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The brain is one of the most important organs in the body. Everything we do is directly connected to our brains; It processes information and responds in kind. The brain has areas that are dedicated to processing different types of information. The front of the brain is the frontal lobe. The sides of the brain make up the temporal lobe. The top-middle of the brain is the parietal lobe. The back of the main form has the occipital lobe. The bulb below the occipital lobe is the cerebellum. The cerebellum leads to the medulla and spinal cord.

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The wrinkles on the brain are called gray matter. It's propose is to allow the brain the ability to process, learn, and increase the brains intelligence. The frontal lobe allows us to think, process, decide, and form personality. The temporal lobes propose is sound processing.

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The parietal lobe assists in the processing of sensations. The occipital lobe processes sight. The cerebellum stores muscle memory, meaning things like walking, breathing, blinking, etc. The medulla manages your heart.

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Learning disabilities are caused by abnormalities within the brain. The abnormality tends to be hypocoherence or hypercoherence.

Hypocoherence in the brain is the phenomenon that describes lack of communication within the brain. Usually, all parts of the brain have areas where they work together to process information. These areas are where axons(refer to picture) deliver information to neurons via the synapse(picture on next slide).

With the case of hypocoherence, the subject would have a specific learning disorder(SLD). Examples of SLD consist of dyslexia(difficulties with word/language processing, anarithmia(difficulties with counting), dysgraphia(difficulties with writing), etc.

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Hypercoherence is the opposite of hypocoherence. Instead of there being too little communication among the brain's sectors, there is too much communication. This usually points to the brain being larger in size when compared to the typical size. This is usually a symptom of the brain of a baby, which is twice as big of that of an adult's, shrinking less than the median as they grow older.

Hypercoherence leads to the subject landing of the autism spectrum. Hypercoherance also occurs in the brains of subjects with OCD, ADHD, etc.

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Learning disorders, in my understanding based on the research that was conducted for this project, are forms of neurodivergence. Neurodivergence is the term used to describe subjects whose brains function differently from the norm. Neurodivergence is not a sickness, so it does not have a cure. Subjects with learning disorders find the processing of different variety of subjects more difficult than a neurotypical person would.

Subjects with learning disorders require more time on subjects to fully understand them. This is how subjects with earning disorders train themselves to align better with the level of learning that they are expected to be at.

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A learning ability which affects the processing of numerates. This would be a hypocoherent learning disability. On top of this, people with Dyscalculia have been observed to have lower quantities of gray matter.

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Center for MR-Research, University Children's Hospital, Zurich, Switzerland

Children's Research Center, University Children's Hospital, Zurich, Switzerland

Clinic for Child and Adolescent Psychiatry, German Red Cross Hospitals, Berlin, Germany

Neuroscience Center Zurich, University of Zurich and ETH Zurich, Zurich, Switzerland

Zurich Center for Integrative Human Physiology, University of Zurich, Zurich, Switzerland

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Affected people show persistent deficits in number processing, which are associated with aberrant brain activation and structure. Reduced gray matter has been reported in DD for the parietal cortex including the intraparietal sulcus (IPS), but also the frontal and occipito-temporal cortex. Furthermore, dyscalculics show white matter differences for instance in the inferior (ILF) and superior longitudinal fasciculus (SLF). However, the longitudinal development of these structural differences is unknown. Therefore, our goal was to investigate the developmental trajectory of gray and white matter in children with and without DD. In this longitudinal study, neuropsychological measures and T1-weighted structural images were collected twice with an interval of 4 years from 13 children with DD (8.2-10.4 years) and 10 typically developing (TD) children (8.0-10.4 years). Voxel-wise estimation of gray and white matter volumes was assessed using voxel-based morphometry for longitudinal data. The present findings reveal for the first time that DD children show persistently reduced gray and white matter volumes over development. Reduced gray matter was found in the bilateral inferior parietal lobes including the IPS, supramarginal gyri, left precuneus, cuneus, right superior occipital gyrus, bilateral inferior and middle temporal gyri, and insula. White matter volumes were reduced in the bilateral ILF and SLF, inferior fronto-occipital fasciculus (IFOF), corticospinal tracts, and right anterior thalamic radiation (ATR). Behaviorally, children with DD performed significantly worse in various numerical tasks at baseline and follow-up, corroborating persistent deficits in number processing. The present results are in line with the literature showing that children with DD have reduced gray and white matter volumes in the numerical network. Our study further sheds light on the trajectory of brain development, revealing that these known structural differences in the long association fibers and the adjacent regions of the temporal- and frontoparietal cortex persist in dyscalculic children from childhood into adolescence. In conclusion, our results underscore that DD is a persistent learning disorder accompanied by deficits in number processing and reduced gray and white matter volumes in number related brain areas.

Introduction

Currently, there is one study that investigated children between 8 and 14 years and aimed to describe how the differences between dyscalculic and control children vary during cortical development ( Ranpura et al., 2013). Relative to TD children, gray matter volume in dyscalculics increases with age in the left dorsolateral prefrontal cortex and the right superior occipital lobe, but decreases slightly in the left primary motor cortex. White matter development of children with DD showed notable delays relative to the control group. Whilst TD children showed an age-related increase in frontal and parietal areas, the white matter volumes of DD children remained stable over time ( Ranpura et al., 2013).

The gray and white matter regions and their relationship with numerical or arithmetical skills were also investigated in TD children. Gray matter volume is positively correlated with arithmetic scores or performance gains specifically in the left IPS and angular gyrus ( Li et al., 2013; Supekar et al., 2013; Evans et al., 2015). Price et al. (2016) showed that gray matter volume in the left IPS measured in first grade predicted the math score at the end of the second grade. This result is not confined to the parietal cortex. Increased gray matter volume in the frontal (dorsal and ventral prefrontal cortices, IFG), occipito-temporal (cuneus, fusiform gyrus) and in the hippocampus also relates to better math performance ( Li et al., 2013; Supekar et al., 2013; Evans et al., 2015; Wilkey et al., 2018). Moreover, associations between brain volume abnormalities and math performance have been reported for the gray matter volume of parietal regions in other populations prone to math difficulties (prematurely born children, very low birth weight, Turner syndrome; Isaacs et al., 2001; Starke et al., 2013; Zhao et al., 2013).

