Mathematical analysis of a nonlinear viscoelastic fluid-structure interaction and wave dynamics in compliant arteries
Phys. Rev. Fluids 11, 043101 – Published 16 April, 2026
DOI: https://doi.org/10.1103/c89k-5fp4
Abstract
The aim of the present study is to perform a comprehensive theoretical and numerical investigation of pressure and flow waves in compliant arteries in order to understand their physiological implications for detecting vascular stiffness. A model of a compliant artery, consisting of a viscoelastic tube containing a Jeffreys-type non-Newtonian fluid and surrounded by external tissue, is studied. The purpose of the work is to understand the coupled influence of fluid and arterial wall viscoelasticity on wave dynamics, flow impedance, and energy dissipation in a compliant artery. The arterial wall deformation is modeled using the Green-Rivlin constitutive law, which accounts for memory kernel and nonlinear viscoelastic effects. With regard to their coupling, the governing equations for the radial and longitudinal motion of an arterial wall are derived separately. The analytical expressions for flow distribution, impedance to flow, and energy estimate are obtained in terms of the frequency functions and the system parameters. A two-dimensional numerical experiment is presented to illustrate the energy distribution, and it utilizes physiological arterial parameters to assess the frequency-dependent impedance and energy dissipation behavior within the fluid-structure model. The obtained results highlight the importance of including both the viscoelasticity of fluid and the arterial wall in the modeling of fluid-structure interaction in arteries. Our results suggest that increasing the vessel radius and stretch ratio enhances damping and dissipates energy more effectively at lower frequencies, while higher stiffness and relaxation times amplify oscillations. Compared to the Newtonian and Maxwell models, the Jeffreys model more accurately captures physiological energy dissipation and dispersive wave behavior in the cardiovascular system for diagnosis and treatment. This study presents a comprehensive model for detailed profiling of vascular mechanics that captures the coupled influence of fluid and arterial wall viscoelasticity, the distribution and dissipation of the energy delivered to arteries, wave impedance, and system stability, with applications in basic future clinical diagnosis.
