A porous media approach for plantar tissue during gait

Recently a new computational model, based on the thermodynamically constrained averaging theory, has been proposed to predict tumor initiation and proliferation and afterwards to study plantar tissue mechanics. The foot tissue is modeled as an elastic porous medium, in large strain regime and completely filled by a fluid phase. In detail, the tissue cells and their extracellular matrix form the solid skeleton with pores saturated by the interstitial fluid. The primary variables of the model are: the interstitial fluid pressure pf , the displacement vector of the solid phase us, and the mass fraction of oxygen dissolved in the interstitial fluid, ωof . With respect to these primary variables, the governing equations are discretized in space by the finite element method, in time by using the θ-Wilson method and then solved numerically. By considering the interstitial fluid, it is possible to mimic the viscoelastic behavior of the plantar tissue observed experimentally by Gefen. This is shown in the simulated cases, where a foot during stance and some gait cycles are modeled. The presented examples integrate experimental data at different scales (patient specific foot geometry, tissue elasticity and permeability, possible tissue vasculopathy, global forces measured during gait, etc.) and allow validating the developed modeling procedure by comparisons between numerical and measured plantar pressures. Being the global response of the bi-phase system viscoelastic, it is shown that the duration of stance as well as of each of gait cycle has an influence on tissue strain and stress fields.