## Abstract

Although male brains have consistently reported to be 8–10% larger than female brains, it remains not well understood whether there are differences between sexes (average or variance) in developmental trajectories. Furthermore, if sex differences in average brain growth or variance are observed, it is unknown whether these sex differences have behavioral relevance. The present longitudinal study aimed to unravel sex effects in cortical brain structure, development, and variance, in relation to the development of educationally relevant cognitive domains and executive functions (EFs). This was assessed with three experimental tasks including working memory, reading comprehension, and fluency. In addition, real-life aspects of EF were assessed with self- and parent-reported Behavior Rating Inventory of Executive Function scores. The full data set included 271 participants (54% female) aged between 8 and 29 years of which three waves were collected at 2-year intervals, resulting in 680 T1-weighted MRI scans and behavioral measures. Analyses of average trajectories confirmed general age-related patterns of brain development but did not support the hypothesis of sex differences in brain development trajectories, except for left banks STS where boys had a steeper decline in surface area than girls. Also, our brain age prediction model (including 270 brain measures) did not indicate delayed maturation in boys compared with girls. Interestingly, support was found for greater variance in male brains than female brains in both structure and development, consistent with prior cross-sectional studies. Behaviorally, boys performed on average better on a working memory task with a spatial aspect and girls performed better on a reading comprehension task, but there was no relation between brain development and cognitive performance, neither for average brain measures, brain age, or variance measures. Taken together, we confirmed the hypothesis of greater males within-group variance in brain structures compared with females, but these were not related to EF. The sex differences observed in EF were not related to brain development, possibly suggesting that these are related to experiences and strategies rather than biological development.

## INTRODUCTION

Many prior studies have reported mean sex differences in brain structure, but the directionality and size of regional effects have been inconsistent (Ruigrok et al., 2014). An initial and well-cited neurodevelopmental study suggested that there are developmental differences in brain structure development between the sexes showing delayed brain development in boys relative to girls (Lenroot et al., 2007), but this effect has not been consistently replicated (Wierenga, Langen, Oranje, & Durston, 2014; Aubert-Broche et al., 2013; Tamnes et al., 2013). Recently, it was demonstrated that inconsistencies between prior studies are possibly related to the way studies have accounted for global brain volume and other scanning parameters (Mills & Tamnes, 2014). Importantly, our work and that of others suggest differences in brain structure between males and females at the variance rather than mean group level: Males show greater variance in brain structure compared with females (Ritchie et al., 2018; Wierenga et al., 2017). This would potentially bias average group-level models.

Moreover, the relation between brain structure development and cognitive development remains poorly understood. If sex differences in brain structure emerge during development, an important question concerns whether individual differences in brain volume are related to cognitive outcomes (Foulkes & Blakemore, 2018). This is especially important in the context of emerging educational implications of differences in brain development, where results may be too quickly translated to the classroom, which may result in neuromyths and unbiased conclusions (Howard-Jones, 2014). The goal of this study was therefore to examine in a three-wave accelerated longitudinal brain imaging study, spanning ages 8–29 years, whether sex differences in brain development were observed in average and variance measures and whether potential differential developmental trajectories are correlated with individual differences in cognitive performance.

An important educational skill concerns our ability to control our thoughts and actions to obtain a future goal, also referred to as executive function (EF; Diamond, 2013). EF is an umbrella term for a variety of subdomains, including working memory, inhibition, cognitive flexibility, and error monitoring (Diamond, 2000), which each showed to have different developmental trajectories. For example, attentional control emerges in infancy showing relative stability in early adolescence, whereas working memory showed protracted development till early adulthood (Huizinga, Dolan, & van der Molen, 2006). Even though marginal sex differences have been identified on specific EF tasks, these findings have not been consistently replicated (Hyde, 2016; Miller & Halpern, 2014). EF domains in which girls, on average, have been reported to outperform boys include verbal fluency, information processing, and spatial organization (Anderson, 2002; Anderson, Anderson, Northam, Jacobs, & Catroppa, 2001; Levin et al., 1991). In contrast, boys, on average, showed better performance than girls on a spatial working memory task (Krikorian & Bartok, 1998).

These different domains of EF are thought to be related to separate but overlapping brain circuitries in the pFC (Crone & Steinbeis, 2017). Moreover, the relative protracted development of pFC has been associated with the development of EF (Bunge & Zelazo, 2006). However, it is currently not known whether and how individual differences in EF relate to the development of the brain. It also remains unclear whether sex differences in EF emerge (Matthews, Ponitz, & Morrison, 2009; Else-Quest, Hyde, Goldsmith, & Van Hulle, 2006) or decrease (Gunzenhauser & von Suchodoletz, 2015) over the course of development and whether this is accounted for by developmental differences in brain development.

• •

The goal of this study was to examine the relation between sex effects in structural brain development and cognitive (EF) development and unravel the ongoing debate about the possible differences between boys and girls in brain development and associated performance. Advances in supervised learning models allow us to model the brain as dynamic, multimodal, circuit-based system, rather than snapshots of individual brain regions in isolation. More specifically, these models are able to accurately predict an individual's developmental stage (e.g., “brain age”), which allows us to test developmental trajectories per individual in more detail, as has been done for functional imaging data (Dosenbach et al., 2010) as well as structural imaging data (Ball, Adamson, Beare, & Seal, 2017; Brown et al., 2012; Khundrakpam, Tohka, Evans, & Brain Development Cooperative Group, 2015). In addition to studying average differences and variance differences, we will also examine individual development relative to the reference group (e.g., males or females). It was previously demonstrated that deviations between predicted “brain age” and chronological age were indicative of cognitive performance in elderly individuals (Erus et al., 2015). As such, these models may help us to better understand whether sex differences in brain development relate to sex differences in cognition.

In this three-wave longitudinal cohort of 299 typically developing children, adolescents, and young adults between ages 8 and 29 years (680 assessments), participants performed a battery of cognitive tasks that was designed for their relation with educational outcomes: working memory, reading comprehension, and fluency (Krom, Jongen, Verhelst, Kamphuis, & Kleintjes, 2010; Huizinga et al., 2006). In addition to these laboratory task-based assessments of cognition, we also include self- and parent-reported “real-life” EF assessments, as these may provide more ecological valid measures of EF because they allow assessment of integrated, multidimensional, complex relativistic, priority-based decision-making that is demanded in real-world situations (Goldberg & Podell, 2000; Burgess, 1997; Shallice & Burgess, 1991). The level of agreement between such questionnaires and well-established EF tasks is, at best, modest (Anderson, Anderson, Jacobs, Northam, & Mickiewicz, 2002), which suggests that each form of assessment provides unique information on EF functioning. Using this combined brain–behavior assessment, we sought to (i) examine whether boys and girls show mean and/or variance differences in developmental brain patterns across the cortical mantle and (ii) test sex effects on performance-based and “real-life” cognitive measures across development and examine their relation to brain development measures. In addition, we used “brain age” prediction models to assess the brain as a circuit-based system and test whether (iii) “brain age” predictions differed between the sexes and (iv) whether “brain age” is predictive of individual differences in cognition.

## METHODS

### Participants

The data in this study are part of a large accelerated longitudinal research project, BrainTime (e.g., Becht et al., 2018; Schreuders et al., 2018; Wierenga et al., 2018; Peters & Crone, 2017). At enrolment, 299 participants were included (51% females); data were collected at three time points with approximately 2-year intervals (see Table 1 for demographics). Based on self-report, neurological, endocrinological, mental health illnesses or use of psychotropic medication at Time Point 1 was excluded. Note that we did not exclude participants who showed these problems at follow-up time points, because from a population science perspective, it is important to include a representative sample from the community. Written informed consent was obtained from all participants at each time point. For participants younger than 18 years, additional consent from their parents was acquired. An independent clinical neuroradiologist evaluated all magnetic resonance imaging (MRI) scans. No gross abnormalities were reported for any of the participants. The study was approved by the institutional review board at Leiden University Medical Centre. A financial reimbursement was granted for participation in the study. IQ was estimated at the first two time points with two subtests (similarities and block design) of the Wechsler Intelligence Scale for Children-III (participants under 16 years) or Wechsler Adult Intelligence Scale-III (participants 16 years and older; Kort et al., 2005; Wechsler, 2000; Van Haasen et al., 1986; Stinissen, Willems, Coetsier, & Hulsman, 1970).