To summarize, gray matter volume in various regions of the frontoparietal network, but specifically in the IPS-which is known as a key area for number processing-has been associated with better performance in numerical processing and arithmetical skills. In line with that, children with DD show reduced gray matter volumes in parietal, but also frontal, occipito-temporal and hippocampal areas. Furthermore, white matter differences have been reported in the main white matter tracts connecting the parietal with the frontal and the temporal cortex in subjects with DD. However, to the author's best knowledge, there is no study investigating the development of these structural differences in children with DD using a longitudinal study design. Therefore, the present work aims to elucidate the developmental trajectory of gray and white brain matter volume in children with and without DD from childhood to adolescence.

Materials and Methods

Participants and Procedure

A total of 35 (23 DD, 12 TD) children between 8 and 11 years were recruited into this longitudinal study, of which 27 took part in a previous study ( Kucian et al., 2011). This longitudinal study included structural and functional MRI data (for the results of fMRI data please see McCaskey et al., 2018). Children were evaluated by neuropsychological tests and MRI at baseline and returned after 4.2 ( SD = 0.46) years for a follow-up measurement. We approached the subjects of our study through the school setting or School psychological Services (DD subjects). The children visited us twice at the Center for MR-Research of the University Children's Hospital Zurich. On both occasions, they first completed a neuropsychological session and then underwent the MRI measurement.

Inclusion criteria for all children were no history of neurological or psychiatric disorders and an IQ ≥ 85, measured by the third edition of the WISC ( Tewes et al., 1999; Similarities, Block Design, Vocabulary, Picture Arrangement). Furthermore, DD children had to score below the 10th percentile in the total score or three subtests of a standardized numerical test battery (ZAREKI-R) at baseline. These criteria are in line with the diagnostic criteria for DD of the ICD-11 (6A03.2 Developmental learning disorder with impairment in mathematics; WHO, 2018). TD children had to perform above the cut-off of value in the test batteries for numerical abilities at baseline and follow-up (10th percentile in the ZAREKI-R and 67 points in the BASIS-MATH 4-8, respectively). Following these criteria, six DD children and one TD child were excluded from the study. For the MRI analysis, two children were excluded due to missing imaging data at baseline or follow-up and three for image quality reasons, resulting in 13 DD and 10 TD complete data sets for the whole study. Groups did not differ in age, gender, handedness, and pubertal status determined by the Edinburgh Handedness Inventory ( Oldfield, 1971) and an adapted version of the Self-administered Rating Scale for Pubertal Development ( Carskadon and Acebo, 1993).

Parental consent and child assent were obtained at the beginning of the study. The study was approved by the Ethics committee of Zurich, Switzerland based on guidelines from the World Medical Association's Declaration of Helsinki ( WMA, 2013).

Neuropsychological Testing

During the neuropsychological assessment, we acquired numerical abilities, general cognitive abilities as well as measures for the most common comorbid disorders such as developmental dyslexia, attention deficit and hyperactivity disorder, and working memory deficits.

Numerical Abilities

At baseline, numerical abilities were assessed using the revised version of the Neuropsychological Test Battery for Number Processing and Calculation in Children (ZAREKI-R; von Aster et al., 2006). The Zareki-R is a multidimensional test, measuring basic numerical skills as well as calculation, and widely used for the diagnosis of DD in the German-speaking area (see Supplementary Material for detailed information about the subtests). Based on this test battery children scoring below the 10th percentile in the total score or three subtests were identified with DD.

Also, the Arithmetic subtest of the Wechsler Intelligence Scale for Children (WISC-III; Tewes et al., 1999) was performed. In this subtest, children had to solve story problems of increasing difficulty within a set time limit (reported test values are IQ scores).

At follow-up, the numerical achievement was assessed with the test for Basic Diagnosis in Mathematics Education for Grades 4-8 (BASIS-MATH 4-8; Moser Opitz et al., 2010). The Basis-Math is a criterion-based test battery measuring various arithmetical abilities such as counting, decimal system, and calculation. Criteria for numerical deficiencies are met if the performance is under a threshold value of 67 points (maximum score of 83 points). This is interpreted as not reaching mastery of basic mathematical concepts (see Supplementary Material for detailed information).

The curriculum-based subtest Quantity Comparison of the Cognitive Abilities Test (KFT 4-12+R; Heller and Perleth, 2000) was performed to assess the arithmetic performance at a peer level. In this subtest, subjects had 10 min to solve as many quantity comparisons as possible of increasing difficulty (reported test values are T scores).

The spatial representation of numbers was measured using a computerized number line task adopted from Kucian et al. ( 2011; for a detailed description see McCaskey et al., 2018). Children had to indicate by mouse-click the position of 20 Arabic digits on a number line with the labeled endpoints 0 and 100. Accuracy was measured by calculating the percentage distance from the marked to the correct position of the given number (reported measures are raw values).

Children also solved 40 basic arithmetic problems (20 addition and 20 subtraction) in the number range 0-1,000 (for a detailed description see McCaskey et al., 2018). Each problem was presented visually on the computer screen and solutions were given via the keyboard. The number of correctly solved items was quantified (reported test values are raw scores, maximum value 20).

Domain General Cognitive Abilities

At baseline, intelligence was measured with the third edition of the WISC (Similarities, Block Design, Vocabulary, Picture Arrangement; Tewes et al., 1999). At follow-up, the fourth edition of the WISC was used (Similarities, Block Design, Matrix Reasoning; Petermann and Petermann, 2007). Table 1 shows the estimated general IQ.

Table 1. Demographic characteristics and scores on numerical abilities, domain-general cognitive abilities, working memory, attention, and reading.

