Diffusion tensor imaging (DTI) allows in vivo, non-invasive mapping of the diffusion process of water molecules in biological tissues. This helps us to can obtain axonal pathways within the brain. Neuroscientists are interested in heritability of such structures. Heritability analysis helps us to know if the development of axons is ruled by genetic or environmental factors. In this talk, we will describe the kind of data involved in such studies. We will then present a new model we have developed that take into account the geometric information of axons fiber bundles for a group of elderly twins. A parallel sliding coordinate system will be built, using a tool called the projection median of a set of points. We will then use genetic information collected on these people to investigate heritability of such structures.