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On the regression of intracranial volume in Fixel-Based Analysis


Abstract and Figures

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
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.
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.
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.
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.
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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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
... Age, sex, and years of education were included as nuisance covariates. Log-transformed ICV (log-ICV) was included as a nuisance covariate for log-FC and FDC (but not FD) to avoid false-positive results with global effects of brain scaling resulting from the registration to a template removed [9,46]. Family-wise error (FWE)-corrected P-values were then assigned to each fixel using nonparametric permutation testing with 10,000 permutations. ...
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Introduction: Metabolic syndrome (MetS) is defined as a complex of interrelated risk factors for type 2 diabetes and cardiovascular disease, including glucose intolerance, abdominal obesity, hypertension, and dyslipidemia. Studies using diffusion tensor imaging (DTI) have reported white matter (WM) microstructural abnormalities in MetS. However, interpretation of DTI metrics is limited primarily due to the challenges of modeling complex WM structures. The present study used fixel-based analysis (FBA) to assess the effect of MetS on the fiber tract-specific WM microstructure in older adults and its relationship with MetS-related measurements and cognitive and locomotor functions to better understand the pathophysiology of MetS. Methods: Fixel-based metrics, including microstructural fiber density (FD), macrostructural fiber-bundle cross-sectional size (FC), and a combination of FD and FC (FDC), were evaluated in 16 healthy controls (no components of metabolic syndrome; four men; mean age, 71.31 ± 5.06 years), 57 individuals with premetabolic syndrome (preMetS; one or two components of MetS; 29 men; mean age, 72.44 ± 5.82 years), and 46 individuals with MetS (three to five components of MetS; 27 men; mean age, 72.15 ± 4.97 years) using whole-brain exploratory FBA. Tract of interest (TOI) analysis was then performed using TractSeg across 14 selected WM tracts previously associated with MetS. The associations between fixel-based metrics and MetS-related measurements, neuropsychological, and locomotor function tests were also analyzed in individuals with preMetS and MetS combined. In addition, tensor-based metrics (i.e., fractional anisotropy [FA] and mean diffusivity [MD]) were compared among the groups using tract-based spatial statistics (TBSS) analysis. Results: In whole-brain FBA, individuals with MetS showed significantly lower FD, FC, and FDC compared with healthy controls in WM areas, such as the splenium of the corpus callosum (CC), corticospinal tract (CST), middle cerebellar peduncle (MCP), and superior cerebellar peduncle (SCP). Meanwhile, in fixel-based TOI, significantly reduced FD was observed in individuals with preMetS and MetS in the anterior thalamic radiation, CST, SCP, and splenium of the CC compared with healthy controls, with relatively greater effect sizes observed in individuals with MetS. Compared with healthy controls, significantly reduced FC and FDC were only demonstrated in individuals with MetS, including regions with loss of FD, inferior cerebellar peduncle, inferior fronto-occipital fasciculus, MCP, and superior longitudinal fasciculus part I. Furthermore, negative correlations were observed between FD and Brinkman index of cigarette consumption cumulative amount and between FC or FDC and the Trail Making Test (parts B-A), which is a measure of executive function, waist circumference, or low-density lipoprotein cholesterol. Finally, TBSS analysis revealed that FA and MD were not significantly different among all groups. Conclusions: The FBA results demonstrate that substantial axonal loss and atrophy in individuals with MetS and early axonal loss without fiber-bundle morphological changes in those with preMetS within the WM tracts are crucial to cognitive and motor function. FBA also clarified the association between executive dysfunction, abdominal obesity, hyper-low-density lipoprotein cholesterolemia, smoking habit, and compromised WM neural tissue microstructure in MetS.
... In line with previous work (Kelly et al., 2020;Pecheva et al., 2019), for each aim we ran additional sensitivity analyses for the FC and FDC metrics adjusting for intracranial volume (ICV; generated from T 1 -weighted images using Statistical Parametric Mapping, version 12 and log transformed; Smith et al., 2019). For the longitudinal analyses, this sensitivity analysis was performed adjusting for the log value of the change in ICV over time. ...
