A stochastic control framework for regulating collective behaviors of an angiogenesis cell population

This paper presents a framework for controlling the development of a vascular system in an in vitro angiogenesis process. Based on on-line measurement of cell growth and a stochastic model of cell population, a closed-loop control system is developed for regulating the process of cell migration and tissue formation. Angiogenesis develops in a wet environment and it is difficult to control each and every cell individually and specifically. Instead, chemical and mechanical stimuli can be applied pervasively to the whole process as global control inputs, which can allow for control of collective behaviors of the cell population. This paper formulates a systems level description of the angiogenesis process and proposes a control scheme that chooses global control inputs to drive collective cell patterns, such as branch density per unit length of sprout, toward a desired goal. In response to control inputs, the k-step ahead prediction of collective cell pattern is evaluated, and the input that is most likely to bring the predicted cell pattern to the desired one is selected for the current control. Simulation demonstrates that the global branch density of a simplified angiogenesis model can be controlled using this technique. To our knowledge, this paper is the first to formulate feedback control for regulating an in vitro angiogenesis process.