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In brain regions containing crossing fibre bundles, voxel-average diffusion MRI measures such as fractional anisotropy (FA) are difficult to interpret, and lack within-voxel single fibre population specificity. Recent work has focused on the development of more interpretable quantitative measures that can be associated with a specific fibre population within a voxel containing crossing fibres (herein we use fixel to refer to a specific fibre population within a single voxel). Unfortunately, traditional 3D methods for smoothing and cluster-based statistical inference cannot be used for voxel-based analysis of these measures, since the local neighbourhood for smoothing and cluster formation can be ambiguous when adjacent voxels may have different numbers of fixels, or ill-defined when they belong to different tracts. Here we introduce a novel statistical method to perform whole-brain fixel-based analysis called connectivity-based fixel enhancement (CFE). CFE uses probabilistic tractography to identify structurally connected fixels that are likely to share underlying anatomy and pathology. Probabilistic connectivity information is then used for tract-specific smoothing (prior to the statistical analysis) and enhancement of the statistical map (using a threshold-free cluster enhancement-like approach). To investigate the characteristics of the CFE method, we assessed sensitivity and specificity using a large number of combinations of CFE enhancement parameters and smoothing extents, using simulated pathology generated with a range of test-statistic signal-to-noise ratios in five different white matter regions (chosen to cover a broad range of fibre bundle features). The results suggest that CFE input parameters are relatively insensitive to the characteristics of the simulated pathology. We therefore recommend a single set of CFE parameters that should give near optimal results in future studies where the group effect is unknown. We then demonstrate the proposed method by comparing apparent fibre density between motor neurone disease (MND) patients with control subjects. The MND results illustrate the benefit of fixel-specific statistical inference in white matter regions that contain crossing fibres.

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Background and Purpose-Blood supply through collateral pathways improves regional cerebral blood flow and may protect against ischemic events. The effect of collaterals on the risk of stroke and transient ischemic attack (TIA), in the presence of angiographic severe internal carotid artery (ICA) stenosis, was assessed. Methods-Angiographic collateral filling through anterior communicating and posterior communicating arteries and retrograde filling through ophthalmic arteries were determined in all patients at entry into the North American Symptomatic Carotid Endarterectomy Trial. Kaplan-Meier event-free survival analyses were performed on 339 medically treated and 342 surgically treated patients. Results-The presence of collaterals supplying the symptomatic ICA increased with severity of stenosis. Two-year risk of hemispheric stroke in medically treated patients with severe ICA stenosis was reduced in the presence of collaterals: 27.8% to 11.3% (Pϭ0.005). Similar reductions were observed for hemispheric TIA (36.1% versus 19.1%; Pϭ0.008) and disabling or fatal strokes (13.3% versus 6.3%; Pϭ0.11). For surgically treated patients, the perioperative risk of hemispheric stroke was 1.1% in the presence of collaterals versus 4.9% when absent. The 2-year stroke risks for surgical patients with and without collaterals were 5.9% versus 8.4%, respectively. Neither comparison in the surgical group was statistically significant. The observed reductions were independent of the degree of ICA stenosis and other vascular risk factors. Conclusions-Collaterals

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