A Biphasic Hyperelastic Model for the Analysis of Fluid and Mass Transport in Brain Tissue

A biphasic hyperelastic finite element model is proposed for the description of the mechanical behavior of brain tissue. The model takes into account finite deformations through an Ogden-type hyperelastic compressible function and a hydraulic conductivity dependent on deformation. The biphasic equations, implemented here for spherical symmetry using an updated Lagrangian algorithm, yielded radial coordinates and fluid velocities that were used with the convective-diffusive equation in order to predict mass transport in the brain. Results of the model were equal to those of a closed-form solution under infinitesimal deformations, however, for a wide range of material parameters, the model predicted important increments in the infusion sphere, reductions of the fluid velocities, and changes in the species content distribution. In addition, high localized deformation and stresses were obtained at the infusion sphere. Differences with the infinitesimal solution may be mainly attributed to geometrical nonlinearities related to the increment of the infusion sphere and not to material nonlinearities.