Combining Local PWV and Quantified Arterial Changes for Calibration-Free Cuffless Blood Pressure Estimation: A Clinical Validation

This study proposes a novel calibration-free cuffless blood pressure monitor (BPM). Unlike the cuffless BPM that requires timing correction with the traditional BPM, the calibration-free cuffless BPM can directly estimate the arterial blood pressure (BP) based on the hemodynamics mathematical model. Our proposed device integrates a pair of piezoelectric ceramics as pressure sensors to sense the pressure wave in the radial artery. It calculates the local pulse wave velocity (PWV) with our waveform detection algorithm of our proposed one. A photoplethysmogram (PPG) probe is set between the pair of pressure wave sensors. This PPG probe is used to monitor the radial artery’s PPG intensity ratio (PIR). We design PPG signal processing algorithms to quantify the PIR. We recruited 129 participants for the BP monitoring experiment. Compared with the reference sphygmomanometer, the error mean ± standard deviations (STDs) systolic BP (SBP) was 2.1 ± 3.4, and the correlation r-value was 0.97. The diastolic BP (DBP) was 0.8 ± 4.2, the correlation r-value was 0.90, and p < 0.05 is taken as statistically significant. A new type of wearable continuous calibration-free BPM can replace the situation that requires the use of traditional ambulatory BPM and reduce patient discomfort. Our proposed BP measurement passed all ANSI/AAMI/ISO 81060-2:20181_5.2.4.1.2 data analysis criterion 1 and 2 standard requirements.


I. INTRODUCTION
A CUFFLESS BPM is a BPM without an occluding cuff [1]. The difference between cuffless BPM and traditional BPM is that it does not need to pressurize the patient's arteries, reducing the discomfort caused by the procedure. Techniques used in this field include measuring physical parameters with electrocardiogram (ECG) and photoplethysmogram (PPG), Chi-Hung Huang is with the Division of Cardiology, Department of Internal Medicine, Cathay General Hospital, Taipei 10630, Taiwan (e-mail: hchbox@cgh.org.tw).
Tung-Li Hsieh is with the Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Sanmin, Kaohsiung City 807618, Taiwan (e-mail: tunglihsieh@gmail.com).
Digital Object Identifier 10.1109/JSEN.2022.3222588 phonocardiographic sensors, elastic modulus, dimensions, and stiffness of the intervening vessels, and establishing mathematical models to estimate blood pressure (BP) according to the sensor technology of choice. Ambulatory BP monitoring (ABPM) is the current gold standard for determining changes in an individual's BP and for determining hypertension [2]. Clinically, ABPM is valuable for controlling hypertension because it can better assess BP in patients with underlying hypertension affected by the white-coat effect [3]. However, patients wearing ABPM suffer from sleep disturbance as well as pain and skin irritation [4], [5]. Since cuffless BPM has no pressure cuff, it can greatly reduce the side effects and the interference of daily life and rest for patients using a traditional ABPM. Current cuffless BPMs [6] use ECG and PPG sensors to measure the pulse arrival time (PAT), convert it to pulse wave velocity (PWV), and then regress the measured PWV and the BP measured by the reference sphygmomanometer to get the correction coefficient [7]. However, studies have shown that PAT is affected by the pre-ejection period (PEP) [8], [9], meaning that PAT cannot accurately estimate PWV and, thus, BP. Moreover, in the current cuffless BPM correction procedure, the correction frequency needs to This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ be determined according to the technical details of different cuffless BPMs [10], and patients still cannot be exempted from the use of a traditional BPM. Even if the regression model is modified to a more complex machine learning model, using various physiological signal characteristics and demographics (e.g., age and sex) as parameters, and matching different hyperparameters to predict BP, it is unclear how much of the attained BP measurement accuracy, especially of the calibration-free device, is due to the actual hemodynamic measurement [11]. The Moens-Korteweg (MK) equation [12] in hemodynamics describes the relationship between PWV and BP, in which the arterial parameters must be considered. The characteristics of arterial hemodynamics differ between individuals, and only considering the correlation between PWV and BP would produce inaccurate BP measurements. To accurately estimate BP, calibration-free cuffless BPMs should not only be able to measure PWV accurately but also be able to monitor arterial distension. Since changes in arterial diameter ( D) correlate with pulse pressure (PP) [13], changes in arterial diameter can be quantified using the PPG intensity ratio (PIR) method. Therefore, this study proposes a calibration-free cuffless BPM measurement method using two piezoelectric sensors to measure the local PWV of the wrist radial artery combined with the physiological characteristics of arterial changes measured by the PPG probe. For this, we used a mathematical model based on hemodynamics to correlate PIR with arterial changes. This approach could integrate the sensor into a wearable device, affording more comfort to patients who require a traditional ABPM for long-term BP monitoring. II. OUR CONTRIBUTION We propose and implement a calibration-free cuffless BPM measurement method that uses a pair of piezoelectric sensors to measure the patient's pulse transit time (PTT) and convert it to local PWV. Also, we use a PPG sensor to detect the patient's PIR signals and quantify artery parameters using a hemodynamics-based mathematical model. Therefore, we have designed a wearable device that integrates these two sensors to achieve calibration-free cuffless BP monitoring. We verified it with ANSI/AAMI/ISO 81060-2, and our proposed BP measurement passed all ANSI/AAMI/ISO 81060-2:20181_5.2.4.1.2 data analysis criterion 1 and 2 standard requirements. This study provides patients with a solution to replace the traditional ABPM monitoring scenario, reducing patients' adverse reactions when BP is monitored for an extended period.

