White matter microstructure correlates with mathematics but not word reading performance in 13-year-old children born very preterm and full-term

Individuals born very preterm (VPT; <32 weeks' gestational age) are at increased risk of impaired mathematics and word reading performance, as well as widespread white matter microstructural alterations compared with individuals born full term (FT; ≥37 weeks' gestational age). To date, the link between academic performance and white matter microstructure is not well understood. This study aimed to investigate the associations between mathematics and reading performance with white matter microstructure in 114 VPT and 36 FT 13-year-old children. Additionally, we aimed to investigate whether the association of mathematics and reading performance with white matter microstructure in VPT children varied as a function of impairment. To do this, we used diffusion tensor imaging and advanced diffusion modelling techniques (Neurite Orientation Dispersion and Density Imaging and the Spherical Mean Technique), combined with a whole-brain analysis approach . Mathematics performance across VPT and FT groups was positively associated with white matter microstructural measurements of fractional anisotropy and neurite density, and negatively associated with radial and mean diffusivities in widespread, bilateral regions. Furthermore, VPT children with a mathematics impairment (>1 standard deviation below FT mean) had significantly reduced neurite density compared with VPT children without an impairment. Reading performance was not significantly associated with any of the white matter microstructure parameters. Additionally, the associations between white matter microstructure and mathematics and reading performance did not differ significantly between VPT and FT groups. Our findings suggest that alterations in white matter microstructure, and more specifically lower neurite density, are associated with poorer mathematics performance in 13-year-old VPT and FT children. More research is required to understand the association between reading performance and white matter microstructure in 13-year-old children.

Related papers:

title: The predictive validity of neonatal MRI for neurodevelopmental outcome in very preterm children.
abstract: Very preterm children are at a high risk for neurodevelopmental impairments, but there is variability in the pattern and severity of outcome. Neonatal magnetic resonance imaging (MRI) enhances the capacity to detect brain injury and altered brain development and assists in the prediction of high-risk children who warrant surveillance and early intervention. This review describes the application of conventional and advanced MRI with very preterm neonates, specifically focusing on the relationship between neonatal MRI findings and later neurodevelopmental outcome. Research demonstrates that conventional MRI is strongly associated with neurodevelopmental outcome in childhood. Further studies are needed to examine the role of advanced MRI techniques in predicting outcome in very preterm children, but early research findings are promising. In conclusion, neonatal MRI is predictive of later neurodevelopment but is dependent on appropriately trained specialists and should be interpreted in conjunction with other clinical and social information.

title: Defining the nature of the cerebral abnormalities in the premature infant: a qualitative magnetic resonance imaging study.
abstract: The aim of this study was to define qualitatively the nature and extent of white and gray matter abnormalities in a longitudinal population-based study of infants with very low birth weight. Perinatal factors were then related to the presence and severity of magnetic resonance imaging (MRI) abnormalities.  From November 1998 to December 2000, 100 consecutive premature infants admitted to the neonatal intensive care unit at Christchurch Women's Hospital were recruited (98% eligible) after informed parental consent to undergo an MRI scan at term equivalent. The scans were analyzed by a single neuroradiologist experienced in pediatric MRI, with a second independent scoring of the MRI using a combination of criteria for white matter (cysts, signal abnormality, loss of volume, ventriculomegaly, corpus callosal thinning, myelination) and gray matter (gray matter signal abnormality, gyration, subarachnoid space). Results were analyzed against individual item scores as well as the presence of moderate-severe white matter score, total gray matter score, and total brain score.  The mean gestational age was 27.9±2.4 weeks (range, 23-32 weeks), and mean birth weight was 1063±292 g. The greatest univariate predictors for moderate-severe white matter abnormality were lower gestational age (odds ratio [OR], 1.3; 95% confidence interval [CI], 1.1-1.7; P P P =0.03), inotropic support (OR, 2.7; 95% CI, 1.5-4.5; P P =.01), grade III/IV intraventricular hemorrhage ( P =.015), and the occurrence of a pneumothorax ( P =.05). There was a significant protective effect of intrauterine growth restriction (OR, 0.51; 95% CI, 0.23-0.99; P =.04). Gray matter abnormality was highly related to the presence and severity of white matter abnormality. A unique pattern of cerebral abnormality consisting of significant diffuse white matter atrophy, ventriculomegaly, immature gyral development, and enlarged subarachnoid space was found in 10 of 11 infants with birth gestation  This MRI study confirms a high incidence of cerebral white matter abnormality at term in an unselected population of premature infants, which is predominantly a result of noncystic injury in the extremely immature infant. We confirm that the major perinatal risk factors for white matter abnormality are related to perinatal infection, particularly maternal fever and infant sepsis, and hypotension with inotrope use. We have defined a distinct pattern of diffuse white and gray matter abnormality in the extremely immature infant.

title: Cognitive Development Trajectories of Very Preterm and Typically Developing Children.
abstract: Cognitive impairment is common among children born very preterm (VPT), yet little is known about how this risk changes over time. To examine this issue, a regional cohort of 110 VPT (≤ 32 weeks gestation) and 113 full-term (FT) born children was prospectively assessed at ages 4, 6, 9, and 12 years using the Wechsler Preschool and Primary Scale of Intelligence-Revised and then Wechsler Intelligence Scale for Children, 4th ed. At all ages, VPT children obtained lower scores than their FT born peers (p < .001). Growth curve modeling revealed stable cognitive trajectories across both groups. Neonatal white matter abnormalities and family socioeconomic adversity additively predicted cognitive risk. Despite some intraindividual variability, cognitive functioning of typically developing and high-risk VPT children was stable and influenced by early neurological development and family rearing context.

