Brain asymmetry is globally different in males and females: exploring cortical volume, area, thickness, and mean curvature

Abstract Brain asymmetry is a cornerstone in the development of higher-level cognition, but it is unclear whether and how it differs in males and females. Asymmetry has been investigated using the laterality index, which compares homologous regions as pairwise weighted differences between the left and the right hemisphere. However, if asymmetry differences between males and females are global instead of pairwise, involving proportions between multiple brain areas, novel methodological tools are needed to evaluate them. Here, we used the Amsterdam Open MRI collection to investigate sexual dimorphism in brain asymmetry by comparing laterality index with the distance index, which is a global measure of differences within and across hemispheres, and with the subtraction index, which compares pairwise raw values in the left and right hemisphere. Machine learning models, robustness tests, and group analyses of cortical volume, area, thickness, and mean curvature revealed that, of the three indices, distance index was the most successful biomarker of sexual dimorphism. These findings suggest that left–right asymmetry in males and females involves global coherence rather than pairwise contrasts. Further studies are needed to investigate the biological basis of local and global asymmetry based on growth patterns under genetic, hormonal, and environmental factors.


Introduction
Brain asymmetry develops before birth (Rajagopalan et al. 2011), with specific range and distribution patterns across males and females still a matter of debate (Gilmore et al. 2007;Guo et al. 2016;Lehtola et al. 2019;Ruigrok et al. 2014).Overall, a series of growth mechanisms are in place (Debat and Peronnet 2013;Lander 2011;Rao et al. 2002;Waddington 1959) for achieving a specific "target size" for body and its component parts (Tanner 1963), including catch up growth in children after malnutrition or sickness (Boersma and Wit 1997;Prader, Tanner, von Harnack 1963;Tanner 1963).Moreover, the size of bilateral body parts such as arms or legs is subject to contralateral regulation (for a review of current debates, see Genikhovich and Technau 2017), such that growth on one side of the body would signal growth on the other side (Roselló-Díez et al. 2018).In sum, both systemic growth retardation and direct left-right communication are driving body symmetry (Busse et al. 2018;Fischerauer et al. 2013) by overriding genetic and environmental variation (Grimes 2019).Nevertheless, certain asymmetries survive, for example at the brain level, including intra-hemispheric gray matter volume (Esteves et al. 2019), cortical thickness (Kong et al. 2018), surface area, and gyrification (Chiarello et al. 2016).The main role of these asymmetries would be to support high-level cognition including episodic memory (Habib et al. 2003), emotion identification (Brunoni et al. 2016), face processing (Zhen et al. 2015), and language (de Courten-Myers 1999; Good et al. 2001;Shapleske et al. 1999).
Whether brain asymmetries are distinct in males and females is far from clear.Moreover, it is unclear what type of asymmetries are specific to (young) adult male and female brains, and current evidence based on weighted pairwise differences remains inconsistent.For example, measurements for the "planum temporale," which subserves language, sometimes supports stronger leftward lateralization in males (Guadalupe et al. 2015), and sometimes stronger leftward lateralization in females (Ruigrok et al. 2014).Overall, few, if any, significant differences are left standing between sexes after controlling for total intracranial volume (cf.review by Sanchis-Segura et al. 2019).Current methods for computing brain asymmetry may be responsible for the stalemate, as they fail to capture potentially different types of structural differences.The "laterality index" (LI) helps determine, for instance, whether the left planum temporale is larger than the right, without considering the impact of other brain areas or underlying growth differences of brain structures in males and females.
Here, we investigated sexual dimorphism in brain asymmetry by comparing the performance of three structural indices measuring distinct qualitative differences between the left and the right hemisphere.We used the Amsterdam Open MRI collection (Snoek et al. 2020) to compute absolute values of the pairwise laterality index for each subject and for each of the 34 regions of interest (ROIs) in the Desikan-Tourville atlas (Desikan et al. 2006).Second, we computed a "subtraction index" (SI) as absolute values of raw pairwise differences between left and the right regions for each of the 34 ROIs.Third, we computed a global "distance index" (DI) by correlating two series of differences-between each ROI and all other ROIs in the left hemisphere, and between each homologous ROI and all other ROIs in the right hemisphere, as described under "Materials and Methods".We repeated the computation of DI, LI, and SI for several gray matter measures, namely cortical volume, area, thickness, and mean curvature, and evaluated their performance using machine learning and robustness analyses drawing on image-quality metrics.
Each index captures specific growth patterns that may depend on proportion, scaling, and/or size regulation of the two hemispheres and their constituent parts.Therefore, an investigation of their capacity to distinguish males from females would help identify which brain growth patterns are ecologically valid.Indeed, the rules governing form and proportion are fundamental to the evolution and development of biological organisms and account for body size growth, interaction among specific tissues, and inherent positional identity of constituent parts (Harris et al. 2021).We therefore expect these rules to also be relevant to hemispheric asymmetry patterns in humans, which remain un(der)explored.Several hypotheses can be put forward on which asymmetry indices could successfully capture sexual dimorphism in cortical asymmetry.First, the laterality index, which relies on weighted pairwise differences, might outperform DI and SI if the 34 brain regions had similar growth rates and proportions across hemispheres in males and females, but with decreased scaling in females, which would require activation of coordinated scaling of growth hormone, growth factors, and thyroid hormone (Harris et al. 2021).Second, the subtraction index, which relies on overall size differences, might outperform DI and LI if the 34 brain regions involved differences in target size across hemispheres for males and females, whether or not regions maintain similar proportions to the right and to the left, as long as metrics are overall different across the sexes (e.g. higher values for males compared with females).Third, the distance index, which relies on global coherence within and across hemispheres, might outperform LI and SI if it were sensitive to hemisphere target size, to interactions among ROIs within each hemisphere, as well as to inherent positional identity of each region, such that effective signaling between ipsilateral and contralateral regions could occur.
A certain overlap in performance can be expected among the three indices, as they all involve differences in asymmetry magnitude between males and females.However, we do not expect conf licting results for sexual dimorphism among indices or cortical measures such that higher metrics are elicited for males, for instance, under random combinations of index and measures, which would question the reliability of (some) indices to capture differences between males and females.Details on how each index were computed as well as on further analyses are presented below.