Table 1.
Demographics
TP1TP2TP3
Total n 299 299 280
Total % females 51 51 55
Age mean (SD14 (3.7) 16 (3.6) 18 (3.7)
IQ mean (SD109 (11) 108 (10.3)
Reading comprehension n 295 281 216
% Females 51 53 50
Mean (SD68 (24.2) 81 (21.2) 91 (18.2)
% Females   52 50
Mean (SD  97 (15.0) 103 (14.8)
Working memory n 288 279 213
% Females 50 52 50
Mean (SD) 0.18 (0.159) 0.86 (0.121) 0.88 (0.117)
BRIEF parent report n 236 201 108
% Females 52 53 52
BRIEF self-report n 23 62 99
% Females 61 53 51
T1 scan n 237 245 198
% Females 54 54 53
TP1TP2TP3
Total n 299 299 280
Total % females 51 51 55
Age mean (SD14 (3.7) 16 (3.6) 18 (3.7)
IQ mean (SD109 (11) 108 (10.3)
Reading comprehension n 295 281 216
% Females 51 53 50
Mean (SD68 (24.2) 81 (21.2) 91 (18.2)
% Females   52 50
Mean (SD  97 (15.0) 103 (14.8)
Working memory n 288 279 213
% Females 50 52 50
Mean (SD) 0.18 (0.159) 0.86 (0.121) 0.88 (0.117)
BRIEF parent report n 236 201 108
% Females 52 53 52
BRIEF self-report n 23 62 99
% Females 61 53 51
T1 scan n 237 245 198
% Females 54 54 53

n = number of individuals; IQ = intelligence quotient; SD = standard deviation; TP = time point; T1 scan = T1-weighted scan.

### Neuroimaging Measures

Good quality MRI scans were collected of 271 participants (53% females) aged between 8 and 26 years. Of these 271 participants, 237 were scanned on Time Point 1, 245 were scanned on Time Point 2, and 198 were scanned on Time Point 3 (see average number of scans per participant in Table 1). Cognitive assessment and MRI scans were acquired at the same day.

MRI scans were acquired on a single 3-T Philips Achieve whole-body scanner, using a six-element SENSE receiver head coil (Philips, Best, The Netherlands) at Leiden University Medical Centre. For definition of all brain measures, a whole-brain T1-weighted anatomical scan was acquired (repetition time = 9.8 msec, echo time = 4.6 msec, flip angle = 8°, 140 slices, 0.875 mm × 0.875 mm × 1.2 mm, and field of view = 224 × 177 × 168 mm). Scan time for this sequence was 4 min 56 sec.

MRI scans were analyzed on the local computer network at the Leiden University Medical Centre. T1 scans were processed using FreeSurfer 5.3, through which volumetric segmentations were estimated. This software suite is well validated and widely used; it is documented and freely available online (surfer.nmr.mgh.harvard.edu/). The technical details of the automated reconstruction scheme are described in detail elsewhere (Fischl et al., 2002; Dale, Fischl, & Sereno, 1999; Fischl, Sereno, & Dale, 1999; Fischl, Sereno, Tootell, & Dale, 1999).

To reduce within-subject scan session variability, a longitudinal stream was developed for FreeSurfer (Reuter, Schmansky, Rosas, & Fischl, 2012; Reuter & Fischl, 2011). This method increases repeatability and statistical power (Reuter, Rosas, & Fischl, 2010). All scans were processed using this procedure. This process includes the creation of an unbiased within-subject template space and image (“base”) using robust, inverse consistent registration (Reuter et al., 2010). The automated processing steps, including skull stripping, atlas registration, and parcellations are next initialized using the common information from the within-subject template. Thickness and surface area measures of the Desikan–Killiany atlas (DK atlas) were included (34 cortical regions per hemisphere). Before quantitative analyses could be performed, output requires qualitative inspection (Dewey et al., 2010). Postprocessing quality control was performed using an in-house developed semiautomatic quality assessment tool (Klapwijk, van de Kamp, van der Meulen, Peters & Wierenga 2019). This resulted in the exclusion of 113 scans from 76 participants, resulting in a final data set of 680 scans from 271 participants (see Table 1).

### Cognitive Measures

Reading fluency was assessed using a subtest of the Dutch “Three-Minute-Test” (Krom et al., 2010). This task aims to asses technical reading skills and was administered at Time Point 2 (n = 281) and Time Point 3 (n = 216). Participants received a list of words and were instructed to read aloud as many words as possible in 1 min. The total score is defined as the number of correct words read minus the number of incorrect words. This test showed high internal consistency (Cronbach's alpha, dependent on age group >.91; Krom et al., 2010).

#### Mental Counters Working Memory

Working memory capacity was measured with the “mental counters” task (Huizinga et al., 2006); this task includes a spatial aspect as the stimuli are presented at different locations (see an example of the task sequence in Peters, van Duijvenvoorde, Koolschijn, & Crone, 2016). This task was assessed at all three time points. The task was completed by 288 participants at Time Point 1, 279 participants at Time Point 2, and 213 participants at Time Point 3.

In this task participants are instructed to keep numerical information online. A computer screen showed two independent “counters,” which were represented by two horizontal bars on the left and right of the screen. The value of each counter was updated if a square appeared above (+1) or below (−1) the bar. The square appeared rapidly and in random order above or below one of the counters. The participants were explicitly instructed to use a verbal counting strategy, updating the values of both counters (e.g., 0–1, 1–1, 1–2, etc.). As soon as one of the counters reached a criterion value (3 or 5), the participants could indicate this with a left or right button press. There were two blocks consisting of 15 series each. Within each series, five or seven stimuli were presented (blocks that appeared randomly and equiprobably above one of the counters). The interval between the squares varied from 1000 to 1300 msec (drawn from a uniform distribution). Participants had 3500 msec to respond when the criterion was reached. The main dependent variable was the proportion of correct trials.

#### Behavior Rating Inventory of EF

Two versions of the Behavior Rating Inventory of Executive Function (BRIEF) were assessed: In participants younger than 18 years, a parent assessment was completed in 62% of the time points; in participants older than 18 years, a self-report questionnaire was assessed. This self-report questionnaire was completed in 60% of the visits where participants were 18 years or older. The BRIEF questionnaire is developed to assess everyday manifestations of executive control functions (Gioia, Isquith, & Guy, 2001; Gioia, Isquith, Guy, & Kenworthy, 2000a). It includes eight subscales: Inhibit (inhibiting distractions and interference); Emotional Control (emotional regulation); Shift (flexibly shifting to new actions); Working Memory (STM); Initiate (initiating action at an appropriate time/context); Plan/Organization (anticipating, planning); Organization of Materials (getting the materials necessary for the planned actions); and Monitor (monitoring the action process through internal and external feedback). These EFs refer to a collection of abilities that direct and control goal-oriented cognitive, behavioral, and emotional function. It is thought to be of high ecologically validity that allows for a “real-world” snapshot of EF that includes aspects of complex, everyday problem-solving demands. A higher score on these subscales indicates more difficulties/problems. The BRIEF has demonstrated good reliability, with high test–retest reliability (.82 for parent report), high internal consistency (Cronbach's alpha .80–.98; Gioia, Isquith, Guy, & Kenworthy, 2000b).

### Analysis

#### Intraclass Correlations

To test the intraindividual variation for each behavioral measure, we tested for homogeneity of the data in this longitudinal sample using intraclass correlations (ICCs) after controlling for age using generalized additive mixed modeling (described in the next section). Residual values were used to compute ICC values by estimating a null model, including a random intercept for each participant. The variance of the intercept is divided by the sum of the variance in intercept and residual variance. The interpretation of high values was ICC > .75, that of moderate values was .50–.75, and that of small values was ICC < .50 (Koo & Li, 2016). Task-based reading measures showed moderate variation, where mental counters working memory showed small ICC (see Table 2A). All parent report real-life EF assessments had moderate ICC values. Self-report real-life EF assessment had small (shifting and emotional control) to moderate ICC values (see Table 2B).

Table 2.
Intraclass Correlation of Cognitive Measures
MeasureICC
Working memory .438

B. ICC BRIEF Scores
Parent Report
Inhibition .535
Shifting .536
Emotional control .572
Initiate .655
Working memory .609
Planning and organization .586
Organization of materials .676
Index behavioral regulation .573
Index metacognition .671
Self-Report
Inhibition .683
Shifting .452
Emotional control .492
Initiate .6
Working memory .539
Planning and organization .544
Organization of materials .747
Index behavioral regulation .587
Index metacognition .704
MeasureICC
Working memory .438

B. ICC BRIEF Scores
Parent Report
Inhibition .535
Shifting .536
Emotional control .572
Initiate .655
Working memory .609
Planning and organization .586
Organization of materials .676
Index behavioral regulation .573
Index metacognition .671
Self-Report
Inhibition .683
Shifting .452
Emotional control .492
Initiate .6
Working memory .539
Planning and organization .544
Organization of materials .747
Index behavioral regulation .587
Index metacognition .704

ICC = intraclass correlation.

