Macroscopic models accounting for cellular effects in natural or engineered tissues may involve unknown constitutive terms that are highly dependent on interactions at the scale of individual cells. Hybrid discrete models, which represent cells individually, were used to develop and apply techniques for modeling diffusive nutrient transport and cellular uptake to identify a nonlinear nutrient loss term in a macroscopic reaction-diffusion model of the system. Flexible and robust numerical methods were used, based on discontinuous Galerkin finite elements in space and a Crank-Nicolson temporal discretization. Scales were bridged via averaging operations over a complete set of subdomains yielding data for identification of a macroscopic nutrient loss term that was accurately captured via a fifth-order polynomial. Accuracy of the identified macroscopic model was demonstrated by direct, quantitative comparisons of the tissue and cellular scale models in terms of three error norms computed on a mesoscale mesh.
Keywords: averaging; discontinuous Galerkin; hybrid discrete model; mesoscale model; model identification; reaction-diffusion model.
Copyright © 2014 John Wiley & Sons, Ltd.