title: Early life predictors of brain development at term-equivalent age in infants born across the gestational age spectrum
abstract: It is well established that preterm infants have altered brain development compared with full‐term (FT; ≥37 weeks' gestational age [GA]) infants, however the perinatal factors associated with brain development in preterm infants have not been fully elucidated. In particular, perinatal predictors of brain development may differ between very preterm infants (VP; <32 weeks' GA) and infants born moderate (MP; 32–33 weeks' GA) and late (LP; 34–36 weeks' GA) preterm, but this has not been studied. This study aimed to investigate the effects of early life predictors on brain volume and microstructure at term‐equivalent age (TEA; 38–44 weeks), and whether these effects differ for GA groups (VP, MP, LP or FT).  Structural images from 328 infants (91 VP, 63 MP, 104 LP and 70 FT) were segmented into white matter, cortical grey matter, cerebrospinal fluid, subcortical grey matter, brainstem and cerebellum. Cortical grey matter and white matter images were analysed using voxel‐based morphometry. Fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD) and radial diffusivity (RD) images from 361 infants (92 VP, 69 MP, 120 LP and 80 FT) were analysed using Tract‐Based Spatial Statistics. Relationships between early life predictors (birthweight standard deviation score [BWSDS], multiple birth, sex, postnatal growth and social risk) and global brain volumes were analysed using linear regressions. Relationships between early life predictors and regional brain volumes and diffusion measures were analysed using voxelwise non‐parametric permutation testing.  Male sex was associated with higher global volumes of all tissues and higher regional volumes throughout much of the cortical grey matter and white matter, particularly in the FT group. Male sex was also associated with lower FA and higher AD, RD and MD in the optic radiation, external and internal capsules and corona radiata, and these associations were generally similar between GA groups. Higher BWSDS was associated with higher global volumes of all tissues and higher regional volumes in much of the cortical grey matter and white matter in all GA groups, as well as higher FA and lower RD and MD in many major tracts (corpus callosum, optic radiation, internal and external capsules and corona radiata), particularly in the MP and LP groups. Multiple birth and social risk also showed associations with global and regional volumes and regional diffusion values which varied by GA group, but these associations were not independent of the other early life predictors. Postnatal growth was not associated with brain volumes or diffusion values.  Early life predictors of brain volumes and microstructure at TEA include sex, BWSDS, multiple birth and social risk, which have different effects based on GA group at birth. This study improves knowledge of the perinatal factors associated with brain abnormalities in infants born across the prematurity spectrum. HighlightsEarly life factors affect regional brain volume and microstructural development.Effects of early life factors on brain development differ by gestational age.Males have higher brain volumes but less organised microstructure than females.Poor prenatal growth is associated with lower volume and less mature white matter.Multiple birth and social risk may also affect brain development.

title: Regional white matter microstructure in very preterm infants: Predictors and 7 year outcomes
abstract: The aims of this study were to investigate regional white matter microstructural differences between very preterm (VPT) (<30 weeks' gestational age and/or <1250 g) and full term (FT) (≥37 weeks' gestational age) infants at term corrected age with diffusion tensor imaging, and to explore perinatal predictors of diffusion measures, and the relationship between regional diffusion measures and neurodevelopmental outcomes at age 7 years in VPT children. Mean (MD) (p = .003), axial (AD) (p = .008), and radial diffusivity (RD) (p = .003) in total white matter were increased in VPT compared with FT infants, with similar fractional anisotropy (FA) in the two groups. There was little evidence that group-wise differences were specific to any of the 8 regions studied for each hemisphere. Perinatal white matter abnormality and intraventricular hemorrhage (grade III or IV) were associated with increased diffusivity in the white matter of VPT infants. Higher white matter diffusivity measures of the inferior occipital and cerebellar region at term-equivalent age were associated with increased risk of impairments in motor and executive function at 7 years in VPT children, but there was little evidence for associations with IQ or memory impairment. In conclusion, myelination is likely disrupted or delayed in VPT infants, especially those with perinatal brain abnormality (BA). Altered diffusivity at term-equivalent age helps explain impaired functioning at 7 years. This study defines the nature of microstructural alterations in VPT infant white matter, assists in understanding the associated risk factors, and is the first study to reveal an important link between inferior occipital and cerebellar white matter disorganization in infancy, and executive and motor functioning 7 years later.

title: Preterm birth and structural brain alterations in early adulthood
abstract: Alterations in cortical development and impaired neurodevelopmental outcomes have been described following very preterm (VPT) birth in childhood and adolescence, but only a few studies to date have investigated grey matter (GM) and white matter (WM) maturation in VPT samples in early adult life. Using voxel-based morphometry (VBM) we studied regional GM and WM volumes in 68 VPT-born individuals (mean gestational age 30 weeks) and 43 term-born controls aged 19–20 years, and their association with cognitive outcomes (Hayling Sentence  Test, Controlled Oral Word Association Test, Visual Reproduction test of the Wechsler Memory Scale-Revised) and gestational age. Structural MRI data were obtained with a 1.5 Tesla system and analysed using the VBM8 toolbox in SPM8 with a customized study-specific template. Similarly to results obtained at adolescent assessment, VPT young adults compared to controls demonstrated reduced GM volume in temporal, frontal, insular and occipital areas, thalamus, caudate nucleus and putamen. Increases in GM volume were noted in medial/anterior frontal gyrus. Smaller subcortical WM volume in the VPT group was observed in temporal, parietal and frontal regions, and in a cluster centred on posterior corpus callosum/thalamus/fornix. Larger subcortical WM volume was found predominantly in posterior brain regions, in areas beneath the parahippocampal and occipital gyri and in cerebellum. Gestational age was associated with GM and WM volumes in areas where VPT individuals demonstrated GM and WM volumetric alterations, especially in temporal, parietal and occipital regions. VPT participants scored lower than controls on measures of IQ, executive function and non-verbal memory. When investigating GM and WM alterations and cognitive outcome scores, subcortical WM volume in an area beneath the left inferior frontal gyrus accounted for 14% of the variance of full-scale IQ (F = 12.9, p < 0.0001). WM volume in posterior corpus callosum/thalamus/fornix and GM volume in temporal gyri bilaterally, accounted for 21% of the variance of executive function (F = 9.9, p < 0.0001) and WM in the posterior corpus callosum/thalamus/fornix alone accounted for 17% of the variance of total non-verbal memory scores (F = 9.9, p < 0.0001). These results reveal that VPT birth continues to be associated with altered structural brain anatomy in early adult life, although it remains to be ascertained whether these changes reflect neurodevelopmental delays or long lasting structural alterations due to prematurity. GM and WM alterations correlate with length of gestation and mediate cognitive outcome.

title: Changes in white matter diffusion anisotropy in adolescents born prematurely
abstract: Being born with very low birth weight (VLBW, birth weight<or=1500 g) or small for gestational age (SGA) carries an increased risk of cerebral white matter damage. The reduced cognitive and motor skills these two groups exhibit suggest that the early injuries to white matter persist into adolescence. White matter integrity was assessed using voxel-wise statistical analysis of fractional anisotropy (FA) maps between three groups of adolescents at age 15; the VLBW group (n=34), the SGA group (n=42) and a control group with normal birth weight (n=47). The FA maps were normalized to a study specific template and group differences were assessed using an analysis of covariance with gender as a confounder (FDR-corrected P<0.05). The main finding is that the VLBW group has significantly reduced FA values in several white matter regions, including the corpus callosum, internal capsule and superior fasciculus compared to the control group. Some of the observed reduction in anisotropy, particularly that observed in the corpus callosum, may have been caused by inaccurate spatial normalization, but this can only explain 30% of the area with reduced anisotropy. Analysis of the eigenvalues of the diffusion tensor show that the reduced FA values in the VLBW group is primarily due to an increase in the two lowest eigenvalues of the diffusion tensor. We speculate that this may be caused by reduced myelination. For the SGA group, we find no statistically significant differences in anisotropy compared to the control group.

