MEDUSA: A GPU-based tool to create realistic phantoms of the brain microstructure using tiny spheres. A GPU-based tool to generate realistic phantoms of the brain microstructure is presented. Using a spherical meshing technique which decomposes each microstructural item into a set of overlapping spheres, the phantom construction is made very fast while reliably avoiding the collisions between items in the scene. This novel method is applied to the construction of human brain white matter microstructural components, namely axonal fibers, oligodendrocytes and astrocytes. The algorithm reaches high values of packing density and angular dispersion for the axonal fibers, even in the case of multiple white matter fiber populations and enables the construction of complex biomimicking geometries including myelinated axons, beaded axons, and glial cells. The method can be readily adapted to model gray matter microstructure.