Blood flow in compliant arteries: an effective viscoelastic reduced model, numerics, and experimental validation.
The focus of this work is on modeling blood flow in medium-to-large systemic arteries assuming cylindrical geometry, axially symmetric flow, and viscoelasticity of arterial walls. The aim was to develop a reduced model that would capture certain physical phenomena that have been neglected in the derivation of the standard axially symmetric one-dimensional models, while at the same time keeping the numerical simulations fast and simple, utilizing one-dimensional algorithms. The viscous Navier-Stokes equations were used to describe the flow and the linearly viscoelastic membrane equations to model the mechanical properties of arterial walls. Using asymptotic and homogenization theory, a novel closed, "one-and-a-half dimensional" model was obtained. In contrast with the standard one-dimensional model, the new model captures: (1) the viscous dissipation of the fluid, (2) the viscoelastic nature of the blood flow - vessel wall interaction, (3) the hysteresis loop in the viscoelastic arterial walls dynamics, and (4) two-dimensional flow effects to the leading-order accuracy. A numerical solver based on the 1D-Finite Element Method was developed and the numerical simulations were compared with the ultrasound imaging and Doppler flow loop measurements. Less than 3% of difference in the velocity and less than 1% of difference in the maximum diameter was detected, showing excellent agreement between the model and the experiment.
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA. canic@math.uh.edu
Suncica
S
Canić
Craig J
CJ
Hartley
Doreen
D
Rosenstrauch
Josip
J
Tambaca
Giovanna
G
Guidoboni
Andro
A
Mikelić
D000465:Algorithms; D000818:Animals; D001158:Arteries / Q000502:physiology*; D001783:Blood Flow Velocity; D004548:Elasticity; D006801:Humans; D008955:Models, Cardiovascular; D018616:Ultrasonography, Doppler, Duplex