1 Introduction

Cardiovascular diseases are considered the leading cause of death globally [17]. The disease is preventable with an early diagnosis and can be stopped with a right treatment [32]. Atherosclerosis is an endovascular disease that causes inflammation of vessel walls and accelerates the stiffening and aging [23] of the arteries. In addition, due to stiffer arteries, the workload of heart is increased [28], which leads to the development of left ventricular hypertrophy and heart failure [31]. In the late stages of the atherosclerosis, the plaques built up to the walls of the arteries, may rupture and cause blockage of blood flow to the other organs [4]. Different methods have been developed to detect changes in the arteries in an early stage [25].

Augmentation index (AIx) is a parameter that has been used to assess the status of the cardiovascular system and arterial stiffness [8]. The AIx can be used to evaluate cardiovascular risk [18]. The SphygmoCor device has been widely used to estimate the aortic AIx in clinical settings [2, 16]. However, the estimation can be time-consuming; it requires a trained operator and it is intermittent.

Photoplethysmographic (PPG) technology is relatively inexpensive and during the last years, it has gained popularity to assess the status of the cardiovascular system [3]. PPG is a non-invasive optical method that can be mainly used to detect relative volume changes in the arteries and the microvascular bed of the tissue. The pulsatile component of the PPG signal is related to the heart activity and the pulsatile waveform is very similar to the pressure waveforms registered by tonometry [10]. The PPG signal waveform analysis has been used to estimate arterial stiffness and vascular aging using time [33] and frequency domain [1] methods. According to [21], the AIx derived from the PPG signal waveform was denoted as PPGAI can be considered as a perspective measure for the AIx and increased arterial stiffness estimation in clinical screenings.

The PPG signal can be registered using a transmission or reflectance mode sensor attached to the body joints or the surface of the skin, respectively. The contact pressure is applied to the sensor in both modes to achieve better signal quality in terms of the higher amplitude of the AC component of the PPG signal [9, 15, 29]. The transmural pressure (Pt) is the difference between the intra-arterial blood pressure (Pa) and the external pressure (Pext):

$${P}_{\text{t}}={P}_{\text{a}}-{P}_{\text{ext}}$$
(1)

The external pressure can be the contact pressure of the PPG sensor. The non-linear relationship between the transmural pressure and the blood volume is known from the theoretical [30] and practical [26] studies. The amplitude of the AC component of the PPG signal is lower at higher and lower transmural pressures, reaching its maximal value around 0 mmHg. This behaviour has been utilized, for example, in the smartphone-based BP measurement via the oscillometric principle [5]. Changes in the morphology of the PPG waveform due to the sensor contact and transmural pressure alteration reported in [15, 26] affect the pulse arrival time measurement for the blood pressure estimation [6], heart rate measurement [24], as well as the second derivative PPG waveform analysis for the arterial stiffness estimation [13].

In the study by Grabovskis et al. [13], the influence of the PPG sensor contact pressure on the variation of the second derivative PPG signal analysis parameter b/a was determined. The PPG signals were registered from the conduit arteries of five subjects and the optimal contact pressure was determined according to the minimal variation of the stiffness related parameter. However, the effect of arterial blood pressure was not taken into account neither were the reference stiffness parameters measured and compared with b/a in order to find the contact pressure suitable for the analysis.

Based on the previous studies, it can be assumed that the transmural pressure, which is related to the sensor contact pressure and the intra-arterial pressure (arterial blood pressure), affects the PPG waveform and the parameters derived for the arterial stiffness estimation. Particularly, the transmural pressure may affect the aortic AIx related PPGAI and therefore impact the assessment of arterial stiffness. None of the previous studies give a recommendation of the transmural pressure suitable for the PPG registration for the pulse waveform analysis to estimate arterial stiffness, which is as well the novelty of the study. Furthermore, it is not known how the transmural pressure affects the AIx that is derived from the PPG signal to assess the status of the cardiovascular system. The aim of this study was to analyse how the transmural pressure affects the PPGAI estimation and its relationship to the aortic AIx estimated by a SphygmoCor device. In addition, suitable transmural pressure was explored as an optimum of the PPGAI determination to estimate arterial stiffness.

