Abstract—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. I. INTRODUCTION NGIOGENESIS is the process of growing or extending a vascular network into a tissue matrix from a preexisting vascular system. Understanding how to control angiogenesis is extremely important in many research areas, ranging from cancer treatment and wound healing to morphogenesis, stem cells, and tissue engineering. During angiogenesis, endothelial cells (EC’s) sprout from existing vasculature and extend into the surrounding tissue. The sprouts extend and branch as a function of local chemical and mechanical conditions. The angiogenesis process has not been completely described via deterministic models and cellular behaviors have been described as stochastic processes Manuscript received April 23, 2008. This material is based on work supported in part by the National Science Foundation under grant number NSF EFRI-0735997. L. B. Wood is with the department of mechanical engineering at the Massachusetts Institute of Technology, Cambridge, MA 02139 USA (phone: 617-258-8013; e-mail: woodl@mit.edu). A. Das is with the department of biological engineering at the Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e- mail: anusuya@mit.edu). R. D. Kamm is with the department of biological engineering and the department of mechanical engineering at the Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: rdkamm@mit.edu). H. H. Asada is with the department of mechanical engineering at the Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e- mail: asada@mit.edu). modulated by conditions local to the cell [1],[2]. Regulating and manipulating the angiogenesis process by actively modulating chemical and mechanical conditions is a truly challenging research issue, which will have a significant impact upon broad biological engineering and medical fields. Angiogenesis and other biological processes are fundamentally different from traditional engineering systems where control technology has been successfully applied. First, the system consists of a vast number of cells that have local controllers to perform a specific class of functions. Collective behavior of the cells exhibits meaningful functionality, such as constructing a vascular network. Second, cells are living in a “wet” environment, where signals propagate through diffusion. Stimuli to the process affect broad regions of cells. In designing a control architecture, it is important to understand that it is not fundamentally possible to control the behavior of each and every cell in the population. The available stimulus is much too limited in specificity. Further, it is not necessary, or even desirable, to control each and every cell. In generating a vascular network, the system as a whole should satisfy certain collective requirements, such a vascular density in the matrix, rate of branching, rate of growth, or others. The behavior of each individual cell does not matter, but correct development of the cellular population as a whole is important in growing a useful vascular system. An additional important feature of the angiogenesis process is that system stimuli do not effect deterministic changes in system behavior. Instead, application of a stimulus modulates cell transition probabilities. The authors have previously developed stochastic broadcast feedback control for control of clouds of independent cells and vast degree of freedom actuators [3],[4]. The authors foresee that insights gained from controlling the meaningful collective behavior of the angiogenesis process will yield insight into better design of vast degree of freedom systems like robotic swarms through engineered randomness. The objective of this paper is to develop a control framework for regulating collective measures of vascular growth. We will pose a systems level description of the angiogenesis process with global outputs that we wish to control. Inspiration for the systems level description must be obtained from mathematical models of the angiogenesis process. In addition, implementing control will require detailed angiogenesis models. It may also be necessary to utilize chemical diffusion models to describe the dynamics A Stochastic Control Framework for Regulating Collective Behaviors of an Angiogenesis Cell Population Levi B. Wood, Anusuya Das, Roger D. Kamm and H. Harry Asada, Member, IEEE A Proceedings of the 2nd Biennial IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics Scottsdale, AZ, USA, October 19-22, 2008 978-1-4244-2883-0/08/$25.00 ©2008 IEEE 390