Working Memory

Visuospatial working memory was measured with the Block-Suppression-Test ( Beblo et al., 2004). The task required subjects to reproduce every second block of a previously presented sequence on a board with nine cubes. The sequences had a length of 3-9 cubes. Three items per sequence were presented. The longest sequence which was reproduced correctly twice was quantified (reported test values are raw scores, maximum value 9). Verbal working memory was measured with the subtest Digit Span of the WISC-IV ( Petermann and Petermann, 2007). In this task, subjects had to repeat an auditorily presented sequence of numerals forward or backward. The sequences had a length of 2-9 numerals (reported test values are IQ scores).

Attention

Levels of attention and inhibition were measured using the subtests Alertness and Go-Nogo of the computerized Test battery for Attentional Performance (TAP; Zimmermann and Fimm, 1993). In the Alertness subtest, subjects had to react as quickly as possible when the target stimulus "x" appeared (intrinsic alertness). Half of the trials were preceded by an acoustic cue stimulus (phasic alertness). The test has four runs and a total of 80 target items. For each subject, the percentile rank of the median RT was quantified (reported test values are percentile ranks). In the Go-Nogo subtest, subjects had to react as quickly as possible to a target stimulus ("x," go condition), but inhibit reactions on a second presented stimulus ("+," nogo condition). The test has a total of 40 items (20 go and 20 nogo items). For each subject, the percentile rank of the median RT was quantified (reported test values are percentile ranks).

Reading Abilities

The 1-Minute-Reading-Task from the Salzburg Reading and Orthography Test (SLRT-II; Moll and Landerl, 2010) assessing word and pseudoword reading fluency was used to estimate the reading performance. Two sheets of paper with either 156 words or 156 pseudowords of increasing length and difficulty were presented. Subjects had 1 min per sheet to read as many words as possible. The amount of correctly read items was quantified (reported test values are percentile ranks). Because of lacking test norms in grades 7 and 8, we interpolated the norms from the test manual (grade 6) and Kronschnabel et al. (2013; grade 9).

Behavioral Data Analysis

Behavioral data were statistically analyzed with SPSS (Version 22). To account for the difficulties regarding the performance of statistical tests of normality in small samples, we performed nonparametric tests (Mann-Whitney U Test) to assess group differences. Effect sizes are reported as Pearson's correlation coefficient r and are interpreted as small ( r = 0.10), medium ( r = 0.30) or large ( r = 0.50).

Brain Imaging

Image Acquisition

MRI data were acquired on a 3T General Electric Signa Scanner (GE Medical Systems, USA) using an 8-channel head coil. T1-weighted structural images (voxel size = 0.94 × 0.94 × 1.00 mm ³) were acquired with a fast spoiled gradient echo sequence (3D FSPGR, slice thickness = 1 mm, no interslice skip, matrix size = 256 × 256, field of view = 240 mm, flip angle = 20°, echo time = 3 ms, repetition time = 10 ms). Participants were carefully instructed and supplied with hearing protection before entering the scanner. To minimize head motion, the head was stabilized with padding.

MRI Data Preprocessing

The data were preprocessed using the Computational Anatomy Toolbox (CAT12, Structural Brain Mapping Group, University of Jena, Germany), which is an extension to Statistical Parametric Mapping (SPM 12, Wellcome Trust Centre for Neuroimaging, University College London, UK) running on Matlab (Release 2012b, The MathWorks Inc., USA).

In a first step, the longitudinal data pair (baseline and follow-up image) of each subject was registered to the mean image for each subject by an inverse-consistent realignment, which also includes a bias correction between the different time points. The mean image of each subject is then segmented and the spatial normalization parameters are estimated with the help of a Dartel Normalization. These spatial normalization parameters (Dartel deformations) are then applied to the gray and the white matter segmentations of the baseline and follow-up image. The white and gray matter segmented images were smoothed with a Gaussian kernel of 8 mm FWHM (full width half maximum). As the last step, the total intracranial volume (TIV) was estimated for the baseline and follow-up image of each subject (please see Supplementary Material for the Matlab scripts of the preprocessing steps).

Quality Control

The CAT12 Toolbox provides image quality measures describing the properties of the images before the preprocessing. The image quality rating (IQR) is a weighted average of the noise contrast ratio, the inhomogeneity contrast ratio and the resolution of the input image. The images all reached ratings above 79 at both measurement time points (baseline range 79-87, follow-up range 81-87). Note that typical scientific (clinical) data is expected to get good to satisfactory ratings (70-90; Gaser and Dahnke, 2016, see also www.neuro.uni-jena.de/cat/). The groups did not differ in their IQR at baseline (DD Mdn = 85.0, TD Mdn = 85.3, U = 46.5, z = −1.15, p = 0.263) or follow-up (DD Mdn = 85.0, TD Mdn = 85.5, U = 48.0, z = −1.05, p = 0.313), and there was no significant difference in the quality measures between the time points (baseline Mdn = 85.1, follow-up Mdn = 85.3, z = −0.69, p = 0.494).

Also, the segmented and normalized gray and white matter images were visually inspected and the sample was checked for homogeneity (mean correlation). Based on the visual inspection and the Mahalanobis distance, which combines a measure of image quality before (weighted overall image quality) and after preprocessing (mean correlation), we excluded two DD and one TD data sets resulting in the final group size of 13 DD and 10 TD.

Statistical Model

For the statistical analyses of the gray and white matter volumes, two separate flexible factorial models with the factors subject, group (DD, TD) and time (baseline, follow-up) including TIV and puberty score as covariates were defined. Statistical results are shown with a threshold of p < 0.05 family-wise error (FWE) correction (see Supplementary Material for the design matrix and the Matlab scripts of the statistical model as well as the defined contrasts). Anatomical localization of the gray matter volume results was attained trough the SPM Anatomy Toolbox v2.0 ( Eickhoff et al., 2005, 2007). White matter regions were labeled according to the JHU (Johns Hopkins University) white-matter tractography atlas ( Hua et al., 2008).

Results

Behavioral Data

The neuropsychological results and the demographic data for all subjects are summarized in Table 1. All participants scored in the normal range of IQ (DD IQ = 93-111, TD IQ = 101-125). However, groups differed in the estimated general IQ at baseline (WISC-III p < 0.001, r = 0.69) and follow-up (WISC-IV p < 0.001, r = 0.72). IQ measures are known not to be fully independent of measures of math ability, and the present sample, therefore, reflects the cognitive pattern typically observed in DD.

