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Flow-induced deformation from pressurized cavities in absorbing porous tissues

Bulletin of Mathematical Biology volume 54, pages 977–997 (1992)Cite this article

Abstract

The behaviour of a cavity during an injection of fluid into biological tissue is considered. High cavity pressure drives fluid into the neighbouring tissue where it is absorbed by capillaries and lymphatics. The tissue is modelled as a nonlinear deformable porous medium with the injected fluid absorbed by the tissue at a rate proportional to the local pressure. A model with a spherical cavity in an infinite medium is used to find the pressure and displacement of the tissue as a function of time and radial distance. Analytical and numerical solutions for a step change in cavity pressure show that the flow induces a radial compression in the medium together with an annular expansion, the net result being an overall expansion of the medium. Thus any flow induced deformation of the material will aid in the absorption of fluid.

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Affiliations

  1. Mathematics Department, University College, University of New South Wales, 2600, Canberra, A.C.T., Australia

    S. I. Barry & G. K. Aldis

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  1. S. I. Barry
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  2. G. K. Aldis
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Correspondence to S. I. Barry.

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Barry, S.I., Aldis, G.K. Flow-induced deformation from pressurized cavities in absorbing porous tissues. Bltn Mathcal Biology 54, 977–997 (1992). https://doi.org/10.1007/BF02460662

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  • DOI: https://doi.org/10.1007/BF02460662

Keywords

  • Porous Medium
  • Applied Pressure
  • Cavity Pressure
  • Nonlinear Diffusion Equation
  • Radial Compression