Improved Vibration-Model-Based Analysis for Estimation of Arterial Parameters From Noninvasively Measured Arterial Pulse Signals

This paper presents a study on using vibration-model-based analysis to estimate arterial parameters from noninvasively measured arterial pulse signals. By modeling the arterial wall as a unit-mass dynamic system, its stiffness and damping are mathematically related to three arterial parameters (elasticity, viscosity, and radius of the arterial wall) and their values are extracted from the key features of an arterial pulse signal and its first-order and second-order derivatives. Arterial pulse signals were measured at the radial artery and carotid artery of four subjects at-rest and post-exercise, and three arterial parameters were estimated from these measured pulse signals using related data-processing algorithms. With at-rest as baseline, relative changes of three arterial parameters post-exercise were found to be consistent with the related findings in the literature.

Arterial pulse signals are noninvasively measured and utilized to obtain various arterial indices for assessing arterial health. Generally speaking, the methodologies underlying various arterial indices fall into two categories: wave propagation (or transmission) theory for pulse wave velocity (PWV) and a viscoelastic material (or pulsation) model for arterial elasticity and viscosity. Arterial radius at diastolic blood pressure (DBP) dictates vascular resistance and is also an important clinical index. While PWV is indicative of arterial elasticity and demands simultaneous pulse signal measurements at two artery sites, a viscoelastic material model requests simultaneous pulsatile pressure and radial wall motion measurements at one artery site. We previously developed a new methodology: a vibration model, for obtaining three arterial parameters from only one measure arterial pulse signal.  In this work, we modify the vibration model for improved physiological consistency and refine the mathematical relations of arterial parameters to the spring stiffness and damping coefficient of the vibration model. The refined relations are further validated by the collected data on six subjects. 

The pulsatile pressure signal in an artery is accompanied by the radial motion of the arterial wall. Owing to its time-harmonic nature, the radial motion of the arterial wall is treated as a vibration signal, and then the arterial wall is modeled as a unit-mass dynamic system. The force analysis of the arterial wall in the radial direction gives rise to the mathematical relations of arterial parameters to its spring stiffness and damping coefficient.  Given that the first-order and second-order derivatives of the radial wall motion represent the velocity and acceleration of the arterial wall, respectively, we conduct a scaling analysis to relate the key features in the radial wall motion and its two derivatives to the spring stiffness and damping coefficient. Consequently, the values of the spring stiffness and damping coefficient can be estimated from a measured pulse signal and then are utilized to estimate arterial parameters. Resulting from a scaling analysis, the estimated values of arterial parameters are relative and are suitable for monitoring changes in arterial parameters in response to external stimuli (e.g., exercise). As such, arterial pulse signals were measured at the radial artery and carotid artery of four subjects at-rest and post-exercise. The related data-processing algorithms were used to estimate arterial parameters from each measured pulse signal. With at-rest as baseline, the relative changes in arterial parameters post-exercise were obtained, showing that arterial elasticity and viscosity increased and arterial radius dropped. The observed changes in arterial elasticity and radius are consistent with the related findings in the literature. However, there are no studies on the changes in arterial viscosity for comparison. The full paper will provide the detailed vibration-model-based analysis and the experimental results of this work.