Participants
A total of 928 healthy participants are included in the freely available ID1000 dataset of the Amsterdam Open MRI collection (https://openneuro.org/datasets/ds003097)following standard ethics procedures.We analyzed structural (T1-weighted) scans for a subset of 826 right-handed individuals (396 males and 430 females), for whom detailed information is available from Snoek and colleagues (https://doi.org/10.1101/2020.06.16.155317).

Asymmetry indices
We computed three asymmetry indices using Matlab 2022a (Mathworks 2022) based on raw values for 34 regions following the Desikan-Tourville atlas (Desikan et al. 2006) across several gray matter measures: volume, surface area, thickness, and mean curvature (henceforth "curvature").We derived the distance index as detailed in equation (1).To obtain a DI value for one region (DI i ), we first computed a vector of absolute differences between that region in the left hemisphere and the other regions ipsilaterally, and then a vector of absolute differences between the same region contralaterally and the other regions in the right hemisphere.After correlating the two vectors, we computed a Pearson correlation coefficient, which we subtracted from 1 to derive DI as the absolute value for that ROI.The higher the DI, the greater the asymmetry (i.e.difference in magnitude between hemispheres) for that region.Conversely, the lower the DI, the smaller the cortical asymmetry.By repeating the computation, we obtained a 34-dimension vector that we compared across two groups of participants (e.g.males and females) in a paired-sample t-test: where For the laterality index for a particular region (LI i ), we computed a modified formula of the classic laterality index, as detailed in equation ( 2), by subtracting the value of that region in the left hemisphere from its counterpart in the right hemisphere before dividing this number by the sum of the two.In a last step, we derived absolute values to obtain the LI for each region.In doing so, we estimated the magnitude of the left-right asymmetry rather than the sign of this difference, as we were not interested which hemisphere was larger than the other.We obtained a series of positive differences, one per ROI, which we further compared between males and females: To compute the subtraction index for a particular region (SI i ), we derived the difference between the raw value of that region and their counterpart in the contralateral hemisphere before deriving the absolute value of this difference, as detailed in equation (3).Again, we aimed to measure the magnitude of the leftright difference instead of the sign of a particular value.Importantly, unlike DI, both LI and SI derive pairwise differences for each region and do not factor in other regions when estimating the asymmetry of a single region.The distinction to be made between LI and SI is that only the former involves proportional/weighted left-right differences, whereas the latter simply measures raw left-right differences.In sum, the three indices provide asymmetry estimates for homologous ROIs across hemispheres in the form of positive differences in magnitude, to be compared between males and females: (3)