title: Neuropsychological outcomes of children born very preterm.
abstract: Considerable research has investigated the consequences of being born very preterm (VP; <32 weeks of gestation), especially in relation to cognitive functioning. While numerous cognitive and neuropsychological outcome studies have been published, it is important to consider methodological issues when reviewing this research, as the generalizability of the studies varies greatly. This article describes the nature of cognitive difficulties confronting VP children, both in terms of the frequency and severity of deficits. The breadth of cognitive difficulties reported in this population implies a generalized cognitive impairment; however, the presence of selective or primary cognitive deficits is discussed. It is concluded that whereas mortality and neonatal morbidity rates have decreased significantly in VP infants in recent decades, these children continue to be at significant risk for cognitive impairments and need to be closely monitored throughout childhood.

title: Development of preschool and academic skills in children born very preterm.
abstract: To examine performance in preschool and academic skills in very preterm (gestational age ≤ 30 weeks) and term-born comparison children aged 4 to 12 years.



Very preterm children (n = 200; mean age, 8.2 ± 2.5 years) born between 1996 and 2004 were compared with 230 term-born children (mean age, 8.3 ± 2.3). The Dutch National Pupil Monitoring System was used to measure preschool numerical reasoning and early linguistics, and primary school simple and complex word reading, reading comprehension, spelling, and mathematics/arithmetic. With univariate analyses of variance, we assessed the effects of preterm birth on performance across grades and on grade retention.



In preschool, very preterm children performed comparably with term-born children in early linguistics, but perform more poorly (0.7 standard deviation [SD]) in numerical reasoning skills. In primary school, very preterm children scored 0.3 SD lower in complex word reading and 0.6 SD lower in mathematics/arithmetic, but performed comparably with peers in reading comprehension and spelling. They had a higher grade repeat rate (25.5%), although grade repeat did not improve their academic skills.



Very preterm children do well in early linguistics, reading comprehension, and spelling, but have clinically significant deficits in numerical reasoning skills and mathematics/arithmetic, which persist with time.

title: School performance at age 7 years in late preterm and early term birth: a cohort study
abstract: To investigate the effect of gestational age, particularly late preterm birth (34–36 weeks gestation) and early term birth (37–38 weeks gestation) on school performance at age 7 years.  Population-based prospective UK Millennium Cohort Study, consisting of linked educational data on 6031 children.  School performance was investigated using the statutory Key Stage 1 (KS1) teacher assessments performed in the third school year in England. The primary outcome was not achieving the expected level (≥level 2) of general performance in all three key subjects (reading, writing and mathematics). Other outcomes investigated subject-specific performance and high academic performance (level 3). Results 18% of full-term children performed below the expected KS1 general level, and risk of poor performance increased with prematurity: compared to children born at full-term, there was a statistically significant increased risk of poor performance in those born very preterm (<32 weeks gestation, adjusted RR 1.78, 95% CI 1.24 to 2.54), moderately preterm (32–33 weeks gestation, adjusted RR 1.71, 95% CI 1.15 to 2.54) and late preterm (34–36 weeks gestation, adjusted RR 1.36, 95% CI 1.09 to 1.68). Early term children performed statistically significantly worse in 4 out of 5 individual subject domains than full-term children, but not in the primary outcome (adjusted RR 1.07, 95% CI 0.94 to 1.23).  Late preterm, and to a lesser extent, early term birth negatively impact on academic outcomes at 7 years as measured by KS1 assessments.

title: Academic performance of children born preterm: a meta-analysis and meta-regression
abstract: Advances in neonatal healthcare have resulted in decreased mortality after preterm birth but have not led to parallel decreases in morbidity. Academic performance provides insight in the outcomes and specific difficulties and needs of preterm children.  To study academic performance in preterm children born in the antenatal steroids and surfactant era and possible moderating effects of perinatal and demographic factors.  PubMed, Web of Science and PsycINFO were searched for peer-reviewed articles. Cohort studies with a full-term control group reporting standardised academic performance scores of preterm children (<37 weeks of gestation) at age 5 years or older and born in the antenatal steroids and surfactant era were included. Academic test scores and special educational needs of preterm and full-term children were analysed using random effects meta-analysis. Random effects meta-regressions were performed to explore the predictive role of perinatal and demographic factors for between-study variance in effect sizes.  The 17 eligible studies included 2390 preterm children and 1549 controls. Preterm children scored 0.71 SD below full-term peers on arithmetic (p<0.001), 0.44 and 0.52 SD lower on reading and spelling (p<0.001) and were 2.85 times more likely to receive special educational assistance (95% CI 2.12 to 3.84, p<0.001). Bronchopulmonarydysplasia explained 44% of the variance in academic performance (p=0.006).  Preterm children born in the antenatal steroids and surfactant era show considerable academic difficulties. Preterm children with bronchopulmonarydysplasia are at particular risk for poor academic outcome.

title: Individual structural differences in left inferior parietal area are associated with schoolchildrens' arithmetic scores
abstract: Arithmetic skill is of critical importance for academic achievement, professional success and everyday life, and childhood is the key period to acquire this skill. Neuroimaging studies have identified that left parietal regions are a key neural substrate for representing arithmetic skill. Although the relationship between functional brain activity in left parietal regions and arithmetic skill has been studied in detail, it remains unclear about the relationship between arithmetic achievement and structural properties in left inferior parietal area in schoolchildren. The current study employed a combination of voxel-based morphometry (VBM) for high-resolution T1-weighted images and fiber tracking on diffusion tensor imaging (DTI) to examine the relationship between structural properties in the inferior parietal area and arithmetic achievement in 10-year-old schoolchildren. VBM of the T1-weighted images revealed that individual differences in arithmetic scores were significantly and positively correlated with the gray matter (GM) volume in the left intraparietal sulcus (IPS). Fiber tracking analysis revealed that the forceps major, left superior longitudinal fasciculus (SLF), bilateral inferior longitudinal fasciculus (ILF) and inferior fronto-occipital fasciculus (IFOF) were the primary pathways connecting the left IPS with other brain areas. Furthermore, the regression analysis of the probabilistic pathways revealed a significant and positive correlation between the fractional anisotropy (FA) values in the left SLF, ILF and bilateral IFOF and arithmetic scores. The brain structure-behavior correlation analyses indicated that the GM volumes in the left IPS and the FA values in the tract pathways connecting left IPS were both related to children's arithmetic achievement. The present findings provide evidence that individual structural differences in the left IPS are associated with arithmetic scores in schoolchildren.