In addition, a correlation analysis between different sets of variables was performed. This allowed us to investigate how the task-based measures relate to real-life assessments of EF using questionnaire data.

To assess age and sex effects on brain and EF measures, generalized additive mixed (gam) modeling was used using the mgcv R package (Wood, 2004, 2017; see also (Wierenga et al., 2018). In short, three models were compared: (1) a model including age as a smooth function (Model 1), (2) a model including a main effect of both age and sex (Model 2), and (3) a model including an age by sex interaction effect (Model 3). More formally, let denote Age of the individual i at time point j. Each cognitive measure is modeled as a smooth function of Age plus a random person effect ui plus errorij:
$yij=β0+s1Ageij+ui+errorij$
(Model 1)
$yij=β0+β1Sexi+s1Ageij+ui+errorij$
(Model 2)
$yij=β0+β1Sexi+s1Ageij+s2AgeijSex+ui+errorij$
(Model 3)
Here, s1 is the essential arbitrary smooth functions, where the linear combination of piecewise cubic B-spline functions k is set to 4. In addition, β0 denotes the random intercepts and β1 denotes the parameter estimate of sex. In Model 3, we tested whether there was an effect of sex by age, where s2 allows to test whether the smooth functions for males and females differ. These three models were compared using the Bayesian information criterion; the model with the smallest Bayesian information criterion value was selected as the best fit model.

#### Computation of Subject-based Cortical Maturation Index

For each participant who had data of three time points (n = 168) for each ROI (max l = 68), we defined the maturational index (MIl) as the average slope values for that ROIl between time points t1 and t2 and between time points t2 and t3 (see details in Khundrakpam et al., 2017). In brief, this holds the following steps:

Let us consider cortical thickness values between time points t1 and t2 for ROIl. The slope for the straight line joining cortical thickness values for ROIl between time points t1 and t2 is computed as
$slope12l=Thick2l−Thick1lt2−t1$
where Thick1l and Thick2l correspond to the average cortical thickness for ROIl for time points t1 and t2, respectively.
We repeat the above procedure for time points t2 and t3 to obtain slope23l. And next compute MIl of ROIl as the average of the two slopes,
$MIi=slope12l+slope23l2$

#### Variance Ratio

To test for sex differences in variance ratio, behavioral measures were averaged across all time points. Also, mean brain measures (cortical thickness and surface area) were averaged across three time points. Next, measures were age-adjusted for mean age, using random forest regression modeling (see Wierenga et al., 2017; Breiman, 2001). Note that maturation index (MI) measures were not adjusted for age.

The differences in variance between males and females were examined where letting yi denote the observed outcome observation number i and its predicted outcome, the residuals were then formed:
$ri=yi−yˆi$
The standard deviations and SDmales and SDfemales were computed separately for males and females and used to form the test statistic
$T=SDmales/SDfemales$
For each outcome, a permutation test of the hypothesis that the sex-specific standard deviations were equal was performed. This was done by random permutation of the sex variable among the residuals. Using B permutations, the p value for the kth outcome was computed as
$pk=∑b=1BITb≥T/B$
where I(TbT) is an indicator function that is 1 when TbT and 0 otherwise. Thus, the p value is the proportion of permuted test statistics (Tb) that were greater than the observed value T of the test statistic above. Here, B was set to 10,000.
The number of comparisons was taken into account by an additional combined test across all outcomes. This was performed for cortical mean surface area and thickness measures and MI measures, using the test statistic
$T=−∑klogpk$
with the permutation distribution of T constructed as described in Pesarin and Salmaso (2010).

#### Effect Size and Bayes Factor

The effect size of sex differences in behavioral measures was assessed by including age corrected values (random forest regression modeling) averaged across all time points. Cohen's d was used to assess the size of the sex difference in EF. Small effect sizes were in the range of .11–.35, moderate effect sizes are between .36 and .65, and large effect sizes are within the .66–1.00 range.

In addition, we performed Bayesian analysis of the mean difference. To do so, we used the BayesFactor package for R (Morey, Rouder, & Jamil, 2015). This package computes BF10 values from a Bayesian t test, where values >1 may be interpreted as stronger support for the alternative than null hypothesis.

#### Mediation Analysis

To test whether sex differences in brain development mediate sex differences in EF, a bootstrapped multiple mediation analysis was performed in R using the lavaan package (Rosseel, 2012; Preacher & Hayes, 2004, 2008). The data are recurrently sampled to estimate indirect effect in each resampled data set (B = 1000). Cortical brain estimates (surface area and thickness measures) that showed sex differences in developmental trajectories were included as potential mediators of the effects between sex and cognition. For these brain estimates, we used MI in as a potential mediator. Cognitive measures that showed significant sex effects were included in the model and were averaged across all time points and age-adjusted using random forest regression modeling.

#### Brain Age Prediction Modeling

Brain age predictions are estimated using random forest modeling; this machine learning algorithm is based on model aggregation introduced by Breiman (2001). The principle of random forests is to combine many binary decision trees using several bootstrap samples coming from a learning sample L and choosing randomly at each node a subset of explanatory variables. At each node, a given number (denoted by mtry) of input variables are randomly chosen, and the best split is calculated only within this subset. Model fits were estimated using five repeats of twofold cross-validation was used.

In this model, we aim to predict age at Time Point 3 (follow-up); this allowed us to compare models including static brain measures in addition to measures of development. As such, input variables included cortical surface area and cortical thickness measures at Time Point 3 for both lobes and all 68 regions of the DK atlas (Klein & Tourville, 2012; Desikan et al., 2006). In addition, developmental trajectories (assessed by MI as described above) of each of the ROIs were included. We first explored whether an increased resolution improved model fit by comparing the four lobe divisions to the DK atlas. We next studied whether cortical thickness, cortical surface area, or a combined model would better predict age. Next, we investigated whether adding information on developmental trajectories (MI) would improve model fit by comparing mean absolute error (MAE) estimates, averaged over the twofolds.

Sex differences in brain age error were assessed using variance ratio, effect sizes, and Bayes factor, as described above. Furthermore, we tested whether brain age predictions explain individual variation in cognitive measures; to do so, we used gam modeling to relate age-corrected average cognition scores to brain age error (predicted brain age minus chronological age).

## RESULTS

### Sex Effects on Cortical Brain Development

#### Developmental and Sex Effects

As expected, almost all age effects were significant with exception of the rostral anterior cingulate surface area and thickness of the pericalcarine region (see Table 3A and B). Both thickness and surface area measures showed curvilinear age-related declines. Main effects of sex on surface area were observed in all cortical regions, where males showed larger surface area. For most regions, there was no main effect of sex on thickness values, with exception of the left pars triangularis, bilateral rostral middle frontal region, right inferior and superior parietal regions, with greater male than female thickness.