III. CALIBRATION-FREE METHOD OF
THE CUFFLESS BPM Our proposed method uses a pair of piezoelectric sensors and a PPG sensor set between them. These two types of sensors measure the pressure waveform and PIR of the patient's radial artery integrated with a PPG sensor, as shown in Fig. 1. The piezoelectric ceramic is rigid, and applying only a small deflection of the material is required to return a good signal. This makes the sensors very robust and tolerant of overpressure conditions and also means that they respond rapidly to changes in pressure [14]. Using a piezoelectric  sensor, rather than a PPG sensor, to measure PWV avoids the need to consider the different characteristics of the PPG signal and the difference in PWV measured by the derivative method [15]. Therefore, PPG is used to measure the patient's PIR in this study and is related to arterial parameters and PP through a mathematical model. Setting the PPG probe between the two piezoelectric sensors ensures that when both piezoelectric sensors sense the pressure of the pulse wave, the PPG sensor is also above the radial artery and can receive the artery expansion signal.

A. Local PWV Measurement
In previous studies, we developed a piezoelectric sensor and algorithm [16] that can be used for PWV detection. Fig. 2 shows the mechanical model of the piezoelectric sensor. The volume change V is generated when the pulse wave is transmitted via the induction period and skin motion. The internal pressure change P of the sensor is the sum of the pressure before pressurization P A and the pulse wave pressure P a . The mass that pushes the rubber to compress the air when the artery expands is S × L multiplied by the air density. Note that the air density is not constant during the pulsed cycle. According to Newton's law, we can find the force of the piezoelectric ceramic. The piezoelectric signal generated by the piezoelectric ceramic is the pulse wave. Fig. 3 shows the pulse wave sensor's analog front end (AFE). Our proposed device uses two pulse wave sensors and AFE. The output of the AFE is sampled by the 12-bit analog-to-digital converter (ADC) integrated into the microcontroller unit (MCU) of the ARM Cortex-M4 architecture. The sampling rate is 10 kHz, making the resolution of PTT in 0.1 ms. The parasitic capacitance of the piezoelectric ceramic is 8000 pF (at 120 Hz) [17]. The AFE can amplify the pulse wave signal, measured by the piezoelectric sensor, and filter it. Our filter design uses the second-order Sallen-Key architecture [18]. The cutoff frequencies of high-pass filters (HPFs) and low-pass filters (LPFs) are 0.58 and 10.6 Hz, respectively. The 12-bit ADC inside the MCU samples the pulse wave output  by the AFE at a sampling rate of 10 000 Hz. Through the finite impulse response (FIR) digital signal filtering algorithm running on the processor, the two-channel pulse wave sensor of the AFE output signal is filtered. Our design uses a bandpass filter of order 128 and uses the Kaiser window function, with the cutoff frequency set from 0.7 to 9.5 Hz [19], [20]. Based on the dynamic PWV detection algorithm developed in our past research, the PWV of the patient can be well detected. The algorithm can detect the feature points of the pulse wave and calculate the peak-to-peak value of the pulse wave signal at two different positions on the radial artery. As shown in the flowchart of Fig. 4, to determine the PWV between two pulse wave peaks, the time difference between the two pulse wave peaks at different positions needs to be converted to PTT after it can calculate PWV with PTT and two sensors' distance [21].

