The human brain is arguably the most mysterious organ in the body. While not the largest or most convoluted brain among mammals, it possesses the highest number of neurons in its cortical layers relative to its size. This aspect has attracted the attention of scientists across various fields, aiming to understand the origin and early-stage development of these neurons in the brain \cite{Zarzor23}. Over the past few decades, neuroscientists have investigated various cell types that play a crucial role during embryonic life. However, the precise mechanisms through which the behavior of these cell types affects the number of neurons in the cortical layer and contributes to cortical folding remain unknown. To fill this knowledge gap, it becomes essential to consider the mechanical forces generated during the folding process. Understanding the interplay between biological processes and these mechanical forces is key to unravel the mechanism of cortical folding. In our research, we seek to explore this correlation through a computational modeling approach. Here, we introduce the cell-density field, which is characterized by a system of advection-diffusion equations (ADE) formulated to mimic the characteristic behavior of different types of cells crucial for brain development. On the other hand, we adopt the theory of finite growth to describe the cell-density-driven expansion process \cite{Zarzor21}. The differential growth of the cortex resulting from neuronal connectivity is controlled by the neuron-density within the cortical layer. Our model serves as a stepping stone to explore and comprehend how the processes of proliferation, migration, and connectivity influence the resultant folding pattern. For instance, changes in the lineage relationship between cell types may result in a smooth brain surface, as observed in lissencephalic malformation, or the appearance of excessively small folds, as seen in polymicrogyria.