A vibration-based approach to quantifying the dynamic elastance of the superficial arterial wall
© Wang et al. 2016
Received: 4 January 2016
Accepted: 16 March 2016
Published: 16 April 2016
The purpose of this study is to propose a novel method for assessing dynamic elastance of the superficial arterial wall using the sinusoidal minute vibration method.
A sinusoidal signal was used to drive a vibrator which induced a displacement of 0.15 mm with a frequency range between 40 and 85 Hz. The vibrator closely contacted with the wall of a superficial radial artery, and caused the arterial wall to shift simultaneously. A force sensor attached to the tip of the vibrator was used to pick up the reactive force exerted by the radial arterial wall. According to the Voigt and Maxwell models, a linear relationship was found between the maximum reactive force and the squared angular frequency of the vibration. The intercept of the linear function represents the arterial wall elastance. In order to validate the feasibility of our method, twenty-nine healthy subjects were recruited and the wall elastances of their radial arteries were measured at room temperature (25 °C), after a 5-min cold stress (4 °C) and a 5-min hot stress (42 °C), respectively.
After the 5-min cold stimulation, the maximum radial wall elastance significantly increased from 0.441 ± 0.182 × 106 dyne/cm to 0.611 ± 0.251 × 106 dyne/cm (p = 0.001). In the 5-min hot stress, the maximum radial wall elastance significantly decreased to 0.363 ± 0.106 × 106 dyne/cm (p = 0.013).
The sinusoidal minute vibration method proposed can be employed to obtain the quantitative elastance of a superficial artery under different thermal conditions, and to help assess the severity of arterial stiffness in conduit arteries.
KeywordsArterial stiffness Dynamic elastance Minute vibration method
Arterial stiffness is frequently associated with the risk of cardiovascular diseases, cerebral vessel disease, diabetes mellitus and end-stage renal disease [1–3]. Some studies have approved that the higher arterial stiffness is a diffuse disease process of the conduit arteries that probably initiates in childhood and young adult life  and has a crucial effect on arterial remodeling in coronary systems . As a result, to detect the alteration in arterial stiffness before the emergence of clinical vascular illness, it may serve as an early prognostic warning for cardiovascular disease.
Several physical indices have been explored to indicate the severity of arterial stiffness in previous investigations. Indices used for assessing global arterial stiffness include the pulse pressure , the capacitive compliance of large arteries and the oscillatory compliance of small arteries . Systemic stiffness indices consist of the pulse wave velocity , characteristic impedance , carotid intima-media thickness , augmentation index of blood pressure  and β variables . Furthermore, there were different indices to describe the local arterial stiffness, such as the arterial compliance , arterial distensibility , volume elastic modulus , Young’s elastic modulus , and spring constant of arterial wall .
It is more important to explore reliable techniques for the arterial stiffness measurement, in which the challenge is how to detect the absolute arterial diameter or the change of arterial diameter. Every technique usually has its own drawbacks and advantages. In the ultrasound echo-tracking technique , although vascular diameter (or blood flow velocity) can be measured, an individual training in the principles and technical skills of ultrasonography would affect its precision and accuracy. In the optical plethysmography , the change of vascular volume can be approximately computed since constituents of tissue have different absorption coefficients of light. The disadvantage is that it is difficult to calibrate the changed volume. Similarly, change in vascular volume can be measured by the impedance plethysmography based on different electrical characteristics of tissue [19, 20]. In the tonometry , the interaction between the peripheral artery and the water chamber of the tonometer, represented the change of arterial volume. In the oscillometry [12, 22], the cuff model was used to transfer the pulse pressure amplitude to the pulse volume amplitude.
Some studies used the indirect method to assess the arterial compliance. In the analysis of pulse transit time , according to the Moens–Korteweg relationship, the pulse wave velocity between two measured points may be proportional to the square root of arterial wall elastance, under the assumption that the wall thickness and lumen radius of the arteries are considered as constants. In the analysis of pressure waveform , the exponentially decayed phenomenon during the diastolic pressure waveform was found to be related to the arterial compliance.
Most of the techniques described above can only provide a rough arterial compliance index for either a part of an artery or for the whole artery system. Furthermore, the arterial characteristic apparently is not a constant, but dependent on the transmural pressure [12, 25]. Therefore, the purpose of the present research was to develop a novel non-invasive vibration-based method for determining the dynamic elastance of the radial artery. The arterial wall elastance was an absolute value and had the unit which could be used to describe the arterial stiffness condition.