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Children born very preterm (VPT; <32 weeks’ gestation) have alterations in brain white matter and poorer math ability than full-term (FT) peers. Diffusion-weighted magnetic resonance imaging studies suggest a link between white matter microstructure and math in VPT and FT children, although longitudinal studies using advanced modelling are lacking. In a prospective longitudinal cohort of VPT and FT children we used Fixel-Based Analysis to investigate associations between maturation of white matter fibre density (FD), fibre-bundle cross‐section (FC), and combined fibre density and cross‐section (FDC) and math computation ability at 7 (n = 136 VPT; n = 32 FT) and 13 (n = 130 VPT; n = 44 FT) years, as well as between change in white matter and math computation ability from 7 to 13 years (n = 103 VPT; n = 21 FT). In both VPT and FT children, higher FD, FC and FDC in visual, sensorimotor and cortico-thalamic/thalamo-cortical white matter tracts were associated with better math computation ability at 7 and 13 years. Longitudinally, accelerated maturation of the posterior body of the corpus callosum (FDC) was associated with greater math computation development. White matter-math associations were similar for VPT and FT children. In conclusion, white matter maturation is associated with math computation ability across late childhood, irrespective of birth group.
... A general linear model (GLM) framework was utilized to compare FD, log FC, and FDC between (i) HC and TD-PD, (ii) HC and PIGD-PD, and (iii) TD-PD and PIGD-PD, with age, sex, and years of education included as nuisance covariates. To avoid false-positive results, additionally, log-ICV was used as a nuisance covariate for log FC and FDC (but not FD) to remove global effects of brain scaling resulting from the registration to a template 14,62 . Connectivity-based fixel enhancement for statistical inference 13 with 2 million streamlines from the template tractogram and default smoothing parameters (smoothing = 10-mm full-width at halfmaximum, C = 0.5, E = 2, and H = 3) 13 was used. ...
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Using a fixel-based analysis (FBA), we assessed the fiber-specific white matter (WM) alterations in nonmedicated patients with early-stage Parkinson’s disease (PD) with tremor-dominant (TD; n = 53; mean age, 61.7 ± 8.7 years) and postural instability and gait disorder (PIGD; n = 27; mean age, 57.8 ± 8.1 years) motor subtypes and age- and sex-matched healthy controls (HC; n = 43; mean age, 61.6 ± 9.2 years) from Parkinson’s Progression Markers Initiative dataset. FBA revealed significantly increased macrostructural fiber cross section and a combination of fiber density and cross section metrics within the corticospinal tract in patients with TD-PD compared with HC. Nonetheless, no significant changes in FBA-derived metrics were found in patients with PIGD-PD compared with HC or patients with TD-PD. Our results may provide evidence of WM neural compensation mechanisms in patients with TD-PD marked by increases in fiber bundle size and the ability to relay information between brain regions.
... For group comparisons involving FD we covaried for sex, age and FWD. For group comparisons involving FC (log) or FDC, we covaried for sex, age, FWD and ICV, since the latter have shown to be associated with individual differences in FC (log) and FDC (Smith et al., 2019). The CFE is the optimum approach for group wise comparisons, with p values provided for each fixel which are permutation-based and family-wise error corrected at the fixel level (Genc et al., 2020;Raffelt et al., 2015). ...
