Intrinsic non-stationarity correction for Fixel-Based
Robert Smith , Dennis Dimond , David Vaughan , Donna Parker , Thijs Dhollander , Graeme Jackson ,
The Florey Institute of Neuroscience and Mental Health, Melbourne, Australia, The University of Melbourne,
Melbourne, Australia, University of Calgary, Calgary, Canada, Austin Health, Melbourne, Australia
The Fixel-Based Analysis (FBA) framework enables data-driven statistical inference of effects in diffusion MRI
measures that is both sensitive and specic to crossing bre geometry ("xel": specic bre bundle element
within a specic voxel) . A fundamental building block of this framework is the Connectivity-based Fixel
Enhancement (CFE) method , which provides enhancement of xel-wise statistical measures according to
xel connectivity estimated through tractography (on the basis that genuine biological effects are likely to appear
along the lengths of affected white matter pathways). This method can however have much greater sensitivity to
effects within the core of major white matter bundles than elsewhere. While non-parametric, permutation-based
non-stationarity correction can theoretically be used to mitigate such effects, this incurs additional
computational time, and can exhibit undesirable numerical instability. We propose an intrinsic normalisation of the
statistical enhancement performed by CFE, which provides superior correction for spatially heterogeneous
statistical power without requiring additional permutations prior to statistical testing.
Non-stationarity correction involves computing an estimate of "expected statistical enhancement in the absence
of an effect", to which values computed during statistical inference can then be normalised. In non-parametric
permutation-based Voxel-Based Analysis (VBA), using e.g. cluster size / cluster mass / Threshold-Free Cluster
Enhancement (TFCE) for statistical enhancement & false positive control , for any particular
voxel in template space it is difcult to accurately estimate a priori the empirical statistical power. In this case the
effects of non-stationarity may instead be estimated in a non-parametric, permutation-based fashion by
computing the "empirical statistic": for some number of permutations, randomly permute the input data, apply
the relevant statistical enhancement algorithm to the resulting statistical map; nally, for each template voxel,
compute some statistic from the values observed across permutations (e.g. the mean of non-zero values)
The empirical statistic may also be generated & utilised in the context of FBA. This however compounds the
computational expense of CFE; and, depending on how the data are generated, may in some instances reduce
1,2 3 1,4 1 1,2 1,4,2
Here we instead make the observation that the xel-xel connectivity matrix utilised by CFE intrinsically captures
the total extent of connected xels by which each individual xel may be statistically enhanced. We therefore
propose a 'normalised' form of the CFE equation, which internally scales the magnitude of statistical
enhancement by the total extent of connectivity present in each xel, providing effective non-stationarity
correction without necessitating permutation-based computation of the empirical statistic.
·Comparison of existing and proposed equations for Connectivity-based Fixel Enhancement (CFE).
The gure compares the outcomes of FBA comparing 13 patients with right hand side Temporal Lobe Epilepsy
(TLE) with Hippocampal Sclerosis (HS) to 30 matched controls, based on the Fibre Density and Cross-section
(FDC) metric quantied as part of the standard FBA processing pipeline , using different methods to
account for heterogeneous statistical power (no correction; non-parametric permutation-based empirical
statistic; proposed intrinsic normalisation).
Use of the proposed normalised CFE equation yields increases in the length and breadth of statistically signicant
bundles, improved spatial continuity of super-threshold xels, and sensitivity to changes in peripheral white
matter bundles (e.g. ipsilateral parahippocampal WM as indicated by arrows in gure - an expected pathological
·Differences in FBA outcomes for example dataset using various non-stationarity correction techniques; arrows
indicate location of right hemisphere parahippocampal white matter.
The proposed change to CFE is a simple yet powerful methodological improvement to the FBA framework.
Disorders of the Nervous System:
Modeling and Analysis Methods:
Diffusion MRI Modeling and Analysis
WHITE MATTER IMAGING - DTI, HARDI, DSI, ETC
Indicates the priority used for review