2 Methods

2.1 Subjects

The study was carried out on 51 volunteers with moderately active lifestyle, without diagnosis of cardiovascular disease and medication. Informed consent was obtained from the subjects and they were interviewed before the study. All the subjects were non-smokers and having normal dietary.

This study has been approved by the Tallinn Ethics Committee on Medical Research at the National Institute for Health Development, Estonia, and the research was conducted in accordance with the Helsinki Declaration.

2.2 Experiment setup

The experiment setup is displayed in Fig. 1a. The Finometer sensor (Finapres Medical Systems, Netherlands) consists of a small cuff that can be wrapped around a finger, an integrated LED, and a photodiode (Fig. 1b). In our study, three Finometer sensors were used. One sensor was wrapped around the middle finger and connected to the Finometer device (Model-1 Pro, Finapres Medical Systems, Netherlands) for blood pressure waveform registration and beat-to-beat finger blood pressure calculation. The second and third sensor were wrapped around the index and ring finger and optical components were connected to the lab-built PPG module for the PPG signal registration. The index finger sensor was used to register the PPG signals at different applied contact pressures. The ring finger sensor was used to register the PPG signals at the contact pressure of 50 mmHg and it served as a reference PPG signal in order to detect changes in the waveform during the experiment. It has been found that there are no statistically significant differences in PPGAI between fingers of the same hand [22].

Fig. 1
figure 1

a Overview of the experiment setup with b Finometer sensor

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Small cuffs of the Finometer sensors enabled us to apply different levels of sensor contact pressure to the index finger and constant contact pressure to the ring finger and simultaneously register the PPG signal as it consisted of an integrated LED and a photodiode. Therefore, in our study, the Finometer sensor was suitable for the PPG signal registration. The integrated LED and the photodiode of the Finometer sensor were located on the opposite sides of the index and ring finger. Therefore, the PPG signal was registered in the transmission mode. The average wavelength of LEDs was 933 ± 1.7 nm, which was detected using an Ocean Optics spectrometer HR2000 (Ocean Optics, USA). The LEDs were pulsed with the frequency of 125 Hz and the duty cycle of 25%. The current of the LEDs was adjusted manually before the recording of the signals in order to keep the PPG signals in the dynamic range of the system. The photo current from the photodiodes was directed to the transimpedance amplifiers of the lab-built PPG module.

The Finometer sensor cuffs wrapped around the index and ring finger were pneumatically (using silicone tubes) connected to the pressure sensors, air reservoirs and syringes to apply different contact pressures.The pressure in the cuffs was adjusted manually using 50 ml syringes. The syringes were filled with air and connected to the system. Thereafter, air was pumped to the system to increase the pressure in the cuffs. The pinch clamps were closed after the pressure was increased to the desired level. The reservoirs were used in order to increase the compliance of the system, which acted as a low pass filter and reduced rapid changes in the pressure of the cuffs. The pressure in the cuffs was measured using two differential pressure sensors (SSCSNBN005PDAA5, Honeywell). The second input of both pressure sensors was left open in order to compensate the changes in the atmospheric pressure. The relationship between the applied pressure and the output voltage of the sensor was determined using a calibrated pressure tester NEO-2 Meter (AUTOMATA Instrumentation, USA) prior to the experiments. The air leakage of the pneumatic system was 1 mmHg per 5 min at 110 mmHg, which was considered sufficient for the experiments.

The Finometer device (Model-1 Pro, Finapres Medical Systems, Netherlands) was used to measure the blood pressure waveform in the finger. The Finometer sensor that was wrapped around the middle finger of the subject was connected to the Finometer device and it registered the continuous pressure waveform from the finger using the volume-clamp method, which was initially introduced by Penaz [19]. The finger pressure waveform was directed to the analogue output of the Finometer device.

The lead II ECG signal was registered using one channel ECG OEM module EG 01000 (Medlab, Germany) for the detection of the cardiac cycle. The analogue signal was directed from the battery powered ECG module to the optocoupler to ensure the galvanic decoupling from the rest of the system for safety reasons of the subject.

