Subject-Independent Cuff-Less Blood Pressure Monitoring via Multivariate Analysis of Finger/Toe Photoplethysmography and Electrocardiogram Data

Abstract

(1) Background: Blood pressure (BP) variability is an important risk factor for cardiovascular diseases. Still, existing BP monitoring methods often require periodic cuff-based measurements, raising concerns about their accuracy and convenience. This study aims to develop a subject-independent, cuff-less BP estimation method using finger and toe photoplethysmography (PPG) signals combined with an electrocardiogram (ECG) without the need for an initial cuff-based measurement. (2) Methods: A customized measurement system was used to record 80 readings from human subjects. Fifteen features with the highest dependency on the reference BP, including time and morphological characteristics of PPG and subject information, were analyzed. A multivariate regression model was employed to estimate BP. (3) Results: The results showed that incorporating toe PPG signals improved the accuracy of BP estimation, reducing the mean absolute error (MAE). Using both finger and toe PPG signals resulted in an MAE of 9.63 ± 12.54 mmHg for systolic BP and 6.76 ± 8.38 mmHg for diastolic BP, providing the lowest MAE compared to previous methods. (4) Conclusions: This study is the first to integrate toe PPG for more accurate BP estimation and proposes a method that does not require an initial cuff-based BP measurement, offering a promising approach for non-invasive, continuous BP monitoring.

1. Introduction

Blood pressure (BP) is a vital indicator of cardiovascular status. High blood pressure (hypertension) can cause several cardiovascular diseases (CVD) including atherosclerosis (thickening of the arteries), heart attack, aneurysms, and cerebrovascular events such as stroke [1,2]. Hypertension is the single most important modifiable risk factor for both CVD and stroke. Besides absolute BP values, evidence from previous studies and trials has shown that these outcomes could also rely on increased blood pressure variability (BPV) [1,2]. It has been reported that increased short-term (24 h period) and long-term (days, weeks, months, etc.) BPV results in the development, progression, and severity of cardiac, vascular, and renal damage [3]. Notably, post hoc analyses of large intervention trials in hypertension revealed that within-patient visit-to-visit BPV is strongly prognostic for cardiovascular morbidity and mortality [1,2,3]. These findings have provided evidence that it is crucial to minimize the risk by monitoring the changes in BP and keeping control in the early stage [2].

The gold standard of BP measurement is through the use of a catheter, but it is invasive and not practical for clinical use. The most commonly performed non-invasive BP measurement is with the use of an inflatable cuff employing either auscultation or oscillometric methods; however, these measurements require at least one minute in between BP measurements, which do not allow for continuous BP recordings [4]. Even conventional 24 h ambulatory BP monitoring can only be performed at regular intervals, and it still requires the use of a cuff [5]. Even though arterial tonometry and volume clamp techniques provide continuous measurements, due to their bulky size and being partly intrusive, they have not found extensive application in clinical practice [2]. There has been a significant research focus on coming up with a non-invasive, accurate, cuff-less and minimally intrusive technology to monitor BP continuously. Even though there are two Food and Drug Administration (FDA)-cleared methods, including Sotera VISI Mobile and SOMNOtouch continuous noninvasive BP monitoring systems, the research on finding a clinically valid cuff-less method is still ongoing since existing methods still struggle with accuracy and calibration concerns [6]. Current methods to achieve cuff-less BP measurements mainly focus on pulse transit time (PTT) and pulse wave velocity (PWV). For these methods, usually, ECG is used in combination with PPG. ECG provides a time reference for the origination of the BP pulse while PPG in reference to ECG provides the PTT (the time for the pulse to arrive at the PPG measurement site). PWV is the propagation velocity of the BP waveform through the arteries; i.e., stiffer arteries will lead to increased PWV. PTT is used for PWV estimation (PWV: the distance between the heart and the peripheral PPG measurement site (finger, toe, etc.) divided by PTT). The main disadvantage of using PTT/PWV technique is that it requires individual patient calibration (measurement with a cuff) that has to be updated periodically.

The majority of the previous studies on cuff-less BP monitoring have required calibration, and they have used different models including mathematical and machine learning algorithms [7,8,9,10,11,12,13,14,15,16]. Additionally, despite using some of the patients’ vital data, they did not have access to the patients’ information including age, height, weight, and body mass index (BMI) which are important parameters for better accuracy [2,10,17]. In addition, it has been shown that the subject’s heart rate shows a significant correlation with temporal parameters from both toe and finger PPG signals while toe PPG has no significant dependency on the subject’s sex [18]. Thus, including toe PPG signal in BP estimator models makes them less dependent on the subject’s sex.

We came up with two methods to improve the accuracy of our BP estimation algorithm by 1—adding/using parameters from toe PPG; 2—including additional parameters with considerable dependence on the BP.

