Three-dimensional (3D) porous tissue scaffolds combined with bioactive molecules and cells offer key advantages for bone repair mechanisms. A functional bone tissue scaffold should provide mechanical support with an adequate combination of porosity and permeability for nutrients, oxygen supply, waste removal, and growth factors release as well as controlled degradation. Although a vast amount of work exist to address these challenges, to the best of our knowledge, a design framework taking tissue differentiation, diffusion, and growth factor (GF) release into account in time-domain simultaneously does not exist. In this paper, we provide an initial effort to address such a need by laying down the foundations for a simulation framework incorporating these effects within a Finite Element Analysis (FEA) model in COMSOL Multiphysics® software. The effectiveness of the numerical model is demonstrated via preliminary mechano-biology analyses on a simulated 3D poroelastic bone scaffold. Initial time-dependent results demonstrate the suitability of this model for an optimization framework. More specifically, it is demonstrated that coupled Multiphysics equations of diffusion, GF release, and differentiation could provide valuable inputs for ideal bone scaffold systems for effective bone repair tasks in the future.