Comparative Study of Viscoelastic Arterial Wall Models in Nonlinear One-Dimensional Finite Element Simulations of Blood Flow

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Rashmi Raghu ◽  
Irene E. Vignon-Clementel ◽  
C. Alberto Figueroa ◽  
Charles A. Taylor
Keyword(s):  
Finite Element ◽  
Blood Flow ◽  
Wave Propagation ◽  
Comparative Study ◽  
Abdominal Aorta ◽  
Elastic Model ◽  
One Dimensional ◽  
Viscoelastic Models ◽  
Wide Range ◽  
Wall Models

It is well known that blood vessels exhibit viscoelastic properties, which are modeled in the literature with different mathematical forms and experimental bases. The wide range of existing viscoelastic wall models may produce significantly different blood flow, pressure, and vessel deformation solutions in cardiovascular simulations. In this paper, we present a novel comparative study of two different viscoelastic wall models in nonlinear one-dimensional (1D) simulations of blood flow. The viscoelastic models are from papers by Holenstein et al. in 1980 (model V1) and Valdez-Jasso et al. in 2009 (model V2). The static elastic or zero-frequency responses of both models are chosen to be identical. The nonlinear 1D blood flow equations incorporating wall viscoelasticity are solved using a space-time finite element method and the implementation is verified with the Method of Manufactured Solutions. Simulation results using models V1, V2 and the common static elastic model are compared in three application examples: (i) wave propagation study in an idealized vessel with reflection-free outflow boundary condition; (ii) carotid artery model with nonperiodic boundary conditions; and (iii) subject-specific abdominal aorta model under rest and simulated lower limb exercise conditions. In the wave propagation study the damping and wave speed were largest for model V2 and lowest for the elastic model. In the carotid and abdominal aorta studies the most significant differences between wall models were observed in the hysteresis (pressure-area) loops, which were larger for V2 than V1, indicating that V2 is a more dissipative model. The cross-sectional area oscillations over the cardiac cycle were smaller for the viscoelastic models compared to the elastic model. In the abdominal aorta study, differences between constitutive models were more pronounced under exercise conditions than at rest. Inlet pressure pulse for model V1 was larger than the pulse for V2 and the elastic model in the exercise case. In this paper, we have successfully implemented and verified two viscoelastic wall models in a nonlinear 1D finite element blood flow solver and analyzed differences between these models in various idealized and physiological simulations, including exercise. The computational model of blood flow presented here can be utilized in further studies of the cardiovascular system incorporating viscoelastic wall properties.

Wave Propagation in Periodic Piezoelectric Elastic Waveguides

2012 ◽  
Author(s):  
D. G. Piliposyan ◽  
K. B. Ghazaryan ◽  
G. T. Piliposian ◽  
A. S. Avetisyan
Keyword(s):  
Wave Propagation ◽  
Stop Band ◽  
Transmission Conditions ◽  
Band Gaps ◽  
Full System ◽  
One Dimensional ◽  
Dynamic Setting ◽  
Floquet Waves ◽  
Wide Range ◽  
Shear Horizontal

The prorogation of electro-magneto-elastic coupled shear-horizontal waves in one dimensional infinite periodic piezoelectric waveguides is considered within a full system of the Maxwell’s equations. Such setting of the problem allows to investigate the Bloch-Floquet waves in a wide range of frequencies. Two different conditions along the guide walls and three kinds of transmission conditions at the interfaces between the laminae of waveguides have been studied. Stop band structures have been identified for Bloch-Floquet waves both at acoustic and optical frequencies. The results demonstrate the significant effect of piezoelectricity on the widths of band gaps at acoustic frequencies and confirm that it does not affect the band structure at optical frequencies. The results show that under electrically shorted transmission conditions Bloch-Floquet waves exist only at acoustic frequencies. For electrically open interfaces the dynamic setting provides solutions only for photonic crystals. In this case the piezoelectricity has no effect on band gaps.

Hypergravity and Multiple Reflections in Wave Propagation in the Aorta

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
J. M. B. Kroot ◽  
C. G. Giannopapa
Keyword(s):  
Blood Flow ◽  
Wave Propagation ◽  
Cerebral Blood Flow ◽  
Total Pressure ◽  
Loss Of Consciousness ◽  
Pressure Waves ◽  
Multiple Reflections ◽  
One Dimensional ◽  
Gravity Changes ◽  
Pressure Part

Hypergravity and gravity changes encountered in, e.g., airplanes, rollercoasters, and spaceflight can result in headaches or loss of consciousness due to decreased cerebral blood flow. This paper describes the effect of hypergravity and gravity changes on the pressure in the aorta and the distension of its wall. The model presented consists of a pressure part caused by gravity and a part representing pressure waves propagating through the vessel. The total pressure is described by a one-dimensional formulation in the frequency domain. To accommodate for geometrical and material variations, the vessel is modeled as a series of sections in which multiple reflections can occur. Results are presented for constant and varying gravity in straight and tapered flexible vessels.