While calibration-based methods need to modify the estimator model for each subject and then track the BP trajectory, designing a subject-independent algorithm –that is not based on an initial or periodic calibration, is one of the challenges in BP estimation. To our knowledge, there are only two studies that have reported calibration-free methods so far. Both of these studies used regression methods in addition to machine learning techniques such as support vector machine (SVM) [17,19]; however, those studies are limited to the available databases including Physionet MIMIC. By developing and customizing our measurement device, we were able to include and analyze additional features, most importantly, the toe PPG signal.

Therefore, the importance of this study is not only based on its ability to estimate continuous BP without any initial cuff-based measurement, but also the integration and assessment of toe PPG signal, and additional subject information such as weight, age, height, and BMI. This study showed that involving these additional parameters results in improved accuracy.

2. Materials and Methods

In studies that are not based on a calibration-free approach, PTT is used as the main indicator of BP. By having an initial measurement of BP, BP at the next heartbeat can be tracked using an equation that maps PTT on BP [7,9,10]. In contrast, due to subject-specific features of the PTT-based algorithms, no universal equation can relate PTT to BP [20,21,22,23].

In this study, we hypothesized that using two PPG sensors, including one for the finger and one for the toe, and additional subject information such as weight, height, BMI, heart rate (HR), etc., would improve the accuracy of BP estimation. The rationale behind the hypothesis is that fingers and toes have different arterial structures, where arterial compliance is the major factor for the toe and the peripheral resistance is the main contributor to the finger PPG signal. Previous studies (with and without calibration) have used the finger PPG signal, none of them have used toe PPG signal, and only one study has used forehead PPG recording [24]. We designed and developed a recording system that allows for two-channel (finger and toe) PPG recordings as well as a single-channel ECG recording.

Most previous cuff-less BP studies have required calibration and used mathematical and machine learning algorithms [7,8,9,10,11,12,13,14,15,16]. Many lacked access to important patient data like age, height, weight, and BMI, which can improve accuracy [2,10,17]. Our study hypothesizes that using two PPG sensors (finger and toe) and this additional subject information will improve BP estimation accuracy.

Our method differs from previous work by (1) integrating toe PPG signals, (2) employing a subject-independent approach, (3) including subject-specific parameters, and (4) utilizing a customized measurement device. This is the first study to use toe PPG in cuff-less BP estimation. Finger PPG is more influenced by peripheral resistance, while toe PPG reflects arterial compliance [18]. Specifically, the rationale for including toe PPG is that the arterial bed in the toes is more representative of the body’s larger arteries, which are less affected by vasoconstriction and more by the elastic modulus changes with BP. This provides information that complements the finger PPG signal, which is more influenced by peripheral resistance in smaller arteries [18]. We developed a calibration-free algorithm, unlike many existing methods [17,19], and incorporated age, height, weight, and BMI, shown to enhance BP estimation [2,10,17]. Finally, we developed a customized device to simultaneously record finger and toe PPG signals.

• Our Recording Device

The recording system consists of two modules: the amplifying module and the controlling module as shown in Figure 1 and Figure 2. The amplifier module includes a two-channel PPG and a single channel ECG signal amplifier. The central processing and control unit utilizes an ARM Cortex-M4 (Tiva Launchpad TM4C123G, Texas Instruments, Dallas, TX, USA) evaluation board and a custom I/O board which also includes analog receivers and analog-to-digital converters (10 bit, 1 kHz). The captured analog signals are conditioned before feeding through the A/D converters in two stages: (I) 2nd-order high pass filter at 0.5 Hz for PPG inputs and 2 Hz for ECG signals; (II) 6th-order low-pass filter at 25 Hz for the PPG signals and 100 Hz for the ECG signal. The circuit was powered by a power bank and the voltage of the input was protected using a DC-DC converter to ensure that there is a voltage isolation barrier. Digital signals were then transmitted to a PC through a Bluetooth link with a speed of 115,200 bytes per second.

The PPG sensors used were 9-pin and reusable SpO2 sensors (DS100A, Nellcor Oximax, Minneapolis, MN, USA), and the ECG electrodes used were chest-lead Ag/AgCl electrodes. The specifications of the recording device are summarized in

Table 1. Specifications of the recording device.

Specification	Description
Amplifier Module	Two-channel PPG and single-channel ECG amplifier
Control Unit	ARM Cortex-M4 (Tiva Launchpad TM4C123G, Texas Instruments)
PPG Filter	2nd order high pass (0.5 Hz), 6th order low pass (25 Hz)
ECG Filter	2nd order high pass (2 Hz), 6th order low pass (100 Hz)
Power Supply	Power bank with DC-DC converter for voltage isolation
Data Transmission	Bluetooth (115,200 bytes per second)
Sensors and Electrodes	Reusable SpO2 sensors (PPG) Chest-lead Ag/AgCl electrodes (ECG)

.

