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Coupled radial and longitudinal displacements and stresses within the arterial wall in pulsatile flow under tethered and free-wall conditions

S. Hodis1 and M. Zamir1,2

  • 1Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A5B7, Canada
  • 2Department of Medical Biophysics, The University of Western Ontario, London, Ontario N6A5B7, Canada

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Phys. Rev. E 83, 051923 – Published 26 May, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.051923

Abstract

An analytical solution is presented of the governing equations for the coupled radial and longitudinal displacements and stresses within the finite thickness of the arterial wall in pulsatile flow. The results are used to examine the extent of coupling between the radial and longitudinal dynamics within the vessel wall, particularly when the wall is fully tethered. In the case of a free wall, it is found that the dynamics in the two directions are fairly decoupled from each other when the wavelength is at least of the order of 100 times the vessel radius. At 10 times the vessel radius, however, there is strong coupling between the two. These findings are consistent with expectations in the case of a free wall where the long-wave approximation has been applied in the past. In the case of a tethered wall, however, the results indicate that in general the long-wave approximation is strictly valid only when the combination of wall material and tethering allow the wave to be long.

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      Information

      Phys. Rev. E 83, 051923– Published 26 May, 2011
      • Received 27 June 2010

      ©2011 American Physical Society

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