Binary classification models
All statistical analyses were carried out in the statistical environment R, version 2022 July 2 (R Core Team 2012) using version 6.0-94 of the Classification and Regression Training ("caret") package for machine learning (Kuhn 2008).We set a unique random seed before building models for each index and for each cortical measure, then split the data into a training set (80%) and a test set (20%).A Random Forest classifier (Breiman 2001) was run for each index and measure including values for all 34 ROIs plus age as predictors.Random Forest is a popular supervised machine learning algorithm that generates and combines multiple decision trees that are trained on different parts of a given set, thereby providing clear advantages over other machine learning methods, such as optimized prediction accuracy and overfitting.Reliability is built into Random Forest models as "bagging," which involves aggregation and bootstrapping.To further enhance reliability, we applied 10-fold grid leave-one-out cross-validation over test data.
A confusion matrix and associated statistics (i.e.model accuracy, Cohen's Kappa, and P-values) was computed for each index and for each cortical measure (i.e.area, volume, thickness, and curvature) to better evaluate the algorithms.A confusion matrix was derived for each model as a 2 × 2 table that summarizes the percentage of correctly and incorrectly classified males and females.The "Cross-Validation for Model Selection" (cvms) package in R (Jeyaraman et al. 2019, https://cran.r-project.org/package=cvms) was used to visualize the confusion matrices.Model accuracy specifies how many correct predictions (i.e.true positives and true negatives) the classification model will make over 100 participants.However, even when accuracy is high, it must be interpreted together with Cohen's Kappa, which corrects for the likelihood that accuracy values might occur accidentally by taking into account both true positives and false positives.The rule of thumb is that Kappa coefficients lower than zero indicate worse-than-chance classification performance, over 0.20 fair performance, over 0.40 good performance, and over 0.60 up to 1 very good classification performance (Fleiss 1981).However, interpreting Kappa values is highly dependent on the research question and may be inadequate when marginals are similar for predicted and target groups (Delgado and Tibau 2019).Accuracy values must also exceed the "no information rate" (NIR), which is the accuracy obtained by always predicting the majority class.The model should thus yield a significant p-value between accuracy and NIR.Further, Random Forest allows us to estimate the relative importance of model predictors that is, the 34 cortical regions plus age.We plotted the six highest ranking predictors on cortical surface maps (cf.Mowinckel and Vidal-Pineiro 2019) for each index and for each cortical measure.

