Time Lapse Observation Based Modeling and Identification of Cell Behaviors in Angiogenic Sprout Development

Abstract

This paper presents a method for deriving dynamic equations for Endothelial Cell (EC) motion and estimating parameters based on time lapse imagery of angiogenic sprout development. Angiogenesis is the process whereby a collection of endothelial cells sprout out from an existing blood vessel, degrade the surrounding scaffold and form a new blood vessel. Sprout formation requires that a collection of ECs all work together and coordinate their movements and behaviors. The process is initiated and guided by a collection of external growth factors. In addition, the individual cells communicate and respond to each other’s movements to behave in a coordinated fashion. The mechanics of cell coordination are extremely complex and include both chemical and mechanical communication between cells and between cells and the matrix. Despite the complexity of the physical system, with many variables that cannot be measured in real time, the ECs behave in a predictable manner based on just a few quantities that can be measured in real time. This work presents a methodology for constructing a set of simple stochastic equations for cell motion dependent only on quantities obtained from time lapse data observed from in vitro experiments. Model parameters are identified from time lapse data using a Maximum Likelihood Estimator.