In the attention, working memory, and reading task no differences between DD and TD children were found (all p > 0.05).

Numerical Achievement

As expected, numerical abilities, assessed by the Zareki-R at baseline, differed significantly between the TD and the DD groups ( p < 0.001, r = 0.84). The groups also differed in the subtest Arithmetic (WISC-II), with the DD subjects scoring significantly lower than the TD group ( p < 0.01, r = 0.55; Table 1).

At follow-up, adolescents of the DD group still performed worse in comparison to their peers (Basis-Math p < 0.001, r = 0.84). In fact, all the subjects identified with DD at baseline still fulfilled the diagnostic criteria for DD at the follow-up measurement. Furthermore, they also scored significantly lower in the curriculum based test Quantity Comparison (KFT 4-12+R p < 0.001, r = 0.83), the number line task ( p < 0.01, r = 0.61) and the basic arithmetic operations (addition p < 0.05, r = 0.52, subtraction p < 0.01, r = 0.62; Table 1).

Pearson's correlations of the whole brain gray and white matter volume with behavioral measures were calculated for baseline and follow-up. At the follow-up, gray matter volume was positively correlated with the Basis-Math ( r = 0.64, p < 0.05) in TD children. However, we found a negative relationship in TD adolescents between performance in addition and gray ( r = −0.69, both p < 0.05) and white matter volume ( r = −0.60, p < 0.05), respectively. For DD children, no significant correlations between numerical abilities and volume of the brain structure were revealed (see Supplementary Material for a complete table of correlations).

Structural Results

Gray Matter

For the gray matter volume, the flexible factorial analysis revealed a significant effect of group ( Figure 1A, Table 2). DD children showed decreased gray matter volumes in the bilateral inferior parietal lobe assigned to the IPS, the bilateral supramarginal gyri, the left precuneus, the left postcentral gyrus, and the right paracentral lobule compared to TD children. In the occipital lobe, differences were found in the left calcarine gyrus/cuneus, the left middle occipital gyrus (MOG), and the right superior occipital gyrus (SOG). Decreased gray matter was found in the bilateral inferior (ITG) and middle temporal gyri (MTG), the left rolandic operculum, and the bilateral insula over the examined time of 4 years.

Figure 1. Group differences in gray and white matter. Results are shown on a pediatric template ( Fonov et al., 2009) with a significance level of p-cluster < 0.05, FWE corrected. (A) Decreased gray matter volumes in dyscalculics compared to typically developing children over both time points. (B) Decreased white matter volumes in dyscalculics compared to typically developing children over both time points. Abbreviations: CST, corticospinal tract; IFOF, inferior fronto-occipital fasciculus; ILF, inferior longitudinal fasciculus; INS, insula; IPS, intraparietal sulcus; ITG, inferior temporal gyrus; MOG, middle occipital gyrus; PCUN, precuneus; SLF, superior longitudinal fasciculus; SMG, supramarginal gyrus.

Table 2. Gray matter.

The main effect of time and the interaction group by time were not significant.

White Matter

For the white matter volume, the flexible factorial analysis revealed a significant effect of the group ( Figure 1B, Table 3). DD children showed reduced white matter volumes in a widespread set of brain regions including the bilateral CST, the bilateral superior and ILF, the bilateral IFOF, and the right ATR. Compared to TD children the DD children further showed increased white matter volumes in the right CST.

Table 3. White matter.

The main effect of time revealed an increase in the left SLF adjacent to the precentral gyrus over both groups. The interaction group by time was not significant.

Discussion

Our study aimed to investigate the neural structural development of children with DD and TD peers using a longitudinal study. Until now, there have only been a handful of studies investigating the structural differences between children with and without DD, and only one study examining changes of regional differences in cortical development ( Rotzer et al., 2008; Rykhlevskaia et al., 2009; Ranpura et al., 2013). However, all of these study results are based on cross-sectional data. To our knowledge, this is the first study investigating the neural developmental trajectory using longitudinal data in children with DD. On the behavioral level, we found that the children of the DD group performed significantly worse in all the numerical and arithmetical tasks. This result remained stable over time. All children that were identified with DD at the beginning of the study still fulfilled the diagnostic criteria of DD 4 years later. On the neural level, children with DD showed reduced gray and white matter volumes in various regions and prominent tracts of the frontoparietal numerical network. These differences do not vanish over time, but persist from childhood into adolescence.

The dyscalculics showed reduced gray matter volumes in the parietal lobes specifically, but also in the occipital, temporal, and frontal parts of the brain, consistent with the results of previous studies. Less gray matter volume in the IPL including the IPS and the SPL have been reported in all studies with dyscalculic children ( Rotzer et al., 2008; Rykhlevskaia et al., 2009; Ranpura et al., 2013). These regions are known from functional studies to be the key areas for number processing and quantity representation (for a meta-analysis see Sokolowski et al., 2017; Arsalidou et al., 2018). Furthermore, we also found reduced gray matter volumes in the bilateral supramarginal gyri, which are thought to play a crucial role in the retrieval of arithmetical facts ( Menon, 2016). Similar to Rykhlevskaia et al. (2009), our results revealed lower gray matter volumes in the MOG/SOG, the cuneus/precuneus, and the temporal gyrus, although our results include bilateral MTG/ITG. Unlike the studies conducted before with DD children ( Rotzer et al., 2008; Rykhlevskaia et al., 2009; Ranpura et al., 2013), we found reduced gray matter volumes in the insula. However, the insula has a high likelihood to be activated when children solve number and calculation tasks and have been proposed to play a role in intrinsic motivation about learning and training ( Arsalidou et al., 2018). Also, our study did not find any volumetric differences in the parahippocampal areas, which was reported in Rykhlevskaia et al. (2009).