The voltage signals from the transimpedance amplifiers, pressure sensors of the cuffs, ECG module and the Finometer device were digitized synchronously with the sampling rate of 5 kHz using the data acquisition card DAQCard-6036E (National Instruments, USA) for PCMCIA. The signals were recorded using the custom made LabView (National Instruments, USA) programme. The ECG, cuff pressure, and Finometer signals were downsampled to 125 Hz. In the LabView algorithm, the optical signal was detected while the LED was turned on and off. The ambient light was removed by subtracting the optical signal while the LED was turned on from the optical signal whereas the LED was turned off. For each cycle, one sample of the PPG signal was obtained. As a result, all the signals were recorded with the sampling rate of 125 Hz. Considering that the PPG signal waveform consists approximately of 10 harmonic components [27] and the maximal heart rate is not exceeding 120 beats per minute while the subject is in supine position, 125 Hz should be a sufficient sampling rate for the PPG signal.

The arterial blood pressure was measured and the aortic AIx was determined separately from the signal acquisition system. The blood pressure was measured from the upper arm using an Omron M3—HEM-7131-E (Omron, Japan) oscillometric blood pressure monitor. The aortic AIx was determined using a SphygmoCor EM3 (AtCor Medical, Australia) device and accompanying software Cardiovascular Management Suite Version 9 (AtCor Medical, Australia). The pressure waveform was registered from the radial artery of the left hand using applanation tonometry. The pressure signal was registered by a trained and experienced operator. The length of each recorded signal was about 10 recurrences. After recording, the SphygmoCor software assesses the signal quality in the scale from 0 to 100. All the recorded waveforms had an operator index of 90 and above. Thereafter, the software converts the radial artery waveform to the aortic waveform using the validated general transfer function [7]. The inflection point is detected from the waveform and the augmentation pressure is calculated (Fig. 2). The aortic AIx is calculated using the following equation:

$$AIx\left(\%\right)=\frac{AP}{\left(SBP-DBP\right)}\cdot 100=\frac{AP}{PP}\cdot 100$$
(2)

where SBP is systolic blood pressure, DBP is diastolic blood pressure, PP is pulse pressure, and AP is augmentation pressure. The SphygmoCor software normalizes the AIx to the heart rate of 75 bpm as the AIx depends on the heart rate according to the study by Wilkinson et al. [34]. The heart rate normalized AIx is denoted as AIx@75.

Fig. 2
figure 2

One period long aortic pressure waveform with the augmentation pressure (AP) and pulse pressure (PP)

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2.3 Experiment protocol

The subjects were in supine position at least for 5 min prior to the experiment. The room temperature was monitored and kept constant at 22 ± 1 °C. The blood pressure was measured from the dominant hand of the subject using Omron oscillometric blood pressure monitor, which was followed by signal registration from the radial artery with a SphymoCor device and the aortic AIx@75 was determined. The blood pressure measurement and AIx@75 determination were carried out consequently for three times. Thereafter, the Finometer sensors for the registration of PPG signals were placed to the index and the ring finger of the left hand. The third Finometer sensor for the beat-to-beat blood pressure measurement was placed to the middle finger of the left hand. The size of the finger cuff was selected according to the circumference of the middle finger. The subject was asked to keep the left hand in a relaxed stationary condition beside the body. The electrodes were attached to the chest of the subject and connected to the ECG module.

After attachment of the sensors and electrodes, the blood pressure signal acquisition with a Finometer device was started. Thereafter, the pressures in the cuffs of Finometer sensors at the index and the ring finger for the PPG signal registration were increased to 20 mmHg and 50 mmHg, respectively. The currents of the LEDs were adjusted manually for the PPG signal registration. The PPG signal was set to half the full dynamic range of the PPG module at the beginning of the experiment. Thereafter, the signal recording started with the LabView programme. The cuff pressure at the index finger was increased from 20 to 120 mmHg with the step of 10 mmHg. At each cuff pressure, at least 1-min long signals were recorded. The feedback resistor in the transimpedance amplifier was decreased manually in case the PPG signal reached the maximal value of the module output. The current of the LED remained unchanged during the whole experiment.