B. PPG Signal Process and PIR Estimate
When the pulse wave sensor detects the arterial pulse wave and can calculate the PWV, showing that the device is placed on the arterial segment of the human body, the PPG sensor is activated to sense the optical signal of arterial expansion. The PPG sensor is the MAX30101 integrated circuit produced by Analog Devices Inc. (ADI), which is a diffuse reflectance spectroscopy (DRS) sensor with three wavelengths of excitation light [22], [23]. The distance between the light-emitting diode (LED) and the photodiode (PD) is 3 mm. We set the ADC sampling rate of the PD to 100 Hz and the resolution to 18 bits. According to the Beer-Lambert law, the light path is arc-shaped. The photons start from the skin surface, penetrate deep into the tissue, before returning to the PD surface, and are converted to an electron signal [24]. The path depth of photons in tissue depends on the wavelength of light. We chose infrared (IR) light with a wavelength of 880 nm as our PPG signal for estimating arterial changes. IR light can penetrate deeper into the tissue than visible wavelength light and can therefore obtain more tissue optical information [25].
Using PIR to estimate changes in arterial diameter is a feasible method [26]. However, it is necessary to filter the PPG signal to quantify the PIR of arterial changes accurately. Also, we would need to design a feature recognition algorithm based on dynamic thresholds to detect the minimal level and highest level of the ac signal of the PPG. To filter the PPG signal, we use the FIR filter algorithm. First, an HPF filters the PPG signal, which is then filtered a second time by an LPF. We set the cutoff frequency of low-pass filtering to 7.5 Hz and the cutoff frequency of high-pass filtering to 0.75 Hz.
The PPG signal after FIR filtering can use the feature detection algorithm, based on the dynamic threshold, to detect the minimal level I L and highest level I H of the PPG signal. We use the window size of half the sampling rate to calculate the dynamic threshold. When the window size is shorter, the response speed of the dynamic threshold is faster, and it is more sensitive to the change rate of the PPG signal. Equation (1) is the calculation method of the dynamic threshold, in which (2) is the formula of covariance (CV), which is used to calculate the previous rate of change of the signal intensity. Before calculating the CV, the average value of the signal needs to be determined by (3). The root mean square (rms) is the amplitude level of the signal, see (4). The gain can be adjusted manually according to the performance of different sensors, and the gain level of the dynamic threshold is set to 1 in this study.
The dynamic threshold of the current PPG signal is determined through (1). This threshold can be input into the feature detection algorithm, which can dynamically identify the features in the PPG signal. The pseudocode of the feature detection algorithm proposed in this study is Algorithm 1 [27]. This algorithm can detect PPG signals of different amplitudes according to the dynamic threshold and label the feature points, as shown in Fig. 5, including the PPG signal's systole and diastole start points as well as the local maximum I H and the local minimum I L of the PPG signal. During the diastole phase, the arterial diameter is at its minimum level D d , the absorption of light by the blood volume in the artery decreases, and the diffuse light intensity is at its highest level I H . Conversely, during the systole phase, as the diameter of the artery increases to D s , the absorption of light due to higher blood volume in the artery increases, causing diffuse light intensity to decrease to the minimum level I L . D is the change in arterial diameter from diastole to systole during cardiac cycles. It should be noted that the definition of the relationship between the PPG signal and the diameter of the artery must differ according to the design of the amplifier for the PD signal of the PPG sensor, specifically whether it is a noninverting amplifier or an inverting amplifier.
To make the IR light penetrate as deep as possible into the tissue and to improve the signal-to-noise ratio (SNR) of the PPG signal, when measuring arterial changes, the system will detect whether I H is close to the saturation current 2 18 measured by the ADC. When it is not close to the saturation current, the system will continue to increase the current of the LED constant current source for the PPG sensor until it reaches the required constant current source. Then, the last unsaturated current parameter will be used as the current setting of the LED constant current source for the PPG sensor