According to Eq. (6), at the specific time T m the ratio of F R_max and A m is negatively and linearly proportional to the square of angular frequency (ω 2). In this linear polynomial function, E(T m ) is the intercept and M is the absolute slope.
Twenty-nine healthy college volunteers (17 M and 12 F, age: 23 ± 3 years, systolic pressure: 113 ± 14 mm Hg, diastolic pressure: 70 ± 10 mm Hg, heart rate: 73 ± 9 beats/min) participated in this study. The clinical trial was approved by the Institutional Review Board of the E-DA Hospital, Kaohsiung, Taiwan (no. EMRP61101 N), and an informed consent was obtained from each participant prior to the initiation of the study. The temperature in the research lab was maintained at 25 °C with air-conditioners. Each subject was put in a sitting position and was asked to take a 5-min rest before the measurement. We measured the blood pressure before and after cold and hot stress tests by OMRON blood pressure monitor. During the measurement, each subject was asked to sit on an adjustable-height chair. The subject’s left hand was placed on a table at the same horizontal height as the heart with the palm pointing upwards and the wrist resting on a soft pillow. The superficial part of the radial artery of the left hand was forced up by the vibrator with a peak displacement of 0.15 mm. The frequency of the vibration was increased from 40 to 85 Hz at a step of 5 Hz. In the experiment, there were three phases, a baseline test, a cold stress test, and a hot stress test. In the baseline test, subjects were measured at room temperature. In the cold stress test, a plastic bag containing a mixture of ice and water (around 4 °C) was put on the inside surface part of the left forearm. Subjects were measured after the 5-min cold stress. Then, subjects were asked to take a 5-min rest in order to make the subjects’ hemodynamic variables stable. Another plastic bag filled with hot water at 42 °C was placed on the left forearm of the subject lasting for 5 min, and subjects were measured again.
The quantitative data are expressed as mean ± SD. To compare the changes of the elastance in the cold stress and hot stress with those at room temperature, a 2-tailed paired t test was used. A p value of 0.05 or less was considered statistically significant. Also, the degree of linear relationship between the two variables was represented by correlation coefficient in linear regression analysis using Sigma Plot 11.0 (Systat Software, Inc., USA).
Comparison of arterial blood pressure measured before and after thecold and hot stresstests
Cold stress (4 °C)
Hot stress (42 °C)
Systolic pressure (mmHg)
113 ± 14
117 ± 16* (p = 0.021)
123 ± 16
118 ± 17** (p = 0.005)
Diastolic pressure (mmHg)
70 ± 10
74 ± 10* (p = 0.016)
74 ± 12
71 ± 12** (p = 0.008)
Heart rate (beats/min)
73 ± 9
72 ± 9 (p = 0.647)
75 ± 12
71 ± 9** (p = 0.003)
Comparison of arterial wall elastance determined in cold stress, room temperature and hot stress conditions
Room temp (25 °C)
Cold stress (4 °C)
Hot stress (42 °C)
Maximum elastance (106 dyne/cm)
0.44 ± 0.182
0.611 ± 0.251*** (p = 0.001)
0.363 ± 0.106* (p = 0.013)
Minimum elastance (106 dyne/cm)
0.378 ± 0.179
0.520 ± 0.242*** (p = 0.001)
0.299 ± 0.107* (p = 0.014)
Change of elastance (106 dyne/cm)
0.063 ± 0.025
0.091 ± 0.038** (p = 0.002)
0.064 ± 0.028 (p = 0.812)
Both maximum elastance and minimum elastance were found to be significantly augmented by the 5-min cold stress (p = 0.001 for both), as compared with those at room temperature. Additionally, the short-term cold stress made the changed range of the arterial wall elastance considerably wider (p = 0.002). In contrast, the 5-min hot stress let the arterial wall elastance significantly decrease (p = 0.013 for maximum elastance, p = 0.014 for minimum elastance). But, the changed range of the arterial wall elastance was the same as the baseline.
In several previous investigations [12, 25] the arterial dynamic compliance follows the change of the transmural pressure. In our method, the reactive force included two forces, the pressure-dependent force and the vibration-dependent force. Although the two forces are time-variant amounts, we only detect the reaction force in each specific time sections. Thus, the vibration-dependent force was considered as a constant force. The change of transmural pressure followed the change of blood pressure. Therefore, in the study, we separated twelve time sections in one cardiac cycle. In Fig. 7, we found that the changes of the radial wall elastance follows the changes of blood pressure. The maximum and minimum elastance values happened at the systolic and diastolic pressures, separately. The results conformed to the Voigt and Maxwell models .
