Porosity and diffusion in biological tissues. Recent advances and further perspectives

We present a review of porosity and diffusion in biological tissues from different perspectives. We first introduce the topic by illustrating experimental evidence related to diffusion in porous media and review a number of state of the art experimental techniques. We then proceed by providing a revisited derivation of the equations of poroelasticity from the microstructure (via asymptotic homogenization), which is especially aimed at giving a first insight on the topic to both students and scientists who are not familiar with the subject. Results based on this kind of models have only recently been presented in the literature and could possibly complement the experiments by getting a more thorough understanding on the complex interplay between porosity and diffusion. We investigate further the matter by exploring the role of diffusion in driving growth and stresses in the context of linear elastic modeling for tumors and cellular automata. We finally conclude the chapter by (a) discussing diffusion in nonlinear, “active” materials, i.e., those which are possibly characterized by growth and remodeling, and (b) offering an overview on cutting edge research problems on diffusion for this class of complex materials