A Finite Element Study of Elasto-Plastic Hemispherical Contact

2003 ◽  
Author(s):  
Robert L. Jackson ◽  
Itzhak Green
Keyword(s):  
Finite Element ◽  
Yield Strength ◽  
Constant Factor ◽  
Elastic Model ◽  
Asperity Contact ◽  
Finite Element Study ◽  
Perfectly Plastic ◽  
Wide Range ◽  
Elastic Perfectly Plastic ◽  
Element Study

This work presents a finite element study of elasto-plastic hemispherical contact. The results are normalized such that they are valid for macro contacts (e.g., rolling element bearings) and micro contacts (e.g., asperity contact). The material is modeled as elastic-perfectly plastic. The numerical results are compared to other existing models of spherical contact, including the fully plastic case (known as the Abbott and Firestone model) and the perfectly elastic case (known as the Hertz contact). At the same interference, the area of contact is shown to be larger for the elasto-plastic model than that of the elastic model. It is also shown, that at the same interference, the load carrying capacity of the elasto-plastic modeled sphere is less than that for the Hertzian solution. This work finds that the fully plastic average contact pressure, or hardness, commonly approximated to be a constant factor (about three) times the yield strength, actually varies with the deformed contact geometry, which in turn is dependant upon the material properties (e.g., yield strength). The results are fit by empirical formulations for a wide range of interferences and materials for use in other applications.

The Wavelet Spectral Finite Element-based user-defined element in Abaqus for wave propagation in one-dimensional composite structures

SIMULATION ◽  
2017 ◽  
Vol 93 (5) ◽  
pp. 397-408 ◽  
Author(s):  
Ashkan Khalili ◽  
Ratneshwar Jha ◽  
Dulip Samaratunga
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Composite Structures ◽  
Impact Damage ◽  
Shear Deformation Theory ◽  
Frequency Wave ◽  
One Dimensional ◽  
Finite Element Software ◽  
Model Complex ◽  
Spectral Finite Element

A Wavelet Spectral Finite Element (WSFE)-based user-defined element (UEL) is formulated and implemented in Abaqus (commercial finite element software) for wave propagation analysis in one-dimensional composite structures. The WSFE method is based on the first-order shear deformation theory to yield accurate and computationally efficient results for high-frequency wave motion. The frequency domain formulation of the WSFE leads to complex-valued parameters, which are decoupled into real and imaginary parts and presented to Abaqus as real values. The final solution is obtained by forming a complex value using the real number solutions given by Abaqus. Four numerical examples are presented in this article, namely an undamaged beam, a beam with impact damage, a beam with a delamination, and a truss structure. A multi-point constraint subroutine, defining the connectivity between nodes, is developed for modeling the delamination in a beam. Wave motions predicted by the UEL correlate very well with Abaqus simulations. The developed UEL largely retains the computational efficiency of the WSFE method and extends its ability to model complex features.

Hyper-Gravity and Multiple Reflections in Wave Propagation in the Aorta

2010 ◽  
Author(s):  
J. M. B. Kroot ◽  
C. G. Giannopapa
Keyword(s):  
Blood Flow ◽  
Wave Propagation ◽  
Cerebral Blood Flow ◽  
Total Pressure ◽  
Loss Of Consciousness ◽  
Pressure Waves ◽  
Multiple Reflections ◽  
One Dimensional ◽  
Gravity Changes ◽  
Pressure Part

Hypergravity and gravity changes encountered in e.g. airplanes, rollercoasters and spaceflight can result in headaches or loss of consciousness due to decreased cerebral blood flow. This paper describes the effect of hypergravity and gravity changes on the pressure in the aorta and the distension of its wall. The model presented consists of a pressure part caused by gravity and a part representing pressure waves propagating through the vessel. The total pressure is described by a one-dimensional formulation in the frequency domain. To accommodate for geometrical and material variations, the vessel is modeled as a series of sections in which multiple reflections can occur. Results are presented for constant and varying gravity in straight and tapered flexible vessels.

Stress Wave Propagation Analysis in One-Dimensional Micropolar Rods with Variable Cross-Section Using Micropolar Wave Finite Element Method

2018 ◽  
Vol 10 (04) ◽  
pp. 1850039 ◽  
Author(s):  
Mohsen Mirzajani ◽  
Naser Khaji ◽  
Muneo Hori
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Cross Section ◽  
Variable Cross Section ◽  
Stress Wave Propagation ◽  
Rotational Degree ◽  
Variable Cross ◽  
One Dimensional ◽  
Element Method

The wave finite element method (WFEM) is developed to simulate the wave propagation in one-dimensional problem of nonhomogeneous linear micropolar rod of variable cross-section. For this purpose, two kinds of waves with fast and slow velocities are detected. For micropolar medium, an additional rotational degree of freedom (DOF) is considered besides the classical elasticity’s DOF. The proposed method is implemented to solve the wave propagation, reflection and transmission of two distinct waves and impact problems in micropolar rods with different layers. Along with new solutions, results of the micropolar wave finite element method (MWFEM) are compared with some numerical and/or analytical solutions available in the literature, which indicate excellent agreements between the results.

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