  In this paper, we introduce a three-dimensional mathematical model of
collagen contraction with microbuckling based on the two-dimensional model
previously developed by the authors. The model both qualitatively and
quantitatively replicates experimental data including lattice contraction over
a time course of 40 hours for lattices with various cell densities, cell
density profiles within contracted lattices, radial cut angles in lattices, and
cell force propagation within a lattice. The importance of the model lattice
formation and the crucial nature of its connectivity are discussed including
differences with models which do not include microbuckling. The model suggests
that most cells within contracting lattices are engaged in directed motion.