2.4 Signal processing

Signal post-processing was carried out in MATLAB (Mathworks, USA). One-minute long PPG, ECG, blood and cuff pressure signal segments were extracted for each level of the index finger cuff pressure. The R-peaks were detected from the ECG signal using the Pan-Tompkins algorithm [20]. The R-peak determines the start of each cardiac cycle; therefore, from the signal processing point of view, it was easier to detect the rest of the distinct points from the blood pressure and PPG waveforms. The PPG signal was filtered with a low- and high-pass filter with the edge frequencies of 30 Hz and 0.5 Hz, respectively. The Parks-McClellan equiripple filter was used with ripples of 0.001 in the pass and stop-band. To determine PPGAI from the index and the ring finger PPG signal waveform, the algorithm from our previous study [21] was used. The length of each period of the signal is normalized to the 1-s long segment. The number of harmonic components of each segment is limited to six. The amplitudes of the PPG signal are determined at the locations, where the ‘b’ and ‘d’ wave peaks of the second derivative PPG signal are detected, as shown in Fig. 3. The second derivative PPG signal was obtained using the Smooth Noise Robust Differentiator [14]. The PPGAI was calculated using the following equation:

$$PPGAI=\frac{{A}_{\text{d}}}{{A}_{\text{b}}}$$
(3)

where Ab and Ad are the amplitudes of the PPG signal at the location of the peaks ‘b’ and ‘d’ of the second derivative signal. As a result, for every cardiac cycle, the PPGAI value was calculated for the index and ring finger PPG signal waveform.

Fig. 3
figure 3

a PPG signal with amplitudes for the PPGAI calculation and b second derivative of the PPG signal with detected waves ‘b’ and ‘d’

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Beat-to-beat systolic and diastolic finger blood pressure values were obtained by detecting the maximal and minimal values of the blood pressure signal for each cardiac cycle, respectively. Each 2 min, the Finometer device carries out two cardiac cycle long calibration of the operating point and therefore the finger pressure signal is flat. All the PPGAI values were excluded during the calibration of the Finometer device.

2.5 Data analysis

For each subject, the average of the three consecutive SphygmoCor AIx@75 measurements was calculated and denoted as AIx@75avg.

The mean blood pressure (PfMAP) of the middle finger was calculated for each cardiac cycle based on the systolic (PfSYS) and diastolic (PfDIA) pressure values from the Finometer signal using the following equation:

$${P}_{\text{fMAP}}={P}_{\text{fDIA}}+0.3\cdot \left({P}_{\text{fSYS}}-{P}_{\text{fDIA}}\right)$$
(4)

Transmural pressure (Pt) was calculated for each cardiac cycle based on the cuff pressure (Pc) and the mean arterial blood pressure of the middle finger:

$${P}_{\text{t}}={P}_{\text{fMAP}}-{P}_{\text{c}}$$
(5)

Data analysis of the PPGAI and Pt is given in Fig. 4. The average transmural pressure (Pt_avg) at the cuff pressure Pc was calculated for each 1-min long signal segment of the subject. In addition, the average transmural pressure over all subjects (Pt_AVG) with a standard deviation SDPt_AVG was calculated at each cuff pressure Pc. The average (PPGAIavg) and standard deviation (SDPPGAI) of the PPGAI values were calculated for every average transmural pressure (Pt_avg) and for each subject. It has to be noted that for each subject, one AIx@75avg value corresponds to every PPGAIavg value at a different cuff pressure as it is assumed that the average AIx does not change during the experiment time. Nevertheless, the PPGAI variation during the experiment was monitored using the reference PPG signal registered from the ring finger. The SDPPGAI was averaged over all subjects for each cuff pressure and denoted as SDPPGAI_AVG. The Pearson correlation coefficient (r) between AIx@75avg and PPGAIavg was calculated for each Pt_AVG with p-values.