Aims: Children with attention deficit hyperactivity disorder (ADHD) often present with deficits in fine motor control. The cortico-spinal tract (CST) is critical for voluntary motor control. Although neuroimaging work has identified anomalous microstructural properties in the CST in ADHD, no study to date has attempted to investigate the link between deficits in fine motor performance and microstructural properties of the CST in children with ADHD. This study aimed to address this gap using a novel fixel-based analysis (FBA). Methods: Participants were 50 right-handed medication naïve children with a history of ADHD and 56 non-ADHD controls aged 9-11 years. Fine motor control was assessed using the Grooved Pegboard task. Children underwent high angular resolution diffusion MRI. Following pre-processing, FBA was performed and the semi-automated deep-learning TractSeg was used to delineate the CST bilaterally. Fibre density (FD), fibre cross-section (FC-log), and fibre density/cross-section (FDC) were extracted for each tract. Results: Children with ADHD performed significantly worse than non-ADHD children on the Grooved Pegboard task when using their non-dominant hand. They also demonstrated widespread significantly lower diffusion metrics in both CSTs compared to non-ADHD controls. However, no correlations were observed between Grooved Pegboard performance and diffusion metrics for the CST in either hemisphere. Conclusions: While we failed to detect a significant relationship between fine motor skill and FBA metrics in either group, this paper extends previous work by showing that children with ADHD and reduced fine motor competence demonstrate atypical microstructure within the CST relative to non-ADHD controls.
Compositionality is a hallmark of human language and other symbolic systems: a finite set of meaningful elements can be systematically combined to convey an open-ended array of ideas. Compositionality is not uniformly distributed over expressions in a language or over individuals’ communicative behavior: at both levels, variation is observed. Here, we investigate the neural bases of interindividual variability by probing the relationship between intrinsic characteristics of brain networks and compositional behavior. We first collected functional resting-state and diffusion magnetic resonance imaging data from a large participant sample (N = 51). Subsequently, participants took part in two signaling games. They were instructed to learn and reproduce an auditory symbolic system of signals (tone sequences) associated with affective meanings (human faces expressing emotions). Signal-meaning mappings were artificial and had to be learned via repeated signaling interactions. We identified a temporoparietal network in which connection length was related to the degree of compositionality introduced in a signaling system by each player. Graph-theoretic analysis of resting-state functional connectivity revealed that, within that network, compositional behavior was associated with integration measures in 2 semantic hubs: the left posterior cingulate cortex and the left angular gyrus. Our findings link individual variability in compositional biases to variation in the anatomy of semantic networks and in the functional topology of their constituent units.
Previous Diffusion Tensor Imaging (DTI) studies in children suggest that developmental improvements in inhibitory control is largely mediated by the degree of white matter organisation within a right-lateralised network of fronto-basal-ganglia regions. Recent advances in diffusion imaging analysis now permit greater biological specificity, both in identifying specific fibre populations within a voxel, as well as in the underlying microstructural properties of that white matter. In the present work, employing a novel fixel-based analysis (FBA) framework, we aimed to comprehensively investigate microstructure within the fronto-basal-ganglia circuit in childhood, and its contribution to inhibition performance. Diffusion MRI data were obtained from 43 healthy children and adolescents age 9–11 years (10.42 ± .41 years, 18 females). Response inhibition for each participant was assessed using the Stop-signal Task (SST) and quantified as a Stop–Signal Reaction Time (SSRT). All steps relevant to FBA were implemented in MRtrix3Tissue, a fork of the MRtrix3 software library. Tracts of the fronto-basal-ganglia circuit were delineated using probabilistic tractography to identify the tracts connecting the subthalamic nucleus, pre-supplementary motor area and the inferior frontal gyrus. Connectivity-based fixel enhancement (CFE) was then used to assess the association between fibre density (FD) and fibre cross-section (FC) with inhibitory ability. Significant negative associations were identified for FD in both the right and left fronto-basal-ganglia circuit whereby greater FD was associated with better inhibition performance. This effect was specifically localised to clusters of fixels within white matter proximal to the right subthalamic nucleus. We did not report any meaningful associations between SSRT and FC. Whilst findings are broadly consistent with prior DTI evidence, current results suggest that SSRT is predominantly facilitated by subcortical microstructure of the connections projecting from the subthalamic nucleus to the cortical regions of the network. Our findings extend current understanding of the role of white matter in childhood response inhibition.
