Optimal Control of 2D Cell Migration
Konstantinos N. Blazakis · European Conference on Mathematical and Theoretical Biology · 2014
In this poster we present an optimal control numerical method for tracking Neutrophil cell migration on a two-dimensional substrate. To-date, the fol- lowing research question is largely unanswered: Given the initial position of the Neutrophil on the substrate at time t = 0 and at time t = T, the nal position and shape of the Neutrophil, can we nd an optimal parame- ter(s) or function (s) (could be time-dependent) such that the cell migrates to the desired nal position according to a formulated mathematical model? This framework naturally leads to inverse problems for cell motility. By using optimal control and phase-eld theory, we formulate and discretize the control of the interface of the moving cell on a 2-dimensional substrate. Then we solve the system of state and adjoint equations by using evolv- ing surface nite element method. A number of numerical experiments are presented which illustrate the validation of our methodology applied to experimental observations on the motion of neutrophils from zebrash Danio rerio larvae, and this poster will illustrate some of these exciting re- sults. Cell migration is a fundamental process in cell biology and is tightly linked to many important physiological and pathological events such as the immune response, wound healing, tissue dierentiation, embryogenesis, in- ammation, tumor invasion and metastasis. Our results oers premises for developing 3D inverse problems for cell motility, a formidable mathematical and computational challenge.