Fig. 4
figure 4

Overview of the data analysis of PPGAI and Pt

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The absolute value of PPGAI varies between the subjects as it is related to the vascular age of the subject. For example, the PPGAI value of the healthy 24- and 54-year old subject is 0.91 and 1.19, respectively [16]. Therefore, the PPGAI value varies due to the transmural pressure around 0.91 and 1.19 and the results are difficult to compare and generalize. Therefore, the PPGAI values for each subject were normalized (PPGAInorm) according to the maximal value over all PPGAIavg at different cuff pressures as follows:

$$PPGA{I}_{\text{norm}}=\frac{PPGAI}{{\text{max}}\left(PPGA{I}_{\text{avg}}\right)}$$
(6)

In addition, for each subject, the averages of PPGAInorm for each averaged transmural pressure (Pt_avg) were calculated, which is denoted as PPGAInorm_avg. Furthermore, the average of PPGAInorm_avg over all the subjects was calculated and denoted as PPGAInorm_AVG.

3 Results

Basic characteristics of the subjects are given in Table 1 and all the values for each subject are given in the supplement material. The signals were successfully recorded from all the 51 healthy volunteers.

Table 1 Basic characteristics and registered physiological parameters of the subjects. Body mass index is denoted as BMI. The values are given as Mean ± SD (min–max)
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The characteristic relationship between the transmural pressure (Pt) and the normalized PPGAI values (PPGAInorm) for all subjects is presented in Fig. 5. The figure shows that the PPGAI value depends on the transmural pressure. It can be seen from the normalized average PPGAI (PPGAInorm_AVG) results that the decrease in the transmural pressure below 38 mmHg causes a decrease in the PPGAI values. The PPGAInorm values become statistically significantly different (p < 0.05) starting from the transmural pressures of 47 mmHg and lower. The PPGAI values from the ring finger PPG signal at the beginning and at the end of the experiment were not statistically significantly different (p = 0.89). The average standard deviation of the reference PPGAI over all the subjects was 0.056.

Fig. 5
figure 5

The relationship between the transmural pressure (Pt) and the normalized PPGAI (PPGAInorm) values for all subjects. Each data point given in black dot represents the PPGAInorm value for one period of one subject. The red data points represent the averaged PPGAI (PPGAInorm_AVG) and the transmural pressure (Pt_AVG) values at each sensor contact pressure (Pc)

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The relationship between the transmural pressure (Pt) and the normalized PPGAI (PPGAInorm) for one subject (28-year old male subject) is presented in Fig. 6. The waveforms show the averages over all the periods during 1-min long signal segment at a given sensor cuff pressure. The normalized PPGAI values tend to scatter at higher transmural pressure values due to the low cuff pressure of the sensor. In addition, it is visible that the waveforms are similar at lower transmural pressures, which could be observed as well in other subjects.

Fig. 6
figure 6

The relationship between the transmural pressure (Pt) and the normalized PPGAI (PPGAInorm) values, and averaged and normalized PPG waveforms with average transmural pressure (Pt_avg) and cuff pressure (Pc) values for a 28-year male subject

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The dependence between the averaged transmural pressure (Pt_AVG) and the averaged PPGAI standard deviation (SDPPGAI_AVG) is shown in Fig. 7. The minimal standard deviation was obtained at the transmural pressure of 10 mmHg, which corresponds to the sensor cuff pressure of 80 mmHg in this study. In addition, low standard deviation could be observed as well at the transmural pressure of 20 mmHg.

Fig. 7
figure 7

The relationship between the transmural pressure (Pt_AVG) and standard deviations (SDPPGAI_AVG) of PPGAI

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The correlation between the AIx@75 and the PPGAI values was calculated for all sensor cuff pressures. Figure 8 shows the relationship between the transmural pressure and the correlation coefficients. Clearly, the correlation coefficients are relatively high (r > 0.79), between transmural pressures of 10 and 60 mmHg. It is visible that the highest correlation coefficient (r = 0.83, p < 0.001) was obtained at the transmural pressure of 20 mmHg, which corresponds to the sensor cuff pressure of 70 mmHg in this study.

Fig. 8
figure 8

The relationship between the transmural pressure (Pt_AVG) and the calculated correlation coefficients (r) of the linear dependence between AIx@75avg and PPGAIavg (p < 0.001)

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The relationships between AIx@75 and PPGAI at the transmural pressures of 10 and 20 mmHg are given in Fig. 9. The regression model (dashed line) from [21] is added to the graphs for the comparison purposes.

