Regional brain development analysis through registration using anisotropic similarity, a constrained affine transformation

We propose a novel method to quantify brain growth in 3 arbitrary orthogonal directions of the brain or its sub-regions through linear registration. This is achieved by introducing a 9 degrees of freedom (dof) transformation called anisotropic similarity which is an affine transformation with constrained scaling directions along arbitrarily chosen orthogonal vectors. This gives the opportunity to extract scaling factors describing brain growth along those directions by registering a database of subjects onto a common reference. This information about directional growth brings insights that are not usually available in longitudinal volumetry analysis. The interest of this method is illustrated by studying the anisotropic regional and global brain development of 308 healthy subjects betwen 0 and 19 years old. A gender comparison of those scaling factors is also performed for 4 classes of age. We demonstrate through these applications the stability of the method to the chosen reference and its ability to highlight growth differences accros regions and gender.