Table 3.
MeasureModelSexAge SplineAge × Sex SplineT
EstimatepEDFFpEDFFp
A. Generalized additive mixed-effects models examining sex and age effects on cortical surface area measures
lh bankssts area Model 3 48.762 .002 2.896 125.388 ** 18.197 **
lh caudalanteriorcingulate area Model 2 32.653 .007 23.573 **
lh caudalmiddlefrontal area Model 2 144.529 ** 2.921 254.657 **       .01
lh cuneus area Model 2 110.283 ** 2.816 31.886 **
lh entorhil area Model 2 33.977 ** 10.853 .001
lh fusiform area Model 2 255.145 ** 2.732 81.198 **
lh inferiorparietal area Model 2 264.974 ** 2.945 433.798 **
lh inferiortemporal area Model 2 243.868 ** 2.398 94.807 **
lh isthmuscingulate area Model 2 93.256 ** 2.371 47.271 **
lh lateraloccipital area Model 2 391.944 ** 2.893 216.09 **
lh lateralorbitofrontal area Model 2 167.541 ** 2.852 39.551 **
lh lingual area Model 2 218.821 ** 2.788 24.88 **
lh medialorbitofrontal area Model 2 155.397 ** 51.198 **
lh middletemporal area Model 2 197.709 ** 2.934 73.8 **
lh parahippocampal area Model 2 42.364 ** 18.145 **
lh paracentral area Model 2 104.467 ** 2.631 132.6 **
lh parsopercularis area Model 2 66.057 .004 2.889 135.92 **
lh parsorbitalis area Model 2 48.868 ** 2.886 33.516 **
lh parstriangularis area Model 2 75.639 ** 2.962 97.291 **
lh pericalcarine area Model 2 95.327 ** 1.725 16.942 **       .019
lh postcentral area Model 2 324.753 ** 2.675 212.973 **
lh posteriorcingulate area Model 2 103.478 ** 2.641 114.553 **
lh precentral area Model 2 360.514 ** 2.867 102.433 **
lh precuneus area Model 2 281.704 ** 2.912 417.952 **       .007
lh rostralanteriorcingulate area Model 2 69.993 ** 6.693 .01
lh rostralmiddlefrontal area Model 2 469.352 ** 2.912 175.898 **
lh superiorfrontal area Model 2 543.608 ** 2.969 161.159 **
lh superiorparietal area Model 2 359.413 ** 2.887 330.065 **
lh superiortemporal area Model 2 305.467 ** 2.418 134.225 **
lh supramargil area Model 2 329.964 ** 2.846 252.089 **
lh frontalpole area Model 2 19.971 ** 18.847 **
lh temporalpole area Model 2 25.24 ** 2.554 .11
lh transversetemporal area Model 2 29.545 ** 1.897 69.068 **
lh insula area Model 2 114.433 ** 2.591 65.67 **
rh bankssts area Model 2 65.058 ** 2.901 357.427 **       .027
rh caudalanteriorcingulate area Model 2 56.935 ** 49.041 **
rh caudalmiddlefrontal area Model 2 102.54 .003 2.94 347.834 **       .05
rh cuneus area Model 2 120.958 ** 2.893 36.181 **
rh entorhil area Model 2 28.948 ** 82.244 **
rh fusiform area Model 2 283.477 ** 2.894 58.344 **
rh inferiorparietal area Model 2 467.265 ** 2.948 405.666 **
rh inferiortemporal area Model 2 261.663 ** 2.873 107.149 **
rh isthmuscingulate area Model 2 73.996 ** 2.605 52.538 **       .049
rh lateraloccipital area Model 2 419.139 ** 2.859 132.829 **       .004
rh lateralorbitofrontal area Model 2 164.056 ** 2.771 26.356 **
rh lingual area Model 2 161.369 ** 2.805 24.657 **
rh medialorbitofrontal area Model 2 110.355 ** 21.623 **
rh middletemporal area Model 2 256.437 ** 2.946 145.792 **
rh parahippocampal area Model 2 52.405 ** 2.616 35.059 **
rh paracentral area Model 2 100.763 ** 2.668 151.735 **
rh parsopercularis area Model 2 75.848 ** 2.857 130.115 **       .042
rh parsorbitalis area Model 2 71.81 ** 2.839 91.071 **
rh parstriangularis area Model 2 100.134 ** 2.969 143.5 **
rh pericalcarine area Model 2 94.56 ** 2.627 15.784 **       .004
rh postcentral area Model 2 287.333 ** 2.91 227.179 **
rh posteriorcingulate area Model 2 112.648 ** 2.728 170.929 **
rh precentral area Model 2 335.74 ** 2.953 94.888 **
rh precuneus area Model 2 366.865 ** 2.897 423.499 **
rh rostralanteriorcingulate area Model 2 61.763 ** 3.034 .082
rh rostralmiddlefrontal area Model 2 523.143 ** 2.921 233.189 **
rh superiorfrontal area Model 2 515.74 ** 2.976 168.601 **
rh superiorparietal area Model 2 314.09 ** 2.833 266.775 **
rh superiortemporal area Model 2 188.724 ** 2.908 143.483 **
rh supramargil area Model 2 269.224 ** 2.798 211.356 **
rh frontalpole area Model 2 19.001 ** 20.865 **
rh temporalpole area Model 1     3.167 .076
rh transversetemporal area Model 2 26.398 ** 2.083 17.172 **
rh insula area Model 2 157.125 ** 2.428 22.568 **