In terms of white matter, our study revealed reduced white matter volume in dyscalculics in the bilateral superior and ILF, the CST, the IFOF, and the ATR. Reduced white matter volumes were also reported in the same tracts by Rykhlevskaia et al. (2009), except that they found additionally reduced volumes in the forceps major and the splenium of the corpus callosum. Moreover, the CST, the ILF and SLF, and the corona radiata (of which the ATR is part) have all been associated with numerical and mathematical processing by numerous studies ( Kucian et al., 2013; for a review see also Matejko and Ansari, 2015). The SLF connects frontal and parietal regions of the brain, which are known to be the main areas activated when solving number and arithmetic related tasks. It has further been proposed that the ILF is involved in visual processing related to numerical or mathematical problem solving ( van Eimeren et al., 2008; Matejko and Ansari, 2015).

Children with DD revealed increased volumes in the right CST. This tract connects the cortex with the brainstem and is typically associated with motor functions. Research has further demonstrated that there is a link between finger and number representation ( Noël, 2005; Matejko and Ansari, 2015). As children with DD often rely on finger counting strategies to compensate for the deficits in fact retrieval, the increased volume in the CST might be related to the frequent finger use during calculation in DD.

However, it is important to note that these observed structural differences in gray and white matter are related to underlying microstructural mechanisms of development and learning. Among the candidate mechanisms explaining gray and white matter plasticity are morphometric changes in the neuron (e.g., axon sprouting, dendritic branching, synaptogenesis, neurogenesis), in fiber organization (e.g., axon branching, sprouting, axon diameter or the number of axons) as well as in the myelination (for detailed information see Zatorre et al., 2012). But also vascular changes (angiogenesis) or changes in morphology and number of glia and astrocytes could explain the increase in gray and white matter volume ( Zatorre et al., 2012). Regarding the structural differences in DD children, one could speculate that DD children show reduced white and gray matter volumes as the underlying microstructural process does not take place to the same extent as in TD peers. This would also be in line with results of functional and DTI studies reporting decreased activation and lower FA values in number related areas and tracks, respectively ( Davis et al., 2009; Kucian et al., 2013; for an overview see Peters and De Smedt, 2018).

Over development, we did not observe a gray matter decrease or prominent white matter increases. The lack of a gray matter decrease can be due to the age of our subjects. We examined children between the ages of 9 and 14. The developmental trajectory of the gray matter volume follows an inverted u-shape and depending on the study the peak of gray matter volume has been reported at age 8 ( Mills et al., 2016), age 12 ( Groeschel et al., 2010), or between ages 11-14 ( Gogtay and Thompson, 2010). The time point of the peak further varies depending on the brain region ( Giedd et al., 1999) and the sex and/or pubertal stage, with females reaching gray matter peaks 1-2 years earlier than males ( Gogtay and Thompson, 2010; Mills and Tamnes, 2014). Therefore, it could be the case that we did not detect developmental changes in the gray matter, because the children and adolescents we studied are around one of the reported gray matter peaks. If we look at the individual trajectories of our study participants, some children still show a gray matter increase, whilst other children show a gray matter decrease or almost no change in the gray matter volume over the 4 years ( Figure 2, upper panel). Moreover, the fact that we controlled for pubertal status and therefore indirectly for sex might be an additional reason why we do not find developmental changes. In the white matter volume, we found a significant increase during development in the left SLF (MNI x = −40, y = −20, z = 28), located right next to the reported developmental changes in the study of Giorgio et al. (2010; MNI x = −42, y = −22, z = 28). However, our results do not show the prominent white matter changes as reported in the literature ( Giorgio et al., 2010). A possible explanation is that our study does not look at the correlations between white matter volume and age. On the other hand, the individual trajectories of our subjects show a clear increase in the total white matter volume ( Figure 2, lower panel), which is in line with previous research ( Aubert-Broche et al., 2013; Mills et al., 2016).

Figure 2. Spaghetti plots of whole brain volumes. Gray matter (top panel) and white matter volumes (lower panel) are plotted against age for children with dyscalculia (left, in blue) and typically developing children (right, in gray). The red line depicts the mean of the group.

The main focus of our study was to find out more about the developmental trajectories of gray and white matter volumes in children with DD. We found no significant interactions, but the group differences in gray and white matter volumes remained stable during the examined time window. Although the differences found between DD and TD children are well in line with the literature ( Rotzer et al., 2008; Rykhlevskaia et al., 2009), and also reflect the known and persistent behavioral differences ( Nelson and Powell, 2018), the developmental trajectories differ from the results reported by Ranpura et al. (2013) in such that we did not find an increase in white matter volume in frontal and parietal areas in TD children only. Studies in adults find no or very subtle differences between the subjects with and without DD ( Cappelletti and Price, 2013; Moreau et al., 2019). Based on these results, one could argue that the volumetric differences should diminish over development. However, Moreau et al. (2019) used a rather lenient criterion for DD, which could also be a reason why volumetric differences were not found. Also, there is an age gap of 10-15 years between our results and the adult studies, in which developmental changes can still take place. Our results, therefore, point towards stable and persistent differences in the dyscalculics gray and white matter volumes from childhood to adolescence. More research, specifically longitudinal studies over a longer time interval, are urgently needed to enable us to conclude the developmental trajectory of the brain structure in DD. However, findings from the present study suggest that development proceeds in a similar manner between DD and TD children.

To better understanding the present findings, it is important that we advance our knowledge about the typical developmental trajectory of the brain structure and its spontaneous variations in numerical cognition. Furthermore, the effects of schooling and specific interventions on brain structure need to be explored more profoundly. This knowledge should build the basis for the investigation and a better understanding of the deviant and/or delayed development as reported in children with DD. In a next step, it would be interesting to investigate if the abnormalities in gray and white matter are a result of a developmental delay or a specific marker of DD. This open question could be tackled by comparing the structural brain development of DD children with TD children that perform on a similar numerical level. Furthermore, the investigation of structural changes caused by a specific intervention could help clarify the questions about the neurobiological cause of dyscalculia.

