Bulletin of Mathematical Biology

, Volume 59, Issue 5, pp 993–1012 | Cite as

The effect of shear stress on solitary waves in arteries

  • Hilmi Demiray
Article
  • 61 Downloads

Abstract

In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materals are depicted in graphical forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissues.

Keywords

Solitary Wave Wave Profile Transmural Pressure Strain Energy Function Elastic Tube 

Nomenclature

Ai

inner cross-sectional area

α

a material constant for soft tissues

b

a material constant for a M-R material

ckl

Finger deformation tensor

γ

thickness parameter for tube wall

λθi

\(\left( {B_i = \lambda _\theta ^{i^2 } } \right)\) circumferential stretch on the inner surface of tube

λz

stretch in the axial direction

P

hydrostatic pressure of elastic solid

Pi*

fluid pressure

ρ0

mass density of solid

ρf

mass density of fluid

tkl

Cauchy stress tensor

w*

axial fluid velocity

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Copyright information

© Society for Mathematical Biology 1997

Authors and Affiliations

  • Hilmi Demiray
    • 1
  1. 1.Faculty of Sciences and Letters, Department of Engineering SciencesIstanbul Technical UniversityMaslak-IstanbulTurkey

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