B. Generalized additive mixed-effects models examining sex and age effects on cortical thickness measures
lh bankssts thickness Model 1     2.894 231.603 **
lh caudalanteriorcingulate thickness Model 1     2.896 166.215 **
lh caudalmiddlefrontal thickness Model 1     2.868 171.62 **
lh cuneus thickness Model 1     2.786 126.385 **
lh entorhil thickness Model 1     2.704 12.968 **
lh fusiform thickness Model 1     2.9 196.137 **
lh inferiorparietal thickness Model 1     2.912 278.985 **
lh inferiortemporal thickness Model 1     2.885 200.46 **
lh isthmuscingulate thickness Model 1     2.944 368.93 **
lh lateraloccipital thickness Model 1     2.66 60.843 **
lh lateralorbitofrontal thickness Model 1     2.84 149.369 **
lh lingual thickness Model 1     2.581 134.348 **
lh medialorbitofrontal thickness Model 1     2.841 86.943 **       .03
lh middletemporal thickness Model 1     2.888 250.654 **
lh parahippocampal thickness Model 1     2.758 99.534 **
lh paracentral thickness Model 1     2.859 163.983 **
lh parsopercularis thickness Model 1     2.871 223.885 **
lh parsorbitalis thickness Model 1     2.795 113.388 **
lh parstriangularis thickness Model 2 0.035 .006 2.846 201.505 **
lh pericalcarine thickness Model 1     34.902 **
lh postcentral thickness Model 1     2.759 95.507 **
lh posteriorcingulate thickness Model 1     2.935 535.136 **       .019
lh precentral thickness Model 1     2.561 75.057 **
lh precuneus thickness Model 1     2.916 356.938 **
lh rostralanteriorcingulate thickness Model 1     2.741 83.122 **       .026
lh rostralmiddlefrontal thickness Model 2 0.03 .006 2.869 214.595 **
lh superiorfrontal thickness Model 1     2.93 251.282 **
lh superiorparietal thickness Model 1     2.873 190.654 **
lh superiortemporal thickness Model 1     2.86 147.559 **
lh supramargil thickness Model 1     2.869 193.908 **
lh frontalpole thickness Model 1     2.648 36.675 **
lh temporalpole thickness Model 1     2.193 6.638 .002
lh transversetemporal thickness Model 1     2.491 38.748 **
lh insula thickness Model 1     2.876 205.232 **
rh bankssts thickness Model 1     2.898 292.973 **
rh caudalanteriorcingulate thickness Model 1     2.797 179.966 **
rh caudalmiddlefrontal thickness Model 1     2.901 160.611 **
rh cuneus thickness Model 1     2.565 104.516 **
rh entorhil thickness Model 1     2.581 7.3 **
rh fusiform thickness Model 1     2.849 173.197 **
rh inferiorparietal thickness Model 2 0.029 .005 2.92 272.51 **       .032
rh inferiortemporal thickness Model 1     2.897 197.834 **
rh isthmuscingulate thickness Model 1     2.943 423.175 **
rh lateraloccipital thickness Model 1     2.722 82.243 **
rh lateralorbitofrontal thickness Model 1     2.817 132.553 **
rh lingual thickness Model 1     2.542 84.812 **
rh medialorbitofrontal thickness Model 1     2.654 111.585 **
rh middletemporal thickness Model 1     2.903 290.44 **       .01
rh parahippocampal thickness Model 1     2.623 100.726 **
rh paracentral thickness Model 1     2.856 164.435 **
rh parsopercularis thickness Model 1     2.86 188.867 **
rh parsorbitalis thickness Model 1     2.721 85.488 **
rh parstriangularis thickness Model 1     2.828 173.939 **
rh pericalcarine thickness Model 1     2.034 .154
rh postcentral thickness Model 1     2.771 126.437 **
rh posteriorcingulate thickness Model 1     2.951 520.943 **       **
rh precentral thickness Model 1     2.752 92.157 **
rh precuneus thickness Model 1     2.929 337.152 **
rh rostralanteriorcingulate thickness Model 1     2.776 54.988 **       .007
rh rostralmiddlefrontal thickness Model 2 0.035 .003 2.873 190.944 **
rh superiorfrontal thickness Model 1     2.904 269.812 **
rh superiorparietal thickness Model 2 0.028 .004 2.857 181.314 **
rh superiortemporal thickness Model 1     2.853 200.965 **
rh supramargil thickness Model 1     2.878 174.392 **
rh frontalpole thickness Model 1     1.742 43.237 **       .018
rh temporalpole thickness Model 1     2.644 6.889 .005
rh transversetemporal thickness Model 1     1.416 48.266 **
rh insula thickness Model 1     2.818 105.785 **
MeasureModelSexAge SplineAge × Sex SplineT
EstimatepEDFFpEDFFp
A. Generalized additive mixed-effects models examining sex and age effects on cortical surface area measures
lh bankssts area Model 3 48.762 .002 2.896 125.388 ** 18.197 **
lh caudalanteriorcingulate area Model 2 32.653 .007 23.573 **
lh caudalmiddlefrontal area Model 2 144.529 ** 2.921 254.657 **       .01
lh cuneus area Model 2 110.283 ** 2.816 31.886 **
lh entorhil area Model 2 33.977 ** 10.853 .001
lh fusiform area Model 2 255.145 ** 2.732 81.198 **
lh inferiorparietal area Model 2 264.974 ** 2.945 433.798 **
lh inferiortemporal area Model 2 243.868 ** 2.398 94.807 **
lh isthmuscingulate area Model 2 93.256 ** 2.371 47.271 **
lh lateraloccipital area Model 2 391.944 ** 2.893 216.09 **
lh lateralorbitofrontal area Model 2 167.541 ** 2.852 39.551 **
lh lingual area Model 2 218.821 ** 2.788 24.88 **
lh medialorbitofrontal area Model 2 155.397 ** 51.198 **
lh middletemporal area Model 2 197.709 ** 2.934 73.8 **
lh parahippocampal area Model 2 42.364 ** 18.145 **
lh paracentral area Model 2 104.467 ** 2.631 132.6 **
lh parsopercularis area Model 2 66.057 .004 2.889 135.92 **
lh parsorbitalis area Model 2 48.868 ** 2.886 33.516 **
lh parstriangularis area Model 2 75.639 ** 2.962 97.291 **
lh pericalcarine area Model 2 95.327 ** 1.725 16.942 **       .019
lh postcentral area Model 2 324.753 ** 2.675 212.973 **
lh posteriorcingulate area Model 2 103.478 ** 2.641 114.553 **
lh precentral area Model 2 360.514 ** 2.867 102.433 **
lh precuneus area Model 2 281.704 ** 2.912 417.952 **       .007
lh rostralanteriorcingulate area Model 2 69.993 ** 6.693 .01
lh rostralmiddlefrontal area Model 2 469.352 ** 2.912 175.898 **
lh superiorfrontal area Model 2 543.608 ** 2.969 161.159 **
lh superiorparietal area Model 2 359.413 ** 2.887 330.065 **
lh superiortemporal area Model 2 305.467 ** 2.418 134.225 **
lh supramargil area Model 2 329.964 ** 2.846 252.089 **
lh frontalpole area Model 2 19.971 ** 18.847 **
lh temporalpole area Model 2 25.24 ** 2.554 .11
lh transversetemporal area Model 2 29.545 ** 1.897 69.068 **
lh insula area Model 2 114.433 ** 2.591 65.67 **
rh bankssts area Model 2 65.058 ** 2.901 357.427 **       .027
rh caudalanteriorcingulate area Model 2 56.935 ** 49.041 **
rh caudalmiddlefrontal area Model 2 102.54 .003 2.94 347.834 **       .05
rh cuneus area Model 2 120.958 ** 2.893 36.181 **
rh entorhil area Model 2 28.948 ** 82.244 **
rh fusiform area Model 2 283.477 ** 2.894 58.344 **
rh inferiorparietal area Model 2 467.265 ** 2.948 405.666 **
rh inferiortemporal area Model 2 261.663 ** 2.873 107.149 **
rh isthmuscingulate area Model 2 73.996 ** 2.605 52.538 **       .049
rh lateraloccipital area Model 2 419.139 ** 2.859 132.829 **       .004
rh lateralorbitofrontal area Model 2 164.056 ** 2.771 26.356 **
rh lingual area Model 2 161.369 ** 2.805 24.657 **
rh medialorbitofrontal area Model 2 110.355 ** 21.623 **
rh middletemporal area Model 2 256.437 ** 2.946 145.792 **
rh parahippocampal area Model 2 52.405 ** 2.616 35.059 **
rh paracentral area Model 2 100.763 ** 2.668 151.735 **
rh parsopercularis area Model 2 75.848 ** 2.857 130.115 **       .042
rh parsorbitalis area Model 2 71.81 ** 2.839 91.071 **
rh parstriangularis area Model 2 100.134 ** 2.969 143.5 **
rh pericalcarine area Model 2 94.56 ** 2.627 15.784 **       .004
rh postcentral area Model 2 287.333 ** 2.91 227.179 **
rh posteriorcingulate area Model 2 112.648 ** 2.728 170.929 **
rh precentral area Model 2 335.74 ** 2.953 94.888 **
rh precuneus area Model 2 366.865 ** 2.897 423.499 **
rh rostralanteriorcingulate area Model 2 61.763 ** 3.034 .082
rh rostralmiddlefrontal area Model 2 523.143 ** 2.921 233.189 **
rh superiorfrontal area Model 2 515.74 ** 2.976 168.601 **
rh superiorparietal area Model 2 314.09 ** 2.833 266.775 **
rh superiortemporal area Model 2 188.724 ** 2.908 143.483 **
rh supramargil area Model 2 269.224 ** 2.798 211.356 **
rh frontalpole area Model 2 19.001 ** 20.865 **
rh temporalpole area Model 1     3.167 .076
rh transversetemporal area Model 2 26.398 ** 2.083 17.172 **
rh insula area Model 2 157.125 ** 2.428 22.568 **

B. Generalized additive mixed-effects models examining sex and age effects on cortical thickness measures
lh bankssts thickness Model 1     2.894 231.603 **
lh caudalanteriorcingulate thickness Model 1     2.896 166.215 **
lh caudalmiddlefrontal thickness Model 1     2.868 171.62 **
lh cuneus thickness Model 1     2.786 126.385 **
lh entorhil thickness Model 1     2.704 12.968 **
lh fusiform thickness Model 1     2.9 196.137 **
lh inferiorparietal thickness Model 1     2.912 278.985 **
lh inferiortemporal thickness Model 1     2.885 200.46 **
lh isthmuscingulate thickness Model 1     2.944 368.93 **
lh lateraloccipital thickness Model 1     2.66 60.843 **
lh lateralorbitofrontal thickness Model 1     2.84 149.369 **
lh lingual thickness Model 1     2.581 134.348 **
lh medialorbitofrontal thickness Model 1     2.841 86.943 **       .03
lh middletemporal thickness Model 1     2.888 250.654 **
lh parahippocampal thickness Model 1     2.758 99.534 **
lh paracentral thickness Model 1     2.859 163.983 **
lh parsopercularis thickness Model 1     2.871 223.885 **
lh parsorbitalis thickness Model 1     2.795 113.388 **
lh parstriangularis thickness Model 2 0.035 .006 2.846 201.505 **
lh pericalcarine thickness Model 1     34.902 **
lh postcentral thickness Model 1     2.759 95.507 **
lh posteriorcingulate thickness Model 1     2.935 535.136 **       .019
lh precentral thickness Model 1     2.561 75.057 **
lh precuneus thickness Model 1     2.916 356.938 **
lh rostralanteriorcingulate thickness Model 1     2.741 83.122 **       .026
lh rostralmiddlefrontal thickness Model 2 0.03 .006 2.869 214.595 **
lh superiorfrontal thickness Model 1     2.93 251.282 **
lh superiorparietal thickness Model 1     2.873 190.654 **
lh superiortemporal thickness Model 1     2.86 147.559 **
lh supramargil thickness Model 1     2.869 193.908 **
lh frontalpole thickness Model 1     2.648 36.675 **
lh temporalpole thickness Model 1     2.193 6.638 .002
lh transversetemporal thickness Model 1     2.491 38.748 **
lh insula thickness Model 1     2.876 205.232 **
rh bankssts thickness Model 1     2.898 292.973 **
rh caudalanteriorcingulate thickness Model 1     2.797 179.966 **
rh caudalmiddlefrontal thickness Model 1     2.901 160.611 **
rh cuneus thickness Model 1     2.565 104.516 **
rh entorhil thickness Model 1     2.581 7.3 **
rh fusiform thickness Model 1     2.849 173.197 **
rh inferiorparietal thickness Model 2 0.029 .005 2.92 272.51 **       .032
rh inferiortemporal thickness Model 1     2.897 197.834 **
rh isthmuscingulate thickness Model 1     2.943 423.175 **
rh lateraloccipital thickness Model 1     2.722 82.243 **
rh lateralorbitofrontal thickness Model 1     2.817 132.553 **
rh lingual thickness Model 1     2.542 84.812 **
rh medialorbitofrontal thickness Model 1     2.654 111.585 **
rh middletemporal thickness Model 1     2.903 290.44 **       .01
rh parahippocampal thickness Model 1     2.623 100.726 **
rh paracentral thickness Model 1     2.856 164.435 **
rh parsopercularis thickness Model 1     2.86 188.867 **
rh parsorbitalis thickness Model 1     2.721 85.488 **
rh parstriangularis thickness Model 1     2.828 173.939 **
rh pericalcarine thickness Model 1     2.034 .154
rh postcentral thickness Model 1     2.771 126.437 **
rh posteriorcingulate thickness Model 1     2.951 520.943 **       **
rh precentral thickness Model 1     2.752 92.157 **
rh precuneus thickness Model 1     2.929 337.152 **
rh rostralanteriorcingulate thickness Model 1     2.776 54.988 **       .007
rh rostralmiddlefrontal thickness Model 2 0.035 .003 2.873 190.944 **
rh superiorfrontal thickness Model 1     2.904 269.812 **
rh superiorparietal thickness Model 2 0.028 .004 2.857 181.314 **
rh superiortemporal thickness Model 1     2.853 200.965 **
rh supramargil thickness Model 1     2.878 174.392 **
rh frontalpole thickness Model 1     1.742 43.237 **       .018
rh temporalpole thickness Model 1     2.644 6.889 .005
rh transversetemporal thickness Model 1     1.416 48.266 **
rh insula thickness Model 1     2.818 105.785 **

For the age spline and the age-by-group splines, the estimated degrees of freedom (EDF), F value, and p values are reported. T = p value significant of Age × Sex interaction effect, but Model 3 not best fitting model. lh = left hemisphere; rh = right hemisphere.

