A nonlinear diffusion equation arising in the study of soft tissue

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Abstract
A nonlinear diffusion equation which describes the deformation of a soft fluid-filled tissue is studied. The nonlinearity in the problem arises from the permeability of the elastic phase which for a number of tissues, such as articular cartilage, is strongly dependent on the strain. Moreover, for most tissues the exact dependence is not known, and so the functional dependence of the permeability on the strain is not determined until after the problem is solved. The approach uses perturbation methods for the diffusive boundary layers that occur in the problem and similarity solutions to solve the reduced problems. Once the solution is obtained, the permeability function is determined and some of the limitations of the present model of soft tissue are discussed.