Multiscale modeling of diffusion hindrance in tissue engineered constructs

Macroscopic mechanical properties of tissue engineered constructs depend on theircomposition, which evolves in time following synthesis, transport, binding and degradationof biomolecules. A thorough understanding of these phenomena is relevant to improve thedevelopment of artificial tissues during culturing. From a purely mechanical point of view,diffusion plays a fundamental role in the transport of newly synthesized material across thetissue. Diffusion mechanisms are highly inhomogeneous in developing biological tissues, inwhich large aggregating matrix molecules such as collagen and GAGs are continuallysynthesized by individuals cells. In these systems, diffusivity decreases due to an increase inthe tortuosity of the extracellular matrix.In this work we address the effects of diffusion hindrance on global mechanical properties oftissue engineered cartilage. We also study the influence of the continuous accumulation ofbound material and the developing microgeometry of the tissue on the diffusion ofaggregating molecules.The study is based on a continuous model for diffusion, binding and a posteriori degradationof matrix components. Diffusion hindrance is modeled in terms of a random walkapproximation. The governing equations are solved using finite element methods at tissueand RVE scales.The numerical results show a significant effect of diffusion hindrance on the concentrationdistribution of immobilized GAG in tissue engineered cartilage as well as on the mechanicalproperties of the construct. Diffusion hindrance causes a higher accumulation of GAGaround the cells, hampering the diffusion of newly synthesized material. On a macroscopicscale, the aggregate modulus and the permeability are sensitive to the distribution of theextracellular matrix. The enhanced localization of the extracellular matrix contributes to asoftening of the construct, which becomes apparent from fifteen days of culture.