Limitations

Our results are important for the field since this is to our knowledge the first study investigating the developmental trajectory of structural white and gray matter volumes using longitudinal data in DD. However, several limitations should be considered when interpreting the results of our study. First of all, due to braces and movement artifacts, the drop-out rates in longitudinal MRI studies with children and adolescents are high. Our study includes only small sample sizes and should for this reason be interpreted with caution. However, the data included had good data quality ratings, as assessed by objective criteria ( Gaser and Dahnke, 2016). Moreover, we replicated the main findings of previous studies examining volumetric gray and white matter differences in DD children ( Rotzer et al., 2008; Rykhlevskaia et al., 2009; Ranpura et al., 2013), which were also performed with larger sample sizes (e.g., Rykhlevskaia et al., 2009). Therefore, we are confident that despite the small sample sizes our results contribute valuable knowledge towards an understanding of the developmental trajectory of brain structure in children with and without DD.

Second, the rather large age range within our sample (at each time point) may attenuate the developmental effects. For methodological reasons, a narrower age range would be much better to examine general developmental effects and detect group differences over time. A closer look at our data revealed that the individual developmental trajectories showed similar trends irrespective of the age at the entry of the study. However, future longitudinal studies should investigate limited age ranges to control better for the effect of schooling and the rapid changes in development.

A third restricting point of our study is the significant difference in IQ between the TD and the DD group. Developmental imaging studies have shown that there is a positive relationship between intellectual abilities and white/gray matter volume, especially in the dorsolateral prefrontal cortex, parietal lobe, the anterior cingulate cortex and in temporal and occipital regions ( Wilke et al., 2003; Tamnes et al., 2011; Brancucci, 2012). For this reason, we ran our analyses with IQ as an additional covariate showing that the main results remained unchanged (see Supplementary Material).

Last, it should be noted that some authors argue that the sensitivity to examine the white matter using voxel-based morphometry is limited, as white matter areas are characterized by large homogenous regions with only subtle changes in intensity ( Kurth et al., 2015).

Conclusion

In conclusion, the present study reveals for the first time the gray and white matter trajectories of the dyscalculic brain. The findings confirm the structural differences as reported in earlier research and support the notion that DD is characterized by persistent structural and behavioral abnormalities. There is an urgent need for longitudinal studies examining the typical and atypical neural development, but also the effect of interventions and therapy on numerical and mathematical abilities. Advancing the knowledge about the developmental course of DD and the effects of schooling, therapy, and intervention would enable us to support affected children and adolescents more effectively.

Data Availability Statement

The datasets generated for this study will not be made publicly available. According to the Ethics committee of Zurich, Switzerland the consent was not obtained for sharing data outside the research team. Therefore we do not have the allowance to make the data publicly available. Requests to access the datasets should be directed to the Ethics committee of Zurich in Switzerland ( Info.KEK@kek.zh.ch, project-number: 2011-0384, title of the project: Plasticity after training and development in children with and without dyscalculia).

Ethics Statement

The present study was reviewed and approved by the Ethics committee of Canton of Zurich, Switzerland. Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.

Author Contributions

All authors have contributed and have approved the final manuscript. UM contributed to the design of the study, the acquisition, analysis, interpretation of the data, and writing the manuscript. MA and RO'G contributed to data interpretation and revised the manuscript. KK contributed to the design of the study, the acquisition, data interpretation, editing, and revision of the manuscript.

Funding

This research was supported by a grant from the NOMIS Foundation.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

We would like to thank all subjects and their parents for participating in this study.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fnhum.2020.00272/full#supplementary-material.

References

Heller, K. A., and Perleth, C. (2000). Cognitive Abilities Test for Grades 4 to 12 - Revised Version. Göttingen: Beltz.

Kurth, F., Luders, E., and Gaser, C. (2015). "Voxel-based morphometry," in Brain Mapping, ed. A. W. Toga (Waltham, MA: Academic Press), 345-349.

Moll, K., and Landerl, K. (2010). Salzburg Reading and Orthography Test - Revised version. Bern: Huber.

von Aster, M., Weinhold Zulauf, M., and Horn, R. (2006). ZAREKI-R. Neuropsychologische Testbatterie für Zahlenverarbeitung und Rechnen bei Kindern, Revidierte Version [Neuropsychological Test Battery for Number Processing and Calculation in Children]. Frankfurt am Main: Harcourt.

WHO. (2018). International classification of diseases for mortality and morbidity statistics (ICD-11). Available online at: https://icd.who.int/browse11/l-m/en. Accessed November 4, 2019.

# data[].attributes.attachment_link.title
Persistent Differences in Brain Structure in Developmental Dyscalculia: A Longitudinal Morphometry Study

# data[].attributes.attachment_link.description
Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Affected people show persistent deficits in number processing, which are associated with aberrant brain activation and structure. Reduced gray matter has been reported in DD for the parietal cortex including the intraparietal sulcus (IPS), but also the frontal and occipito-temporal cortex.

# data[].attributes.body
Dysgraphia points to issues with writing and language coherency. Dysgraphia is hypocoherent. Subjects with dysgraphia usually find their shortcoming of connections in the parietal lobe.

# data[].attributes.attachment_link.readable_text
What is dysgraphia?

Dysgraphia is a neurological condition in which someone has difficulty turning their thoughts into written language for their age and ability to think, despite exposure to adequate instruction and education. Dysgraphia can present with many different symptoms at different ages. It's considered a learning difference.

Writing is a complex process that involves many skills and brain functions, including:

Fine motor skills.

Spatial perception (ability to perceive the space around you).

Working memory (ability to hold and manipulate information in your mind).

Orthographic coding (ability to form, store and recall letters, numbers and symbols).

Language processing.

Conceptualization.

Organization.

Because of this, dysgraphia is somewhat of a catch-all term to diagnose issues with writing and can be difficult to diagnose.

Dysgraphia generally appears when children are first learning to write. This is called developmental dysgraphia. People can also develop dysgraphia suddenly after some type of head or brain trauma. This is called acquired dysgraphia.

Dysgraphia is considered a "specific learning disorder" - more specifically, a "specific learning disorder in written expression."

Is dysgraphia a form of dyslexia?

Dyslexia and dysgraphia are two distinct neurological conditions, though they're easy to confuse because they share symptoms and often occur together.

