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

Abstract

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 × 10(6) dyne/cm to 0.611 ± 0.251 × 10(6) dyne/cm (p = 0.001). In the 5-min hot stress, the maximum radial wall elastance significantly decreased to 0.363 ± 0.106 × 10(6) 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.

Keywords: Arterial stiffness; Dynamic elastance; Minute vibration method.

Fig. 1

A three-component arterial model that characterizes the wall viscoelastic properties. E is an elastance component; M is an effect mass; η is a viscosity component; x is a displacement of the arterial wall; F _E is an external force; F _R is a reactive force

Fig. 2

Schematic diagram of the dynamic elastance measurement system

Fig. 3

Explanation for acquiring maximum reactive force (Fm). a Sinusoidal displacement of 40 Hz; b Reactive force of the arterial wall in response to the sinusoidal vibration; c Reactive force signal of one-cardiac cycle extracted from (b); d One-vibration cycle reactive force waveform extracted form (c)

Fig. 4

The elastances of the arterial wall were estimated by Eq. (6). The intercept represents E and the slope represents M.F_{R_max} = the maximum reactive force; Am = the maximum amplitude of sinusoidal displacement

Fig. 5

Typical time course of (a) the vibrator signal with 0.15 mm displacement and 40 Hz vibration, b the reactive force signal, c the arterial pressure-dependent force without the vibrator effect, d the sinusoidal vibration-dependent force, e the electrocardiogram (ECG) signal

Fig. 6

The linear relationship between ω² and F_{R_max}/Am in the systolic and diastolic durations of one heart beat was used to determine the arterial wall elastance. The data was taken from Fig. 5. aThe five regression lines correspond to T1–T5 in the systolic duration, respectively. b The eight regression lines correspond to T5 and to T12 in diastolic duration, respectively.The intercept of the linear regression represents the arterial wall elastance. Different dot symbols denote the experimental data and the solid lines are the regression lines with this data

Fig. 7

Typical elastance curves of one cardiac cycle measured from one subject at the cold stress, the baseline and the hot stress. Data points represent the measuring values of wall elastance