C. PIR-Arterial Change Estimation Based on Hemodynamic Model
The feature detection algorithm can accurately determine I H and I L of the PPG signal, and the PIR signal of the artery can be estimated. However, to build a correlation model of PIRarterial diameter and PIR-PP, the arterial parameter D and arterial PP should be considered as hemodynamic parameters, and the mathematical model must be based on hemodynamics.
In a study on the PPG analysis of arteries wrapped under tissue by the Monte Carlo simulation [28], arteries of different sizes had different rates of change for the PPG ac signal, and the amount of photons absorbed depended on blood volume. Blood volume is directly related to arterial size, so larger diameter arteries have higher absorption, which can be quantified and used to determine the arterial size, see (5), by normalizing the ac and dc signals of the PPG signal. The artery is under 1 cm of tissue. There is, therefore, an obvious relationship between the diameter of the artery and the normalized PPG signal. Furthermore, the blood vessel phantom experiment was used to verify that the variation of the artery and the arterial diameter was proportional to the rate of change of the signal, which was consistent with the results of the Monte Carlo simulation. However, in practice, the dynamic removal of the dc signal of the PPG signal is not easy [29], affecting the ratio of the normalized signal and causing a deviation. Therefore, a more accurate PIR method is used to normalize the PPG.
The relationship between arterial diameter change versus I H and I L can be expressed as (6) and (7) by the Beer-Lambert law [30]. The arterial expansion and blood volume changes produced by the cardiac cycle allow the DRS sensor to receive an ac signal. The dc signal is a tissue component, including the optical tissue information of the subject's epidermis, muscle, fat, and arterial tissue. α DC = ε × c, where ε is the absorbance coefficient of human tissue and c is the material concentration of tissue and blood. d DC is the dc component of the optical path of photons in human tissue, including the optical properties of refraction and reflection produced by different layers of tissue media. The product of the two contributes to the dc signal source of the tissue's diffuse reflectance spectrum. D s and D d are the systolic and diastolic states of the artery with the progression of the cardiac cycle, respectively. Through (8), I H and I L can be expressed as a function of the diffuse reflection light signal for arterial expansion, as the ratio of I H to I L is the PIR signal of the DRS sensor. Therefore, we can express the systole diameter D s and the diastole diameter D d as formula (9) [31], which means that the PIR changes with the artery diameter change of the cardiac cycle. α is a constant related to the optical absorption coefficients in the light path. The subject's arterial expansion volume can be estimated by modeling the correlation function between the normalized PIR signal and the arterial expansion volume D The normalized PIR signal was obtained and used to build a PIR-arterial diameter correlation model. We used an ultrasonic imaging device (M-turbo ultrasound system from Sonosite Inc.) to obtain the radial artery's diastolic diameter and record the normalized PIR signal for modeling the PIR-arterial diameter correlation model. In previous studies, the arterial diameter D and the instantaneous diastolic arterial diameter D d differed by about 10% in each cardiac cycle, so it can be assumed that the two are approximately equivalent [32]. The MK equation of the hemodynamics model assumes an ideal circular and straight cylinder. Therefore, we selected different measurement points on the radial artery segment and averaged the artery diameter and wall thickness of the measurement points as the arterial parameters for building a correlation model to estimate the arterial expansion D and arterial diameter D, as shown in Fig. 6. We used an ultrasound probe to measure and annotate the diameter and wall thickness of the radial artery [33]. We measured the ultrasound probe pressure-free on the surface between 2 and 6 cm above the styloid process [34] and referenced the method used to assess the radial artery in systemic disease to measure the arterial diameter and intima thickness [35] (the method for assessing the radial artery in systemic disease). Previous studies have shown that the arterial change rate is correlated with PP [36]. The PIR-PP correlation model of this study uses the difference between the values of systolic BP (SBP) and diastolic BP (DBP), measured by aneroid sphygmomanometer to reference PP, and is precomputed with the normalized PIR signal.