**

p < .001.

The next question we examined was whether boys and girls showed differences in developmental patterns across the cortical mantle. Model 3 (including the age by sex interaction effect) was never the best fitting model with the exception of one structure: the surface area of the left banks superior temporal gyrus. This region showed a steeper decline in boys than girls (see Figure 1 and Table 3A). For the following regions, we observed significant age by sex interaction effects showing steeper declines for boys than girls, but this was not the best fitting model: surface area of the bilateral caudal middle frontal gyrus, left pericalcarine gyrus, left precuneus, right banks superior temporal gyrus, right isthmus cingulate gyrus, right lateral occipital cortex, right pars opercularis, right pericalcarine region (see Table 3A). Thickness showed significant age by sex interaction effects (but not best model fits) for the bilateral posterior cingulate gyrus, bilateral rostral anterior cingulate gyrus, left medial orbitofrontal gyrus, right inferior parietal gyrus, right middle temporal gyrus, and right frontal pole (see Table 3B).

Figure 1.

Age by sex effects on the left banks superior temporal gyrus surface area estimated using gam modeling. Steeper declines in surface area were observed for boys than girls.

Figure 1.

Age by sex effects on the left banks superior temporal gyrus surface area estimated using gam modeling. Steeper declines in surface area were observed for boys than girls.

#### Sex Effects in Variance

Next, we assessed sex differences in variance for mean surface area and mean thickness (averaged across three time points). Mean surface area did not show significant sex differences in overall variance (p = .0617). However, regional effects showed that, for the following regions, there was significant greater male than female variance in “surface area”: right caudal anterior cingulate gyrus, left precentral region, left supra marginal region, right banks superior temporal gyrus, left middle temporal gyrus, and right inferior parietal gyrus (see Figure 2A). Cortical thickness did not show a significant difference in overall variance between boys and girls (p = .299). However, regional average thickness effects showed variance differences favoring males in the following regions: right temporal pole, left superior frontal gyrus, left insula, right isthmus cingulate gyrus, and left pars opercularis. In addition, there were regions that showed significant greater female than male variance in cortical thickness, including the right superior parietal gyrus, right middle temporal gyrus, left lateral occipital gyrus, and right rostral middle frontal gyrus (see Figure 2B).

Figure 2.

Variance ratio's favoring males (green) and females (yellow). (A) Mean surface area estimates of 68 cortical regions. (B) Mean thickness estimates of 68 cortical regions (DK atlas). *p < .05. **p < .01. *** p < .001.

Figure 2.

Variance ratio's favoring males (green) and females (yellow). (A) Mean surface area estimates of 68 cortical regions. (B) Mean thickness estimates of 68 cortical regions (DK atlas). *p < .05. **p < .01. *** p < .001.

As a next step, we compared variance of boys and girls for cortical brain development, using the MI. Separate analyses were performed for cortical surface area and thickness development. A combined p value did not show sex differences in overall variance of surface area MI (p = .073) or thickness MI (p = .126). However, regional variance effects again showed greater male than female variance in maturation in the “surface area” of the left insula, right posterior cingulate gyrus, and right precentral gyrus and “thickness” of the left medial orbitofrontal gyrus, right lateral occipital gyrus, right precentral gyrus, and right temporal pole. In addition, significant greater female than male variability was observed for the “surface area” of the rostral anterior cingulate gyrus and supra marginal gyrus and “thickness” of the right insula and posterior cingulate gyrus (see Figure 3A and B).

Figure 3.

Variance ratio's favoring males (green) and females (yellow). (A) MI estimates of surface area of 68 cortical regions. (B) MI estimates of mean thickness estimates of 68 cortical regions (DK atlas). *p < .05. **p < .01. ***p < .001.

Figure 3.

Variance ratio's favoring males (green) and females (yellow). (A) MI estimates of surface area of 68 cortical regions. (B) MI estimates of mean thickness estimates of 68 cortical regions (DK atlas). *p < .05. **p < .01. ***p < .001.

### Sex Effects on “Brain Age” Predictions

#### Model Selection

Results show that the DK atlas (d) yielded better age predictions than a parcellation based on the four lobes (a). This indicates that regional heterogeneity in cortical measures led to improved prediction performance (see Table 4). Cortical thickness (b) showed better performance than surface area (c), yet a combined model (d) had the best model fit (mean MAE = 2.422, SD MAE = 0.070). A model including information on developmental trajectories (MI) (e) showed even better model fit than models including brain measures at Time Point 3 only (follow-up; mean MAE = 2.015, SD MAE = 0.181). Nevertheless, a combined model (f) including both information on maturation (MI) and follow-up estimates showed the best performance (mean MAE = 1.976, SD MAE = 0.085). This indicates that MI holds additional information on developmental stage. As such, Model f was used for further analysis.

Table 4.
MAE Model Comparison
ModelsMean MAESD MAE
a. Lobes mean thickness and area 2.481 0.132
b. DK mean thickness 2.422 0.102
c. DK mean area 2.865 0.111
d. DK mean thickness and area 2.422 0.07
e. DK MI thickness and area 2.015 0.181
f. DK mean thickness, area and MI 1.976 0.085
ModelsMean MAESD MAE
a. Lobes mean thickness and area 2.481 0.132
b. DK mean thickness 2.422 0.102
c. DK mean area 2.865 0.111
d. DK mean thickness and area 2.422 0.07
e. DK MI thickness and area 2.015 0.181
f. DK mean thickness, area and MI 1.976 0.085

DK = Desikan-Killiany atlas.

#### Sex Effects

Model f included 270 brain estimates of mean cortical thickness and surface area in addition to MI of 68 cortical brain regions. This model accounted for almost 80% of the individual differences in brain structure and variability (Rho = .7964, adjusted R2 = .7952; see Figure 4). There was significant greater male variance in brain age error (p = .013). Note that this was significant in the absence of a mean sex difference in brain age error (p = .159).

Figure 4.

Anatomical prediction of age (predicted age) by chronological age for 168 individuals. The model to predict age includes estimates of 270 variables including cortical surface area and thickens mean estimates as well as MI. Colors correspond to males (green) and females (yellow). A linear model (solid line) between chronological age and predicted age is plotted.

Figure 4.

Anatomical prediction of age (predicted age) by chronological age for 168 individuals. The model to predict age includes estimates of 270 variables including cortical surface area and thickens mean estimates as well as MI. Colors correspond to males (green) and females (yellow). A linear model (solid line) between chronological age and predicted age is plotted.

### Sex Effects and Age Effects in EF

#### Developmental and Sex Effects

Mental counters working memory, reading comprehension, and reading fluency performance all showed significant increases with age (see Table 5A and Figure 5A). In addition, main effects of sex were observed (Model 2). Girls performed significantly better than boys on reading comprehension, and boys performed better than girls on the mental counters working memory task. Reading fluency showed no differences between boys and girls. There were no significant age by sex interaction effects.

