<p>Embryonic development is a complicated phenomenon influenced by genetic regulation and biomechanical cellular behaviors. However, the relative influence of these factors on spatiotemporal morphogen distributions is not well understood. Bone Morphogenetic Proteins (BMPs) are the primary morphogen guiding the dorsal-ventral (DV) patterning of the early zebrafish embryo, and BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands.  Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however, it is not clear how the source-sink mechanism shapes patterns in 3D, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo.</p><p> Throughout blastulation and gastrulation, major cell movement, known as epiboly, happens along with the BMP mediated DV patterning. The layer of epithelial cells begins to thin as it spreads toward the vegetal pole of the embryo until it has completely engulfed the yolk cell. This dynamic domain may influence the distributions of BMP network members. This project aims to investigate the multiscale regulatory network of the BMP signaling dynamics along with the biophysical deformation of the embryo tissue during epiboly. </p><p> In this study, we present a three-dimensional (3D) growing domain mathematical modeling framework to simulate the BMP patterning and epiboly process during the blastula to gastrula stage zebrafish embryo, with both finite difference and finite element approaching. These models provide a starting point to elucidate how different mechanisms and components work together in 3D to create and maintain the BMP gradient in the zebrafish embryo. We are interested in how the cellular movements impact the formation of gradients by contributing an advective term whereby the morphogens are swept with the moving cells as they move vegetally. Dynamic cell imaging data are used to quantify the cell movement during the epiboly. We evaluated the accuracy of the mesh updating compared to the advection caused by cell movement and its role in embryonic patterning. Quantitative whole-mount RNA scope data of BMP2b, Chordin, Noggin, Sizzled, and phosphorylated-SMAD data are collected and analyzed precisely to test the hypotheses of the gradient formation mechanism in our model. We also present a novel approach of Neuro Network model to accelerate the computationally intensive PDE simulations. Our goal is to develop a complete advection-diffusion-reaction model that incorporates all stages of zebrafish embryonic development data. By combining the biophysics of epiboly with the regulatory dynamics of the BMP network, we can test complex models to investigate the consistent spatiotemporal DV patterning in the early zebrafish embryo.</p>