title: Left fronto-parietal white matter correlates with individual differences in children's ability to solve additions and multiplications: A tractography study
abstract: Functional neuroimaging data have pointed to the activation of a fronto-parietal network during calculation tasks, the activity of which is modulated by arithmetic operation and arithmetical competence. As the cortical brain regions of this network are distant, it is crucial to investigate the white matter connections between them and to examine how these connections are related to different arithmetic operations and individual differences in arithmetical competence. By using diffusion tensor imaging (DTI) tractography in eighteen 12-year-olds, we tested whether white matter pathways connecting these distant regions were related to children's arithmetical competence and how this association was modulated by operation. For each child, we delineated the three subcomponents of the arcuate fasciculus, a bundle of pathways linking frontal and temporo-parietal regions that are commonly active during calculation tasks. Fractional anisotropy in the left anterior portion of the arcuate fasciculus was positively correlated with addition and multiplication, but not with subtraction and division, suggesting a specific role of this left anterior segment in the solution of those problems that are expected to be solved with fact retrieval. The observed correlation was not explained by age, intelligence and working memory. Follow-up control analyses using different types of reading measures revealed that the observed correlation only disappeared when measures that draw heavily on phonological processing, such as non-word reading, were controlled for, suggesting that the association between the left arcuate fasciculus-anterior and addition/multiplication reflects the involvement of phonological processing. These results are the first to demonstrate that individual differences in fronto-parietal white matter are associated with arithmetical competence in typically developing children of a very narrow age range and indicate that this association is modulated by arithmetic operation.

title: Left lateralized white matter microstructure accounts for individual differences in reading ability and disability
abstract: Diffusion tensor imaging (DTI) was used to investigate the association between variation in white matter microstructure and individual differences in reading skill within children. Unlike previous DTI studies of reading, our sample examined children in both the average reading range as well as several children in the performance range of reading disability (RD). Results replicate previous findings of a strong correlation between fractional anisotropy (FA) values in a left temporo-parietal white matter region and standardized reading scores of typically developing children. Furthermore, FA values in this same region accounted for differences between children scoring in the average range and children scoring in the RD range, suggesting that the role of white matter tract microstructure is best characterized as an extreme range on a continuum of typical variation. Furthermore, significant correlations between working memory and frontal white matter tract regions were present in this same population, yet were demonstrated to be independent of the relationships found between reading and more posterior regions. Results form a "correlational double dissociation" that demonstrates domain specificity in the influence of white matter tract structures to individual differences in cognitive performance.

title: Imaging brain connectivity in children with diverse reading ability
abstract: Reading is a complex cognitive skill that requires the coordination of multiple brain regions. Although functional neuroimaging studies highlight the cortical brain regions associated with a specific cognitive task like reading, they do not directly address the underlying neural connections necessary for efficient performance of this task. Adults with reading disability have demonstrated lower regional white matter connectivity, but it is not known whether this relationship between neuronal wiring and reading performance also holds in younger readers. Using diffusion tensor magnetic resonance imaging (DTI) that highlights the structural integrity of the brain wiring, we show that regional brain connectivity in the left temporo-parietal white matter correlates with a wide range of reading ability in children as young as 8-12 years old. Diffusion tensor tractography suggests that the posterior limb of the internal capsule is consistent with the location of the largest cluster of correlation between reading ability (Word Identification subtest) and fractional anisotropy. The maturation of the white matter may play a key role in the development of cognitive processes such as reading.

title: Children's Reading Performance is Correlated with White Matter Structure Measured by Diffusion Tensor Imaging
abstract: We investigated the white matter structure in children (n = 14) with a wide range of reading performance levels using diffusion tensor imaging (DTI), a form of magnetic resonance imaging. White matter structure in a left temporo-parietal region that had been previously described as covarying with reading skill in adult readers also differs between children who are normal and poor readers. Specifically, the white matter structure measured using fractional anisotropy (FA) and coherence index (CI) significantly correlated with behavioral measurements of reading, spelling, and rapid naming performance. In general, lower anisotropy and lower coherence were associated with lower performance scores. Although the magnitude of the differences in children are smaller than those in adults, the results support the hypothesis that the structure of left temporoparietal neural pathways is a significant component of the neural system needed to develop fluent reading.

title: NODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain
abstract: This paper introduces neurite orientation dispersion and density imaging (NODDI), a practical diffusion MRI technique for estimating the microstructural complexity of dendrites and axons in vivo on clinical MRI scanners. Such indices of neurites relate more directly to and provide more specific markers of brain tissue microstructure than standard indices from diffusion tensor imaging, such as fractional anisotropy (FA). Mapping these indices over the whole brain on clinical scanners presents new opportunities for understanding brain development and disorders. The proposed technique enables such mapping by combining a three-compartment tissue model with a two-shell high-angular-resolution diffusion imaging (HARDI) protocol optimized for clinical feasibility. An index of orientation dispersion is defined to characterize angular variation of neurites. We evaluate the method both in simulation and on a live human brain using a clinical 3T scanner. Results demonstrate that NODDI provides sensible neurite density and orientation dispersion estimates, thereby disentangling two key contributing factors to FA and enabling the analysis of each factor individually. We additionally show that while orientation dispersion can be estimated with just a single HARDI shell, neurite density requires at least two shells and can be estimated more accurately with the optimized two-shell protocol than with alternative two-shell protocols. The optimized protocol takes about 30 min to acquire, making it feasible for inclusion in a typical clinical setting. We further show that sampling fewer orientations in each shell can reduce the acquisition time to just 10 min with minimal impact on the accuracy of the estimates. This demonstrates the feasibility of NODDI even for the most time-sensitive clinical applications, such as neonatal and dementia imaging.

title: Wide Range Achievement Test 4
abstract: This machine consists primarily of a frame, which is supported by wheels, and the frame supports three spaced-apart self-placing form units, which operate in conjunction with finishing rollers. The self-placing form units of the machine are faced with endless synthetic rubber belts, which are backed up by hinged steel pads, and the top and bottom of the self-placing form units are sealed with a plate having a lip at the edge, to overlap the synthetic rubber, so as to repel any foreign matter, or concrete mix, from entering the inside of the units. The machine is reversible in direction when desired, and is used for concrete curb and gutter construction.

title: Rates of early intervention services in very preterm children with developmental disabilities at age 2 years
abstract: Preterm birth is increasing in prevalence and long‐term follow‐up studies have documented high rates of neurosensory, intellectual, academic and behavioural disabilities. The importance of early intervention (EI) is well recognised but significant barriers to receiving EI exist in the community. This study explores the association of levels of disability at age 2 years with EI services and social risk in a large cohort of very preterm children.

