Computational methods for the analysis of cell migration and motility - Havenhill, Eric Colton, author; Ghosh, Soham, advisor; Heyliger, Paul, committee member; McGilvray, Kirk, committee member; Zhao, Jianguo, committee member (Colorado State University. Libraries, 2024)
Collective cell migration (CCM) is necessary for many biological processes, such as in the formation or regeneration of tissue, fibroblast movement in wound healing, and the movement of macrophages and neutrophils in the body's immune response, to name a few. CCM is commonly modeled with PDEs, however these equations usually model the population density, rather than the displacement field describing the movement of any arbitrary cell. One unknown aspect of this movement is the various methods that cells use to facilitate communication to each other. Chemical communication plays a substantial role in directed cell movement, however, other mechanical methods, such as the propagation of stresses through a shared substrate to neighboring cells and cell behavior in a crowded environment, also play an important role which is less understood. The quantification of the kinematic and dynamic characteristics in CCM would present several novel advancements in understanding the collective cell behavior. First, the dynamic mode decomposition (DMD) framework is utilized. DMD allows for the recovery of a dynamic system, in the form of an ODE or PDE, by sampling the states of a system. In the context of the cell migration, the displacements of fibroblasts during a scratch-wound assay are obtained, which result in a governing PDE through the DMD process. This PDE is used in conjunction with modern optimal control theory to develop a 2D and 3D trajectory for the migration of controllable cells to a target. On an individual level, with the hybrid use of modern static structural optimization and simple non-linear control, a cell's cytoskeleton during migration can be studied, providing for the quantification of the traction force exerted on the substrate. The results of this analysis are compared with stress and structural optimization models in ANSYS and FEBio, which uses the finite element method, so that a reasonable range of these stresses during CCM can be provided. To further study the individual mechanics of cell migration, the proposed hybrid model is extended to a fully dynamic model which predicts the cytoskeletal stress fiber formations over time that require the minimal amount of material with the use of optimal control theory. The results of this research could provide useful applications in many real-world situations, from the generating of a trajectory for microrobots during drug delivery to the study of the collective migration of organisms including cells.
Keywords: generative design; morphogenesis; structural optimization; mechanosensing; dynamics; optimal control