B.

Subjects and Experiments

A total number of 80 participants, with 39 female and 41 male subjects, were included in this study (

Table 2. Anthropometric characteristics of subjects.

Parameter	Mean	Standard Deviation
Age (years)	25	7.9
Height (cm)	171	9.4
Weight (kg)	75.8	18.9
BMI (kg/m2)	25.8	5.7

). The average age of the subjects was 25.0 ± 7.6 years old (18–53 years old). Written informed consent was obtained from all subjects prior to their participation in the study. The consent form detailed the purpose of the research, the experimental procedures, the potential risks and benefits, the confidentiality of their data, and their right to withdraw from the study at any time. Participants were given ample opportunity to ask questions and were provided with a copy of the signed consent form for their records. The subjects also completed a digital questionnaire to obtain a general health background. Out of the 80 subjects, only 1 reported a history of cardiac arrhythmia. Seven of the subjects indicated they had hypertension. All of the testing procedures with human subjects and the recording place were approved by the Office of Compliance and Risk Management Institutional Review Board (IRB Approval Number: 18-030) at Florida Institute of Technology, Melbourne, FL, USA and this study was conducted according to Declaration of Helsinki ethical principles for medical research on human subjects.

Three single-use dynamic ECG–/EMG electrodes, (PB-50-060, Myovision, Seattle, WA, USA) were placed: one was placed about 2 inches below the left underarm; the second electrode was placed approximately 2 inches below the right underarm. These two locations were selected instead of the arms to reduce motion artifacts. The ground electrode was placed on the right side of the abdominal cavity, above the iliac crest to minimize power line noise from interfering with the ECG signal. The best positions arbitrated for optimal PPG recordings were the left index finger and the right hallux. The duration of the testing was 3 min. Each subject was seated in an armed chair and the subject’s right foot was placed on a footrest, with their leg fully extended. A fully automatic BP monitor (Bloeddrukmeter M3, Omron, Kyoto, Japan) was used to measure the BP 30 s after the onset of the recording process. The device has a mean error of 1.9 ± 3.0 and −1.0 ± 2.3 mmHg for systolic and diastolic BP, respectively [25]. The room temperature was fixed at 25 °C, and the lights were dimmed.

C.

Features and Feature Selection

The extracted and analyzed features were categorized based on the following classes:

1. Heart Rate and PPG-based: latency/time and morphology features from finger and toe PPGs.

2. Subject information-based features: weight, height, age, and BMI.

3. Other features.

• Heart Rate and PPG Features

Heart rate: HR is an indicator of ANS activity. It also controls the cardiac output. NN is the length of successive R-R intervals.

Latency/Time: When the blood arrives at the distal PPG site, the blood volume rapidly changes [26,27,28,29]. PPG signal, as the indicator of this change in volume, consists of consecutive peaks, inflection points, and a distinctive notch, which highlight distinguishable events in the cardiovascular system (Figure 3). These sites allow for the extraction of the latency/time features from the PPG signal. The first peak is called the systolic peak and the second one is known as the diastolic peak. The moment when the blood volume starts to increase is the onset of the PPG signal (the first derivative of the signal becomes positive), as shown in Figure 3.

The time delay from the ECG R peak to the onset is measured as pulse arrival time (PAT) (Figure 4a). It is shown that PAT and BP are inversely correlated. The maximum rate in blood volume change can be observed when the first derivative of the PPG signal is at its maximum. This point is called the rising point and the time delay between the R peak and the rising point is called PTT [7,9,10,11,12,17,19,21,22,23,30]. The time delay between R peak and systolic and diastolic peaks is measured as systolic pulse transit time (SPTT) and diastolic pulse transit time (DPTT), respectively, as shown in Figure 4a [7,9,10,20,21,22]. Since subject height is related to the distance between the source (heart) and the distal site (i.e., finger/toe), the latencies (i.e., PTT) were normalized by dividing them by the subject’s height.

Morphology features: It was shown that the stiffer arteries exhibit longer delays between systolic and diastolic peaks (ΔT) [31,32,33,34]. Large artery stiffness index (LASI) represents the ratio obtained by dividing the height by ΔT [28,29,34,35]. AI is a feature that is measured by dividing the systolic-to-diastolic peak difference by the systolic peak amplitude [28,34]. AI is an indicator of arterial stiffness, hypertension, and mortality [28,34]. This feature is directly correlated to the arterial compliance [28,34]. Each PPG cycle can be divided into two parts: one from onset to dicrotic notch (A1) and the other from the dicrotic notch to the end of the cycle (A2). The A2/A1 ratio is called the inflection point area ratio (IPA) [17,19,23,28,36]. The total peripheral resistance is related to the A2/A1 ratio [17,19,23,28,36]. PPG cycles can also be represented by 4 areas indicated as S1, S2, S3, and S4 as illustrated in Figure 4b. Since the PPG signal amplitude changes with the posture, these values (S1–S4) were normalized over the total area

2.