title: How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging
abstract: Diffusion tensor imaging is often performed by acquiring a series of diffusion-weighted spin-echo echo-planar images with different direction diffusion gradients. A problem of echo-planar images is the geometrical distortions that obtain near junctions between tissues of differing magnetic susceptibility. This results in distorted diffusion-tensor maps. To resolve this we suggest acquiring two images for each diffusion gradient; one with bottom-up and one with top-down traversal of k-space in the phase-encode direction. This achieves the simultaneous goals of providing information on the underlying displacement field and intensity maps with adequate spatial sampling density even in distorted areas. The resulting DT maps exhibit considerably higher geometric fidelity, as assessed by comparison to an image volume acquired using a conventional 3D MR technique.

title: An integrated approach to correction for off-resonance effects and subject movement in diffusion MR imaging
abstract: In this paper we describe a method for retrospective estimation and correction of eddy current (EC)-induced distortions and subject movement in diffusion imaging. In addition a susceptibility-induced field can be supplied and will be incorporated into the calculations in a way that accurately reflects that the two fields (susceptibility- and EC-induced) behave differently in the presence of subject movement. The method is based on registering the individual volumes to a model free prediction of what each volume should look like, thereby enabling its use on high b-value data where the contrast is vastly different in different volumes. In addition we show that the linear EC-model commonly used is insufficient for the data used in the present paper (high spatial and angular resolution data acquired with Stejskal–Tanner gradients on a 3 T Siemens Verio, a 3 T Siemens Connectome Skyra or a 7 T Siemens Magnetome scanner) and that a higher order model performs significantly better. The method is already in extensive practical use and is used by four major projects (the WU-UMinn HCP, the MGH HCP, the UK Biobank and the Whitehall studies) to correct for distortions and subject movement.

title: Advances in functional and structural MR image analysis and implementation as FSL
abstract: The techniques available for the interrogation and analysis of neuroimaging data have a large influence in determining the flexibility, sensitivity, and scope of neuroimaging experiments. The development of such methodologies has allowed investigators to address scientific questions that could not previously be answered and, as such, has become an important research area in its own right. In this paper, we present a review of the research carried out by the Analysis Group at the Oxford Centre for Functional MRI of the Brain (FMRIB). This research has focussed on the development of new methodologies for the analysis of both structural and functional magnetic resonance imaging data. The majority of the research laid out in this paper has been implemented as freely available software tools within FMRIB's Software Library (FSL).

title: The B‐matrix must be rotated when correcting for subject motion in DTI data
abstract: To estimate diffusion tensor MRI (DTI) measures, such as fractional anisotropy and fiber orientation, reliably, a large number of diffusion‐encoded images is needed, preferably cardiac gated to reduce pulsation artifacts. However, the concomitant longer acquisition times increase the chances of subject motion adversely affecting the estimation of these measures. While correcting for motion artifacts improves the accuracy of DTI, an often overlooked step in realigning the images is to reorient the B‐matrix so that orientational information is correctly preserved. To the best of our knowledge, most research groups and software packages currently omit this reorientation step. Given the recent explosion of DTI applications including, for example, neurosurgical planning (in which errors can have drastic consequences), it is important to investigate the impact of neglecting to perform the B‐matrix reorientation. In this work, a systematic study to investigate the effect of neglecting to reorient the B‐matrix on DTI data during motion correction is presented. The consequences for diffusion fiber tractography are also discussed. Magn Reson Med, 61:1336–1349, 2009.

title: A global optimisation method for robust affine registration of brain images
abstract: Registration is an important component of medical image analysis and for analysing large amounts of data it is desirable to have fully automatic registration methods. Many different automatic registration methods have been proposed to date, and almost all share a common mathematical framework - one of optimising a cost function. To date little attention has been focused on the optimisation method itself, even though the success of most registration methods hinges on the quality of this optimisation. This paper examines the assumptions underlying the problem of registration for brain images using inter-modal voxel similarity measures. It is demonstrated that the use of local optimisation methods together with the standard multi-resolution approach is not sufficient to reliably find the global minimum. To address this problem, a global optimisation method is proposed that is specifically tailored to this form of registration. A full discussion of all the necessary implementation details is included as this is an important part of any practical method. Furthermore, results are presented for inter-modal, inter-subject registration experiments that show that the proposed method is more reliable at finding the global minimum than several of the currently available registration packages in common usage.

title: Regression models for twin studies: a critical review.
abstract: Twin studies have long been recognized for their value in learning about the aetiology of disease and specifically for their potential for separating genetic effects from environmental effects. The recent upsurge of interest in life-course epidemiology and the study of developmental influences on later health has provided a new impetus to study twins as a source of unique insights. Twins are of special interest because they provide naturally matched pairs where the confounding effects of a large number of potentially causal factors (such as maternal nutrition or gestation length) may be removed by comparisons between twins who share them. The traditional tool of epidemiological 'risk factor analysis' is the regression model, but it is not straightforward to transfer standard regression methods to twin data, because the analysis needs to reflect the paired structure of the data, which induces correlation between twins. This paper reviews the use of more specialized regression methods for twin data, based on generalized least squares or linear mixed models, and explains the relationship between these methods and the commonly used approach of analysing within-twin-pair difference values. Methods and issues of interpretation are illustrated using an example from a recent study of the association between birth weight and cord blood erythropoietin. We focus on the analysis of continuous outcome measures but review additional complexities that arise with binary outcomes. We recommend the use of a general model that includes separate regression coefficients for within-twin-pair and between-pair effects, and provide guidelines for the interpretation of estimates obtained under this model.

title: Permutation inference for the general linear model
abstract: 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.

title: Threshold-free cluster enhancement: Addressing problems of smoothing, threshold dependence and localisation in cluster inference
abstract: Many image enhancement and thresholding techniques make use of spatial neighbourhood information to boost belief in extended areas of signal. The most common such approach in neuroimaging is cluster-based thresholding, which is often more sensitive than voxel-wise thresholding. However, a limitation is the need to define the initial cluster-forming threshold. This threshold is arbitrary, and yet its exact choice can have a large impact on the results, particularly at the lower (e.g., t, z < 4) cluster-forming thresholds frequently used. Furthermore, the amount of spatial pre-smoothing is also arbitrary (given that the expected signal extent is very rarely known in advance of the analysis). In the light of such problems, we propose a new method which attempts to keep the sensitivity benefits of cluster-based thresholding (and indeed the general concept of "clusters" of signal), while avoiding (or at least minimising) these problems. The method takes a raw statistic image and produces an output image in which the voxel-wise values represent the amount of cluster-like local spatial support. The method is thus referred to as "threshold-free cluster enhancement" (TFCE). We present the TFCE approach and discuss in detail ROC-based optimisation and comparisons with cluster-based and voxel-based thresholding. We find that TFCE gives generally better sensitivity than other methods over a wide range of test signal shapes and SNR values. We also show an example on a real imaging dataset, suggesting that TFCE does indeed provide not just improved sensitivity, but richer and more interpretable output than cluster-based thresholding.