Table 5.
MeasureModelSexAge SplineAge × Sex Spline
EstimatepEDFFpEDFFp
A. Generalized additive mixed-effects models examining sex and age effects on task-based cognitive measures
Reading comprehension Model 2 −7.032 ** 2.964 665.858 **
Reading fluency Model 1     2.703 32.535 **
Working memory Model 2 0.016 ** 2.381 35.864 **

B. Sex and age effects on parent report BRIEF data
Inhibition Model 1     16.011 **
Shifting Model 1     0.143 .706
Emotional control Model 1     16.367 **
Initiate Model 2 1.3 ** 1.865 1.729 .163
Working memory Model 2 0.986 ** 1.231 0.081 .769
Planning and organization Model 2 1.598 ** 1.512 .219
Organization of materials Model 1     5.714 .017
Index behavioral regulation Model 1     11.557 **
Index metacognition Model 2 4.959 ** 1.635 1.236 .362

C. Sex and age effects on self report BRIEF data
Inhibition Model 1 0.839 .014 1.81 .18
Shifting Model 1     0.308 .58
Emotional control Model 2 −1.175 .003 1.991 .16
Initiate Model 2 1.121 ** 1.026 .312
Working memory Model 1     2.407 .123
Planning and organization Model 2 1.146 .002 2.424 .121
Organization of materials Model 1     0.56 .455
Index behavioral regulation Model 1     0.082 .775
Index metacognition Model 2 4.102 .004 5.765 .017
MeasureModelSexAge SplineAge × Sex Spline
EstimatepEDFFpEDFFp
A. Generalized additive mixed-effects models examining sex and age effects on task-based cognitive measures
Reading comprehension Model 2 −7.032 ** 2.964 665.858 **
Reading fluency Model 1     2.703 32.535 **
Working memory Model 2 0.016 ** 2.381 35.864 **

B. Sex and age effects on parent report BRIEF data
Inhibition Model 1     16.011 **
Shifting Model 1     0.143 .706
Emotional control Model 1     16.367 **
Initiate Model 2 1.3 ** 1.865 1.729 .163
Working memory Model 2 0.986 ** 1.231 0.081 .769
Planning and organization Model 2 1.598 ** 1.512 .219
Organization of materials Model 1     5.714 .017
Index behavioral regulation Model 1     11.557 **
Index metacognition Model 2 4.959 ** 1.635 1.236 .362

C. Sex and age effects on self report BRIEF data
Inhibition Model 1 0.839 .014 1.81 .18
Shifting Model 1     0.308 .58
Emotional control Model 2 −1.175 .003 1.991 .16
Initiate Model 2 1.121 ** 1.026 .312
Working memory Model 1     2.407 .123
Planning and organization Model 2 1.146 .002 2.424 .121
Organization of materials Model 1     0.56 .455
Index behavioral regulation Model 1     0.082 .775
Index metacognition Model 2 4.102 .004 5.765 .017

For the age spline and the age-by-group splines, the estimated degrees of freedom (EDF), F value, and p values are reported.

**

p value < .001.

Figure 5.

Best gam model fits of age and sex for (A) task-based cognitive measures, (B) parent report EF assessment using BRIEF questionnaire, and (C) self-report EF assessment using BRIEF questionnaire. Best fit models are indicated where Model 1 is a model including age and Model 2 is a model including both age and sex effects.

Figure 5.

Best gam model fits of age and sex for (A) task-based cognitive measures, (B) parent report EF assessment using BRIEF questionnaire, and (C) self-report EF assessment using BRIEF questionnaire. Best fit models are indicated where Model 1 is a model including age and Model 2 is a model including both age and sex effects.

BRIEF parent report measures showed significant age-related improvement, indicated by a negative age-related change in inhibition, emotional control, and behavioral regulation (see Table 5B and Figure 5B). Stable sex effects (Model 2) were observed for initiative, working memory, planning and organization, and metacognition, where girls scored significantly lower than boys, indicating fewer problems in these domains. There was no significant interaction effect between age and sex.

BRIEF self-report measures showed no significant change with age, with the exception of metacognition, which showed an improvement with increasing age (see Table 5C and Figure 5C). In addition, similar to parent report measures, stable sex effects (Model 2) were observed for initiative, planning and organization, and metacognition. Additionally, stable sex effects were observed for inhibition (lower scores in females) and emotional control (lower scores in males). There were no significant age by sex interaction effects for any of these measures.

#### Effect Sizes and Variance Differences

Next, we tested the size of sex effects in addition to variance differences between males and females on average age-adjusted cognitive measures, by averaging scores across time points (Table 6A, B, and C). Effect sizes of sex effects were large for reading comprehension (d = .669) and small for mental counters working memory (d = .328). None of the cognitive tasks showed significant sex differences in variance (Table 6A).

Table 6.
Variance Effects and Bayes Factors
MeasureMean FMean MpCohen's dBFVRp VR
Reading comprehension 0.229 −0.212 ** 0.669 539090.8 0.053 ns
Reading fluency 0.109 −0.098 ns 0.207 0.5 −0.104 ns
Working memory −0.123 0.153 ** 0.328 5.7 −0.329 ns

B. Parent report BRIEF measures
Inhibition 0.007 −0.025 ns 0.031 0.1 −0.25 ns
Shifting 0.056 −0.091 ns 0.152 0.3 −0.451 ns
Emotional control 0.112 −0.133 ns 0.243 0.8 −0.287 ns
Initiate −0.284 0.293 ** 0.525 460.5 0.179 ns
Working memory −0.148 0.136 ns 0.259 0.187 ns
Planning and organization −0.274 0.275 ** 0.51 291.1 0.478 **
Organization of materials 0.092 −0.108 ns 0.177 0.4 0.037 ns
Index behavioral regulation 0.079 −0.1 ns 0.176 0.4 −0.463 ns
Index metacognition −0.22 0.241 ** 0.412 21.3 0.231 ns

C. Self-report BRIEF measures
Inhibition −0.238 0.251 * 0.469 3.1 0.263 ns
Shifting −0.04 0.081 ns 0.121 0.2 0.435 **
Emotional control 0.182 −0.181 ns 0.364 1.1 0.02 ns
Initiate −0.212 0.268 * 0.451 2.5 0.039 ns
Working memory −0.183 0.224 ns 0.392 1.4 0.089 ns
Planning and organization −0.29 0.336 ** 0.617 21.9 0.343 *
Organization of materials −0.137 0.187 ns 0.268 0.5 0.032 ns
Index behavioral regulation −0.077 0.082 ns 0.162 0.3 0.215 ns
Index metacognition −0.272 0.337 * 0.571 11.4 0.188 ns
MeasureMean FMean MpCohen's dBFVRp VR
Reading comprehension 0.229 −0.212 ** 0.669 539090.8 0.053 ns
Reading fluency 0.109 −0.098 ns 0.207 0.5 −0.104 ns
Working memory −0.123 0.153 ** 0.328 5.7 −0.329 ns

B. Parent report BRIEF measures
Inhibition 0.007 −0.025 ns 0.031 0.1 −0.25 ns
Shifting 0.056 −0.091 ns 0.152 0.3 −0.451 ns
Emotional control 0.112 −0.133 ns 0.243 0.8 −0.287 ns
Initiate −0.284 0.293 ** 0.525 460.5 0.179 ns
Working memory −0.148 0.136 ns 0.259 0.187 ns
Planning and organization −0.274 0.275 ** 0.51 291.1 0.478 **
Organization of materials 0.092 −0.108 ns 0.177 0.4 0.037 ns
Index behavioral regulation 0.079 −0.1 ns 0.176 0.4 −0.463 ns
Index metacognition −0.22 0.241 ** 0.412 21.3 0.231 ns

C. Self-report BRIEF measures
Inhibition −0.238 0.251 * 0.469 3.1 0.263 ns
Shifting −0.04 0.081 ns 0.121 0.2 0.435 **
Emotional control 0.182 −0.181 ns 0.364 1.1 0.02 ns
Initiate −0.212 0.268 * 0.451 2.5 0.039 ns
Working memory −0.183 0.224 ns 0.392 1.4 0.089 ns
Planning and organization −0.29 0.336 ** 0.617 21.9 0.343 *
Organization of materials −0.137 0.187 ns 0.268 0.5 0.032 ns
Index behavioral regulation −0.077 0.082 ns 0.162 0.3 0.215 ns
Index metacognition −0.272 0.337 * 0.571 11.4 0.188 ns

BF = Bayes factor; VR = variance ratio.

*

p < .05.

**

p < .01.

Parent report on the BRIEF questionnaire showed moderate effect sizes of sex differences in initiative (d = .525), working memory (d = .259), planning and organization (d = .510), and metacognition (d = .412; Table 6B). For the other scales, Bayes factors were <1, supporting the null mode of no significant sex differences. In addition, there was significant greater male than female variance for planning and organization.

Self-report measures of EF showed medium effect sizes for sex differences in inhibition (d = .469), initiative (d = .451), planning and organization (d = .617), and metacognition (d = .571). In addition, greater male variance was observed for planning and organization. For the other scales, Bayes factors were <1, supporting the null model of no significant sex differences. Furthermore, significant greater male variance effects were observed in shifting, in the absence of a mean sex difference.