Fig. 9
figure 9

The relationship between PPGAI and AIx@75 with the regression line (black continuous line) for the transmural pressure of a 20 mmHg (cuff pressure 70 mmHg) and b 10 mmHg (cuff pressure 80 mmHg). The dashed line and the lower model represent the regression model from the previous study [21]

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4 Discussion

In the current study, the dependence of the arterial stiffness index PPGAI on the transmural pressure has been demonstrated. Rapid changes in the PPGAI values can be observed at transmural pressures between − 25 and 10 mmHg, which is around the mean blood pressure, where transmural pressure is equal to 0 mmHg. At higher levels, the PPGAI values became less dependent on the transmural pressure. The maximal Pearson’s correlation coefficient of the linear relationship between PPGAI and AIx@75 and nearly minimal standard deviation of the PPGAI values was observed at the transmural pressure of 20 mmHg (Figs. 7 and 8). Similar results were found for the transmural pressure at 10 mmHg. The high correlation coefficients can be observed as well at higher transmural pressures; however, the standard deviation of PPGAI is increased in this region. As the PPGAI depends in the region between 10 and 20 mmHg on the transmural pressure, the optimal transmural pressure for the PPGAI determination to estimate arterial stiffness can be suggested as 20 mmHg. According to Eq. (5), the transmural pressure is dependent on the mean arterial blood pressure of the finger. Therefore, to record the finger PPG signal for the waveform analysis purposes, the sensor contact pressure should be selected according to the arterial blood pressure of the finger.

All the subjects in this study were without any diagnosis of cardiovascular diseases; however, three of the male subjects had systolic arterial blood pressure above 140 mmHg during the experiment. Furthermore, 12 subjects (nine female and three male) had their body mass index (BMI) above 30 kg/m2. Two subjects (two female subjects) were regularly engaged in sport activities and had large muscle weight. Two subjects (one male and one female subject) were big-boned. The rest of the subjects were obese. The subjects with high blood pressure did not have higher BMI at the same time. The AIx and AIx@75 were higher for female subjects due to their higher average age (Table 1) and gender differences [12]. The subjects with obesity and high blood pressure did not have notably higher AIx and AIx@75 values from the rest of the subjects within their age region. The stiffness of the arteries is increased due to the increase of the age of the subject. As the age of the subjects in the study group has a relatively wide coverage, the stiffness of the arteries variation is large as well.

In a previous study [21], a relatively strong correlation between the PPGAI and the heart rate normalized AIx@75 was demonstrated. In the current study, we have shown that there is relatively strong linear relationship between the PPGAI and the AIx@75 at the transmural pressures of 10 and 20 mmHg (Fig. 9). Both regression models between the PPGAI and the AIx@75 in our study are similar to the earlier results [21]. However, there is a noticeable shift between the regression models in Fig. 9b, which is due to the averagely lower PPGAI values at the transmural pressure of 10 mmHg (Fig. 5). Therefore, the selection of the sensor contact pressure according to the finger arterial blood pressure is important in order to avoid the bias in the PPGAI values. It is as well visible that the data points deviate from the regression lines, which can have multiple reasons. The PPG signal and the pressure waveform were registered from different locations on the body. In addition, the PPG signal is related non-linearly to the pressure waveform [26, 30].

Figure 5 shows that the PPGAI increases noticeably between the transmural pressure values of − 25 mmHg to 10 mmHg. It is clearly visible as well for one subject from Fig. 6 how the change of the mean blood pressure affects the PPGAI as the cuff pressure of the sensor remains constant. Even though, the PPGAI changes due to breathing [22] and other vasoactive processes, the reference PPGAI values from the ring finger at the beginning and at the end of the experiment showed no statistical difference. The increase in the PPG sensor contact pressure causes changes in the signal waveform, which has been also reported in earlier studies [15, 26]. Based on the observed PPG waveform changes illustrated in Fig. 6, it can be debated that the transmural pressure might affect as well the other waveform parameters used for the estimation of the arterial stiffness [33] or blood pressure [11]. However, a separate study should be carried out to analyse those dependencies.

