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On the regression of intracranial volume in Fixel-Based Analysis

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Fixel-Based Analysis (FBA) enables robust whole-brain statistical analysis of both microscopic and macroscopic white matter properties that is both sensitive and specific to crossing fibre geometry. Given the influence of macroscopic brain differences in such experiments, interest has been expressed in how best to account for variations in brain volume across participants. Here we demonstrate the effect of brain volume on FBA by synthetically modulating brain sizes within a healthy cohort and statistically testing FBA metrics with various regressions of estimated intracranial volume. We conclude with recommendations for regression of the influence of global brain size differences in FBA when desired.
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On the regression of intracranial volume in Fixel-Based Analysis
Robert Elton Smith , Thijs Dhollander , and Alan Connelly
The Florey Institute of Neuroscience and Mental Health, Heidelberg, Australia, The Florey Department of Neuroscience and Mental Health, The University of Melbourne, Heidelberg, Australia
Synopsis
Fixel-Based Analysis (FBA) enables robust whole-brain statistical analysis of both microscopic and macroscopic white matter properties that is both sensitive and specific to crossing fibre geometry. Given the
influence of macroscopic brain differences in such experiments, interest has been expressed in how best to account for variations in brain volume across participants. Here we demonstrate the effect of brain volume
on FBA by synthetically modulating brain sizes within a healthy cohort and statistically testing FBA metrics with various regressions of estimated intracranial volume. We conclude with recommendations for
regression of the influence of global brain size differences in FBA when desired.
Introduction
Fixel-Based Analysis (FBA) enables robust whole-brain statistical analysis of both microscopic and macroscopic white matter properties that is both sensitive and specific to crossing fibre geometry . Given the influence of
macroscopic brain differences in such experiments, interest has been expressed in how best to account for variations in brain volume across participants. In particular, the Fibre Cross-section (FC) metric, which quantifies
morphological changes orthogonal to the local white matter fibre orientation, may demonstrate a widespread effect that is in fact driven by variations in gross total brain volume; thus it may be desirable within certain contexts to first
remove the effect of this global scaling, in order for statistical analysis to be sensitive to local effects only.
To address this question, we performed an experiment where gross variations in brain size were introduced synthetically. The premise of this experiment is that if the effects of global brain scaling are properly accounted for within the
statistical model, based on a scalar estimate of intracranial volume for each subject, then the image data should contain no residual effects of these modulations of brain size following regression of the global scaling effect.
Methods
100 healthy subjects from the Human Connectome Project (HCP) minimally pre-processed data were used . Subjects were split randomly into “expanded” and “contracted” groups, where the provided DWI and mask images were
expanded or contracted by a factor of 10% along each image axis respectively, then re-sampled back onto the original 1.25mm isotropic grid (Figure 1). The estimated intracranial volume (eICV) of each subject was extracted from
FreeSurfer processing output , and modulated appropriately so as to reflect the spatial expansion / contraction of the subject’s DWI data (Figure 1). Processing of this cohort included: multi-shell multi-tissue (MSMT) constrained
spherical deconvolution (CSD) using group-average tissue response functions ; multi-tissue intensity normalization ; population-specific Fibre Orientation Distribution (FOD) template generation using FOD-based registration ;
segmentation of template FODs to define discrete fixels (fibre bundle elements in specific voxels) ; FOD segmentation and extraction of subject per-fixel FBA quantitative metrics ; derivation of a template analysis fixel mask based
on a combination of fibre density threshold, whole-brain streamlines tractography in template space, and consistency of subject-template fixel correspondence.
For all three conventional FBA metrics (“FD”: an estimate of microscopic Fibre Density; “FC”: the macroscopic modulation of Fibre Cross-section, of which the logarithm is conventionally applied prior to statistical testing; “FDC”: Fibre
Density and Cross-section, the product of FD and FC, which provides a combined measure of “the white matter’s capacity to transmit information”) , we fit the General Linear Model (GLM) in each template fixel, incorporating some
numerical transformation of the eICV as a nuisance regressor using the Freedman-Lane method , repeating for different transformations of the eICV. We obtained familywise-error (FWE)-corrected p-values for differences between
the expanded and contracted groups using permutation testing in each case, and calculated the fraction of fixels in the template for which p<0.05 as a measure of “effectiveness of nuisance regression”. Numerical transformations
applied to the eICV values prior to statistical testing included various powers between 0 and 1, and the logarithm transform; tests without the inclusion of eICV as a nuisance regressor were also performed.
