A lattice-based approach to model distraction osteogenesis.

Distraction osteogenesis is a well-known technique in which new bone tissue is created when a distraction displacement is applied through an external frame. This orthopedic process is nowadays focus of intense research, both experimentally and numerically, as there are still many aspects not well understood. The aim of this study is to simulate bone distraction by means of a combined discrete-continuum approach based on a lattice formulation. Existing computational models simulate the main processes of distraction osteogenesis from a continuum perspective, considering as state variables the population of cells and tissue distributions. Results of the continuum and lattice-based approaches are similar with respect to the global evolution of the different cells but rather different in terms of the type of ossification process. Differences in the size of the soft interzone in the gap have also been found. In addition, the discrete-continuum formulation allows including a more realistic approach of the migration/proliferation process with a discrete random walk model instead of the Fick's law used in continuum approaches. Also, blood vessel growth can be simulated explicitly in this model with the inclusion of the endothelial cells. Further study is needed to provide additional insights to understand coupled phenomena at different scales in the cell-tissue interactions. However this work provides a first preliminary step for improving multiscale models.