Subject Information-Based Features

Physiological and physical features such as weight, height, BMI, and age were also gathered from the questionnaire each subject filled out.

3.

Other Features

The PPG signals recorded from the finger and the toe follow the wave propagation equation described in Equation (1) [21,22].

$$P(x,t)=f(x\pm {\displaystyle \frac{t}{\sqrt{LC\left(P\right)}}})$$

(1)

$$L={\displaystyle \frac{\rho }{A}}$$

(2)

where P, L, t, A, ρ, and P(x,t) are pressure, arterial inertance per unit length, time, distance, arterial cross-section area (πr²), blood viscosity and BP function, respectively. C(P) is the compliance of the arteries and represents the elasticity and the dynamical change of the cross-sectional area that is influenced by the BP [21,22].

Studies on C(P) show that it is not only related to the geometry of the artery but also to the elastic modulus (E) of the arterial wall as follows [21,22]:

$$C(P)={\displaystyle \frac{2\pi r^3}{E_0.e^{\alpha P}}}$$

(3)

$$PTT=\sqrt{LC(P)}={\displaystyle \frac{2r(\Delta x^2+\rho )}{E_0.e^{\alpha P}}}$$

(4)

$$PT{T}^2={\displaystyle \frac{\rho +\Delta x^2}{A}}.C(P)$$

(5)

$$PT{T}^2={\displaystyle \frac{2r(\rho +\Delta x^2)}{E_0{e}^{\alpha P}}}$$

(6)

Based on Equation (6), PTT² is related to the arterial radius, stiffness, and compliance. So, Equation (6) can be re-written for pressure as:

$$P={\displaystyle \frac{-1}{\alpha }}[\ln ({\displaystyle \frac{2r\rho }{E_0}})+\ln ({\displaystyle \frac{2r}{E_0}}\Delta x^2.PT{T}^{-2})]$$

(7)

$$P={\displaystyle \frac{-1}{\alpha }}[{\gamma }_1+{\gamma }_2\ln (\Delta x^2.PT{T}^{-2})]$$

(8)

As described by Equation (8), the natural logarithm of squared PWV is used as one of the features.

Table 2 shows the anthropometric characteristics of the subjects, and

Table 3. List of features used in analysis.

Features	Symbol	Mean ± SD		Equation/Definition	Source
		Finger	Toe
Normalized PTT (ms/m)	PTTn	176.7 ± 15.1	232.5 ± 16.7	${\displaystyle \frac{PTT}{Height}}$	ECG, finger and toe PPG
Pulse Acceleration (cm/s2)	ACC	19.2 ± 3.3	11.0 ± 1.6	${\displaystyle \frac{Height}{PT{T}^2}}$	ECG, finger and toe PPG
S2/S1 Ratio	S2S1	7.8 ± 1.6	5.5 ± 0.7	${\displaystyle \frac{S_{2}Area}{S_{1}Area}}$	finger and toe PPG
IPA	IPA	2.1 ± 0.5	0.2 ± 0.1	${\displaystyle \frac{A_{2}Area}{A_{1}Area}}$	finger and toe PPG
LASI (ms)	LASI	220.6 ± 39.4	260.1 ± 56.7	Sys. to dia. peak latency	finger and toe PPG
Heart Rate (beats/min)	HR	78.6 ± 14.4		-	ECG
NN (s)	NN	0.8 ± 0.1		-	ECG
Weight (kg)	W	76.2 ± 18.4		-	Questionnaire
Height (cm)	H	171.6 ± 9.4		-	Questionnaire
Body Mass Index (kg/m2)	BMI	25.8 ± 5.5		${\displaystyle \frac{W}{H^2}}$	Questionnaire
Age (years)	AGE	24.9 ± 7.9		-	Questionnaire
Ln of Squared PWV	LnPWV2	9.2 ± 0.2	8.6 ± 0.2	$Ln{({\displaystyle \frac{H}{PTTn}})}^2$	ECG, finger and toe PPG

provides the detailed hemodynamic, anthropometric, and temporal features that were used in this study. Other than the mentioned parameters, all of the products of feature pairs with a high dependency on BP were also selected. These pair-products included powers from −2 to 2 for each feature. So, any possible orthogonal, polynomial combination of the features was added to the features list.

D.

Estimation Algorithms

As the number of features grows in size, finding the best estimation algorithm becomes more challenging. In this study, we used multivariate regression analysis (MR) analysis which is currently being used in various studies [37,38,39].