Robustness and reliability analyses
The quality of magnetic resonance (MR) images may depend on operator errors, patient movement, equipment performance, as well as by contrast and brightness as indexed by T1-weighted (T1w) sequences.Image-quality metrics are typically not included in brain imaging studies, but failure to control for data quality was shown to bias estimates of lifespan brain development (Rosen et al. 2018;Zuo et al. 2017) and age (Power et al. 2012;Roalf et al. 2016).Evidence of negligible impact of image-quality metrics on index values would support index robustness.Indeed, analyses are robust when they do not vary strongly with external parameters (e.g.image quality), and they are reliable when they do not vary across repeated testing of the same sample (Jansen et al. 2006).In our study, reliability is part of the Random Forest algorithm, which involves bootstrapping as well as cross validation.In addition, obtaining similar result patterns for indices across several cortical measures, namely volume, area, thickness, and mean curvature, would further support index reliability.
The AOMIC database provides five of the 14 fully automated image-quality metrics described by Esteban and colleagues (Esteban et al. 2017).The five metrics are based on specific artifacts, structural image quality, and information theory.Measures targeting specific artifacts are the intensity nonuniformity metric (INU) and the white matter to maximum intensity ration (WM2MAX).The former describes the inhomogeneity of the magnetic field, with values around 1.0 indicating less motion and smaller bias in the magnetic field.The latter measures median intensity of white matter over 95% of full intensity distribution and captures artifacts generated by carotid vessels and fat.Values between 0.6 and 0.8 indicate ideal white matter brightness.Structural image quality measures evaluate the impact of noise and include the coefficient of joint variation (CJV) of white and gray matter and the contrast-to-noise ratio (CNR).The former is an objective function for optimizing INU correction algorithms (Ganzetti et al. 2016a), with higher values indicating head motion and important INU artifacts.The latter evaluates the degree of separation between gray matter and white matter, with higher values indicating better tissue separation.Finally, information theory measures evaluate the spatial distribution of information.In particular, the entropyfocus criterion (EFC) estimates ghosting and blurring caused by head motion; hence, lower values are preferable (Atkinson et al. 1997).
To evaluate the impact of image-quality metrics on the robustness of the three asymmetry indices, we selected two equal subsamples for each metric and for each group, as follows.First, data were organized in lower and upper levels for each imagequality metric, and 80 participants (approx.20%) were selected for each level, while matching the metrics values across males and females.As a rule, the first and the last 80 participants and corresponding index values were selected for each metric.EFC was an exception, as values were highly homogeneous in females compared with males, and therefore upper and lower groups could only be delineated by strongly polarizing the samples.As a result, two groups of only 35 participants each were selected.In a last step, paired-sample t-tests were run between males and females index values across the 34 ROIs for each metric and for each level.Several outcomes are possible, bearing in mind that some image-quality metrics are better when higher (e.g.CNR, INU), whereas others are better when lower (i.e.CJV, EFC).First, differences between males and females could be significant only for the preferred level, which would indicate that a particular index, either DI, LI, or SI, is sensitive to image quality metrics.Second, analyses of asymmetry indices for males and females could be significant for both upper and lower metrics levels, in which case the index is a robust biomarker of sexual dimorphism.Third, there may be no significant differences for a given index between males and females for associated lower or upper imagemetrics, which would indicate that the index is not a robust biomarker or brain asymmetry.

Group analyses and correlations with males/females
Group analyses as paired t-tests between males and females for each index and for each cortical measure were performed, whose results could support the output of binary classification models.Pearson correlations between sex and whole-brain index values were computed, allowing for an informal comparison of asymmetry indices and their potential to distinguish males from females across cortical measures.For each ROI, we computed index values (separately for DI, LI, and SI) across subjects and correlated them with males/females (coded as "0" and "1," respectively) before averaging over correlation coefficients for that particular region and for each index.In a last step, we obtained a grand average over all 34 ROI for each index and represented the three values in graphical format.Another informal analysis was performed over raw ROI values for each hemisphere, to determine the potential of each hemisphere alone to provide cues for binary classification.As before, correlations with males/females were averaged for each ROI and for each hemisphere, followed by a grand average computed for each hemisphere and cortical measure before representing values in graphical format.