As shown in Fig. 6, the waveforms are relatively similar at higher transmural pressure (lower sensor contact pressures) and the waveform starts to change from the transmural pressure of 12 mmHg and below. Figures 7 and 8 show the correlation coefficient decreases and standard deviation increases noticeably at transmural pressures lower than 10 mmHg, respectively. A similar change in PPGAI standard devation is visible at transmural pressures higher than 20 mmHg; however, the correlation coefficient remains high until the transmural pressure of 60 mmHg. As the standard deviation of PPGAI is nearly minimal and the correlation coefficient is highest at the transmural pressure of 20 mmHg, it can be suggested that the PPG signal for the PPGAI assessment should be registered at the transmural pressures of 20 mmHg.

Earlier studies show that the optimal contact pressure of the PPG sensor for the heart rate [24] and the pulse arrival time [6] detection is 54 mmHg. In our study, the transmural pressure of 20 mmHg corresponds to the sensor contact pressure of 70 mmHg. However, it should be mentioned that the transmural pressure is dependent on the mean blood pressure of the subject and therefore this comparison is not fully relevant for different studies. Nevertheless, it can be seen from Fig. 5 that there are no large differences in the PPGAI values at higher transmural pressures over 38 mmHg (sensor cuff pressures < 52 mmHg).

According to [9], the pulsatile volume change in the blood vessels decreases due to the increased transmural pressure (decreased sensor contact pressures). The blood volume change related to the PPG signal amplitude is decreased as well and the signal to noise ratio is increased. Consequently, the increased signal to noise ratio also increases the standard deviation of PPGAI (Fig. 7). Decrease of Pearson’s correlation coefficient at higher transmural pressures (Fig. 8) can be related to the increased PPGAI standard deviation values and as well due to the insufficient contact pressure to obtain PPG signal with high signal to noise ratio.

At higher transmural pressures in Fig. 5, the data points that are noticeably lower from the average belong to a 26-year old male subject with the lowest AIx@75 values (AIx@75avg =  − 14.33%) and one of the highest arterial systolic blood pressure values (SBP = 144 mmHg, DBP = 79 mmHg) in the whole study group. It has to be mentioned that the standard deviation of the PPGAI was relatively large at higher transmural pressures, which could be caused by the cold fingers of the subject. Nevertheless, the PPGAI value of the subject reaches maximal value around the transmural pressure of 11 mmHg. At lower transmural pressures, the deviated data points from the average line correspond to the results of three subjects. The PPGAI remained almost stable even though the transmural pressure was decreased (sensor cuff pressure was increased). All three subjects were female with age between 49 and 50 years, normal arterial blood pressure and AIx@75 index values were between 20 and 23%. Apart from the mentioned subjects, the PPGAI dependence on the transmural pressure was similar for all the other subjects. There were no notable differences in the relationship between the transmural pressure and the PPGAI in subjects with obesity and high blood pressure compared to other subjects. However, in the case of subjects with high blood pressure, there were less data points below the transmural pressure of 0 mmHg, as the mean blood pressure was higher.

4.1 Limitations of the study

In the current study, the PPG sensor contact pressure was changed circumferentially using the cuff wrapped around the finger. However, in many PPG signal registration setups for the waveform analysis, a finger clip sensor is used. It can be assumed that the changes in the PPG waveform recorded with the finger clip sensor are similar to the results of this study. Nevertheless, it should be clarified in the futures studies.

5 Conclusions

This study suggests that the transmural pressure of 20 mmHg is suitable for the PPG signal registration from the finger to assess the arterial stiffness index PPGAI. The PPGAI was compared with the arterial stiffness related aortic augmentation index (AIx@75) at different transmural pressures. Strong linear relation between AIx@75 and PPGAI, and low standard deviations of PPGAI were found at the transmural pressures of 10 and 20 mmHg. In addition, the relationship between AIx@75 and PPGAI at the transmural pressure of 20 mmHg was found similar to the regression model from the previous study, where the PPGAI was shown to discriminate the subjects with raised arterial stiffness from healthy persons [21]. Based on the results, the contact pressure of the sensor should be selected according to the finger mean blood pressure of the subject to achieve the optimal transmural pressure for the PPGAI and arterial stiffness assessment.