MR is an approach that models a system to find the relationship between the inputs and the outputs. The simplest form of regression analysis is linear regression analysis as represented in Equation (11). Although a linear method was used in this study, since several non-linear features were used as the inputs, the behavior of the method is similar to polynomial models. If P is the matrix of features and B is the recorded BP, 1st-order (linear) MR analysis finds an equation that maps P on B, where a and b are coefficient and intercept matrices, respectively. $\widehat{a}$, $\widehat{b}$, and $\widehat{B}$ are the estimated values of a, b, and B. Eventually, MAE can be calculated using Equation (13).

$$P_{f\times n}=\mathit{Features}\mathit{Matrix}$$

(9)

where f is the number of features, and n is the number of subjects.

$$B_{1\times n}=\mathit{Measured}\mathit{Cuff}\mathit{Pressure}$$

(10)

$$B=a+bP$$

(11)

$$\widehat{B}=\widehat{a}+\widehat{b}P$$

(12)

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|\widehat{B}(1,l)-B(1,l)\right|}$$

(13)

When dealing with a large number of features, reducing the dimension of the matrices is crucial. The two common options to reduce the complexity are dimension reduction and feature selection [40,41]. In this study, the feature selection is employed. In parallel to finding a and b, the p-values of each feature are calculated. Then, the features with p-values greater than 0.07 are removed from the features matrix, P. Then, the regression analysis is performed on the validation group, and the overall p-value is calculated. If the p-value is not acceptable, a new set of training data is selected. When the validation is passed, SBP and DBP are estimated for the test group. Also, the values of MAE, r², and p-value are measured to check the performance.

In order to check the system performance, the ratio of mean arterial pressure (MAP) error lower than 5, 10, and 15 mmHg to the entire population of the test group are calculated. According to “The British and Irish Health Society (BIHS)” standard, the performance of BP monitoring devices can be evaluated in three grades: A, B, and C; where in a grade B device, 90% of the estimations for MAP have a cumulative error of less than 15 mmHg, 70% of the estimations have a cumulative error of less than 10 mmHg, and 50% of the estimations have a cumulative error of less than 5 mmHg [42].

E.

QRS Complex Detection

The QRS complex detection method is based on the first derivative of the ECG signal [43,44].

$$v_r[n]={\displaystyle \frac{1}{8}}(2u[n]+u[n-1]-u[n-3]-2u[n-4])$$

(14)

where u is the ECG signal and n is the sample number. Equation (14) applies a derivative-based filter and calculates vr (filter output) that distinguishes QRS complexes. Equation (14) is used to prevent the output to be affected by high-frequency noise [43,44]. After passing the signal through the filter, it was squared and a moving average window with 32-sample width was applied. Then, the peaks were detected by comparing v_r² with a certain threshold value.

F.

Dataset Construction

The dataset for this study was acquired using a custom-designed data acquisition system to simultaneously capture ECG and PPG signals from multiple sites. A total of 80 participants were enrolled in the study. Prior to participation, subjects completed a health questionnaire.

To ensure sufficient data for training, validation, and testing of the BP estimation models, the dataset was partitioned into three subsets: a training set (45 recordings), a validation set (10 recordings), and a test set (25 recordings). This partitioning strategy allowed for robust model development and evaluation. All data were stored in a structured database to facilitate efficient access and analysis.

G.

Experimental Testbed

The experimental setup was designed to mimic a controlled clinical setting. Participants were positioned in a seated posture to minimize movement artifacts and ensure consistent signal acquisition. ECG was recorded using three electrodes placed in a modified lead configuration to optimize signal quality. Simultaneous PPG recordings were obtained from the left index finger and the right hallux using optical sensors. Each recording session lasted for 3 min, during which participants were instructed to remain still and breathe normally. Reference BP measurements were taken using a calibrated automated sphygmomanometer (Omron) at the midpoint of each recording session.

3. Results

• Dataset Division and Preprocessing

The collected data were divided into three groups: training, validation, and test. The test group was kept separate, and all the analyses were performed on the training and validation groups. The training group included 45 recordings and the validation and the test groups had 10 and 33 recordings, respectively. There was no special rule to select the members of the training and test groups as they were randomly selected.

A Windows application was built with Visual C# 2017 (Microsoft, Seattle, WA, USA) that stored all of the recordings, subject information (i.e., weight), and record information (i.e., recording time) in a database that was designed using MySQL workbench 6.3 CE (Oracle, Redwood Shores, CA, USA).

The ECG signals were filtered based on Equation (13) and then were squared. The detected R peaks of ECG signals were also visually checked by a specialist to identify the false positive and negative points. The R peaks detection algorithm had an excellent performance of 100%.

