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.
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This content will become publicly available on November 1, 2024
A Vibrating-String Model for Closed-Loop Wave Transmission and Reflection Between the Aorta and Periphery
Abstract A tube-load model is used to reconstruct aortic pressure waveform from peripheral pressure waveform. Yet, the reconstructed aortic pressure waveform is greatly affected by load impedance used. In this work, a vibrating-string model for closed-loop wave transmission and reflection between the aorta and periphery is developed to examine the roles of all the parameters involved in aortic pressure waveform. The arterial pulsatile wave theory gives rise to the standard one-dimensional wave equation for a vibrating string. A vibrating-string model based on radial displacement of the arterial wall is developed to relate aortic pressure waveform to peripheral pressure waveform, relate load impedance to input impedance, and derive theoretical expressions for associated clinical indices. The vibrating-string model is extended to incorporate blood velocity and is further connected to the left ventricle (LV) to study the role of the LV in aortic pressure waveform. The difference between the vibrating-string model and the tube-load model is also examined. Load impedance is identified as an indispensable independent parameter for reconstruction of aortic pressure waveform with accuracy, and its physiologically realistic harmonic dependence can only be obtained from the measured input impedance. The derived expressions for clinical indices interpret some clinical findings and underscore the role of harmonics in clinical indices. Some misconceptions in the tube-load model are revealed, including load impedance and characteristic impedance. This work clarifies the role of harmonics-dependence of load impedance and harmonics of aortic pressure waveform in determining clinical indices.
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- Award ID(s):
- 1936005
- NSF-PAR ID:
- 10415164
- Date Published:
- Journal Name:
- Journal of Engineering and Science in Medical Diagnostics and Therapy
- Volume:
- 6
- Issue:
- 4
- ISSN:
- 2572-7958
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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