No Evidence for an Association Between Variability in Sulcal Pattern and Academic Achievement

Investigating how the brain may constrain academic achievement is not only relevant to understanding brain structure but also to providing insight into the origins of individual differences in these academic abilities. In this pre-registered study, we investigated whether the variability of sulcal patterns, a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning, accounted for individual differences in reading and mathematics. Participants were 97 typically developing 10-year-olds. We examined (a) the association between the sulcal pattern of the intraparietal sulcus (IPS) and mathematical ability; (b) the association between the sulcal pattern of the occipitotemporal sulcus (OTS) and reading ability; and (c) the overlap and specicity of sulcal morphology of IPS and OTS and their associations with mathematics and reading. Despite its large sample, the present study was unable to replicate a previously observed relationship between the IPS sulcal pattern and mathematical ability and a previously observed association between the Left posterior OTS sulcal pattern and reading. We found no evidence for a possible overlap or specicity in the effect of sulcal morphology on mathematics and reading. Possible explanations for this absence of an association between sulcal morphology and academic achievement and suggestions for future research are discussed.


Introduction
Understanding how academic abilities, such as reading and math, develop but also mapping the various constraints, including biological factors, that may in uence its development is of great importance for both science and society. Especially since research suggests that these academic abilities are important factors in determining career success, income and even psychological well-being (e.g., Parsons & Bynner, 2005). Yet, the 2018 Program for International Student Assessment (PISA) results show that more than one in ve pupils in the EU has insu cient pro ciency in these key academic skills (OECD, 2019).
Investigating how the brain may constrain academic achievement is not only relevant to understanding brain structure but also to providing insight into the origins of individual differences in these academic abilities.
Research has extensively studied the function of key regions for processing mathematics and reading, . The aim of this study was to replicate and extend these ndings of an association between the sulcal morphology of the IPS and math abilities as well as the sulcal morphology of the OTS and reading.
Research has strived to delineate the brain regions functionally supporting mathematical ability. This body of literature converges to suggest that a fronto-parietal network is engaged during arithmetic in both children and adults (Arsalidou & Taylor, 2011;Rivera et al., 2005). Consistent across these data is the activation of the bilateral IPS during arithmetic (e.g., Arsalidou  Studies have also investigated which brain structures are related to individual differences in mathematical ability, with the majority of studies focusing on the role of white and grey matter. Individual differences in math ability were found to be associated with higher fractional anisotropy, a parameter related to white matter microstructure, in white matter tracts connecting frontal lobes with basal ganglia and parietal regions (Matejko et al., 2013;Navas-Sánchez et al., 2014;van Eimeren et al., 2008).
Additionally, grey matter volume of the Left IPS at the end of rst grade has been found to be related to math competence a year later at the end of Grade 2 (Price et al., 2016). Similarly, Evans et al. (2015) reported that grey matter volume of posterior parietal areas, including the Left IPS, predicted the growth in arithmetic across primary school. However, in a recent study, Polspoel et al. (2020) examined grey matter volume using voxel-based morphometry, as did previous studies, but also cortical complexity. They did not nd a signi cant association between children's arithmetic uency and the grey matter volume or the complexity of parietal regions such as the IPS.
Reading, on the other hand, systematically activates the Left lateral Occipitotemporal sulcus (OTS) at a xed location known as the Visual Word Form Area (VWFA, Cohen et al., 2002) relative to a reproducible mosaic of regions partially specialized for objects, faces, bodies and places (Downing et al., 2006). The specialization of the VWFA site appears progressively as children start to learn to read (Dehaene-Lambertz et al., 2018). Additionally, word-induced activation found at the site of the VWFA in good readers has been found to be cross-culturally consistent. Bolger et al.( 2005) found that the peak activation of the VWFA in Japanese kana, Japanese logographic kanji, Chinese and roman alphabet readers was all within the millimeter of each other. Furthermore, children and adults with developmental dyslexia, a speci c disorder of reading acquisition (American Psychiatric Association, 2013), show an under-activation (Cao et al., 2006;Shaywitz et al., 2003) and a dysfunction in the VWFA whilst processing visual words (van der Mark et al., 2011).
