Abstract
Vascular remodeling, the adaptive reshaping of the vascular network in response to changing demands of the tissue, plays a critical role in embryo development and various pathologies. Biochemical signals present in the extravascular region, such as vascular endothelial growth factor (VEGF), are key regulators in the vascular remodeling process. Although the role of these signals has been well studied in vitro, in vivo quantification of VEGF transport during vascular remodeling remains challenging since it requires computing VEGF transport on a growing, topologically changing geometry. In this work, we propose a computational method to compute the VEGF concentration inside the extraembryonic tissue of a growing quail embryo during early vascular development. The evolving vascular geometry is obtained from time-lapse images of a growing quail embryo and represented implicitly via a phase field formulation, which tracks complex topological changes without mesh regeneration, enabling accurate simulation of VEGF transport in the growing extraembryonic tissue. Our simulations demonstrate that tissue growth can significantly influence VEGF distribution, which in turn affects the spatial cues driving vascular remodeling. This effect arises because the timescale of VEGF production and binding mechanics is comparable to the timescale of the impact of tissue growth on VEGF.