D. Calibration-Free Cuffless BP Measurement
During a cardiac cycle, the physiological changes of the radial artery can be described as a mathematical model composed of arterial dimensions, stiffness indices, and PTT. The model can quantify the elastic modulus of the artery and describe the compliance of the arterial segment. The hemodynamics theoretical model of the physiological characteristics can be extended and applied to cardiovascular system research [37]. The relationship between arterial pressure P and arterial diameter D can be expressed as (10), where P d and D d are the end-diastolic pressure and diameter, respectively, and β constant is the stiffness parameter usually related to the elasticity coefficient of human arteries. Equation (11) shows that the change of arterial pressure difference and arterial diameter are the primary variables that determine stiffness. Therefore, we can calculate the variation of the arterial diameter through the differential equation of the arterial pressure in (12), for the arterial diameter. Since the arterial diameter D and the instantaneous diastolic arterial diameter D d differ by about 10% in each cardiac cycle, we can replace the arterial diameter term with the arterial cross-sectional area dA, as in (13), where the cross-sectional area A of the artery is calculated as A = (π/4) D 2 [38]. According to the Bramwell-Hill (BH) model [39], pressure pulses in the arteries produce local PWV. The local PWV can be expressed as intra-arterial pressure changes, and the PP is a function of the change in the arterial crosssectional area, as in the modified BH model of (14), where ρ is the blood density. This study used the density of healthy human whole blood at 1.06 g/mL to calculate the parameter [40]. Equations (13) and (14) can be combined to obtain (15), which determines the value of the arterial local PWV in a cardiac cycle, dependent on the cross-sectional area gradient and the intra-arterial pressure level The BH model relates PWV to arterial compliance dA/dP, blood density ρ, and arterial cross-sectional area A, derived from the MK equation [41]. The MK equation is based on hemodynamics, such as with (16), (17), and (19). The MK equation describes the relationship between PWV and BP, where D is the diameter of the radial artery and h is the wall thickness of the radial artery, otherwise called intima-media thickness (IMT), ρ is the average density of whole blood, PTT is the pulse wave time difference measured by the relative distance L between the sensors, E is Young's modulus, P is the pressure, and E 0 and γ are coefficients with values of 1428.7 and 0.031, respectively [42]. Although E 0 and γ depend on the stiffness of the radial artery and vary between individuals [43], this study used mean values from previous clinical studies, assuming that E 0 , γ , and ρ are constants, for validation. We combined (16) and (17) to obtain (18), where P in the MK equation approximates mean arterial pressure (MAP) [44]. So far, combining the PIR-arterial diameter correlation model and the PIR-PP correlation model, we can estimate the subject's MAP, PP, D, and arterial diameter D. Also, we can use the MK equation to enumerate the possible radial artery wall thickness h by assuming a reasonable range for MAP and using the recalculated MAP to track SBP and DBP with PP Fig. 7 shows the calculation flow of the calibration-free cuffless BPM proposed in this study with the aforementioned theoretical model. First, the sensor detects the participant's pulse wave and PIR signal at the same time. The participant's local PWV can be calculated from the two pulse wave signals through our proposed algorithm, and the PIR can be measured using the DRS sensor. The normalized PIR signal is input into the prebuild PIR-arterial diameter and PIR-PP correlation models and a participant's estimated values of PP, D, and D d can be obtained. Since the wall thickness h of the participant's radial artery cannot be measured and estimated by the diffuse reflection light sensor, we refer to the known clinical research literature, assuming that the human MAP has a reasonable range under normal conditions [45]. Therefore, the MAP calculated by the MK equation has upper and lower bounds. Through the MK equation, the arterial wall thickness can be increased in 0.01 mm increments according to the arterial characteristics measured for different individuals. The possible range of the participant's arterial wall thickness can be enumerated, and the average value can be taken as the individual wall thickness parameter h. As shown in the enumeration algorithm of Algorithm 2, with h ranging from 0.01 to 1 mm in the MK equation calculation of MAP, if MAP exceeds the reasonable range, the value of the wall thickness must be unreasonable and vice versa. Therefore, the wall thickness value is considered reasonable if the MAP is within the reasonable MAP range. Since the MK equation is a nonlinear function, this enumeration can find a reasonable range of wall thickness according to the parameters of different individuals. This study chose to average this reasonable range as the individual radial artery wall thickness h. Finally, our proposed calibration-free cuffless BPM will extend the MAP and PP calculated by the MK equation to SBP and DBP with the formula of (20) [46]. The coefficient k in this study was set according to the clinical results and here is 0.76 IV. CLINICAL STUDY AND RESULT This study was approved by the Institutional Review Board (IRB) of the Cathay General Hospital, Taipei, Taiwan, and conducted according to the Declaration of Helsinki ethical principles for medical research on human participants. Each participant signed an informed consent form as defined by the IRB. The study protocol is retrospectively registered with the Taiwan Food and Drug Administration (IRB protocol number: CGH-P108003). In the clinical analysis in this section, our proposed calibration-free cuffless BPM is called Accurate24 BPM, and the sphygmomanometer for reference is called SM. The participants were equipped with Accurate24 BPM on the left wrist, sitting position with the wrist at heart level to remove hydrostatic pressure differences. A sphygmomanometer cuff of appropriate size was positioned on the participant's left upper arm at heart level. Study participants were comfortably seated with their backs and arms supported.