Random Forest binary classification
The trained model was tested on the test dataset to obtain singlesubject predictions in the form of accuracy percentages and counts of correct and incorrect classification.Figure 1 illustrates a series of 2 × 2 confusion matrices summarizing the outcomes of Random Forest models, one for each index and cortical measure.The following associated statistics are reported underneath each matrix: accuracy ("Acc"), P-value when comparing accuracy with no-information rate, and Cohen's Kappa.By combining target (raw) values over two columns and predicted values over two rows, four quadrants are defined, as follows: correct classification over the upper left and lower right quadrants (true positives for cases where males are predicted to be males and true negatives for cases where females are predicted to be females) and incorrect classification over the upper right and lower left quadrants (false positives in cases where females are predicted to be males and false negatives in cases where males are predicted to be females).Each quadrant in a matrix includes several numbers, starting with the overall percentage in the middle and overall count underneath.Column percentages are given at the bottom of each quadrant: if we consider the first matrix summarizing binary classifications for DI volume, of all the observations where Target is male, 59.5% were predicted to be male and 40.5% were predicted to be female.Row percentages are given to the right of the quadrants: if we consider the upper quadrants, of all the observations where Prediction is male, 61% of them were actually male, while 39% were female.
The color intensity of the quadrants corresponds to counts, from deeper oranges (higher counts) to pale oranges (lower counts).Highly accurate classifications are therefore cases where the upper left-lower right diagonal is intensely colored, which was true for DI volume, area, and curvature, for LI area and curvature, and for SI volume and area.Accuracy levels exceeded 50% except for SI curvature, with DI scoring the highest for area, thickness, and curvature.Cohen's Kappa values were above 20% only for DI volume area, and thickness, for LI volume and area, and for SI volume and area.As for p-values, they were significant for DI volume, area, and curvature, for LI area, and for SI volume and area, indicating that LI underperformed compared with the other two indices.DI curvature also featured reasonable statistics (56% accuracy and P = 0.004, despite a lower Kappa value of 0.13), whereas binary classifications based on cortical thickness fared poorly across indices.
Brain maps of lateral and medial surfaces above each confusion matrix in Fig. 1 present the six ROIs whose variance contributed to binary classification the most.Color intensity goes from light blue (highest rank) to dark blue (lowest rank).If we exclude thickness, for which classification was poor, we may conclude that successful classification relies mostly on prefrontal and temporal areas, as well as on the temporo-parietal junction, with slight variations across indices.Of the ROIs with highest differences in DI asymmetry between males and females, we singled out the rostral anterior cingulate for volume and area and the rostral middle frontal for mean curvature.For LI and SI, the inferior parietal ranked highly for volume and area, and even for mean curvature for LI.These areas are among those previously associated with male-female differences (i.e.Gomez et al. 2019;Lotze et al. 2019;Sowell et al. 2007), but their relevance to brain asymmetry was not established.
An important goal of the AOMIC database was to provide a homogeneous sample size and, therefore, only individuals in their early twenties were recruited.This goal was met, as we included "age" as a predictor of sex, alongside the 34 ROIs but found it among the lowest ranked predictors in the output of all models.

Robustness analysis: Impact of image quality metrics on index values
Figure 2(A) summarizes five image-quality metrics (CJV, CNR, EFC, INU, and WM2MAX) associated with the 826 right-handed male and female participants in the AOMIC dataset.Overall, image quality was similar or even better compared with other large datasets, for example ABIDE (Di Martino et al. 2014).However, the values were different in males and females, which could bias the analysis of associated indices.To preclude biases when evaluating the impact of image quality metrics on index values, two subsamples were selected for each index and for each measure, corresponding with upper and lower image-quality levels.For each set of 34 ROIs at upper and lower levels, paired sample ttests were run between males and females.Associated p-values were designated in Fig. 2(C) with " * " if less than 0.001, with "x" if less than 0.05 but higher than 0.001, and with "ns" if higher than 0.05.Distance index scores were significantly higher in males compared with females for each cortical measure (volume, area, thickness, and curvature) across both lower and upper CJV and EFC, across lower and upper CNR and WM2MAX except for thickness, where differences were significant only for lower CNR, and finally for lower INU except volume.The results of t-test between males and females for the laterality index were significant only for a quarter of all t-tests run, namely for lower CJV area and Overall, asymmetry was again higher in males compared with females.Unlike DI scores, LI scores followed the optimal level of image-quality that is, they were significant if associated with lower CJV and EFC, as well as with higher CNR and INU.As for the subtraction index, scores were not significantly different for males and females across the board, suggesting low robustness for this index.