title: Tract probability maps in stereotaxic spaces: Analyses of white matter anatomy and tract-specific quantification
abstract: Diffusion tensor imaging (DTI) is an exciting new MRI modality that can reveal detailed anatomy of the white matter. DTI also allows us to approximate the 3D trajectories of major white matter bundles. By combining the identified tract coordinates with various types of MR parameter maps, such as T2 and diffusion properties, we can perform tract-specific analysis of these parameters. Unfortunately, 3D tract reconstruction is marred by noise, partial volume effects, and complicated axonal structures. Furthermore, changes in diffusion anisotropy under pathological conditions could alter the results of 3D tract reconstruction. In this study, we created a white matter parcellation atlas based on probabilistic maps of 11 major white matter tracts derived from the DTI data from 28 normal subjects. Using these probabilistic maps, automated tract-specific quantification of fractional anisotropy and mean diffusivity were performed. Excellent correlation was found between the automated and the individual tractography-based results. This tool allows efficient initial screening of the status of multiple white matter tracts.

title: Mapping Human Cortical Areas In Vivo Based on Myelin Content as Revealed by T1- and T2-Weighted MRI
abstract: Noninvasively mapping the layout of cortical areas in humans is a continuing challenge for neuroscience. We present a new method of mapping cortical areas based on myelin content as revealed by T1-weighted (T1w) and T2-weighted (T2w) MRI. The method is generalizable across different 3T scanners and pulse sequences. We use the ratio of T1w/T2w image intensities to eliminate the MR-related image intensity bias and enhance the contrast to noise ratio for myelin. Data from each subject were mapped to the cortical surface and aligned across individuals using surface-based registration. The spatial gradient of the group average myelin map provides an observer-independent measure of sharp transitions in myelin content across the surface—i.e., putative cortical areal borders. We found excellent agreement between the gradients of the myelin maps and the gradients of published probabilistic cytoarchitectonically defined cortical areas that were registered to the same surface-based atlas. For other cortical regions, we used published anatomical and functional information to make putative identifications of dozens of cortical areas or candidate areas. In general, primary and early unimodal association cortices are heavily myelinated and higher, multimodal, association cortices are more lightly myelinated, but there are notable exceptions in the literature that are confirmed by our results. The overall pattern in the myelin maps also has important correlations with the developmental onset of subcortical white matter myelination, evolutionary cortical areal expansion in humans compared with macaques, postnatal cortical expansion in humans, and maps of neuronal density in non-human primates.

title: The development of brain white matter microstructure
abstract: Throughout infancy, childhood, and adolescence, our brains undergo remarkable changes. Processes including myelination and synaptogenesis occur rapidly across the first 2–3 years of life, and ongoing brain remodeling continues into young adulthood. Studies have sought to characterize the patterns of structural brain development, and early studies predominately relied upon gross anatomical measures of brain structure, morphology, and organization. MRI offers the ability to characterize and quantify a range of microstructural aspects of brain tissue that may be more closely related to fundamental neurodevelopmental processes. Techniques such as diffusion, magnetization transfer, relaxometry, and myelin water imaging provide insight into changing cyto‐ and myeloarchitecture, neuronal density, and structural connectivity. In this review, we focus on the growing body of literature exploiting these MRI techniques to better understand the microstructural changes that occur in brain white matter during maturation. Our review focuses on studies of normative brain development from birth to early adulthood (˜25 years), and places particular emphasis on longitudinal studies and newer techniques that are being used to study microstructural white matter development. All imaging methods demonstrate consistent, rapid microstructural white matter development over the first 3 years of life, suggesting increased myelination and axonal packing. Diffusion studies clearly demonstrate continued white matter maturation during later childhood and adolescence, though the lack of consistent findings in other modalities suggests changes may be mainly due to axonal packing. An emerging literature details differential microstructural development in boys and girls, and connects developmental trajectories to cognitive abilities, behaviour, and/or environmental factors, though the nature of these relationships remains unclear. Future research will need to focus on newer imaging techniques and longitudinal studies to provide more detailed information about microstructural white matter development, particularly in the childhood years.

title: Working Memory
abstract: Working memory, the ability to transiently keep, process, and use information as part of ongoing mental processes is an essential feature of cognitive functioning. The largest number of items that people can hold in their working memory, referred to as the capacity of working memory, is limited and varies substantially among individuals. Uncovering the biological factors that underlie these two defining properties of working memory capacity remains a key undertaking of modern cognitive neuroscience since capacity strongly predicts how well we reason, learn, and even do math. In this work we review data that highlights the role white matter, which provides the wiring of the extensive neural networks that activate during working memory tasks, may play in interindividual variations in capacity. We also describe advanced diffusion imaging methods, which may be uniquely suited in capturing those white matter features that are most relevant to capacity. Finally, we discuss several possible mechanisms through which white matter may both contribute to and limit working memory.

title: THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING
abstract: Did evolution endow the human brain with a predisposition to represent and acquire knowledge about numbers? Although the parietal lobe has been suggested as a potential substrate for a domain-specific representation of quantities, it is also engaged in verbal, spatial, and attentional functions that may contribute to calculation. To clarify the organisation of number-related processes in the parietal lobe, we examine the three-dimensional intersection of fMRI activations during various numerical tasks, and also review the corresponding neuropsychological evidence. On this basis, we propose a tentative tripartite organisation. The horizontal segment of the intraparietal sulcus (HIPS) appears as a plausible candidate for domain specificity: It is systematically activated whenever numbers are manipulated, independently of number notation, and with increasing activation as the task puts greater emphasis on quantity processing. Depending on task demands, we speculate that this core quantity system, analogous to an internal “number line,” can be supplemented by two other circuits. A left angular gyrus area, in connection with other left-hemispheric perisylvian areas, supports the manipulation of numbers in verbal form. Finally, a bilateral posterior superior parietal system supports attentional orientation on the mental number line, just like on any other spatial dimension.

