An Innovative Method to Measure the Peripheral Arterial Elasticity: Spring Constant Modeling Based on the Arterial Pressure Wave with Radial Vibration

Noninvasive Measurement of Time-Varying Arterial Wall Elastance Using a Single-Frequency Vibration Approach

The arterial wall elastance is an important indicator of arterial stiffness and a kind of manifestation associated with vessel-related disease. The time-varying arterial wall elastances can be measured using a multiple-frequency vibration approach according to the Voigt and Maxwell model. However, such a method needs extensive calculation time and its operating steps are very complex. Thus, the aim of this study is to propose a simple and easy method for assessing the time-varying arterial wall elastances with the single-frequency vibration approach. This method was developed according to the simplified Voigt and Maxwell model. Thus, the arterial wall elastance measured using this method was compared with the elastance measured using the multiple-frequency vibration approach. In the single-frequency vibration approach, a moving probe of a vibrator was induced with a radial displacement of 0.15 mm and a 40 Hz frequency. The tip of the probe directly contacted the wall of a superficial radial artery, resulting in the arterial wall moving 0.15 mm radially. A force sensor attached to the probe was used to detect the reactive force exerted by the radial arterial wall. According to Voigt and Maxwell model, the wall elastance (E_single) was calculated from the ratio of the measured reactive force to the peak deflection of the displacement. The wall elastances (E_multiple) measured by the multiple-frequency vibration approach were used as the reference to validate the performance of the single-frequency approach. Twenty-eight healthy subjects were recruited in the study. Individual wall elastances of the radial artery were determined with the multiple-frequency and the single-frequency approaches at room temperature (25 °C), after 5 min of cold stress (4 °C), and after 5 min of hot stress (42 °C). We found that the time-varying E_single curves were very close to the time-varying E_multiple curves. Meanwhile, there was a regression line (E_single = 0.019 + 0.91 E_multiple, standard error of the estimate (SEE) = 0.0295, p < 0.0001) with a high correlation coefficient (0.995) between E_single and E_multiple. Furthermore, from the Bland-Altman plot, good precision and agreement between the two approaches were demonstrated. In summary, the proposed approach with a single-frequency vibrator and a force sensor showed its feasibility for measuring time-varying wall elastances.

A vibration-based approach to quantifying the dynamic elastance of the superficial arterial wall

Background

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.

Methods

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.

Results

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).

Conclusions

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.

Developing an effective arterial stiffness monitoring system using the spring constant method and photoplethysmography

This study aimed to develop a fast and effective arterial stiffness monitoring system for diabetic patients using the spring constant method and photoplethysmography (PPG). The experimental group comprised 70 patients (4 type 1 diabetes mellitus patients and 66 type 2 diabetes mellitus patients); 23 participants suffered from atherosclerosis. All were subjected to the measurements of both the carotid-femoral pulse wave velocity (cfPWV) and the spring constants evaluated using the PPG pulse as well as the radial pulse. The control group comprised 70 normal participants (39 men and 31 women) who did not have diabetes mellitus, with an age range of 40-84 years. All control group members were only subjected to the measurement by the spring constant method. For the experimental group, statistical analysis indicated a significantly high correlation between the spring constants computed using PPG and the radial pulse (p < 0.001, correlation coefficient =0.89). The result also showed a significant negative correlation between the cfPWV and the spring constant of PPG (p < 0.001, correlation coefficient = - 0.72); multivariate analysis similarly indicated a close relationship. In addition, we used Student's t test to examine the difference between the experimental and control groups for the spring constant of PPG. A P value less than 0.05 confirmed that the difference between the two groups was statistically significant. In the receiver operating characteristic curve, area under curve (=0.82) indicates a good discrimination, and a spring constant of PPG below 516 (g/s (2)) may imply a risk of arterial stiffness for diabetic patients. These findings imply that the spring constant of PPG could effectively identify normal versus abnormal characteristics of elasticity in normal and diabetic participants. As a result of some excellent characteristics in clinical monitoring, the spring constant computed using PPG shows the effectiveness and feasibility in the monitoring system of arterial stiffness.

Using the spring constant method to analyze arterial elasticity in type 2 diabetic patients

BACKGROUND

This study tests the validity of a newly-proposed spring constant method to analyze arterial elasticity in type 2 diabetic patients.

METHODS

The experimental group comprised 66 participants (36 men and 30 women) ranging between 46 and 86 years of age, all with diabetes mellitus. In the experimental group, 21 participants suffered from atherosclerosis. All were subjected to the measurements of both the carotid-femoral pulse wave velocity (cfPWV) and the spring constant method. The comparison (control) group comprised 66 normal participants (37 men and 29 women) with an age range of 40 to 80 years who did not have diabetes mellitus. All control group members were subjected to measurement by the spring constant method.

RESULTS

Statistical analysis of the experimental and control groups indicated a significant negative correlation between the spring constant and the cfPWV (P < .001; r = - 0.824 and - 0.71). Multivariate analysis similarly indicated a close relationship. The Student's t test was used to examine the difference in the spring constant parameter between the experimental and control groups. A P-value less than .05 confirmed that the difference between the 2 groups was statistically significant. In receiver operating characteristic curve (ROC), the Area Under Curve (AUC, = 0.85) indicates good discrimination. These findings imply that the spring constant method can effectively identify normal versus abnormal characteristics of elasticity in normal and diabetic participants.

CONCLUSIONS

This study verifies the use of the spring constant method to assess arterial elasticity, and found it to be efficient and simple to use. The spring constant method should prove useful not only for improving clinical diagnoses, but also for screening diabetic patients who display early evidence of vascular disease.