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An evolution of pulse speed in arteries

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Abstract

In this work, treating the artery as a thick-walled cylindrical shell made of an incompressible, isotropic and elastic solid, utilizing the large deformation theory and the stress-strain relation proposed by Demiray (1976b,Trans. ASME Ser. E, J. Appl. Mech.,98, 194–197), an explicit expression for the pulse speed is obtained and the effect of lumen pressure and the axial stretch on wave speed is discussed. Numerical results indicate that the wave speed increases with lumen pressure but decreases with the axial stretch. The results of the present model are compared with our previous work (Demiray, 1988,J. Biomech. 21, 55–58) on the same subject.

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Abbreviations

t kl :

Cauchy stress tensor

P :

Hydrostatic pressure

P i :

Lumen pressure

c kl :

Finger deformation tensor

F k K :

Deformation gradient

g kl :

Reciprocal metric tensor of the spatial frame

G KL :

Reciprocal metric tensor of the material frame

Σ:

Strain energy density function

I 1,I 2,I 3 :

Basic invariants of Finger deformation tensor

λ z :

Stretch ratio in the axial direction

λθ :

Stretch ratio in circumferential direction

λ iθ :

Stretch ratio on the inner surface

λ 0θ :

Stretch ratio on the outer surface

r i :

Deformed inner radius

r o :

Deformed outer radius

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Author notes

  1. Hilmi Demiray

    Present address: Faculty of Sciences and Letters, Department of Engineering Sciences, Istanbul Technical University, Maslak 80626, Istanbul, Turkey

Authors and Affiliations

  1. Research Institute for Basic Sciences, Department of Mathematics, Marmara Research Centre, P.O. Box 21, Gebze-Kocaeli, Turkey

    Hilmi Demiray

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  1. Hilmi Demiray
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Demiray, H. An evolution of pulse speed in arteries. Bltn Mathcal Biology 58, 129–140 (1996). https://doi.org/10.1007/BF02458285

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  • DOI: https://doi.org/10.1007/BF02458285

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