  We introduce a stress/total-pressure formulation for poroelasticity that
includes the coupling with steady nonlinear diffusion modified by stress. The
nonlinear problem is written in mixed-primal form, coupling a perturbed twofold
saddle-point system with an elliptic problem. The continuous formulation is
analysed in the framework of abstract fixed-point theory and Fredholm
alternative for compact operators. A mixed finite element method is proposed
and its stability and convergence analysis are carried out. We also include a
few illustrative numerical tests. The resulting model can be used to study
waste removal in the brain parenchyma, where diffusion of a tracer alone or a
combination of advection and diffusion are not sufficient to explain the
alterations in rates of filtration observed in porous media samples.