Studies have also examined the brain's structure supporting reading, again focusing largely on white and grey matter data. In their study, Myers et al. (2014) found that increases in the volume of two left temporo-parietal white matter clusters are unique predictors of reading outcomes above and beyond family history, socioeconomic status and cognitive and preliteracy measure at baseline. Similarly, Niogi & McCandliss (2006) found a strong correlation between fractional anisotropy values in a Left tempoparietal white matter region and standardized reading scores of typically developing children. Additionally, they found that fractional anisotropy values in that region accounted for differences in reading score between typically developing children and children with dyslexia children.
Turning to the role of grey matter, Altarelli et al. (2013) examined whether cortical thickness of the ventral occipitotemporal regions differed between dyslexic and typically developing children. They found a reduction in thickness in dyslexic compared with controls in the VWFA, i.e., the Left posterior OTS. In their meta-analysis, Richlan et al. (2013) found converging evidence of reduced grey matter in the bilateral superior temporal sulcus in dyslexic participants compared to typically developing controls. They also found evidence of structural and functional abnormalities in the Left occipitotemporal region in prereaders with a family history of developmental dyslexia (Richlan et al., 2013).
One limitation of the existing body of data is that it does not furnish information on the in uence of early cerebral constraints on academic achievement. Indeed, nearly all studies on the relation between neuroanatomy and academic achievement have focused on structural brain characteristics, such as grey matter density or white matter tracts (Dehaene et al., 2015;, that are affected by brain maturation and learning (e.g., Zatorre et al., 2012). To evaluate early cerebral constraints on mathematical or reading achievement, it is important to examine neuroanatomical characteristics that are not affected by brain maturation and learning. Researchers have recently turned to the study of sulcal pattern of the brain as this qualitative feature of the cortex anatomy is determined in utero (Mangin, Jouvent, & Cachia, 2010) and is stable during development (Tissier et al., 2018). Studying brain sulcal pattern thus allows researchers to further unravel the question of causes of individual differences that are independent of learning and development.
Applying this methodology to the study of individual differences in mathematical cognition, in a recent pre-registered study (https://osf.io/w3zvc) Roell et al. (in prep) examined whether the IPS sulcal pattern explains individual differences in number processing in sample of grade 1 to grade 4 children (n = 77) and adults (n = 21). They characterized the Left and Right IPS sulcal pattern as "sectioned" vs "not sectioned" based on the presence or absence of branches completely sectioning the IPS using Zlatkina & Petrides' (2014) classi cation. They found that IPS sulcal pattern explains part of the variance in both the children's and adult's symbolic number comparison and math uency abilities but not in their nonsymbolic number abilities. As with the data on the association between sulcal morphology and reading, it appears of importance to be able to replicate the association between the sulcal morphology of the IPS and symbolic number processing and arithmetic ability in a large sample of participants with a narrower age range.
Using In addition to studies that either focus on reading or on mathematics, it would be of interest to examine potential overlap or speci city of the sulcal pattern effect of the IPS on mathematical abilities and OTS on reading. Indeed, mathematical and reading abilities have been found to be correlated (Grimm, 2008). Comorbidity or co-occurrence of speci c learning disorders in reading (dyslexia) and in math (dyscalculia) is remarkably high (Peters & Ansari, 2019). Furthermore, functional neural overlap of arithmetic and reading has been reported (Evans et al., 2016). Children with dyslexia have been reported to show atypical brain activation patterns during arithmetic in arithmetic-related regions, such as the supramarginal gyrus (Evans et al., 2014) and there is evidence to suggest that children with dyslexia and dyscalculia show highly overlapping patterns of brain activity during the processing of number (e.g., .