The histogram of cuff-measured SBP and DBP are shown in Figure 5 where the mean of SBP and DBP were 123.96 ± 13.08 mmHg and 77.15 ± 8.88 mmHg, respectively.

B.

PPG Timing Analysis and PTT Comparison

Estimation of SBP and DBP was performed for three scenarios:

1: ECG and finger PPG;

2: ECG and toe PPG;

3: ECG, finger and toe PPG.

The PTT features of finger and toe PPGs are one of the features used in our method. As expected, the results indicate that the PTT of the finger PPG is shorter than the PTT of the toe PPG for all of the subjects as shown in Figure 6.

C.

Feature Selection and Model Construction

The features were then extracted from the collected data using MATLAB R2017a. Next, the dimension was reduced based on the significance of each feature in SPSS Statistics 25 (IBM, Armonk, NY, USA). Accepted variables (p-values< 0.07) are listed in

Table 4. Features from toe PPG.

Toe PPG Features	Coefficient
	SBP	DBP
Intercept	−322.53	56.16
Height	1.84	-
BMI	5.44	-
ACCtoe	−28.20	-
ACCtoe × HR	0.42	-
W2	−7.9 × 10−3	-
S2S1toe	6.55	-
(S2S1toe × AGE)2	-	−128.27
PTTntoe−1	-	145.66
PTTntoe2 × NN	-	−2.31
1/(S2S1toe × LnPTTtoe2)	-	−293.12
(LASItoe2)/AGE	-	−1.4 × 10−3
W/(LASItoe2)	-	−622.44

,

Table 5. Features from finger PPG.

Finger PPG Features	Coefficient
	SBP	DBP
Intercept	−241.15	110.20
Height	0.88	-
BMI	3.34	-
ACCtoe	−17.67	-
ACCtoe × HR	0.04	-
W2	5.1 × 10−3	-
S2S1toe	−0.40	-
(S2S1toe × AGE)2	-	−93.01
PTTntoe	-	17.77
PTTntoe × NN	-	−0.20
LnPWV2	20.61	-

and

Table 6. Features from combined (finger +toe) PPG.

Combined PPG Features	Coefficient
	SBP	DBP
Intercept	−973.61	132.06
Height	−0.27	-
BMI	4.95	-
ACCfinger	−66.27	-
ACCtoe	24.09	-
ACCtoe + ×HR	1.1 × 10−3	-
Weight2	−7.4 × 10−3	-
S2S1toe	7.37	-
(S2S1toe/AGE)2	-	−4.52
(LnPTTtoe)2/LnPTTfinger	-	10.08
LnPTTfinger/(LnPTTtoe)2	-	−7.89
(PTTntoe)2 × NN	-	−2.71
1/(LnPTTtoe2 × S2S1toe)	-	−211.40
(LASIfinger)2/AGE	-	−2.9 × 10−3
W/(LASIfinger)2	-	1.3 × 10−3
LnPWV2finger	122.38	-

to estimate the values for three different scenarios mentioned above. The calculations were performed with ‘automatic linear modeling’ of SPSS to extract p-values.

The value of the coefficients and the intercept were calculated with SPSS software. The relation between the pressure and multivariate regression (MR) features is described by Equation (15) [37,38,39], where n is the number of features, is the estimated blood pressure, I is the intercept, P_i is the ith feature, and α is the calculated coefficient represented in Table 4, Table 5 and Table 6.

$$\widehat{B}=I+{\displaystyle \sum _{i=1}^n({\alpha }_i\times P_i)}$$

(15)

D.

Estimation Accuracy and Comparison with Prior Work

The results from the proposed method are shown in

Table 7. Comparison of the mean and standard deviation of estimation error between two subject independent studies and our method, where: $MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|{\widehat{B}}_i-B_i\right|} \& SDE={\displaystyle \frac{1}{n}}{{\displaystyle \sum _{i=1}^n\left({\widehat{B}}_i-B_i\right)}}^2$.

Study	Signal	Method	SBP MAE ± SDE	DBP MAE ± SDE
Calibration-free Method#1 [19]	ECG and finger PPG	RLRLF	14.73 ± 18.5	7.24 ± 9.2
		RLRPF	14.46 ± 18.2	7.42 ± 10.0
		ANN	13.78 ± 17.5	6.86 ± 9.0
		SVM	12.38 ± 16.2	6.34 ± 8.4
Calibration-free Method#2 [17]	ECG and finger PPG	Linear regression	14.71 ± 10.8	6.74 ± 6.1
		Decision tree	16.28 ± 16.3	7.75 ± 8.5
		SVM	12.26 ± 10.3	5.91 ± 5.8
		AdaBoost	11.17 ± 10.1	5.35 ± 6.1
Our study	ECG, finger PPG, and toe PPG	MRfinger	10.28 ± 13.31	7.08 ± 9.18
		MRtoe	9.70 ± 12.62	6.93 ± 8.84
		MRboth	9.63 ± 12.54	6.76 ± 8.38

. The MAE and standard deviation of error (SDE) represent the accuracy and precision of the method, respectively.

