Modeling Viscoelastic Behavior of Arterial Walls and Their Interaction with Pulsatile Blood Flow

A horizontal rotary table is provided and a mounting arm is supported above the table and generally parallels the latter. The arm extends along a path paralleling an axis of rotation of the table and an upright shaft is journalled from the mounting arm for rotation about an upright axis coinciding with the axis of rotation of the table. Drive structure drivingly connects the table and the upright shaft for rotation of the latter at twice the speed of rotation of the table and a support is mounted on the support arm for guided movement therealong. A scribe tool is carried by the support for engagement with and scribing a workpiece disposed on the table for rotation with the latter and motion converting and drive structure is operatively connected between the upright shaft and the support for effecting oscillation of the support along the arm responsive to and an in timed relation with rotation of the shaft. The motion converting and drive structure includes operational features which function to continuously vary the linear displacement rate of the support along the arm during constant angular velocity of the upright shaft.

[1]  M. Olufsen,et al.  Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions , 2000, Annals of Biomedical Engineering.

[2]  V. V. Novozhilov,et al.  Thin shell theory , 1964 .

[3]  Philippe G. Ciarlet,et al.  Asymptotic analysis of linearly elastic shells. III. Justification of Koiter's shell equations , 1996 .

[4]  P. Plotnikov,et al.  HOPF SOLUTIONS TO A FLUID-ELASTIC INTERACTION MODEL , 2008 .

[5]  A. Cemal Eringen,et al.  Mechanics of continua , 1967 .

[6]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[7]  R. D. Bauer,et al.  Separate determination of the pulsatile elastic and viscous forces developed in the arterial wall in vivo , 2004, Pflügers Archiv.

[8]  H. B. Veiga On the Existence of Strong Solutions to a Coupled Fluid-Structure Evolution Problem , 2004 .

[9]  G. Pontrelli A mathematical model of flow in a liquid-filled visco-elastic tube , 2006, Medical and Biological Engineering and Computing.

[10]  J. Grotberg,et al.  BIOFLUID MECHANICS IN FLEXIBLE TUBES , 2001 .

[11]  Daniel Coutand,et al.  The Interaction between Quasilinear Elastodynamics and the Navier-Stokes Equations , 2006 .

[12]  Antonin Chambolle,et al.  Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate , 2005 .

[13]  Andro Mikelić,et al.  The derivation of a nonlinear filtration law including the inertia effects via homogenization , 2000 .

[14]  J D Humphrey,et al.  Mechanics of the arterial wall: review and directions. , 1995, Critical reviews in biomedical engineering.

[15]  Andro Mikelić,et al.  Effective equations describing the flow of a viscous incompressible fluid through a long elastic tube , 2002 .

[16]  R Armentano,et al.  Effects of hypertension on viscoelasticity of carotid and femoral arteries in humans. , 1995, Hypertension.

[17]  Fabio Nobile,et al.  Numerical approximation of fluid-structure interaction problems with application to haemodynamics , 2001 .

[18]  S. Čanić,et al.  A two-dimensional effective model describing fluid–structure interaction in blood flow: analysis, simulation and experimental validation , 2005 .

[19]  R. Vito,et al.  Blood vessel constitutive models-1995-2002. , 2003, Annual review of biomedical engineering.

[20]  S. Čanić,et al.  Mathematical analysis of the quasilinear effects in a hyperbolic model blood flow through compliant axi‐symmetric vessels , 2003 .

[21]  J. F. Doyle Thin Plates and Shells , 2020, Encyclopedia of Continuum Mechanics.

[22]  M. Lupo,et al.  Unsteady Stokes Flow in a Distensible Pipe , 1991 .

[23]  Anne M. Robertson,et al.  A DIRECTOR THEORY APPROACH FOR MODELING BLOOD FLOW IN THE ARTERIAL SYSTEM: AN ALTERNATIVE TO CLASSICAL 1D MODELS , 2005 .

[24]  Alfio Quarteroni,et al.  Computational vascular fluid dynamics: problems, models and methods , 2000 .

[25]  Philippe G. Ciarlet,et al.  Asymptotic analysis of linearly elastic shells: ‘Generalized membrane shells’ , 1996 .

[26]  Herbert Reismann,et al.  Elastic Plates: Theory and Application , 1988 .

[27]  B. Miara,et al.  Asymptotic analysis of linearly elastic shells , 1996 .

[28]  Suncica Canic,et al.  Self-Consistent Effective Equations Modeling Blood Flow in Medium-to-Large Compliant Arteries , 2005, Multiscale Model. Simul..

[29]  George E Taffet,et al.  Noninvasive cardiovascular phenotyping in mice. , 2002, ILAR journal.

[30]  Y C Fung,et al.  New experiments on shear modulus of elasticity of arteries. , 1994, The American journal of physiology.

[31]  G. C. Lee.,et al.  Numerical simulation for the propagation of nonlinear pulsatile waves in arteries. , 1992, Journal of biomechanical engineering.

[32]  Daniel Coutand,et al.  Motion of an Elastic Solid inside an Incompressible Viscous Fluid , 2005 .

[33]  R. Armentano,et al.  Arterial wall mechanics in conscious dogs. Assessment of viscous, inertial, and elastic moduli to characterize aortic wall behavior. , 1995, Circulation research.

[34]  Suncica Canic,et al.  Effective Equations Modeling the Flow of a Viscous Incompressible Fluid through a Long Elastic Tube Arising in the Study of Blood Flow through Small Arteries , 2003, SIAM J. Appl. Dyn. Syst..

[35]  R. Temam Navier-Stokes Equations , 1977 .

[36]  Timothy J. Pedley,et al.  Large Axisymmetric Deformation of a Cylindrical Shell Conveying a Viscous Flow , 1995 .

[37]  Josip Tambača,et al.  Effective Model of the Fluid Flow through Elastic Tube with Variable Radius , 2005 .

[38]  Philippe Destuynder,et al.  A classification of thin shell theories , 1985 .

[39]  A. Mikelić Homogenization theory and applications to filtration through porous media , 2000 .

[40]  U. Hornung Homogenization and porous media , 1996 .

[41]  Gerald Wempner,et al.  Mechanics of Solids and Shells: Theories and Approximations , 2002 .

[42]  G. Kuiken,et al.  Wave propagation in a thin-walled liquid-filled initially stressed tube , 1983, Journal of Fluid Mechanics.

[43]  W. Nichols,et al.  McDonald's Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles , 1998 .