Research aims
The aim of this study is threefold. For our rst aim, Aim 1, we focus on the association between sulcal morphology of the IPS and individual differences in arithmetic and number processing. We wish to conceptually replicate in a larger dataset of participants in the same age range and extend our previous study (Roell et al., in prep). In continuation of Roell et al.'s study, we expect that IPS sulcal morphology explains part of the variability observed in arithmetic and symbolic number ability in typically developing children. That is, we hypothesize that children with a "sectioned" IPS will have greater symbolic number comparison and arithmetic abilities than children with a "not sectioned" IPS. In order to further our understanding of the relationship between symbolic number processing, arithmetic and the sulcal arithmetic ability. As such, it would appear interesting to examine whether the relationship between IPS sulcal morphology and arithmetic ability is mediated by symbolic number processing. We hypothesize that symbolic number processing mediates the association between IPS sulcal morphology and arithmetic ability. That is, participants with a "sectioned" IPS will have greater symbolic number comparison abilities; these greater symbolic number comparison abilities will in turn be associated with greater arithmetic abilities. Our third aim, Aim 3, is to examine whether the effect of sulcal morphology on academic abilities is speci c. As discussed above, studies examining behaviour, learning disorders and functional networks point towards an overlap between reading and mathematical abilities. Additionally, the speci city of the IPS for number and arithmetic processing (Fias et al., 2007) and the VWFA for reading (Vogel et al., 2014) remains controversial. As such, in view of the existing overlap, it becomes relevant to determine whether the effect of the IPS sulcal pattern on numerical abilities is speci c, as well as the effect of the OTS sulcal pattern on reading is speci c. The overlap and speci city of the IPS and OTS will be examined through three different analyses. Firstly, we shall test whether the sulcal pattern of IPS predicts reading and the sulcal pattern of Left posterior OTS predicts arithmetic abilities. Secondly, we shall run the same analyses as in Aim 1 and 2 but we shall add the other academic ability as a covariate. That is, we shall examine the effect of IPS sulcal morphology on mathematical ability whilst controlling for reading ability. Similarly, we shall examine the effect of OTS sulcal morphology on reading ability whilst controlling for mathematical ability. Thirdly, we shall use a third sulcal pattern, which is much less related to reading or mathematical ability, as a control region. More speci cally we will examine if the sulcal morphology of the ACC (anterior cingulate cortex) is related to math and reading abilities. Studies have found that an asymmetrical ACC sulcal pattern, that is each hemisphere had a different ACC sulcal pattern, was associated with higher inhibitory control e ciency in both children Cachia et al., 2017) and adults (Fornito, 2004;Huster et al., 2009;Tissier et al., 2018). Against this background, we predict that, if the association between sulcal patterns and academic achievement is speci c, this sulcal pattern of the ACC will be much less related to math abilities or reading ability. Finally, we also tested whether a relationship between the sulcal pattern of the IPS and that of the OTS could be found. That is, are participants with an "interrupted" OTS more likely to have a "sectioned" IPS and vice-versa?
To address the three aims outlined above, we will utilize structural MRI data from two existing samples collected in the same age range. These structural data were previously collected for a variety of different studies (Bellon et al., 2020;Polspoel et al., 2017) and all have the same structural image scans as well as academic achievement measures (Tempo Test Arithmetic task, symbolic number comparison task, Dutch one-minute reading test). We selected behavioural measures common to all samples that measured academic achievement. It is of note that both datasets initially focused on mathematical ability. As such, the datasets contained more common mathematical tasks which allow us to also investigate the cognitive correlates of mathematical ability (through our mediation analysis) in a more ne-grained way as compared to reading ability. The functional data has already been published (  sulcus and extending at least 20 mm (interruptions or gaps in the PCS course will not be taken into account for the length measure). PCS length was measured in a standard (MNI) space.

Analysis
A statistical analysis plan for this study was preregistered on the Open Science Framework (https://osf.io/cqsu9). Analyses were performed using the R (R Core Team, 2013) and JASP software (JASP Team, 2020). For each of the analyses, we reported effect size in terms of Cohen's d for t-tests and eta-square for ANOVAs. Bayesian analysis were also used to quantify the evidence against (BF 10 ) or for (BF 01 ) the null hypothesis.
Before conducting analyses relevant to the 3 aims, we rst assessed whether sex and IQ were associated with the academic measures. If associations were found to be signi cant, we included these variables as covariates in the regression models. We also assessed whether there was any database difference in the academic measures [2]. If database differences were found to be signi cant, we included database as a covariate in the regression model.