Dyslexia is a learning difference that makes it harder for people to learn to read. If you have dyslexia, you may read more slowly or have trouble recognizing words. Often, people with dyslexia read at a lower level than expected. People with dyslexia may struggle to break words into sounds or relate letters to sounds when reading.

Dysgraphia involves difficulty with the act of writing. Difficulties can range from issues with physically writing words to issues with organizing and expressing thoughts in written form.

Is dysgraphia a form of autism?

Dysgraphia isn't a form of autism spectrum disorder (ASD). Though dysgraphia commonly occurs in people with autism, you can have dysgraphia without having autism.

Autism spectrum disorder is a neurodevelopmental condition characterized by:

Difficulties in social communication differences.

Deficits in social interactions.

Restricted, repetitive patterns of behavior, interests or activities.

Sensory problems.

Who does dysgraphia affect?

Dysgraphia can affect children and adults. As with many neurodevelopmental conditions, dysgraphia is more common in children assigned male at birth (AMAB) than in children assigned female at birth (AFAB).

You're more likely to have dysgraphia if other family members also have it, and dysgraphia is common in children with autism spectrum disorder (ASD) and/or attention deficit hyperactivity disorder (ADHD).

How common is dysgraphia?

Dysgraphia is common. Researchers estimate that 5% to 20% of people have dysgraphia. The estimated range is large because dysgraphia often goes undiagnosed or misdiagnosed.

# data[].attributes.attachment_link.title
Dysgraphia: What It Is, Symptoms, Diagnosis & Treatment

# data[].attributes.attachment_link.description
Dysgraphia is a neurological condition in which someone has difficulty with writing skills for their age despite exposure to adequate instruction.

# data[].attributes.body
ADHD is a hypercoherent learning disorder. People with ADHD have difficulties with paying attention and controlling impulsive behaviours. The extra connections associated with ADHD are mostly in the brain's gray matter.

# data[].attributes.attachment_link.provider_name
Centers for Disease Control and Prevention

# data[].attributes.attachment_link.readable_text
ADHD symptoms may look different across the lifetime.

People with ADHD may have trouble paying attention, controlling impulsive behaviors (may act without thinking about what the result will be), or be overly active. Although ADHD can't be cured, it can be successfully managed and some symptoms may improve as the child ages.

Data and resources for states.

Learn about CDC's initiative to support children with ADHD.

Learn about symptoms of ADHD, how ADHD is diagnosed, and treatment recommendations including behavior therapy, medication, and school support.

# data[].attributes.attachment_link.description
ADHD is one of the most common neurobehavioral disorders of childhood. It is usually first diagnosed in childhood and often lasts into adulthood. Children with ADHD have trouble paying attention, controlling impulsive behaviors (may act without thinking about what the result will be), and in some cases, are overly active.

# data[].attributes.headline
Phonologic Dyslexia, Surface Dyslexia, and Dyslexia

# data[].attributes.subject
Phonologic Dyslexia, Surface Dyslexia, and Dyslexia

# data[].attributes.body
Phonologic Dyslexia is difficulty in processing non-word reading (numbers, symbols, etc). Surface Dyslexia is difficulty processing words by exception(some come easy, some come hard). Dyslexia is difficulty with word processing(misspelling, mispronouncing, etc). All of these are hypocoherent learning disabilities. The lack of connections occur in the temporal lobe, as well as in the occipital lobe.

# data[].attributes.body
This learning disability highlights the difficulty the subject would have with mathematics. This would be a hypocoherent learning disability.

# data[].attributes.body
This is when the subject has a difficulty with counting. It is a hypocoherent learning disorder.

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loss of the ability to count (as resulting from a brain lesion)… See the full definition

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Anomic Aphasia means the subject has difficulty with recognizing and finding words. This would be a hypocoherent learning disorder. The lack of connected points to the parietal lobe, specifically the left one.

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Most people have never heard about aphasia until they or someone they know are impacted personally. Here is what you need to know.

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This encapsulates a wide variety of difficulties, but autism in general is a hypercoherent learning disability.

# data[].attributes.attachment_link.provider_name
Centers for Disease Control and Prevention

# data[].attributes.attachment_link.readable_text
Autism spectrum disorder (ASD) is a developmental disability caused by differences in the brain. People with ASD often have problems with social communication and interaction, and restricted or repetitive behaviors or interests. People with ASD may also have different ways of learning, moving, or paying attention. It is important to note that some people without ASD might also have some of these symptoms. But for people with ASD, these characteristics can make life very challenging.
Learn more about ASD
Social Communication and Interaction Skills

Social communication and interaction skills can be challenging for people with ASD.

Examples of social communication and social interaction characteristics related to ASD can include

Avoids or does not keep eye contact

Does not respond to name by 9 months of age

Does not show facial expressions like happy, sad, angry, and surprised by 9 months of age

Does not play simple interactive games like pat-a-cake by 12 months of age

Uses few or no gestures by 12 months of age (for example, does not wave goodbye)

Does not share interests with others by 15 months of age (for example, shows you an object that they like)

Does not point to show you something interesting by 18 months of age

Does not notice when others are hurt or upset by 24 months of age

Does not notice other children and join them in play by 36 months of age

Does not pretend to be something else, like a teacher or superhero, during play by 48 months of age

Does not sing, dance, or act for you by 60 months of age

Restricted or Repetitive Behaviors or Interests

People with ASD have behaviors or interests that can seem unusual. These behaviors or interests set ASD apart from conditions defined by problems with social communication and interaction only.

