New approximation of a scale space kernel on SE(3) and applications in neuroimaging

We provide a new, analytic kernel for scale space filtering of dMRI data. The kernel is an approximation for the Green’s function of a hypo-elliptic diffusion on the 3D rigid body motion group SE(3), for fiber enhancement in dMRI. The enhancements are described by linear scale space PDEs in the coupled space of positions and orientations embedded in SE(3). As initial condition for the evolution we use either a Fiber Orientation Distribution (FOD) or an Orientation Density Function (ODF). Explicit formulas for the exact kernel do not exist. Although approximations well-suited for fast implementation have been proposed in literature, they lack important symmetries of the exact kernel. We introduce techniques to include these symmetries in approximations based on the logarithm on SE(3), resulting in an improved kernel. Regarding neuroimaging applications, we apply our enhancement kernel (a) to improve dMRI tractography results and (b) to quantify coherence of obtained streamline bundles. Keywords: Scale space on SE(3); Contextual enhancement; Left-invariant diffusion; Group convolution; Tractograph

Abnormalities in normal-appearing white matter from which multiple sclerosis lesions arise

Normal-appearing white matter is far from normal in multiple sclerosis; little is known about the precise pathology or spatial pattern of this alteration and its relation to subsequent lesion formation. This study was undertaken to evaluate normal-appearing white matter abnormalities in brain areas where multiple sclerosis lesions subsequently form, and to investigate the spatial distribution of normal-appearing white matter abnormalities in persons with multiple sclerosis. Brain MRIs of pre-lesion normal-appearing white matter were analysed in participants with new T2 lesions, pooled from three clinical trials: SYNERGY (NCT01864148; n = 85 with relapsing multiple sclerosis) was the test data set; ASCEND (NCT01416181; n = 154 with secondary progressive multiple sclerosis) and ADVANCE (NCT00906399; n = 261 with relapsing-remitting multiple sclerosis) were used as validation data sets. Focal normal-appearing white matter tissue state was analysed prior to lesion formation in areas where new T2 lesions later formed (pre-lesion normal-appearing white matter) using normalized magnetization transfer ratio and T2-weighted (nT2) intensities, and compared with overall normal-appearing white matter and spatially matched contralateral normal-appearing white matter. Each outcome was analysed using linear mixed-effects models. Follow-up time (as a categorical variable), patient-level characteristics (including treatment group) and other baseline variables were treated as fixed effects. In SYNERGY, nT2 intensity was significantly higher, and normalized magnetization transfer ratio was lower in pre-lesion normal-appearing white matter versus overall and contralateral normal-appearing white matter at all time points up to 24 weeks before new T2 lesion onset. In ASCEND and ADVANCE (for which normalized magnetization transfer ratio was not available), nT2 intensity in pre-lesion normal-appearing white matter was significantly higher compared to both overall and contralateral normal-appearing white matter at all pre-lesion time points extending up to 2 years prior to lesion formation. In all trials, nT2 intensity in the contralateral normal-appearing white matter was also significantly higher at all pre-lesion time points compared to overall normal-appearing white matter. Brain atlases of normal-appearing white matter abnormalities were generated using measures of voxel-wise differences in normalized magnetization transfer ratio of normal-appearing white matter in persons with multiple sclerosis compared to scanner-matched healthy controls. We observed that overall spatial distribution of normal-appearing white matter abnormalities in persons with multiple sclerosis largely recapitulated the anatomical distribution of probabilities of T2 hyperintense lesions. Overall, these findings suggest that intrinsic spatial properties and/or longstanding precursory abnormalities of normal-appearing white matter tissue may contribute to the risk of autoimmune acute demyelination in multiple sclerosis