Aim 1: Associations between number/arithmetic and IPS sulcal morphology
For our rst aim, we determined whether the sulcal patterns of the Right and Left IPS were associated with the participant's symbolic number processing abilities and arithmetic abilities.
We rst assessed the relationship between IPS sulcal pattern (Left and Right IPS) and symbolic number processing as well as the arithmetic through t-tests. If an association was found between number/arithmetic and IPS sulcal pattern, subsequent regressions tested whether the association holds when the abovementioned covariates (IQ, sex and database) are included.
Finally, we assessed whether participants' scores in the TTA task were correlated with the symbolic number comparison task. If these were indeed correlated and we nd an association between IPS and arithmetic abilities, we ran a mediation model, to examine whether symbolic number processing mediates the relationship between IPS sulcal morphology and arithmetic ability. We hypothesized a direct effect between IPS sulcal pattern and arithmetic ability as well as an indirect effect between IPS sulcal pattern and arithmetic ability through symbolic number abilities, see gure 4. was found between reading and OTS sulcal pattern, subsequent regressions examined whether the association holds when the abovementioned covariates are included.
If we found that participants with interrupted Left posterior OTS had better reading skills than participants with a continuous Left posterior OTS, we then examined whether we may nd a positive correlation between the length of the interruption and reading ability as was found in (Cachia et al., 2017).
Aim 3: Overlap and speci city of sulcal morphology related to mathematics and reading Three analyses were performed to evaluate the speci city of the effect of the IPS sulcal pattern on mathematical abilities and of the speci city of the effect of the OTS sulcal pattern on reading abilities. Firstly, we investigated whether the sulcal pattern of the IPS might be related to reading ability and whether the sulcal pattern of the OTS might be related to mathematical ability via t-tests. Secondly, we tested whether the association between IPS sulcal pattern and mathematical ability remains when reading ability is controlled for. Likewise, we examined whether the association between OTS sulcal pattern and reading ability remains when mathematical ability is controlled for. Thirdly, we examined whether mathematical and reading ability are associated to the sulcal pattern of the ACC, a sulcus unrelated to both academic skills. To do so, we investigated whether ACC pattern groups ("single type" vs "double parallel type") differ in their mathematical and reading ability. Finally, we also tested whether a relationship between the sulcal pattern of the IPS and that of the OTS could be found. That is, are participants with an "interrupted" OTS more likely to have a "sectioned" IPS and vice-versa. Footnote: [1] The pre-registration protocol initially expected to use a third database. However, the T1 MRI data had too much movement for the BrainVisa software to read it, the database was therefore excluded from the study.
[2] Pre-registration protocol initially indicated that we would add database as a covariate in the nal models without assessing whether we found any database differences in the academic measures.
However, for the sake clarity we chose to rst assess whether there were any database difference and only add them if these were signi cant Findings with and without the inclusion of database as a covariate were exactly the same.

General description
We rst explored the data for potential outliers, de ned as values larger or smaller than one and a half times the interquartile range. Four outliers were identi ed and excluded in the symbolic number measure.
In the arithmetic measure, one outlier was identi ed and excluded. In the reading measure, two outliers were identi ed and excluded. Notably, our data was analyzed both with and without the outliers, including the outliers did not affect the results.
We then analyzed whether sex and IQ were associated with arithmetic, symbolic number and reading abilities. Sex was not found to be associated with arithmetic abilities, t(87)= -1.65 , p = . 10 and for IQ and reading, BF 01 = 6.18. To conclude, neither sex nor IQ were associated with the academic skills measured in this study, and therefore they were not included as covariates in the subsequent models.
We also analyzed whether there were any database differences in arithmetic, symbolic number comparison and reading abilities (see Table 1). No database differences were found in arithmetic abilities, t(87) = 0.26, p = .79, and the evidence for this absence of an association was substantial BF 01 = 4.37. No database differences were found in symbolic number comparison abilities, t(84) = 0.61, p = .53, and the evidence for this absence of an association was substantial BF 01 = 3.76. No database differences were found in reading abilities, t(62) = 0.62, p = .52, and the evidence for this absence of an association was substantial BF 01 = 3.29. Since we did not nd any database differences in the academic measures, we did not include database as a covariate in the subsequent models. We also examined the distribution of sulcal patterns of the IPS (Table 2), OTS ( Table 3) and ACC ( Table  4).  Table 4. Distribution of participants with a "Single type" or a "Double type" Left and Right ACC.

