There is a growing demand for fast, accurate computation of clinical markers to improve renal function and anatomy assessment with a single study. However, conventional techniques have limitations leading to overestimations of kidney function or failure to provide sufficient spatial resolution to target the disease location. In contrast, the computer-aided analysis of dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) could generate significant markers, including the glomerular filtration rate (GFR) and time-intensity curves of the cortex and medulla for determining obstruction in the urinary tract. This paper presents a dual-stage fully modular framework for automatic renal compartment segmentation in 4D DCE-MRI volumes. (1) Memory-efficient 3D deep learning is integrated to localise each kidney by harnessing residual convolutional neural networks for improved convergence; segmentation is performed by efficiently learning spatial-temporal information coupled with boundary-preserving fully convolutional dense nets. (2) Renal contextual information is enhanced via non-linear transformation to segment the cortex and medulla. The proposed framework is evaluated on a paediatric dataset containing 60 4D DCE-MRI volumes exhibiting varying conditions affecting kidney function. Our technique outperforms a state-of-the-art approach based on a GrabCut and support vector machine classifier in mean dice similarity (DSC) by 3.8% and demonstrates higher statistical stability with lower standard deviation by 12.4% and 15.7% for cortex and medulla segmentation, respectively.