A non-conservative Lagrangian framework for statistical fluid registration: SAFIRA

In this paper, we used a non-conservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3D brain images. This algorithm is named SAFIRA, acronym for Statistically-Assisted Fluid Image Registration Algorithm. A non-statistical version of this algorithm was implemented [9], where the deformation was regularized by penalizing deviations from a zero rate of strain. In [9], the terms regularizing the deformation included the covariance of the deformation matrices () and the vector fields (q). Here we used a Lagrangian framework to re-formulate this algorithm, showing that the regularizing terms essentially allow non-conservative work to occur during the flow. Given 3D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the non-statistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the non-conservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms performance on 92 3D brain scans from healthy monozygotic and dizygotic twins; 2D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for largescale neuroimaging studies