Left ACC Right ACC
Single type 32 54 Double type 58 36 Aim 1: Associations between number/arithmetic and IPS sulcal morphology We rst examined whether the sulcal pattern of the Left and Right IPS was associated with arithmetic abilities. There was no association between Left IPS and arithmetic, t(87) = 1.63 , p = .10, and the evidence for this absence of an association was weak BF 01 = 1.35, see Figure 5. Similarly no association between Right IPS and arithmetic was found, t(87) = 1.32, p = .18, and the evidence for this absence of an association was weak BF 01 = 2.07, see Figure 5.
We then analyzed whether the sulcal pattern of the Left and Right IPS was associated with symbolic number ability. The Left IPS was not found to be signi cantly associated with symbolic number abilities, t < 1, and the evidence for this absence of an association was substantial BF 01 = 4.18. Contrastingly, Right IPS was found to be signi cantly associated with symbolic number ability, t(84) = -2.07, p = .04, and the evidence for this association was weak BF 10 = 1.44. Participants with a sectioned Right IPS had signi cantly longer reaction times in the symbolic number comparison task than participants with a not sectioned IPS, see Figure 6.
Next, we assessed whether participants' scores in the arithmetic task are correlated with the symbolic number comparison task. Arithmetic ability was found to be correlated with symbolic number ability, r(83) = -0.35, p < .001 and the evidence for this association was very strong with BF 10 = 44.70. Although arithmetic ability and symbolic number ability are indeed correlated, we did not nd an association between IPS and mathematical abilities (arithmetic and symbolic ability). As such, it was not appropriate to conduct mediation analyses examining whether symbolic number processing mediates the relationship between IPS sulcal morphology and arithmetic ability (but see Supplementary Section 1 for mediation analyses).

Aim 2: Associations between reading and sulcal morphology OTS
The Left posterior and anterior OTS were not found to be signi cantly associated with reading ability, t(1,62) = 1.69, p = .09, and t < 1, respectively, see Figure 7. The evidence for this association was weak for both the Left posterior, BF 01 = 1.14 and Left anterior OTS, BF 01 = 2.49. Similarly, the Right posterior OTS was not found to be signi cantly associated with reading ability, t < 1 (see Figure 7) and the evidence for this absence of an association was weak BF 01 = 2.58. The Right anterior OTS was found to be moderately associated with reading ability with t(1,62)= -2.03, p = .05 (see Figure 7), the evidence for this association was weak BF 10 = 1.47.

Aim 3: Overlap and speci city of sulcal morphology related to mathematics and reading
Our third aim was to examine the speci city of the effect of the IPS sulcal pattern on numerical abilities as well as the speci city of the effect of the OTS sulcal pattern on reading. However, this study failed to nd a clear effect of the IPS sulcal pattern on arithmetic and symbolic number comparison abilities, nor did the study nd a clear effect of the OTS sulcal pattern on reading abilities. As such, it seemed illguided to study the speci city of both these effects (but see Supplementary Section 2 for the results of the analyses of Aim 3).

