Abstract This study examines radial and axial displacement of the arterial wall under the influence of harmonics and wave reflection for the role of axial wall displacement in pulsatile wave propagation. The arterial wall is modeled as an initially-tensioned thin-walled orthotropic tube. In conjunction with three pulsatile parameters in blood flow, a free wave propagation analysis is conducted on the governing equations of the arterial wall and no-slip conditions at the blood-wall interface to obtain the frequency equation and pulsatile parameter expressions under different harmonics. The influence of wave reflection is then added to pulsatile parameter expressions. With the harmonic values of measured pulsatile pressure and blood flow rate at the ascending aorta in the literature, the waveforms of radial wall displacement, axial wall displacement, and wall shear stress are calculated under different orthotropicity and axial initial tension. The developed theory and calculated results indicate that (1) difference in waveform between blood flow rate, wall shear stress, and axial wall displacement is caused by harmonics, rather than wave reflection; (2) Axial wall displacement does not affect blood flow rate, radial wall displacement, and wall shear stress; (3) Besides wall shear stress, radial wall displacement gradient also contributes to axial wall displacement and its contribution is adjusted by axial initial tension; (4) different wave reflections only noticeably affect the maximum and minimum values of wall shear stress; and (5) The amplitude and waveform of axial wall displacement are predominantly dictated by axial elasticity and axial initial tension, respectively.
more »
« less
Relations of Radial Vibration of the Arterial Wall to Pulsatile Parameters in Blood Flow for Extraction of Arterial Indices
Abstract Given the wide utility of radial vibration of the arterial wall for clinical values, this paper presents a theoretical study on the relations of radial vibration of the arterial wall to pulsatile parameters in blood flow. Pulse wave propagation in an artery is formulated as a combination of the governing equations of blood flow and the arterial wall and no-slip conditions at the blood-wall interface and is analyzed to obtain the wave velocity and the theoretical expressions for blood flow rate and radial wall displacement in terms of pulsatile pressure. With the harmonics of a pulse signal, theoretical relations of radial vibration of the arterial wall to pulsatile parameters in blood flow are derived under two conditions: without and with wave reflection. These theoretical relations identify the assumptions for the simplified relations employed in the utility of radial vibration of the arterial wall for clinical values. With the arterial wall treated as a unit-mass vibration system, these simplified relations are utilized for extraction of arterial indices from radial vibration of the arterial wall. Other applications of such relations for clinical values are discussed, and the interaction between the arterial wall and blood flow is further revealed from the perspective of energy and one-dimensional wave equations. With harmonics and wave reflection considered, the derived theoretical expressions for radial wall vibration, pulsatile parameters in blood flow, and the relations between them provide theoretical guidance for improving their interpretation of clinical values with clearly defined physiological implications and assumptions.