.

E.

Regression Analysis of Estimated vs. Measured BP

Figure 7 illustrates the regression plot of estimated values versus the measured references. The R values of regression analyses for SBP and DBP estimations are 0.73 (SBP-finger), 0.72 (DBP-finger), 0.72 (SBP-toe), 0.78 (DBP-toe), 0.78 (SBP-both), and 0.73 (DBP-both), respectively.

F.

Bland–Altman and Error Distribution Analysis

Figure 8 shows the Bland–Altman plot of the estimators for finger DBP, finger SBP, toe DBP, toe SBP, both (finger + toe) DBP and both (finger + toe) SBP. Figure 9 illustrates the histogram of estimation error for finger DBP, finger SBP, toe DBP, toe SBP, both (finger + toe) DBP and both (finger + toe) SBP.

4. Discussion

• Device Innovation and Inclusion of Toe PPG

In this study, a continuous, cuff-less, and subject-independent BP estimation method is proposed based on features extracted from lead-I ECG in combination with both finger and toe PPG signals.

All the previous studies to estimate BP have used only finger PPG (except one that included forehead PPG signal [24]) in combination with ECG. None of that research has included measurements from the toe PPG. One practical reason behind this is that they have used open-source databases such as Physionet.org, and none of these databases have simultaneous finger and toe PPG data. For that purpose, we designed and developed a measurement device that is customized for this application. This device includes two PPG and one ECG inputs/amplifiers. We conducted an experimental study with human subjects to combine ECG measurements with simultaneous finger and toe PPG recordings. Importantly, our findings showed that the most accurate BP measurements are obtained when toe PPG is included in the calculations based on the physiological nature of the toe BP (SBP and DBP) (Table 7). Peripheral resistance and arterial compliance are directly affected by BP. As explained in Section II, finger PPG indicates more peripheral resistance, while the toe PPG displays more arterial compliance. According to Equation (6), arterial compliance is directly related to arterial BP and is also affected by arterial radius and stiffness. The arteries that provide blood to the toe PPG are larger and stiffer than the arteries that provide blood to the finger PPG. This results in more dependency on BP. Therefore, one major novelty of the study was to incorporate the toe PPG into the BP estimation which enhanced the system’s accuracy.

B.

Feature Extraction and Selection

The first group of features was extracted from the latencies between the QRS complex of ECG and distinguishable points of PPG signals including PAT, PTT, SPTT, and DPTT. The second group of features was measured based on the morphology of PPG signals such as LASI, IPA, and S2/S1 (see Section 2). Additional features involving height, weight, BMI, and gender were recorded from the questionnaires that were filled out by the subjects before taking the test. Features with the highest dependency on the output were selected, and the others were removed from the database. Previous calibration-based methods have specifically focused on PTT, PAT, HR, augmentation index (AI), LASI, IPA, S1, S2, S3, and S4 (see Section 2). However, in some studies, BP has been shown to be correlated to age, weight, height, gender, and BMI, which have never been used in any calibration-free techniques [31,32,33,35]. Therefore, another contribution of this study was to include, combine and analyze those features in relation to BP estimation. We thoroughly assessed each feature and calculated the p-values of their contribution to BP estimation, and we used only features that played a substantial part in the estimation, as shown in Table 3, Table 4 and Table 5.

C.

Performance of the Estimation Model

The strategy to check the performance of estimation was based on MR analysis which is the easiest technique to find the regression equation of a multivariate model. Using MR analysis, SBP estimation MAE was 10.28 ± 13.31 (finger), 9.70 ± 12.62 (toe), and 9.63 ± 12.54 (both) mmHg. The MAEs for DBP estimation were 7.08 ± 9.18 (finger), 6.93 ± 8.84 (toe), and 6.76 ± 8.38 (both) mmHg. According to the BIHS standard, this device can be categorized as a grade B automated BP monitor.

MR analysis techniques are powerful in modeling linear models but sometimes may have limitations in dealing with non-linear models. However, non-linear forms of inputs were included to obtain a better fit.

The results from MR analysis demonstrated that the toe PPG displays better results than finger PPG. Moreover, using both signals from the finger and toe PPGs further improved the performance of the estimator, as shown in Table 7.

D.