Results
Figure 2 presents, for each of the three conventional FBA metrics, the fraction of template fixels for which p<0.05 (i.e. false positives) when different transformations of the subject eICV values were used as nuisance regressors.
Discussion / Conclusion
Based both on minimisation of false positives in our experimental results and mathematical derivation, our suggestions for when the regression of intracranial volume is sought in FBA are as follows:
FD: Unless there is a strong hypothesis that FD will vary across subjects as a function of intracranial volume, we advocate omitting this variable from the design matrix, as the inclusion of non-useful factors within the GLM
may lead to false positives.
FC: Since it is in fact log(FC) that is pre-calculated prior to statistical testing, if FC co-varies with eICV (or some power thereof), then log(FC) is expected to co-vary with log(eICV). Although such regression was not the
absolute optimum in our testing, we believe this difference to be within experimental error, and so advocate regressing by log(eICV) in this case.
FDC: While an initial hypothesis was that regressing by (eICV) would perform well for this metric (considering brain expansion / contraction as an inflating / deflating sphere, where measurement of FC is akin to the radius
being proportional to the cube root of the volume), regression by log(eICV) provided the best empirical performance for this metric.
Acknowledgements
We are grateful to the National Health and Medical Research Council (NHMRC) (400121) of Australia and the Victorian Government’s Operational Infrastructure Support Program for their support.
Data were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint
for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.
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Figures
Figure 1: Flowchart of experiment. 100 subjects were split randomly into 2 groups, where images were either expanded or contracted by 10% in all three spatial axes; each subject’s estimated intracranial volume (eICV) was
modulated by the same factor. Upon building a population template, fixels were tested for a residual group difference (i.e. expanded vs. contracted) after having regressed out a column containing some numerical transformation of
the eICVs (relevant GLM details highlighted in red); experiment was repeated independently for a range of various such transformations.
Figure 2: Results of experiment. Height of bar is fraction of fixels within the template with p<0.05 after regressing for some numerical transformation of estimated intracranial volume (eICV), considered to be false positive results; note
logarithmic scale. Bar colours represent Fixel-Based Analysis (FBA) metrics tested. Bars are grouped according to the mathematical transformation of the eICV that was placed into the GLM design matrix.
Proc. Intl. Soc. Mag. Reson. Med. 27 (2019) 3385
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Constrained spherical deconvolution (CSD) has become one of the most widely used methods to extract white matter (WM) fibre orientation information from diffusion-weighted MRI (DW-MRI) data, overcoming the crossing fibre limitations inherent in the diffusion tensor model. It is routinely used to obtain high quality fibre orientation distribution function (fODF) estimates and fibre tractograms and is increasingly used to obtain apparent fibre density (AFD) measures. Unfortunately, CSD typically only supports data acquired on a single shell in q-space. With multi-shell data becoming more and more prevalent, there is a growing need for CSD to fully support such data. Furthermore, CSD can only provide high quality fODF estimates in voxels containing WM only. In voxels containing other tissue types such as grey matter (GM) and cerebrospinal fluid (CSF), the WM response function may no longer be appropriate and spherical deconvolution produces unreliable, noisy fODF estimates. The aim of this study is to incorporate support for multi-shell data into the CSD approach as well as to exploit the unique b-value dependencies of the different tissue types to estimate a multi-tissue ODF. The resulting approach is dubbed multi-shell, multi-tissue CSD (MSMT-CSD) and is compared to the state-of-the-art single-shell, single-tissue CSD (SSST-CSD) approach. Using both simulations and real data, we show that MSMT-CSD can produce reliable WM/GM/CSF volume fraction maps, directly from the DW data, whereas SSST-CSD has a tendency to overestimate the WM volume in voxels containing GM and/or CSF. In addition, compared to SSST-CSD, MSMT-CSD can substantially increase the precision of the fODF fibre orientations and reduce the presence ofspurious fODF peaks in voxels containing GM and/or CSF. Both effects translate into more reliable AFD measures and tractography results with MSMT-CSD compared to SSST-CSD.
