP, Netherlands) device placed on the middle finger of the left hand, and the ultimate output values of the blood pressure estimation model, representing the systolic and diastolic blood pressures, were computed within the ranges of 70 190 mmHg and 30 100 mmHg, respectively. For enhanced computational efficiency, the initially measured signals at 1 kHz underwent down-sampling process to 250 Hz after the frequency filtering process and were segmented into 4-second data intervals. Subsequently, the preprocessed signal was fed into a graph-based neural network model for the blood pressure estimation ^[13]. The graph is represented by nodes and edges with features extracted from ECG, PPG, and the 2-channel BCG signals, as illustrated in Fig. 2.

Fig. 2. Graph structure consisting of ECG, PPG and 2-channel BCG signals.

2.1. Graph Neural Networks

In this study, a graph-based graph neural network (GNN) was employed for the blood pressure estimation model. The model utilized the relationships among the collected signals to improve the blood pressure estimation performance. The effectiveness of the graph-based network model is affected by the edge information representing the relationships among the nodes. This edge information is described as a matrix indicating the strength of the connections among the nodes, commonly called an adjacency matrix. GNN applies this adjacency matrix, representing the relationship among the multi-channel signals, to the neural networks. In other words, by assigning weights between two signals, the model incorporates the relationships among multiple signals into the learning process. The structure of the GNN model applied in this study is illustrated in Fig. 3.

Fig. 3. Graph-based graph convolutional network model structure.

3. Performance Evaluation

Blood pressure estimation performance was evaluated using three metrics: root mean squared error (RMSE), mean absolute error (MAE), and the Pearson correlation coefficient. RMSE is defined as the square root of the mean squared difference between the observed and predicted values, as shown in Eq. (3).

where $N$ represents the total number of segments, $y_i$ is the observed value for the $i^{th}$ observation, and $\hat{y}_i$ is the predicted value for the $i^{th}$ observation. MAE calculates the average absolute difference between the observed and predicted values, as shown in Eq. (4).

The Pearson correlation coefficient is denoted by $r$ and is calculated as shown in Eq. (5).

where $x_i$ and $y_i$ represent the individual observations of the two variables, and $\bar{x}$ and $\bar{y}$ represent their respective mean values.

4. Results

In Blood pressure estimation results are provided through the three indicators introduced earlier for the systolic blood pressure and diastolic blood pressure. The results are presented in Table 1.

In the blood pressure estimation results for all subjects, applying the adjacency matrix created through the two-way directionality between signals using Euclidean distance, the SBP RMSE through the intra-subject test was confirmed to be 2.161, the MAE 2.485, and $r$ 0.481. For DBP, the RMSE was 1.767, MAE 2.405, and $r$ 0.598. In the individual blood pressure estimation results inter-subject test, SBP RMSE was confirmed to be 2.655, MAE 6.392, and $r$ 0.4263. For DBP, the RMSE was 2.442, MAE 7.785, and $r$ 0.537. In the blood pressure estimation results for all subjects through intra-subject test, applying the adjacency matrix generated using PDC that consider the causality in one-way direction, the SBP RMSE was confirmed to be 2.225, MAE 3.486, and $r$ 0.391. For DBP, the RMSE was 2.153, MAE 3.159, and $r$ 0.398. In the inter-subject blood pressure estimation results, SBP RMSE was confirmed to be 3.196, MAE 10.429, and $r$ 0.320. For DBP, the RMSE was 3.046, MAE 10.321, and $r$ 0.328.

5. Conclusion

Research in the field of blood pressure estimation is increasingly focusing on enhancing accuracy and reliability by incorporating various physiological signals. In this study, we propose a method for estimating blood pressure that employs a graph-based network model. This model utilizes the correlations among diverse physiological signals to assess their impact on the estimation results, thereby providing insights into the interconnected influences of these signals on blood pressure. The proposed technique aims to demonstrate improved performance in blood pressure estimation by leveraging the relationships between simultaneously measured signals. This was achieved by quantifying the strength of the connections between signals, which builds the adjacency matrix that expresses the relationship among the signals. The experimental results showed promising outcomes, suggesting that the relationship among signals positively affects the accuracy of blood pressure estimation results.