Wei et al. had used the theorem of spring constant to estimate the arterial elastance by the radial blood pressure waveform  and photoplethysmogram waveform . In their study, they have proposed two hypotheses, the blood pressure forced the extension of the arterial wall and their relation was linear. Therefore, the displacement, velocity, and acceleration of the arterial wall movement were obtained from the blood pressure waveform. Then the spring constant of the arterial wall could be detected. But, this method has two problems. One is that the arterial wall elastance is not a constant. Using the change of blood pressure waveform to replace the displacement of the arterial wall is a rough transformation. Second, the spring constant in their method had no proper units. It only was called an “index of arterial stiffness”. But, in the present study, we used the ratio of F m and A m (dyne/cm) at the different trasmural pressures to describe the elastic characteristic of arterial wall as the arterial stiffness index.
Many non-invasive and non-image methods have been used to indirectly or directly estimate the local arterial stiffness or the systematic compliance, including pulse wave velocity , pulse wave analysis [10, 24], impedance plethysmography [11, 14], photoplethysmography , and oscillometry . But, in these methods, the largest challenge is how to calibrate the parameter’s unit and measure the parameter’s absolute value. In our method, the force sensor and the vibrator all have been calibrated by the manufacturers. Thus, it is believed that the measured force and the moving distance of vibrator are reasonably accurate, and then the elastance (F m /A m ) should be reliable. The measured elastance has a proper unit and is an absolute value which depends on the transmural pressure. However, the measured ratio of F m and A m could not fully describe the elastance of arterial wall because there are some mediums between the radial arterial wall and the tip of the sensing probe. The mediums really have some contribution (probably a DC component) to the measured elastance. Thus, the measured wall elastance by the current method can be considered as an arterial stiffness index which may be applied to evaluate the arterial stiffness condition. Other drawbacks of the present method include the difficulties in setting the optimal measurement location and in installing the measurement system, as well as the lack of a precise calibration procedure.
In order to validate the feasibility of our method, we did the 5 min cold and hot water stimulation trials to compare with the results at room temperature. In Table 1, it is found that the radial wall elastance significantly rose after the cold water stimulation, the mean of minimum radial wall elastance (0.520 ± 0.242·106 dyne/cm) in the cold stress was greater than maximum radial wall elastance (0.441 ± 0.182·106 dyne/cm) in room temperature. Moreover, it also significantly descended after the hot water stimulation, the mean of maximum radial wall elastance (0.363 ± 0.106·106 dyne/cm) in the hot stress was smaller than the minimum radial wall elastance (0.378 ± 0.179·106 dyne/cm) in room temperature. The response of the arterial wall elastance in these trials completely matched the physiological response.
The mediums between the radial arterial wall and the tip of the sensing probe have the skin, tissue, and muscle which could affect the accuracy of the arterial wall elastance measurement in this study. Thus, the tip of the vibrator and force sensor must be placed at the superficial radial artery. The area used on the wrist to measure the radial wall elastance is very small. Moreover, the displacement of the vibrator is very small (0.15 mm). If the subject’s hand has a slight motion, the reaction force has a big reaction. Thus, in the experiment, we continuously recorded many heart beat cycles, and extracted the most perfect signal to detect the wall elastance.
With the proposed method, it is clear that the higher the frequency of sinusoidal vibration, the better resolution to describe the dynamic elastic characteristics of arterial wall. However, it is very hard for a mechanical device to produce high-frequency minute vibrations without any distortion. In this study, when the vibration frequency became greater than 100 Hz, more distortion existed in the sinusoidal displacement waveform. Such distorted sinusoidal waveform will no longer satisfy the requirement of Eqs. (2)–(6). Therefore, we have to make a compromise between the selection of higher frequency and the distortion of the sinusoidal waveform in applying the proposed vibration method. After several trial and error experiments, we have done our best to adjust the frequency and waveform of the vibrator to yield the better results.
The proposed vibration method is successfully applied to calculate the dynamic and absolute values of radial arterial wall elastance under different thermal situations. The measured wall elastance may be considered as a local arterial stiffness index and the elastance curve corresponding to an entire cardiac cycle, obtained with the novel method, may be helpful for diagnosis of peripheral arterial disease.
JJW was the principle investigator in this study. SHL wrote the manuscript. HMS and SC carried out the system manufacture, and the signal measurement in the experiment. WKT performed the statistical analysis and medicine introduction. All authors read and approved the final manuscript.
This work was supported by the Ministry of Science and Technology, Taiwan, under Grants, NSC 102-2221-E-214-005-MY3 and MOST 104-2221-E-324-030-MY2.
The authors declare that they have no competing interests.
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