Our work aims to develop a biomechanical model of hydrocephalus both intended to perform clinical research and to assist the neurosurgeon in diagnosis decisions. Recently, we have defined a new MR imaging sequence based on SPACE (Sampling Perfection with Application optimized Contrast using different flip-angle Evolution). On these images, the cerebrospinal fluid (CSF) appears as a homogeneous hypersignal. Therefore such images are suitable for segmentation and for volume assessment of the CSF. In this paper we present a fully automatic 3D segmentation of such SPACE MRI sequences. We choose a topological approach considering that CSF can be modeled as a simply connected object (i.e. a filled sphere). First an initial object which must be strictly included in the CSF and homotopic to a filled sphere, is determined by using a moment-preserving thresholding. Then a priority function based on an Euclidean distance map is computed in order to control the thickening process that adds "simple points" to the initial thresholded object. A point is called simple if its addition or its suppression does not result in change of topology neither for the object, nor for the background. The method is validated by measuring fluid volume of brain phantoms and by comparing our volume assessments on clinical data to those derived from a segmentation controlled by expert physicians. Then we show that a distinction between pathological cases and healthy adult people can be achieved by a linear discriminant analysis on volumes of the ventricular and intracranial subarachnoid spaces.