Evaluation of developed simulator using robotic tonometry system
To verify that the developed cam-based pulsation simulator can accurately reproduce the average radial pulse profile of a human measured by RTS, the radial pulse generated at the wrist region of the simulator was measured again using RTS. Figure 7 shows the overall experimental setup for evaluating the developed simulator. The simulator’s wrist part was laid and fixed on the base plate of the RTS similar to the location of the human arm. The developed simulator can modulate the pulse pressure and heart rate generated by the cam-based mechanism by changing the length of the air tube and the rotational speed of the cam. In the experiments, the simulator pulse pressure increased from 50 to 60 mmHg, and the heart rate values increased from 65 to 75 bpm. The generated radial pulse was measured by RTS. While working for 5 min, the simulator showed a repeatability of CV = 0.23% and CV = 0.82% for the heart rate and the pulse pressure, respectively.
As shown in Fig. 8, since the artificial arm of the simulator was fixed on the base of the robotic tonometry device, the contact force direction of the pulse sensor could be kept constant when the pulse sensor surface angles with the gravitational axis were controlled by the constant target values α = − 5.0° and β = 2.0°. In the experiment, the two contact angles between the pulse sensor surface and the base plane of the simulator were controlled with error bounds of ± 0.21° and ± 0.37°, respectively.
Figure 9 shows the raw data of the pulse wave measured from the time that the pulse sensor reached the artificial wrist surface to the pressurization of the artificial radial artery. The center of the pulse sensor was laid on the same contact point of the surface, and the radial artery was incrementally pressured until the maximum pulse pressure values were found. When the maximum pulse pressure was detected, the tonometry device maintained the contact force for about 30 s to reliably record the raw signals of the maximum pulse pressure of the radial artery pulse. Approximately 30 pulse waveforms obtained in the reliable region were averaged to analyze the dynamic characteristics between the artificial radial pulse and the reference signal obtained from clinical data.
Analysis
In order to analyze how accurately the developed cam-based pulsation simulator can regenerate the human representative radial pulse waveforms shown in Fig. 4, error analyses were performed among the representative pulse waveforms of the human (Fig. 4), the pulse wave measured by the RTS on the skin above the simulator wrist (Fig. 9), and pressure sensor outputs built into the simulator’s vessel.
First, these error analyses were performed by comparing the radial AI calculated from each radial pressure waveform. This is because the radial AI has a significantly high correlation with the central aortic AI, which is a very important indicator for predicting cardiovascular diseases such as atherosclerosis and vascular aging [5, 23, 24]. Next, these error analyses were also conducted by comparing the phase delay between the first peaks of the representative human pulse wave and the simulator’s measured pulse data.
The first peak of the radial artery pressure waveform was used to reconstruct the early systolic shoulder of the aortic pressure wave through a generalized transfer function [6]. Since the upstroke slope of the early systolic shoulder is related to the left ventricular contractility whose abnormality can initiate a clinically significant heart failure syndrome [25, 26], the slope of the first peak as well as the magnitude ratio (radial AI) were evaluated to be in good agreement with the upstroke slope of the representative human waveform.
Radial augmentation index (AI)
For the various comparative analyses shown in Fig. 10, the heart rate was adjusted to 65 bpm and 75 bpm by changing the rotational speed of the built-in motor in the simulator. The pulse pressure was regulated to 50 mmHg and 60 mmHg, respectively, by adjusting the internal volume of the simulator. In each case, the measured pulses were stored using the RTS on the skin of the wrist of the simulator. At the same time, the pulses measured by a pressure sensor built into the simulator’s silicone vessel were stored. In each case, the average waveforms were generated from the stored pulses, and then the magnitude and period were normalized to 1 and compared with the representative waveform of a human (Fig. 4) as shown in Fig. 10.
Figure 10a shows the results obtained by measuring the heart rate and pulse pressure of the simulator at 65 bpm and 50 mmHg, respectively. In the figure, the measured data with the RTS and pressure sensor were compared with the representative waveform of a human. Figure 10b shows the comparison results when the simulator heart rate and pulse pressure were set to 65 bpm and 60 mmHg, respectively, and Fig. 10c shows the comparison results at 75 bpm and 50 mmHg. Figure 10d shows the comparison results at 75 bpm and 50 mmHg.
As shown in Fig. 10a, it was confirmed that the waveform measured by the RTS on the wrist of the simulator and the waveform measured by the pressure sensor are in good agreement with the human representative waveform. This result implies that the proposed three-peak cam generating the pressure waveform in the simulator is designed to accurately regenerate the human pulse waveform. As shown in Fig. 10b–d, similar trends were observed when the same comparisons were made by changing the heart rate and pulse rate.
