Flow-induced deformation from pressurized cavities in absorbing porous tissues.

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.

[1]  M. Biot.  THEORY OF ELASTICITY AND CONSOLIDATION FOR A POROUS ANISOTROPIC SOLID , 1955 .

[2]  H J Grootenboer,et al.  In vitro compression of a soft tissue layer on a rigid foundation. , 1987, Journal of biomechanics.

[3]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[4]  W M Lai,et al.  Drag-induced compression of articular cartilage during a permeation experiment. , 1980, Biorheology.

[5]  G. Aldis,et al.  Fluid flow over a thin deformable porous layer , 1991 .

[6]  M. Holmes.  Finite deformation of soft tissue: analysis of a mixture model in uni-axial compression. , 1986, Journal of biomechanical engineering.

[7]  Matthew R. Glucksberg.  Mechanics of the perialveolar interstitium of the lung , 1990 .

[8]  Mark H. Holmes,et al.  COMPARISON THEOREMS AND SIMILARITY SOLUTION APPROXIMATIONS FOR A NONLINEAR DIFFUSION EQUATION ARISING IN THE STUDY OF SOFT TISSUE , 1984 .

[9]  S. I. Barry,et al.  Unsteady flow induced deformation of porous materials , 1991 .

[10]  M. H. Friedman,et al.  General theory of tissue swelling with application to the corneal stroma. , 1971, Journal of theoretical biology.

[11]  D. E. Kenyon,et al.  A mathematical model of water flux through aortic tissue. , 1979, Bulletin of mathematical biology.

[12]  D. E. Kenyon.  Consolidation in Compressible Mixtures , 1978 .

[13]  M. Biot.  MECHANICS OF DEFORMATION AND ACOUSTIC PROPAGATION IN POROUS MEDIA , 1962 .

[14]  R. M. Bowen,et al.  Incompressible porous media models by use of the theory of mixtures , 1980 .

[15]  Y Lanir,et al.  Biorheology and fluid flux in swelling tissues. I. Bicomponent theory for small deformations, including concentration effects. , 1987, Biorheology.

[16]  G Jayaraman,et al.  Water transport in the arterial wall--a theoretical study. , 1983, Journal of biomechanics.

[17]  Van C. Mow,et al.  A Finite Deformation Theory for Nonlinearly Permeable Soft Hydrated Biological Tissues , 1986 .

[18]  M. M. Helland.  Samson Wright’s Applied Physiology 12th ed , 1972 .

[19]  M. Holmes.  A theoretical analysis for determining the nonlinear hydraulic permeability of a soft tissue from a permeation experiment. , 1985, Bulletin of mathematical biology.

[20]  van Dh Dick Campen,et al.  A mixture approach to the mechanics of skin. , 1987, Journal of biomechanics.

[21]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[22]  J. Tarbell,et al.  Modeling water flow through arterial tissue. , 1987, Bulletin of mathematical biology.

[23]  W M Lai,et al.  Fluid transport and mechanical properties of articular cartilage: a review. , 1984, Journal of biomechanics.

[24]  W M Lai,et al.  Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications. , 1989, Journal of biomechanical engineering.

[25]  Charles Nicholson,et al.  Diffusion from an injected volume of a substance in brain tissue with arbitrary volume fraction and tortuosity , 1985, Brain Research.

[26]  V C Mow,et al.  The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. , 1990, Journal of biomechanics.

[27]  Y Lanir,et al.  In-vivo indentation of human skin. , 1990, Journal of biomechanical engineering.

[28]  Van C. Mow,et al.  Mechanics of Animal Joints , 1979 .

[29]  G. Jayaraman,et al.  A theoretical model for water flux through the artery wall. , 1987, Journal of biomechanical engineering.

[30]  D. E. Kenyon,et al.  The theory of an incompressible solid-fluid mixture , 1976 .

[31]  G. Aldis,et al.  Comparison of models for flow induced deformation of soft biological tissue. , 1990, Journal of biomechanics.

[32]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[33]  S. Middleman,et al.  Transport phenomena in the cardiovascular system , 1972 .

[34]  D. E. Kenyon.  Transient Filtration in a Porous Elastic Cylinder , 1976 .

[35]  Mark H. Holmes.  A nonlinear diffusion equation arising in the study of soft tissue , 1983 .