Brain magnetic resonance imaging (MRI) in patients with Multiple Sclerosis (MS) shows regions of signal abnormalities, named plaques or lesions. The spatial lesion distribution plays a major role for MS diagnosis. In this paper we present a 3D MS-lesion segmentation method based on an adaptive geometric brain model. We model the topological properties of the lesions and brain tissues in order to constrain the lesion segmentation to the white matter. As a result, the method is independent of an MRI atlas. We tested our method on the MICCAI MS grand challenge proposed in 2008 and achieved competitive results. In addition, we used an in-house dataset of 15 MS patients, for which we achieved best results in most distances in comparison to atlas based methods. Besides classical segmentation distances, we motivate and formulate a new distance to evaluate the quality of the lesion segmentation, while being robust with respect to minor inconsistencies at the boundary level of the ground truth annotation.