Optimization-based synthesis with directed cell migration.

Collective behavior of biological agents from cells to herds of organisms is a fundamental feature in systems biology and in the emergence of new phenomena in the biological environment. Collective cell migration (CCM) under a physical or chemical cue is an example of this fundamental phenomenon where the individual migration of a cell is driven by the collective behavior of the neighboring cells and vice versa. The goal of this research is to discover the mathematical rules of collective cell migration with dynamic mode decomposition (DMD) with the use of experimental data and to test the predictive nature of the models with independent experimental data sets subject to Dirichlet, Neumann, and mixed boundary conditions. Both single and multi-cellular systems are investigated in this process. Additionally, the goal of this research is to create an optimal trajectory for microscopic robots in the presence of an obstacle course made of both static and dynamic obstacles. Such an optimization is made possible by synthesizing the discovered dynamics for cell migration with a numerical approach to dynamic optimization known as collocation by augmenting the discovered dynamics to the constraint equations. The optimal trajectory results presented in silico have potential design applications for the path planning of microrobots for therapeutic purposes such as cancer cell drug delivery, microsurgery, microsensing for early disease detection, and cleaning of toxic substances.