Ultrasound is the mainstay of imaging for pediatric hydronephrosis, which appears as the dilation of the renal collecting system. However, its potential as diagnostic tool is limited by the subjective visual interpretation of radiologists. As a result, the severity of hydronephrosis in children is evaluated by invasive and ionizing diuretic renograms. In this paper, we present the first complete framework for the segmentation and quantification of renal structures in 3D ultrasound images, a difficult and barely studied challenge. In particular, we propose a new active contour-based formulation for the segmentation of the renal collecting system, which mimics the propagation of fluid inside the kidney. For this purpose, we introduce a new positive delta detector for ultrasound images that allows to identify the fat of the renal sinus surrounding the dilated collecting system, creating an alpha shape-based patient-specific positional map. Finally, we incorporate a Gabor-based semi-automatic segmentation of the kidney to create the first complete ultrasound-based framework for the quantification of hydronephrosis. The promising results obtained over a dataset of 13 pathological cases (dissimilarity of 2.8 percentage points on the computation of the volumetric hydronephrosis index) demonstrate the potential utility of the new framework for the non-invasive and non-ionizing assessment of hydronephrosis severity among the pediatric population.