Limited cell ingrowth is a major problem for tissue engineering and the clinical application of porous biomaterials as bone substitutes. As a first step, migration and proliferation of an interacting cell population can be studied in two-dimensional culture. Mathematical modelling is essential to generalize the results of these experiments and to derive the intrinsic parameters that can be used for predictions. However, a more thorough evaluation of theoretical models is hampered by limited experimental observations. In this study, experiments and image analysis methods were developed to provide a detailed spatial and temporal picture of how cell distributions evolve. These methods were used to quantify the migration and proliferation of skeletal cell types including MG63 and human bone marrow stromal cells (HBMSCs). The high level of detail with which the cell distributions were mapped enabled a precise assessment of the correspondence between experimental results and theoretical model predictions. This analysis revealed that the standard Fisher equation is appropriate for describing the migration behaviour of the HBMSC population, while for the MG63 cells a sharp front model is more appropriate. In combination with experiments, this type of mathematical model will prove useful in predicting cell ingrowth and improving strategies and control of skeletal tissue regeneration.

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A multilevel finite element approach is applied to predict local cell deformations in engineered tissue constructs. Cell deformations are predicted from detailed nonlinear FE analysis of the microstructure, consisting of an arrangement of cells embedded in matrix material. Effective macroscopic tissue behavior is derived by a computational homogenization procedure. To illustrate this approach, we simulated the compression of a skeletal muscle tissue construct and studied the influence of microstructural heterogeneity on local cell deformations. Results show that heterogeneity has a profound impact on local cell deformations, which highly exceed macroscopic deformations. Moreover, microstructural heterogeneity and the presence of neighboring cells leads to complex cell shapes and causes non-uniform deformations within a cell.