Mathematical and mechanical models of cell motion

Metastasis plays a significant role in many of breast cancer deaths. The traditional route for metastasis involves several steps including successful penetration of a vessel (intravasation), passage through the circulatory system to the site of metastasis (translocation), and exiting of that vessel (extravasation). Decreasing the frequency of any of these events can help mitigate the effects of breast cancer on the approximately 3.5 million Americans affected by the disease. Experiments also suggest that mechanotransduction, a process by which mechanical forces initiate cellular processes, may play an important role in such events. Because of these observations, we have begun developing a mechanical model of breast cancer cell dynamics that is force-based and, therefore, readily informs us about force levels cells may experience during events like intravasation, translocation, and extravasation. We will share results where the model is used to simulate breast cell passage through a tapered microfluidic channel. These results show that a two-dimensional network of damped springs (viscoelastic elements) submersed in surrounding Stokes flow can be used to reproduce qualitative agreement with experiments. They further show that such a model can be used with sensitivity analysis to consider how different cell properties affect cellular dynamics. While such results are focused on translocation and physical forces (without biochemistry), additional extensions of the model are currently in progress. We will share these extensions including development of a three-dimensional version of the model as well as use of an alternative approach, the immersed boundary method, to model such cells. Both of these efforts suggest this particular modeling approach is relatively versatile and useful for considering cell migration, osteocyte dynamics, and mechanically transduced biochemical products.