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The Human Connectome Project (HCP) faces the challenging task of bringing multiple magnetic resonance imaging (MRI) modalities together in a common automated preprocessing framework across a large cohort of subjects. The MRI data acquired by the HCP differ in many ways from data acquired on conventional 3 Tesla scanners and often require newly developed preprocessing methods. We describe the minimal preprocessing pipelines for structural, functional, and diffusion MRI that were developed by the HCP to accomplish many low level tasks, including spatial artifact/distortion removal, surface generation, cross-modal registration, and alignment to standard space. These pipelines are specially designed to capitalize on the high quality data offered by the HCP. The final standard space makes use of a recently introduced CIFTI file format and the associated grayordinate spatial coordinate system. This allows for combined cortical surface and subcortical volume analyses while reducing the storage and processing requirements for high spatial and temporal resolution data. Here, we provide the minimum image acquisition requirements for the HCP minimal preprocessing pipelines and additional advice for investigators interested in replicating the HCP's acquisition protocols or using these pipelines. Finally, we discuss some potential future improvements to the pipelines.
Article
This article proposes a new measure called Apparent Fibre Density (AFD) for the analysis of high angular resolution diffusion-weighted images using higher-order information provided by fibre orientation distributions (FODs) computed using spherical deconvolution. AFD has the potential to provide specific information regarding differences between populations by identifying not only the location, but also the orientations along which differences exist. In this work, analytical and numerical Monte-Carlo simulations are used to support the use of the FOD amplitude as a quantitative measure (i.e. AFD) for population and longitudinal analysis. To perform robust voxel-based analysis of AFD, we present and evaluate a novel method to modulate the FOD to account for changes in fibre bundle cross-sectional area that occur during spatial normalisation. We then describe a novel approach for statistical analysis of AFD that uses cluster-based inference of differences extended throughout space and orientation. Finally, we demonstrate the capability of the proposed method by performing voxel-based AFD comparisons between a group of Motor Neurone Disease patients and healthy control subjects. A significant decrease in AFD was detected along voxels and orientations corresponding to both the corticospinal tract and corpus callosal fibres that connect the primary motor cortices. In addition to corroborating previous findings in MND, this study demonstrates the clear advantage of using this type of analysis by identifying differences along single fibre bundles in regions containing multiple fibre populations.
Article
Registration of diffusion-weighted images is an important step in comparing white matter fibre bundles across subjects, or in the same subject at different time points. Using diffusion-weighted imaging, Spherical Deconvolution enables multiple fibre populations within a voxel to be resolved by computing the fibre orientation distribution (FOD). In this paper, we present a novel method that employs FODs for the registration of diffusion-weighted images. Registration was performed by optimising a symmetric diffeomorphic non-linear transformation model, using image metrics based on the mean squared difference, and cross-correlation of the FOD spherical harmonic coefficients. The proposed method was validated by recovering known displacement fields using FODs represented with maximum harmonic degrees (l(max)) of 2, 4 and 6. Results demonstrate a benefit in using FODs at l(max)=4 compared to l(max)=2. However, a decrease in registration accuracy was observed when l(max)=6 was used; this was likely caused by noise in higher harmonic degrees. We compared our proposed method to fractional anisotropy driven registration using an identical code base and parameters. FOD registration was observed to perform significantly better than FA in all experiments. The cross-correlation metric performed significantly better than the mean squared difference. Finally, we demonstrated the utility of this method by computing an unbiased group average FOD template that was used for probabilistic fibre tractography. This work suggests that using crossing fibre information aids in the alignment of white matter and could therefore benefit several methods for investigating population differences in white matter, including voxel based analysis, tensor based morphometry, atlas based segmentation and labelling, and group average fibre tractography.
Article
Diffusion-weighted (DW) MR images contain information about the orientation of brain white matter fibres that potentially can be used to study human brain connectivity in vivo using tractography techniques. Currently, the diffusion tensor model is widely used to extract fibre directions from DW-MRI data, but fails in regions containing multiple fibre orientations. The spherical deconvolution technique has recently been proposed to address this limitation. It provides an estimate of the fibre orientation distribution (FOD) by assuming the DW signal measured from any fibre bundle is adequately described by a single response function. However, the deconvolution is ill-conditioned and susceptible to noise contamination. This tends to introduce artefactual negative regions in the FOD, which are clearly physically impossible. In this study, the introduction of a constraint on such negative regions is proposed to improve the conditioning of the spherical deconvolution. This approach is shown to provide FOD estimates that are robust to noise whilst preserving angular resolution. The approach also permits the use of super-resolution, whereby more FOD parameters are estimated than were actually measured, improving the angular resolution of the results. The method provides much better defined fibre orientation estimates, and allows orientations to be resolved that are separated by smaller angles than previously possible. This should allow tractography algorithms to be designed that are able to track reliably through crossing fibre regions.