Inverted colloidal crystal geometry has been recently utilized in the design of highly organized 3D cell scaffolds. The regularity of the resulting scaffolds enables computational modeling of scaffold properties. In this work we probe the resistance offered by these scaffolds to nutrient transport, by using Brownian dynamics and Monte Carlo simulations to model the effective nutrient diffusivity. Brownian dynamics simulations indicate that the effective diffusivity for small nutrients in the scaffold, D(eff)=0.3D(0), where D(0) is the free solution diffusivity. Further, results of Monte Carlo simulations for dilute solutions of larger particles show that the D(eff) decreases linearly with the size of the particles.