more »
« less
- Award ID(s):
- 1936005
- PAR ID:
- 10415163
- Date Published:
- Journal Name:
- Journal of Engineering and Science in Medical Diagnostics and Therapy
- Volume:
- 6
- Issue:
- 1
- ISSN:
- 2572-7958
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
With the arterial wall modeled as an initially-tensioned thin-walled orthotropic tube, this study aims to analyze radial and axial motion of the arterial wall and thereby reveal the role of axial motion and two initial tensions of the arterial wall in arterial pulse wave propagation. By incorporating related clinical findings into the pulse wave theory in the literature, a theoretical study is conducted on arterial pulse wave propagation with radial and axial wall motion. Since the Young wave is excited by pulsatile pressure and is examined in clinical studies, commonly measured pulsatile parameters in the Young wave are expressed in terms of pulsatile pressure and their values are calculated with the well-established values of circumferential elasticity (E) and initial tension (T0) and assumed values of axial elasticity (Ex) and initial tension (Tx0) at the ascending aorta and the carotid artery. The corresponding values with exclusion of axial wall motion are also calculated. Comparison of the calculated results between inclusion and exclusion of axial wall motion indicates that 1) axial wall motion does not affect radial wall motion and other commonly measured pulsatile parameters, except wall shear stress; 2) axial wall motion is caused by wall shear stress and radial wall displacement gradient with a factor of (Tx0T0), and enables axial power transmission through the arterial wall; and 3) while radial wall motion reflects E and T0, axial wall motion reflects Ex and (Tx0T0).more » « less
-
more » « less
Abstract Pulsatile pressure at an artery is a collection of harmonics of the heartbeat. This study examines harmonics of pulsatile pressure at different ages and its effect on other pulsatile parameters and waveform-based clinical indices. Based on a vibrating-string model of the arterial tree, wave velocity and characteristic impedance are related to arterial stiffness and radius. Blood velocity, wall shear stress (WSS), and driving force on the left ventricle (LV) are related to pulsatile pressure. Reflection magnitude and return time are related to input impedance. These relations are applied to pulsatile pressure and blood velocity at the ascending aorta (AA) and the carotid artery (CA) at different ages in a database to calculate harmonics of all the pulsatile parameters and reflection magnitude and return time at each harmonic. Harmonics of pulsatile pressure varies with aging and between the two arteries. Reflection magnitude and return time vary between harmonics. While wave reflection manifests the arterial tree (i.e., arterial stiffness and radius) and termination, harmonics of pulsatile pressure is a combination of the LV, the arterial tree, and termination. Harmonics of pulsatile pressure dictates harmonics of WSS and affects endothelial function. Harmonics of pulsatile pressure needs to serve as an independent clinical index indicative of the LV function and endothelial function. Reflection magnitude and return time of the 1st harmonic of pulsatile pressure serve as clinical indices indicative of arterial stiffness and radius.
-
This work is aimed to establish engineering theories of the coupled longitudinal and radial motion of the arterial wall. By treating the arterial wall as a piano string in the longitudinal direction and as a viscoelastic material in the circumferential direction, and considering pulsatile pressure and wall shear stress from axial blood flow in an artery, the fully-formed governing equations of the coupled motion of the arterial wall are obtained and are related to the engineering theories of axial blood flow for a unified engineering understanding of blood circulation in the cardiovascular (CV) system. The longitudinal wall motion and the radial wall motion are essentially a longitudinal elastic wave and a transverse elastic wave, respectively, traveling along the arterial tree, with their own propagation velocities dictated by the physical properties and geometrical parameters of the arterial wall. The longitudinal initial tension is essential for generating a transverse elastic wave in the arterial wall to accompany the pulsatile pressure wave in axial blood flow. Under aging and subclinical atherosclerosis, propagation of the two elastic waves and coupling of the two elastic waves weakens and consequently might undermine blood circulation.more » « less
-
null (Ed.)With the goal of achieving consistence in interpretation of an arterial pulse signal between its vibration model and its hemodynamic relations and improving its physiological implications in our previous study, this paper presents an improved vibration-model-based analysis for estimation of arterial parameters: elasticity (E), viscosity (), and radius (r0) at diastolic blood pressure (DBP) of the arterial wall, from a noninvasively measured arterial pulse signal. The arterial wall is modeled as a unit-mass vibration model, and its spring stiffness (K) and damping coefficient (D) are related to arterial parameters. Key features of a measured pulse signal and its first-order and second-order derivatives are utilized to estimate the values of K and D. These key features are then utilized in hemodynamic relations, where their interpretation is consistent with the vibration model, to estimate the value of r0 from K and D. Consequently, E, , and pulse wave velocity (PWV) are also estimated from K and D. The improved vibration-model-based analysis was conducted on pulse signals of a few healthy subjects measured under two conditions: at-rest and immediately post-exercise. With E, r0, and PWV at-rest as baseline, their changes immediately post-exercise were found to be consistent with the related findings in the literature. Thus, this improved vibration-model-based analysis is validated and contributes to estimation of arterial parameters with better physiological implications, as compared with its previous counterpart.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4055390