Comparison with Previous Calibration-Free Studies

Two of the key concerns regarding cuff-less and continuous BP measurement systems are their accuracy and requirement for periodic BP cuff-based readings. There are only a couple of studies that have come up with a calibration-free BP estimation [17,19]. No requirement for calibration can theoretically widen the clinical use of these methods and that was our motivation to introduce a technique that is subject-independent and does not rely on an initial cuff-based measurement. The results from one of the related previous studies, [19], reported MAE of 6.34 mmHg (DBP) and 12.83 (SBP) mmHg from a support vector machine (SVM) method, which provided the lowest error rate between the algorithms they covered. That study was based on machine learning strategies such as ANN, SVM as well as linear regression analysis. In a related study from the same team [17], they updated their algorithms and found the lowest MAE of 5.35 (DBP) and 11.17 (SBP) mmHg from their radial basis function (RBF) kernel SVM calibration-free method. The estimation error (MAE) from our method for DBP is 1.54 mmHg higher, and for SBP is 1.41 mmHg lower than the previous calibration-free studies. In addition, the r values of regression analyses showed that our method fitted the SBP estimation values on the reference values relatively better than other proposed methods [17,19]. Table 7 compares our results with the two other calibration-free studies [17,19]. Finally, the biggest difference of our work from those two studies was to include other parameters such as the toe PPG, HR, as well as anthropometric features (weight, height, BMI, etc.).

5. Limitations

There are several limitations to this study. The majority of the subjects were young students between the ages of 18 and 25, even though other age groups were also involved in the study. Cardiovascular physiology and arterial properties change with age, and our findings may not be directly applicable to older populations, who typically have a higher prevalence of hypertension and increased arterial stiffness. In addition, only eight subjects indicated they had cardiovascular conditions. While this number allowed us to include some hypertensive data in our analysis, it may not be sufficient to fully validate the method’s performance across the full spectrum of blood pressure ranges. A larger, more balanced sample, including a greater proportion of hypertensive individuals, would provide a more comprehensive evaluation of the method’s accuracy and reliability in this clinically important subgroup. Third, while our study demonstrates the potential of the proposed cuff-less BP monitoring technique, further research is needed to validate its performance in diverse real-world settings. Factors such as individual variability, physiological conditions, and environmental influences can affect the accuracy of BP estimation.

6. Future Work

The cuff-less blood pressure monitoring device developed in this study is portable, user-friendly, and equipped with Bluetooth data transmission capability, making it suitable for use beyond traditional clinical settings. Its practicality extends to outpatient monitoring and even self-monitoring at home, offering a convenient and less intrusive alternative to conventional methods. Future research should therefore focus on optimizing data transmission capabilities to facilitate seamless integration into daily life and personal health management. Further studies should also address the long-term reliability and accuracy of the device under diverse real-world conditions, including variations in environmental factors and user activity levels, to ensure its effectiveness for continuous and out-of-clinic blood pressure monitoring.

In future research, we plan to address the limitations of the current study by recruiting a larger and more diverse sample population with a wider age range and a higher proportion of individuals with hypertension, including subjects with diagnosed cardiovascular diseases, to validate the algorithm’s performance across a broader range of health conditions. We will extend our future study to include more subjects and subjects with cardiovascular disease history. We will also conduct studies in real-world settings, such as during daily activities and in clinical environments, and at different postures to evaluate the method’s robustness and generalizability. The testing was performed while the subjects were sitting in a chair, and their signals were not recorded at different postures. The effect of posture on BP estimation will also be investigated in another study. Further research will involve investigating the effects of various physiological and environmental factors on the accuracy of BP estimation and exploring methods to improve the accuracy and reliability of the algorithm for individual subjects, potentially through personalized calibration or adaptive algorithms. Exploring advanced machine learning techniques such as deep learning could potentially improve the accuracy and robustness of BP estimation. Investigating additional PPG features and their relationship to BP could lead to a more comprehensive model. Additionally, we plan to conduct long-term studies to assess the algorithm’s performance in real-world, ambulatory settings, and develop more compact and wearable sensors to facilitate continuous and unobtrusive BP monitoring. Finally, we aim to compare the proposed method with other cuff-less BP monitoring techniques and with the gold standard cuff-based measurements in a larger clinical trial.

7. Conclusions

In conclusion, the highlights of this study are to integrate the toe PPG measurements into cuff-less BP estimations; a unique customized design and development of a two PPG and one-channel ECG recording system; demonstration of enhanced BP accuracy when the toe PPG is included, and even better accuracy when both toe and finger PPG recordings are performed; a subject-independent system that uses an MR-based method towards the goal of improving the performance of cuff-less BP devices in clinical uses. This study also analyzes a total number of 15 features and selects those that meet dependency criteria.

The ability to monitor sudden changes in BP continuously and managing hypertension in the early stage can be significant to reduce cardiovascular events as well as costs related to cardiovascular diseases. Therefore, this study represents a novel effort towards a reliable, continuous, calibration-free BP device with improved estimation accuracy, and can potentially allow for wider clinical use of BP monitoring including ambulatory and home health care [20].