title: Processing Pathways in Mental Arithmetic—Evidence from Probabilistic Fiber Tracking
abstract: Numerical cognition is a case of multi-modular and distributed cerebral processing. So far neither the anatomo-functional connections between the cortex areas involved nor their integration into established frameworks such as the differentiation between dorsal and ventral processing streams have been specified. The current study addressed this issue combining a re-analysis of previously published fMRI data with probabilistic fiber tracking data from an independent sample. We aimed at differentiating neural correlates and connectivity for relatively easy and more difficult addition problems in healthy adults and their association with either rather verbally mediated fact retrieval or magnitude manipulations, respectively. The present data suggest that magnitude- and fact retrieval-related processing seem to be subserved by two largely separate networks, both of them comprising dorsal and ventral connections. Importantly, these networks not only differ in localization of activation but also in the connections between the cortical areas involved. However, it has to be noted that even though seemingly distinct anatomically, these networks operate as a functionally integrated circuit for mental calculation as revealed by a parametric analysis of brain activation.

title: Considering structural connectivity in the triple code model of numerical cognition: differential connectivity for magnitude processing and arithmetic facts
abstract: The current study provides a generalizable account of the anatomo-functional associations as well as the connectivity of representational codes underlying numerical processing as suggested by the triple code model (TCM) of numerical cognition. By evaluating the neural networks subserving numerical cognition in two specific and substantially different numerical tasks with regard to both grey matter localizations as well as white matter tracts we (1) considered the possibility of additional memory-related cortex areas crucial for arithmetic fact retrieval (e.g., the hippocampus); (2) specified the functional involvement of prefrontal areas in number magnitude processing, and, finally; (3) identified the connections between these anatomo-functional instantiations of the representations involved in number magnitude processing and arithmetic fact retrieval employing probabilistic fiber tracking. The resulting amendments to the TCM are summarized in a schematic update, and ideas concerning the possible functional interplay between number magnitude processing and arithmetic fact retrieval are discussed.

title: Drawing connections between white matter and numerical and mathematical cognition: A literature review
abstract: In this review we examine white matter tracts that may support numerical and mathematical abilities and whether abnormalities in these pathways are associated with deficits in numerical and mathematical abilities. Diffusion tensor imaging (DTI) yields indices of white matter integrity and can provide information about the axonal organization of the brain. A growing body of research is using DTI to investigate how individual differences in brain microstructures relate to different numerical and mathematical abilities. Several tracts have been associated with numerical and mathematical abilities such as the superior longitudinal fasciculus, the posterior segment of the corpus callosum, inferior longitudinal fasciculus, corona radiata, and the corticospinal tract. Impairments in mathematics tend to be associated with atypical white matter structures within similar regions, especially in inferior parietal and temporal tracts. This systematic review summarizes and critically examines the current literature on white matter correlates of numerical and mathematical abilities, and provides directions for future research.

title: White matter microstructure correlates of mathematical giftedness and intelligence quotient
abstract: Recent functional neuroimaging studies have shown differences in brain activation between mathematically gifted adolescents and controls. The aim of this study was to investigate the relationship between mathematical giftedness, intelligent quotient (IQ), and the microstructure of white matter tracts in a sample composed of math‐gifted adolescents and aged‐matched controls. Math‐gifted subjects were selected through a national program based on detecting enhanced visuospatial abilities and creative thinking. We used diffusion tensor imaging to assess white matter microstructure in neuroanatomical connectivity. The processing included voxel‐wise and region of interest‐based analyses of the fractional anisotropy (FA), a parameter which is purportedly related to white matter microstructure. In a whole‐sample analysis, IQ showed a significant positive correlation with FA, mainly in the corpus callosum, supporting the idea that efficient information transfer between hemispheres is crucial for higher intellectual capabilities. In addition, math‐gifted adolescents showed increased FA (adjusted for IQ) in white matter tracts connecting frontal lobes with basal ganglia and parietal regions. The enhanced anatomical connectivity observed in the forceps minor and splenium may underlie the greater fluid reasoning, visuospatial working memory, and creative capabilities of these children. Hum Brain Mapp 35:2619–2631, 2014.

title: Neuroanatomical Correlates of Developmental Dyscalculia: Combined Evidence from Morphometry and Tractography
abstract: Poor mathematical abilities adversely affect academic and career opportunities. The neuroanatomical basis of developmental dyscalculia (DD), a specific learning deficit with prevalence rates exceeding 5%, is poorly understood. We used structural MRI and diffusion tensor imaging (DTI) to examine macro- and micro-structural impairments in 7- to 9-year-old children with DD, compared to a group of typically developing (TD) children matched on age, gender, intelligence, reading abilities and working memory capacity. Voxel-based morphometry (VBM) revealed reduced grey matter (GM) bilaterally in superior parietal lobule, intra-parietal sulcus, fusiform gyrus, parahippocampal gyrus and right anterior temporal cortex in children with DD. VBM analysis also showed reduced white matter (WM) volume in right temporal-parietal cortex. DTI revealed reduced fractional anisotropy (FA) in this WM region, pointing to significant right hemisphere micro-structural impairments. Furthermore, FA in this region was correlated with numerical operations but not verbal mathematical reasoning or word reading. Atlas-based tract mapping identified the inferior longitudinal fasciculus, inferior fronto-occipital fasciculus and caudal forceps major as key pathways impaired in DD. DTI tractography suggests that long-range WM projection fibers linking the right fusiform gyrus with temporal-parietal WM are a specific source of vulnerability in DD. Network and classification analysis suggest that DD in children may be characterized by multiple dysfunctional circuits arising from a core WM deficit. Our findings link GM and WM abnormalities in children with DD and they point to macro- and micro-structural abnormalities in right hemisphere temporal-parietal WM, and pathways associated with it, as key neuroanatomical correlates of DD.

title: Arithmetic ability and parietal alterations: a diffusion tensor imaging study in velocardiofacial syndrome.
abstract: Velocardiofacial syndrome (VCFS) is a congenital anomaly that causes somatic as well as cognitive and psychiatric impairments. Previous studies have found specific deficits in arithmetic abilities in subjects with VCFS. In this study, we investigated whether abnormalities in white matter pathways are correlated with reduced arithmetic ability. Nineteen individuals with VCFS aged 7-19 years received diffusion-weighted magnetic resonance imaging (MRI) scans. A linear regression model was used to correlate fractional anisotropy (FA) values with scores of the arithmetic subscale on the WISC/WAIS on a voxel-by-voxel basis, after covarying for any IQ- and age-related effects. There was a statistically significant positive correlation between the arithmetic score on the WISC/WAIS and FA values in white matter tracts adjacent to the left supramarginal and angular gyri, as well as along the left intraparietal sulcus. Inferior parietal lobe white matter structural aberrations may contribute to reduced arithmetic ability in VCFS.