Examples of restricted or repetitive behaviors and interests related to ASD can include

Lines up toys or other objects and gets upset when order is changed

Repeats words or phrases over and over (called echolalia)

Plays with toys the same way every time

Is focused on parts of objects (for example, wheels)

Gets upset by minor changes

Has obsessive interests

Must follow certain routines

Flaps hands, rocks body, or spins self in circles

Has unusual reactions to the way things sound, smell, taste, look, or feel

Other Characteristics

Most people with ASD have other related characteristics. These might include

Delayed language skills

Delayed movement skills

Delayed cognitive or learning skills

Hyperactive, impulsive, and/or inattentive behavior

Epilepsy or seizure disorder

Unusual eating and sleeping habits

Gastrointestinal issues (for example, constipation)

Unusual mood or emotional reactions

Anxiety, stress, or excessive worry

Lack of fear or more fear than expected

It is important to note that children with ASD may not have all or any of the behaviors listed as examples here.
Learn more about screening and diagnosis of ASD Learn more about treating the symptoms of ASD

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Signs & Symptoms | Autism Spectrum Disorder (ASD) | NCBDDD | CDC

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Autism Spectrum Disorder (ASD) are a group of developmental disabilities that can cause significant social, communication and behavioral challenges. CDC is working to find out how many children have ASDs, discover the risk factors, and raise awareness of the signs.

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OCD is a hypercoherent learning disorder. OCD causes the subject to have unwanted patterns in their behaviour, and causes unwanted thoughts. Like ADHD, the over-connections occur in the brain's gray matter.

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Overview

Obsessive-compulsive disorder (OCD) features a pattern of unwanted thoughts and fears known as obsessions. These obsessions lead you to do repetitive behaviors, also called compulsions. These obsessions and compulsions get in the way of daily activities and cause a lot of distress.

Ultimately, you feel driven to do compulsive acts to ease your stress. Even if you try to ignore or get rid of bothersome thoughts or urges, they keep coming back. This leads you to act based on ritual. This is the vicious cycle of OCD.

OCD often centers around certain themes, such as being overly fearful of getting contaminated by germs. To ease contamination fears, you may wash your hands over and over again until they're sore and chapped.

If you have OCD, you may be ashamed, embarrassed and frustrated about the condition. But treatment can be effective.

Symptoms

Obsessive-compulsive disorder usually includes both obsessions and compulsions. But it's also possible to have only obsession symptoms or only compulsion symptoms. You may or may not know that your obsessions and compulsions are beyond reason. But they take up a great deal of time, reduce your quality of life, and get in the way of your daily routines and responsibilities.

Obsession symptoms

OCD obsessions are lasting and unwanted thoughts that keeping coming back or urges or images that are intrusive and cause distress or anxiety. You might try to ignore them or get rid of them by acting based on ritual. These obsessions usually intrude when you're trying to think of or do other things.

Obsessions often have themes, such as:

Fear of contamination or dirt.

Doubting and having a hard time dealing with uncertainty.

Needing things to be orderly and balanced.

Aggressive or horrific thoughts about losing control and harming yourself or others.

Unwanted thoughts, including aggression, or sexual or religious subjects.

Examples of obsession symptoms include:

Fear of being contaminated by touching objects others have touched.

Doubts that you've locked the door or turned off the stove.

Intense stress when objects aren't orderly or facing a certain way.

Images of driving your car into a crowd of people.

Thoughts about shouting obscenities or not acting the right way in public.

Unpleasant sexual images.

Staying away from situations that can cause obsessions, such as shaking hands.

Compulsion symptoms

OCD compulsions are repetitive behaviors that you feel driven to do. These repetitive behaviors or mental acts are meant to reduce anxiety related to your obsessions or prevent something bad from happening. But taking part in the compulsions brings no pleasure and may offer only limited relief from anxiety.

You may make up rules or rituals to follow that help control your anxiety when you're having obsessive thoughts. These compulsions are beyond reason and often don't relate to the issue they're intended to fix.

As with obsessions, compulsions usually have themes, such as:

Washing and cleaning.

Checking.

Counting.

Ordering.

Following a strict routine.

Demanding reassurance.

Examples of compulsion symptoms include:

Hand-washing until your skin becomes raw.

Checking doors over and over again to make sure they're locked.

Checking the stove over and over again to make sure it's off.

Counting in certain patterns.

Silently repeating a prayer, word or phrase.

Trying to replace a bad thought with a good thought.

Arranging your canned goods to face the same way.

Severity varies

OCD usually begins in the teen or young adult years, but it can start in childhood. Symptoms usually begin over time and tend to vary in how serious they are throughout life. The types of obsessions and compulsions you have also can change over time. Symptoms generally get worse when you are under greater stress, including times of transition and change. OCD, usually thought to be a lifelong disorder, can have mild to moderate symptoms or be so severe and time-consuming that it becomes disabling.

When to see a doctor

There's a difference between being a perfectionist - someone who needs flawless results or performance - and having OCD. OCD thoughts aren't simply excessive worries about real issues in your life or liking to have things clean or arranged in a specific way.

If your obsessions and compulsions affect your quality of life, see your doctor or mental health professional.

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Causes

The cause of obsessive-compulsive disorder isn't fully understood. Main theories include:

Biology. OCD may be due to changes in your body's natural chemistry or brain functions.

Genetics. OCD may have a genetic component, but specific genes have yet to be found.

Learning. Obsessive fears and compulsive behaviors can be learned from watching family members or learning them over time.

Risk factors

Factors that may raise the risk of causing obsessive-compulsive disorder include:

Family history. Having parents or other family members with the disorder can raise your risk of getting OCD.

Stressful life events. If you've gone through traumatic or stressful events, your risk may increase. This reaction may cause the intrusive thoughts, rituals and emotional distress seen in OCD.

Other mental health disorders. OCD may be related to other mental health disorders, such as anxiety disorders, depression, substance abuse or tic disorders.

Complications

Issues due to obsessive-compulsive disorder include:

Excessive time spent taking part in ritualistic behaviors.

Health issues, such as contact dermatitis from frequent hand-washing.

Having a hard time going to work or school or taking part in social activities.

Troubled relationships.

Poor quality of life.

Thoughts about suicide and behavior related to suicide.

Prevention

There's no sure way to prevent obsessive-compulsive disorder. However, getting treated as soon as possible may help keep OCD from getting worse and disrupting activities and your daily routine.

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Obsessive-compulsive disorder (OCD) - Symptoms and causes

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OCD features unwanted thoughts and fears, or obsessions. These obsessions lead to repetitive behaviors, also known as compulsions, that get in the way of daily activities.

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