#### Correlation Matrix EF Measures

Significant correlations between all cognitive measures (p < .05) are shown in Figure 6. Strong correlations were observed within the different scales of the BRIEF subscales (range r = .17–.92). Moderate correlations were observed between tasks and BRIEF data (range r = .14–.61), where stronger correlations were observed for reading comprehension and fluency (r = .61) than mental counters working memory (range r = .13–.38).

Figure 6.

Correlation matrix between task-based assessment of cognitive performance (first three columns) and real-life assessment of EF as assed by the BRIEF questionnaire data (parent report Columns 4–12, self-report Columns 13–21). Positive correlations are indicated in red; negative correlations are indicated in purple. The stronger the correlation, the darker the color. Only significant correlations are reported (p < .05).

Figure 6.

Correlation matrix between task-based assessment of cognitive performance (first three columns) and real-life assessment of EF as assed by the BRIEF questionnaire data (parent report Columns 4–12, self-report Columns 13–21). Positive correlations are indicated in red; negative correlations are indicated in purple. The stronger the correlation, the darker the color. Only significant correlations are reported (p < .05).

### Sex Differences in Brain Development in Relation to Sex Difference in EF

To test whether the observed sex differences in brain maturation were related to sex differences in cognition, we performed a bootstrap mediation analysis. It was tested whether sex differences in MI of surface area development of the left banks superior temporal gyrus mediated the sex differences in EF measures. We additionally tested whether any other of the brain measures that showed significant interaction effects (but not best fit for Model 3) between age and sex mediated sex differences in behavior. None of the indirect effects were significant.

### EF Effects on “Brain Age” Predictions

We tested using gam modeling whether individual variation in cognitive measures (averaged across time points and age corrected) were related to the brain age error prediction model. There were no significant relations between brain age error and cognitive measures.

## DISCUSSION

The aim of this study was to unravel several inconsistencies concerning sex differences in brain development based on prior studies (Wierenga et al., 2014; Tamnes et al., 2013; Lenroot et al., 2007). We confirmed age-related changes in brain development as shown in prior studies (Wierenga et al., 2014; Tamnes et al., 2013) and confirmed main sex differences in brain sizes (Kaczkurkin, Raznahan, & Satterthwaite, 2019; Ruigrok et al., 2014), but we disconfirmed the presumed age by sex interaction in brain development, except for one cortical brain regions in the temporal cortex. However, we confirmed and extended previous findings of greater male variance in brain structure (Ritchie et al., 2018; Wierenga et al., 2017) by showing greater male variance in brain both structure and development of cortical thickness and surface area, as a larger number of regions showed significant greater male than female variance in cortical maturation. This was further supported by the findings on “brain age” predictions, which showed greater male than female variance. These results show that sex differences in variance are present in the absence of average sex differences in brain structure. Furthermore, behavioral outcomes favored girls for reading and boys for mental counters working memory, but these results were not consistently related to brain development trajectories. The latter finding may suggest that average sex differences in cognition are more strongly related to experience than biological predispositions.

The focus on EF measures was driven by the implications that these findings may have for educational settings. Indeed, consistent with many prior studies, this longitudinal study confirmed significant developmental improvements in all three cognitive tasks: mental counters working memory, reading comprehension, and reading fluency. Similar developmental improvements were observed for parent-reported and self-reported EF measures, which showed significant improvement in a number of domains including inhibition, emotional control, and behavioral regulation. All observed sex effects in cognition were stable across development, where girls in general performed better at reading comprehension, initiative, working memory, planning and organization, and metacognition. In older individuals (>18 years), females reported better performance of inhibition than males. The effect sizes of these female biased cognitive measures were small to moderate (Cohen's d = .412–.617). Males, on the other hand, performed better at two cognitive domains, mental counters working memory task (small effect size) and emotional control (>18 years), although the latter effect was no longer significant when averaged across time points.

An important question that we aimed to address was whether there was evidence that the observed sex differences in performance and EF reports were related to brain development. First of all, we showed that brain age prediction models were improved by including information on developmental trajectories; this improved age prediction with 0.5 years precision. This confirms the added value of longitudinal assessment over single assessments (Foulkes & Blakemore, 2018). We found no evidence that male brains were estimated “younger” than female brains, although there was significant greater male variance in estimations of brain age than in females, consistent with prior reports (Ritchie et al., 2018; Wierenga et al., 2017). Most importantly, we found no evidence for an association between cognition and brain age error, which corresponds with earlier findings in two cross-sectional samples with overlapping age ranges on cognitive performance (Ball et al., 2017; Brown & Jernigan, 2012).

Taken together, we observed sex differences in behavioral cognitive performance and sex difference in brain variance, but no evidence for a relation between these two patterns. Previous studies have linked the variance effect in cortical thickness to genetic components. As such, the results may reveal target regions where cortical thickness development is under control of X-linked genes (e.g., medial OFC, precentral gyrus, temporal pole, post central gyrus). This is in line with research showing that, independent of, for example, social factors or sex steroids, X-chromosome-linked genes play a substantial role in the brain. X-linked genes may herewith directly influence sex variability differences. For example, X-linked genes show relatively high expression rates in brain tissue compared with somatic tissue (Nguyen & Disteche, 2006; Graves, Gécz, & Hameister, 2002).

Given that these effects are not significantly related to cognitive outcomes suggests this relation warrants further investigation, as relations may exist with other behavioral outcomes such as those associated with male-dominant psychiatric disorders. Identifying where and in what way male and female brains differ and how this relates to behavior will help illuminate associated mechanisms. This is important to, for example, our understanding of sex differences in the prevalence of neurodevelopmental disorders (Bao & Swaab, 2010).

The presence of sex differences in cognitive performance without a clear relation to structural brain development may suggest that boys and girls rely on different strategies to perform EF tasks, while relying on the same neural structure. Given that some functions are better in boys and others in girls also argues against general sex differences in cognitive potential in the current sample. There is now increasing evidence that EF can be trained (Diamond & Lee, 2011), which is correlated with difference in neural recruitment as measured with functional MRI (Erickson et al., 2006). Possibly, the sex differences are therefore the result of different cognitive experiences or parental expectations, although this is still a speculative interpretation that should be addressed in future research. A better understanding of sex differences could promote cognitive potential in developing individuals and address pressing societal issues, such as education programs that are based on a presumed difference in brain development between boys and girls.

This study has a number of strengths, including a large sample, longitudinal assessments of MRI and behavioral data, in addition to both task and questionnaire data. In addition, this study explored sex effects beyond mean differences by including variance analysis. However, the study also had a number of limitations. First, two tasks (reading comprehension and mental counters working memory) showed potential ceiling effects in performance. Although there are a number of procedures described in the literature to deal with such effects (excluding top scores, e.g., log transformations), these procedures are all suboptimal. Moreover, they may introduce systematic bias that may relate to our variables of interest (e.g., reading comprehension scores would be affected to a larger extent in girls than boys). As such, our findings should be interpreted with caution. Second, the size of our sample may be limited to detect variance effects in brain developmental trajectories. It is therefore encouraged to replicate these findings in a larger longitudinal data set. Last, an increased sample size of longitudinal data could also improve our brain age prediction model as previous studies showed that larger (but cross-sectional) data sets had improved MAE (Ball et al., 2017; Brown et al., 2012). A prior study showed that brain development in the OFC was influenced by testosterone levels, with different relations to behavioral measures in boys and girls (Peper, Koolschijn, & Crone, 2013). It would be interesting in future studies to not only look at age developmental trajectories but also take into account measures of puberty in relation to behavioral development.

In conclusion, the results of this study do not support the hypothesis of sex difference in cortical development trajectories. The only structure showing a sex difference in cortical maturation did not relate to sex differences in cognition. We did, however, extend previous findings of greater variability in male brain structure by showing greater male than female variability in cortical development. Observed performance differences in cognition may be related to training and educational experiences, an important question to address in future research. Our study provides a novel perspective to better understand brain–behavioral differences between males and females and how these develop.

## Acknowledgments

We thank all the participants for their valuable contribution to this longitudinal study. We would additionally like to thank Prof. Dr. C. Espin for her valuable contribution to the cognitive task data set. This work was supported by the European Council starting grand scheme (ERC-2010-StG_263234 to E. A. C.).

Reprint requests should be sent to Lara M. Wierenga, Brain and Development Research Center, Leiden University, PO Box 9600, 2300 RB, Leiden, The Netherlands, or via e-mail: l.m.wierenga@fsw.leidenuniv.nl.

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