Discussion
The present study sought to investigate the impact of neuroanatomical constraints on key academic abilities, namely mathematical and reading ability. We examined a speci c neuroanatomical characteristic that is not affected by brain maturation and learning, sulcal patterns of the brain Mangin et al., 2010). Speci cally, we focused on the sulcal pattern of the IPS and the OTS as both regions have consistently been associated with mathematical processes and reading respectively (Dehaene & Cohen, 2011;Menon, 2014;. Through this approach we wished to gain some insight as to biological constraints that in uence the development of reading and mathematics. The rst aim focused on the relationship between the IPS sulcal pattern and mathematical ability. We hypothesized in accordance with Roell et al.'s (in prep) ndings, that IPS sulcal morphology would explain part of the the variability observed in symbolic number comparison and arithmetic tasks in typically developing children. In contrast to our expectations, no signi cant association between arithmetic ability and IPS sulcal morphology (Left and Right) were found. A signi cant association was found between the Right IPS sulcal morphology and symbolic number abilities. However, this association was the opposite to what we had hypothesized and what Roell et al. (in prep) found. We found that participants with a "sectioned" Right IPS had worse symbolic number abilities, here reaction time, than participants with a "not sectioned" Right IPS. Importantly, we were able to replicate the well-know association between symbolic number ability and arithmetic ability, hereby assuring the validity of both measures.
The second aim of this study centered on the relationship between OTS sulcal pattern and reading ability. We expected that in line with the ndings of Cachia et al. (2017) and Borst et al. (2016), participants with an interrupted Left posterior OTS, in particular in its posterior portion hosting the visual word form area (VWFA), will have better reading performance than participants who have a continuous Left OTS. In contrast to our expectations, we did not nd such an effect.
Our third aim was to examine the speci city of the effect of the IPS sulcal pattern on numerical abilities as well as the speci city of the effect of the OTS sulcal pattern on reading. However, since we were unable to nd an effect of either the IPS sulcal pattern in numerical abilities nor of the OTS sulcal pattern on reading abilities, we did not pursue such aim.
The present study was unable to replicate a previously observed relationship between the IPS sulcal pattern and mathematical ability Roell et al., (in prep), and a previously observed association between the Left posterior OTS sulcal pattern and reading Cachia et al., 2017). It is unlikely that the lack of ndings is due to our methods. Indeed, we followed the protocol for labelling the IPS (Roell et al., The lack of ndings might be due to the fact that the sample in this study might have been too homogenous in terms of its academic performance. All participants came from the same grade and they were from fairly high socio-economic backgrounds. As such, it may be that the performance in the math and reading task may not have been varied enough. It may be that there lacked enough variability in the academic measures to be explained by the OTS and IPS sulcal measures. Past studies have selected speci c samples that were more varied in their performance. Cachia et al.'s (2017) sample consisted of participants that learnt to read as children and participants that had learnt to read as adults, thereby assuring a great variability in reading ability. In addition, the participants' background was extremely diverse with participants from both low and high socio-economical backgrounds. In Roell et al.'s (in prep) study, variability in mathematical ability was assured through a sample age range, as participants in the children group range from Grade 1 to Grade 4. On the other hand, although by selecting heterogeneous samples the previous studies have been able to measure variability in the academic skills, the ndings might have been confounded by age and SES differences in the sample rather than real differences in the association between academic skills and sulcal morphology. Future studies should examine speci cally the possible effect of age and SES differences on the relationship between sulcal morphology and academic abilities.
It may also be that there was an effect of sulcal morphology, but it was too subtle for us to pick up.
Indeed, the Bayesian effects observed were all predominantly small thus pointing towards anecdotal or weak evidence. Which would mean that either the effects of sulcal morphology on academic achievements are not there or are too small and a much larger samples are needed to pick them up.
Currently the data presented here cannot unravel this point, a study with a larger sample would be needed. Note that our sample was su ciently powered to detect a medium effect size (d = .30, power = .86), it was not for detecting small effects (d = .10, power = .17).
Although we followed extremely closely the protocols elaborated by Borst et al. (2016), Cachia et al. (2017) and Roell et al. (in prep), we were not able to replicate their results. Another possible explanation for the lack replication is the country-based and language-based educational differences. As mentioned above, children in Flemish school have notably high math uency whereas children from Roell et al.'s (in prep) study came from Ontario (Canada). Importantly, children from Ontario (Canada) have signi cantly lower than average math uency levels (Archibald et al., 2013). Future studies should examine the potential effect of language and educational differences on the relationship between sulcal morphology and academic abilities.
In conclusion, our study was unable to nd a relationship between the IPS sulcal pattern and mathematical ability, nor did we observe an effect of the Left posterior OTS sulcal pattern on reading. It might be that such effects are only observable in heterogenous samples (as in previous work). On the other hand, it might be explained by differences in background and the education of the sample as compared to previous work. Future studies might want to explore this effect further by conducting a study with samples from different countries with different educational levels.

Declarations
Funding Margot Roell and Elien Bellon are both supported by the Postdoctoral Mandate (PDM) under the Katholieke Universiteit Leuven program.

Con icts of interest
The authors declare that they have no con ict of interest.

Availability of data and materials
Not applicable   Example of different ACC sulcal patterns. The "single type", with only the cingulate sulcus (depicted in yellow) and the "double parallel type", with an additional PCS (depicted in blue).

Figure 4
Mediation model for the relationship between IPS sulcal pattern and arithmetic ability as mediated by symbolic number ability.

Figure 5
Page 27/28 Effect of the Left and Right IPS pattern on arithmetic ability.

Figure 6
Effect of the Left and Right IPS pattern on symbolic number reaction time (in ms).