Spatial normalization of diffusion models and tensor analysis

Diffusion tensor imaging provides the ability to study white matter connectivity and integrity noninvasively. The information contained in the diffusion tensors is very complex. Therefore a simple way of dealing with tensors is to compute rotationally invariant scalar quantities. These scalar indices have been used to perform population studies between controls and patients with neurological and psychiatric disorders. Implementing the scalar values may reduce the information contained in the whole tensor. A group analysis using the full tensors may give better estimate of white matter changes that occur in the diseased subjects. For spatial normalization of diffusion tensors, it is necessary to interpolate the tensor representation as well as rotate the diffusion tensors after transformation to keep the tensors consistent with the tissue reorientation. Existing reorientation methods cannot be directly used for higher order diffusion models (e.g. q-ball imaging). A novel technique called gradient rotation is introduced where the rotation is directly applied to the diffusion sensitizing gradients providing a voxel by voxel estimate of the diffusion gradients instead of a volume of by volume estimate. The technique is validated by comparing it with an existing method where the transformation is applied to the resulting diffusion tensors. For better matching of diffusion tensors a novel multichannel registration method is proposed based on a non-parametric diffeomorphic demons algorithm. The channels used for the registration include T1-weighted volume and tensor components. A fractional anisotropy (FA) channel is used for defining the contribution of each channel. Including the anatomical data together with the tensors, allows the registration to accurately match the global brain shape and the underlying white matter architecture simultaneously. Using this multichannel registration framework, 10 healthy controls and 9 patients of schizophrenia were spatially normalized. For the group analysis, the tensors were transformed to log-euclidean space. Linear regression analysis was performed on the transformed tensors. Results show that there is a significant difference in the anisotropy between patients and controls especially in the anterior regions that include genu of the corpus callosum and anterior and superior corona radiata, forceps minor and anterior limb on the internal capsule.