title: Reading performance correlates with white‐matter properties in preterm and term children
abstract: We used diffusion tensor imaging to investigate the association between white‐matter integrity and reading ability in a cohort of 28 children. Nineteen preterm children (14 males, five females; mean age 11y 11mo [SD 1y 10mo], mean gestational age 30.5wks (SD 3.2), mean birthweight was 1455g [SD 625]); and nine term children (five males, four females; mean age 12y 8mo [SD 2y 5mo], mean gestational age 39.6wks (SD 1.2), and mean birthweight 3877g [SD 473]).

title: Cerebellar white matter pathways are associated with reading skills in children and adolescents
abstract: Reading is a critical life skill in the modern world. The neural basis of reading incorporates a distributed network of cortical areas and their white matter connections. The cerebellum has also been implicated in reading and reading disabilities. However, little is known about the contribution of cerebellar white matter pathways to major component skills of reading. We used diffusion magnetic resonance imaging (dMRI) with tractography to identify the cerebellar peduncles in a group of 9‐ to 17‐year‐old children and adolescents born full term (FT, n = 19) or preterm (PT, n = 26). In this cohort, no significant differences were found between fractional anisotropy (FA) measures of the peduncles in the PT and FT groups. FA of the cerebellar peduncles correlated significantly with measures of decoding and reading comprehension in the combined sample of FT and PT subjects. Correlations were negative in the superior and inferior cerebellar peduncles and positive in the middle cerebellar peduncle. Additional analyses revealed that FT and PT groups demonstrated similar patterns of reading associations within the left superior cerebellar peduncle, middle cerebellar peduncle, and left inferior cerebellar peduncle. Partial correlation analyses showed that distinct sub‐skills of reading were associated with FA in segments of different cerebellar peduncles. Overall, the present findings are the first to document associations of microstructure of the cerebellar peduncles and the component skills of reading. Hum Brain Mapp 36:1536–1553, 2015.

title: Methodological considerations on tract-based spatial statistics (TBSS)
abstract: Having gained a tremendous amount of popularity since its introduction in 2006, tract-based spatial statistics (TBSS) can now be considered as the standard approach for voxel-based analysis (VBA) of diffusion tensor imaging (DTI) data. Aiming to improve the sensitivity, objectivity, and interpretability of multi-subject DTI studies, TBSS includes a skeletonization step that alleviates residual image misalignment and obviates the need for data smoothing. Although TBSS represents an elegant and user-friendly framework that tackles numerous concerns existing in conventional VBA methods, it has limitations of its own, some of which have already been detailed in recent literature. In this work, we present general methodological considerations on TBSS and report on pitfalls that have not been described previously. In particular, we have identified specific assumptions of TBSS that may not be satisfied under typical conditions. Moreover, we demonstrate that the existence of such violations can severely affect the reliability of TBSS results. With TBSS being used increasingly, it is of paramount importance to acquaint TBSS users with these concerns, such that a well-informed decision can be made as to whether and how to pursue a TBSS analysis. Finally, in addition to raising awareness by providing our new insights, we provide constructive suggestions that could improve the validity and increase the impact of TBSS drastically.

title: Deformable registration of diffusion tensor MR images with explicit orientation optimization
abstract: In this paper, we present a novel deformable registration algorithm for diffusion tensor MR images that enables explicit optimization of tensor reorientation. The optimization seeks a piecewise affine transformation that divides the image domain into uniform regions and transform each region affinely. The objective function captures both the image similarity and the smoothness of the transformation across region boundaries. The image similarity enables explicit orientation optimization by incorporating tensor reorientation, which is necessary for warping diffusion tensor images. The objective function is formulated in a way that allows explicit implementation of analytic derivatives to drive fast and accurate optimization using the conjugate gradient method. By explicitly optimizing tensor reorientation, the algorithm is designed to take advantage of similarity measures comparing tensors as a whole. The optimal transformation is hierarchically refined in a subdivision framework. A comparison with affine registration for inter-subject normalization of 8 subjects shows that the proposed algorithm improves the alignment of several major white matter structures examined: the anterior thalamic radiations, the inferior fronto-occipital fasciculi, the corticospinal/corticobulbar tracts and the genu and the splenium of the corpus callosum. The alignment of white matter structures is assessed using a novel scheme of computing distances between the corresponding fiber bundles derived from tractography.

title: The effect of filter size on VBM analyses of DT-MRI data
abstract: Voxel-based morphometry (VBM) has been used to analyze diffusion tensor MRI (DT-MRI) data in a number of studies. In VBM, following spatial normalization, data are smoothed to improve the validity of statistical inferences and to reduce inter-individual variation. However, the size of the smoothing filter used for VBM of DT-MRI data is highly variable across studies. For example, a literature review revealed that Gaussian smoothing kernels ranging in size (full width at half maximum) from zero to 16 mm have been used in DT-MRI VBM type studies. To investigate the effect of varying filter size in such analyses, whole brain DT-MRI data from 14 schizophrenic patients were compared with those of 14 matched control subjects using VBM, when the filter size was varied from zero to 16 mm. Within this range of smoothing, four different conclusions regarding apparent patient control differences could be made: (i) no significant patient-control differences; (ii) reduced FA in right superior temporal gyrus (STG) in patients; (iii) reduced FA in both right STG and left cerebellum in patients; and (iv) reduced FA only in left cerebellum in patients. These findings stress the importance of recognizing the effect of the matched filter theorem on VBM analyses of DT-MRI data. Finally, we investigated whether one of the underlying assumptions of parametric VBM, i.e., the normality of the residuals, is met. Our results suggest that, even with moderate smoothing, a large number of voxels within central white matter regions may have non-normally distributed residuals thus making valid statistical inferences with a parametric approach problematic in these areas.

title: Spatial and orientational heterogeneity in the statistical sensitivity of skeleton-based analyses of diffusion tensor MR imaging data
abstract: Group comparisons of indices derived from diffusion tensor imaging are common in the literature. An increasingly popular approach to performing such comparisons is the skeleton-projection based approach where, for example, fractional anisotropy (FA) values are projected onto a skeletonized version of the data to minimize differences due to spatial misalignment. In this work, we examine the spatial heterogeneity of the statistical power to detect group differences, and show that there is an intrinsic spatial heterogeneity, with more 'central' structures having less variance within a population. Importantly, we also demonstrate a previously unreported feature of skeleton-based analysis methods, that is that the width of the skeleton depends on the relative orientation to the imaging matrix. Due to the way in which the inferential statistics are performed, this means that structures that are obliquely oriented to the imaging matrix are more likely to show significant differences than when aligned with the imaging matrix. This has profound implications for the interpretation of results obtained from such analysis, especially when there are no a priori hypotheses concerning the spatial location of any group differences. For a uniform (DC) offset between two groups, the skeleton projection-based approaches will be most likely to reveal a difference in centrally located white matter structures oriented obliquely to the imaging matrix.