Preterm birth is connected to impairments and altered brain growth. Compared to their term born peers, preterm infants have a higher risk of behavioral and cognitive problems since most part of their brain development is in extra-uterine conditions. This paper presents different deep learning approaches with the objective of quantifying the volumes of 8 brain tissues and 5 other image-based descriptors that quantify the state of brain development. Two datasets were used: one with 86 MR brain images of patients around 30 weeks PMA and the other with 153 patients around 40 weeks PMA. Two approaches were evaluated: (1) using the full image as 3D input and (2) using multiple image slices as 3D input, both achieving promising results. A second study, using a dataset of MR brain images of rats, was also performed to assess the performance of this method with other brains. A 2D approach was used to estimate the volumes of 3 rat brain tissues.