A. Study Protocol and Population
This comparative study followed ANSI/AAMI/ISO 81060-2:20181 [47]. Male and female volunteers totaling 129 subjects were included. The algorithm passed Criterion 2. The distribution of SBP and DBP is shown in Fig. 8(a) and (b), respectively. BP measurements were taken by trained observers in stations. The clinical study method stated that observers shall be trained in using the proper methodology for performing a resting BP reading with the SM (reference reading) and an Accurate24 BPM device reading (subject under test) lasting at least 60 s, interchanging the reference and subject devices, with three replications of the process.
All data from a subject were excluded if the following conditions hold. 1) Any two reference SBP values differed by more than 12 mmHg (160 kPa).

B. Statistical Analysis
In this study, two measurement methods were compared: the novel method in this study (the Accurate24 BPM device) and an established one (a standard Korotkoff manometry device). We aimed to determine whether these two methods could be used interchangeably and whether our novel method could replace the established one.
In this study, the collected data for BP measurements were analyzed for mean, maximum, minimum, median, standard deviation (STD), and confidence values (Tables I and II). If the novel measurement technique agreed sufficiently with the established technique, it would be possible to replace it. Agreement between these techniques was analyzed using the Bland-Altman method, which calculates the mean difference between two methods of measurement (the "bias") and looks at the 95% limit of agreement of the mean difference 2STD. It is expected that the 95% limit includes 95% of differences between the two measurement methods. The presentation of the 95% limits of agreement allows for visual judgment of how well two methods of measurement agree. The smaller the range between these two limits, the better the agreement. Linear correlation is a measure of dependence or association between two random variables. The correlation provides a measure of the degree to which these two variables tend to "move together." The Pearson correlation coefficient is bounded between −1 and 1 making it easy to understand the intensity of the linear dependence between two random variables. The closer the correlation coefficient is to 1, the greater the positive linear dependence between the variables, and the closer it is to −1, the greater the negative linear dependence between them. When the correlation equals zero, the variables do not display any of these two tendencies. The Accurate24 BPM device application was compared to a standard Korotkoff manometry device and the differences between their readings were analyzed as explained in the following.

C. Result
One hundred twenty-nine subjects had valid data sets and were included in the analyses, of which there were 40 females and 89 males. The Pearson correlation and Bland-Altman  analysis between Accurate24 BPM and SM are shown in Table III. For the SBP analysis, we found that R 2 = 0.94, which means that R = 0.97, showing that 97% of the data sets are, or are very close to, equal. For the DBP analysis, we found that R 2 = 0.81, which means that R = 0.90, showing that 90% of the data sets are, or are very close to, equal.
The Mean and SD of the validation study results of criterions 1 and 2 between the reference SM and subject device readings are shown in Table IV.
The ANSI/AAMI/ISO 81060-2:2018 Standard Criterion 1 requires a mean ±SD difference of ≤5 ± 8 mmHg. The Midmark algorithm clearly passed this criterion. Criterion 2 requires a smaller SD value, using a sliding scale depending on the mean SBP and DBP differences. For SBP, the mean value of 2.15 mmHg gives an upper limit for SD of 6.58, and for the DBP difference of 0.75, the upper limit for SD is 6.89. The algorithm passed criterion 2. The required Bland-Altman plots of SBP and DBP are shown in Fig. 9(a) and (b), respectively.
The Accurate24 BPM device was compared to the gold standard SM device by plotting a visual chart expressing the correlation between their readings in Fig. 10(a) and (b).
Another protocol, from the European Hypertension Society, expresses the data distribution as the percent of readings within 5, 10, and 15   BPM measurements according to the international protocol (revision 2010) [48], data are shown in Table V and Fig. 11.

