Quantitative modeling and control of nascent sprout geometry in in vitro Angiogenesis

Abstract

Nascent blood vessel growth in angiogenesis is a complex process involving cellular response to biochemical growth factors, degradation of the surrounding matrix, and coordinated migration of multiple endothelial cells up a growth factor gradient. Mechanistic understanding and quantitative modeling of the dominant dynamics involved in nascent vessel growth will enable new strategies for regulating vessel growth rate and geometry, and will have implications in controlling growth of complete vascular networks in many research areas, ranging from cancer treatment and wound healing to tissue engineering. In this thesis, we investigate the dynamics of nascent vessel growth in 3D microfluidic assays, formulate a quantitative process model based on our experimental characterization, and formulate a feedback approach to regulate growth. We begin by developing a new microfluidic assay consisting of a collagen gel scaffold with features to reduce assay-to-assay variability and increase experimental throughput. This high throughput assay reveals that there is an inverse relationship between nascent vessel elongation rate and diameter under diverse biochemical conditions. This finding is supported by immuno-fluorescent staining and biochemical inhibition studies, which give insight into the dominant mechanisms determining nascent vessel diameter. Based on our experimental characterization, we formulate a simple quantitative reaction-diffusion model that relates vessel diameter to elongation rate, and supports our understanding of the relevant dynamics. We conclude by formulating a model-based optimization approach for planning the optimal trajectory of elongation rate vs. time needed to obtain desired sprout geometry, and illustrate in simulation that model predictive feedback control can be used to correct for noise in the response of elongation rate to growth factor inputs.