Previous studies investigating white matter organization in attention deficit hyperactivity disorder (ADHD) have adopted diffusion tensor imaging (DTI). However, attempts to derive pathophysiological models from this research have had limited success, possibly reflecting limitations of the DTI method. This study investigated the organization of white matter tracts in ADHD using fixel based analysis (FBA), a fiber specific analysis framework that is well placed to provide novel insights into the pathophysiology of ADHD. High angular diffusion weighted imaging and clinical data were collected in a large paediatric cohort (N = 144; 76 with ADHD; age range 9–11 years). White matter tractography and FBA were performed across 14 white matter tracts. Permutation based inference testing (using FBA derived measures of fiber density and morphology) assessed differences in white matter tract profiles between children with and without ADHD. Analysis further examined the association between white matter properties and ADHD symptom severity. Relative to controls, children with ADHD showed reduced white matter connectivity along association and projection pathways considered critical to behavioral control and motor function. Increased ADHD symptom severity was associated with reduced white matter organization in fronto-pontine fibers projecting to and from the supplementary motor area. Providing novel insight into the neurobiological foundations of ADHD, this is the first research to uncover fiber specific white matter alterations across a comprehensive set of white matter tracts in ADHD using FBA. Findings inform pathophysiological models of ADHD and hold great promise for the consistent identification and systematic replication of brain differences in this disorder.
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Purpose Despite the important role of manual dexterity in child development, the neurobiological mechanisms associated with manual dexterity in childhood remain unclear. We leveraged fixel-based analysis (FBA) to examine the longitudinal association between manual dexterity and the development of white matter structural properties in the corticospinal tract (CST). Methods High angular diffusion weighted imaging (HARDI) data were acquired for 44 right-handed typically developing children (22 female) aged 9-13 across two timepoints (timepoint 1: mean age 10.5 years ± 0.5 years, timepoint 2: 11.8 ± 0.5 years). Manual dexterity was assessed using the Grooved Pegboard Test, a widely used measure of manual dexterity. FBA-derived measures of fiber density and morphology were generated for the CST at each timepoint. Connectivity-based fixel enhancement and mixed linear modelling were used to examine the longitudinal association between manual dexterity and white matter structural properties of the CST. Results Longitudinal mixed effects models showed that greater manual dexterity of the dominant hand was associated with increased fiber cross-section in the contralateral CST. Analyses further demonstrated that the rate of improvement in manual dexterity was associated with the rate of increase in fiber cross-section in the contralateral CST between the two timepoints. Conclusion Our longitudinal data suggest that the development of manual dexterity in late childhood is associated with maturation of the CST. These findings significantly enhance our understanding of the neurobiological systems that subserve fine motor development and provide an important step toward mapping normative trajectories of fine motor function against microstructural and morphological development in childhood.
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To overcome the fact that the fibre orientation distribution (FOD) from constrained spherical deconvolution (CSD) assumes a single-fibre white matter (WM) response function—and is thus inappropriate and distorted in voxels containing grey matter (GM) or cerebrospinal fluid (CSF)—multi-shell multi-tissue CSD (MSMT-CSD) was proposed. MSMT-CSD can resolve WM, GM and CSF signal contributions, but requires multi-shell data. Very recently, we proposed a novel method that can achieve the same results using just single-shell data. We refer to this method as "single-shell 3-tissue CSD" (SS3T-CSD). Both MSMT-CSD and SS3T-CSD require WM, GM and CSF response functions. These can be obtained from manually selected exemplary voxels of the tissue classes, or via the procedure described initially in the MSMT-CSD paper, which relies on a highly accurately co-registered T1 image. We propose an unsupervised procedure that does not depend on a T1 image, nor registration, and works for both single-shell and multi-shell data.
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Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (glms) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on glm parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm - the "randomise" algorithm - for permutation inference with the glm.
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.
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.
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.
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.
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.