The growth of solid grains during the solidification of a liquid alloy is accompanied by the ejection of chemical species into their environment. Nearby grains interact via the diffusion field in the liquid phase. These interactions depend heavily on the spatial arrangement of the grains. The influence of the diffusive interactions is not limited to the shapes and sizes of grains but extends to controlling the overall kinetics of the transformation. In current mean-field models of dendritic growth these interactions are overly simplified, since the mean-field models completely neglect the spatial arrangement aspect. In this study we show the limitations of state-of-the-art mean-field models in the prediction of dendritic growth, by comparing their predictions with full-field simulations using the grain envelope model (GEM). Different periodic and random arrangements of grains are examined. We also explain why mean-field models poorly predict the behavior of realistic systems with randomly dispersed grains. This explanation is based on analyzing the behavior of individual grains in their local neighborhood, defined by a Voronoi tessellation. We plan on using these analyses to integrate the grain spatial arrangement aspect in order to formulate better mean-field models of dendritic growth.