Figure 11a shows the error between the representative waveform of a human (Fig. 4) and the pressure waveform measured by a pressure sensor inside the simulator’s vessel in terms of the radial AI. Here, since the error value of the radial AI is very small at less than 8.14E−3, it was confirmed that the radial AI values of both waveforms were matched well. On the other hand, in Fig. 11b, the error value of the radial AI between the representative waveform of a human (Fig. 4) and the waveform measured by the RTS on the skin of the wrist of the simulator was about 4.85E−2, which is relatively large. The reason why the error value (waveform measured by the RTS) is relatively large is that the proposed simulator generates the pressure waveform using air pressure instead of an incompressible liquid similar to blood. Because the compressibility of air is different from that of blood, the pressure waveform measured by the tonometry method using the RTS has a slightly different radial AI value from that of the human radial AI. Although this error value is larger than the value in Fig. 11a, this error value is small enough to conclude that the developed simulator can reproduce a pulse waveform similar to the human waveform while ensuring the value of the radial AI.
Phase Delay
As shown in Fig. 10, when comparing the upstroke slopes of early systolic pressure in the three measured waveforms, it can be seen that the slope of the representative pressure waveform of the human is the steepest. This is because the proposed simulator generates a pressure waveform by compressing and tensioning air instead of an incompressible liquid similar to blood. Owing to the nature of the air, which is a compressible fluid, the slope of the upstroke becomes less steep, resulting in a phase delay. To ensure that this phase delay effect is small enough to be ignored, an error analysis of the phase delay was performed among the representative pulse waveforms of a human, the pulse wave measured by the RTS on the skin above the simulator’s wrist, and the pressure sensor outputs built into the simulator’s vessel, as described in Fig. 10.
Figure 12 shows the amplitude of Fourier transform at each frequency in the frequency domain when a discrete Fourier transform was applied to the pulse waveforms measured in the human and the simulator. The results of the discrete Fourier transform showed almost no difference between the amplitudes obtained from the human waveform and simulator waveform. The results also showed that the pulse waveforms measured in the human and the simulator had a dominant amplitude in the low-frequency range. Thus, we investigated the difference in phase angle at low frequencies of 1 Hz and 2 Hz to determine the phase delay between pulse waveforms.
If \( y^{h} \) is the pulse shape of a human, and \( y^{c} \) is the waveform generated by the cam simulator, the discrete Fourier transform is defined as follows:
$$ \begin{aligned} \widehat{y}^{h} \left( f \right) = \mathop \sum \limits_{n = 1, \ldots ,N} y^{h} (x_{n} )e^{{ - \frac{2\pi i}{N}fn}} \hfill \\ \widehat{y}^{c} \left( f \right) = \mathop \sum \limits_{n = 1, \ldots ,N} y^{c} (x_{n} )e^{{ - \frac{2\pi i}{N}fn}} \hfill \\ \end{aligned} $$
(4)
Here, \( x_{n} = x/N \) (N = 200). If \( \widehat{y}^{h} \left( f \right) \) and \( \widehat{y}^{c} \left( f \right) \) in Eq. (4) are expressed in the complex domain, the angles determined by the real parts and imaginary parts are denoted by \( \theta \left( {\widehat{y}^{h} \left( f \right)} \right) \) and \( \theta \left( {\widehat{y}^{c} \left( f \right)} \right) \), respectively. Here, the phase angle delay is defined as Eq. (5):
$$ Phase\;Angle \;Delay = \theta \left( {\widehat{y}^{h} \left( f \right)} \right) - \theta \left( {\widehat{y}^{c} \left( f \right)} \right) $$
(5)
At low frequencies of 1 Hz and 2 Hz, the phase angle delays are calculated as Eq. (6):
$$ \begin{aligned} Phase\;Angle \;Delay_{{\left( {f = 1Hz} \right)}} = \theta \left( {\widehat{y}^{h} \left( 1 \right)} \right) - \theta \left( {\widehat{y}^{c} \left( 1 \right)} \right) \hfill \\ Phase\; Angle\; Delay_{{\left( {f = 2Hz} \right)}} = \theta \left( {\widehat{y}^{h} \left( 2 \right)} \right) - \theta \left( {\widehat{y}^{c} \left( 2 \right)} \right) \hfill \\ \end{aligned} $$
(6)
In four cases where the heart rate is adjusted to 65 bpm and 75 bpm and the pulse pressure is adjusted to 50 mmHg and 60 mmHg as shown in Fig. 10. Figure 13 illustrates the phase angle at \( f = 1 {\text{Hz and }}f = 2 {\text{Hz}} \) of each pulse waveform measured in the human and the simulator. In all figures, the difference in phase angle is positive, indicating that the phase of the waveform is delayed.
Figure 14 shows the error of the phase angle delay owing to heart rate and pulse pressure changes. The error value of the phase delay of the waveform measured on the skin of the simulator (Fig. 14b) is larger than the error value of the phase delay of the waveform measured by the pressure sensor (Fig. 14a). The reason is that the proposed simulator produces a pressure waveform using air pressure with compressibility characteristics, which results in a decrease in the pressure transfer efficiency to the skin.
A maximum phase angle delay of 11.4° occurs at a heart rate of 65 bpm and a pulse pressure of 60 mmHg, as shown in Fig. 14b. This phase angle delay is small enough to be 3.2% when converted to a percentage error in one cycle (360°). As a result, the phase delay effect caused by using air instead of incompressible liquid in the proposed simulator is sufficiently small, thus proving that a very accurate pulse pressure waveform can be reproduced using the air-based three-peak cam simulator.