D. Discussion
The data demonstrated that the Accurate24 Noninvasive BP monitor (BPM) for BP measurement passed all ANSI/AAMI/ISO 81060-2:20181_5.2.4.1.2 data analysis criterion 1 and 2 standard requirements. The Accurate24 Noninvasive BPM also surpassed requirements for the European Hypertension Society protocol data analysis for both SBP and DBP. These tests in adults show that the Accurate 24 BPM sensors and applications achieved the required range and were defined as having acceptable error levels by the European international protocol for BP devices, as shown in Table V. For accuracy in ≤5 mmHg, the proportion of Accurate24 BPM in SBP and DBP is 86.8% and 85.8%, respectively, both of which meet the European international protocol (73%). For accuracy in ≤10 mmHg, the proportion of Accurate24 BPM in SBP and DBP is 99.0% and 98.7%, respectively, both of which meet the European international protocol (87%). For accuracy in ≤15 mmHg, the proportion of Accurate24 BPM in SBP and DBP is 100% and 100%, respectively, both of which meet the European international protocol (96%).

V. LIMITATIONS AND FUTURE WORKS
Although the calibration-free cuffless BPM proposed in this study passed the clinical gold standard, according to the   estimation. Therefore, finding a feasible technical means to measure the arterial stiffness of subjects noninvasively, and to calculate the nonlinear function of the arterial stiffness for each subject, would reduce the overall BP estimation bias. Normal subjects' arterial blood contains dyshemoglobin, which is a hemoglobin derivative. The two dyshemoglobins that affect tissue oxygenation are methemoglobin (MetHb) and carboxyhemoglobin (COHb), which are usually present in low concentrations in normal subjects in the blood [49]. The main substances that absorb IR light in the blood are oxyhemoglobin and hemoglobin. The absorption ratio of MetHb and COHb is low. However, when the subject is carbon monoxide poisoning or exposed to some chemical, it may increase MetHb and COHb [50]. In this study, using single-wavelength quantitative technology may cause errors, so multiwavelength quantitative technology is a future research direction that can quantify more substances to reduce inaccurate factors.

VI. CONCLUSION
This study proposes a new calibration-free cuffless BPM technique, which uses a pair of high-sensitivity piezoelectric sensors to measure the local PWV, and a DRS sensor to quantify the PIR signal, of the radial artery. With this, we used principles based on hemodynamics and tissue optics to estimate BP. Our proposed calibration-free cuffless BPM has been clinically validated, showing that the technology passed all ANSI/AAMI/ISO 81060-2:20181_5.2.4.1.2 data analysis criterion 1 and 2 standard requirements. In the trend of popularization of home medical care in the future, we believe that the sensing technology in this study can be integrated into wearable devices, with measurements based on hemodynamics, making it possible to provide beat-to-beat BP monitoring. This advantage could enable future research on hypertension to shorten the monitoring period from every hour to every minute. The improved performance of BP monitoring technology provides a powerful new tool for research in hypertension.

ACKNOWLEDGMENT
Cheng-Yan Guo, Chi-Hung Huang, Chia-Chi Chang, Tung-Li Hsieh, and Kuan-Jen Wang conceived the presented idea. Chia-Chi Chang and Cheng-Yan Guo developed the theory and performed the computations. Chia-Chi Chang, Tung-Li Hsieh, and Cheng-Yan Guo verified the analytical methods. Chi-Hung Huang and Kuan-Jen Wang encouraged the investigation (a specific aspect) and supervised the findings of this work. All authors discussed the results and contributed to the final manuscript.