Group analyses and correlations with males/females
As seen in Fig. 3(A), correlation coefficients with males/females were similar for the left and the right hemisphere.Paired t-tests between them for each cortical measures were not significant, showing that neither hemisphere provides robust cues for binary classification.Figure 3(B) summarizes whole brain averages for males and females across indices for surface area, cortical volume, thickness, and mean curvature.Overall, index values in these group analyses were higher for males than for females.For DI, were highly significant (under 0.001) across all cortical measures.For LI, P-values were highly significant only for volume, they were significant (under 0.05 but over 0.001) for area and thickness, and non-significant for mean curvature.For SI, P-values were highly significant for volume and area, significant for thickness, and non-significant for mean curvature.
The analyses contrasting males and females revealed that DI yielded the best outcomes, followed by SI, and then by LI.These results are confirmed by correlation analyses, as seen in Fig. 3(C), which presents an informal comparison of Pearson correlation Fig. 2. Image-quality metrics and their impact on asymmetry indices DI, LI, and SI.Average metric values (CJV, CNR, EFC, INU, and WM2MAX) are given for males and females in the full sample (all 826 right-handed participants) and in two subsamples corresponding to upper and lower metric levels (A).Average index values corresponding to upper and lower image-quality levels are given for males and females for cortical measures-volume, area, thickness, and curvature (B).Significance levels of t-tests between males and females are marked as " * " if less than 0.001, as "x" if less than 0.05 but higher than 0.001, and as "ns" if higher than 0.05.Note that SI scores are all "ns." coefficients for each asymmetry index and males/females across cortical measures.Higher values indicate better classification performance.Overall, DI (light orange) has associated the highest coefficients, especially for mean curvature, with SI (mid-orange) a good second, especially for average volume and surface area.Of the three, LI (deep orange) yielded the lowest coefficients and therefore the poorest classification.

Discussion
We provided evidence that brain asymmetry is globally different in males and females, with the distance index being the most suitable methodological tool for evaluating these differences.Machine learning and robustness analyses contrasted the distance index with the laterality index and the subtraction index, which are based on local pairwise differences between brain regions, in their ability to distinguish males from females.Random Forest models performed overall better in terms of accuracy, non-randomness, and Cohen's Kappa for DI volume, area, and curvature compared with SI and especially to LI, which fared poorly.Interestingly, binary classification failed for cortical thickness across indices, suggesting the existence of regional differences in thickness that cannot be captured by whole-brain analyses.
For each index, t-test results between males and females were significant, especially for the distance index.Moreover, unlike DI values, LI and SI values did not differ significantly in males and females for mean curvature-incidentally, DI correlation coefficients with males/females were highest for mean curvature.When investigating index robustness in upper and lower subsamples corresponding to highest and lowest image-quality metrics, DI yielded the highest percentage of significant t-tests (80%) in group analyses of males versus females.LI scores were significant in only 25% of the tests, and SI scores were not significant.Moreover, informal correlation analyses between sex and index measures illustrated in Fig. 3(C) underscore the robustness of DI as a global coherence index for encoding sexual dimorphism.Fig. 3. Group analyses and correlations of males/females with index values.Pearson correlation coefficients are given for sex versus raw values in the left and right hemisphere over aggregated regions of interest for all cortical measures-volume, area, thickness, and curvature (A).Significance levels of paired t-tests between male and female index values for cortical measures are marked as " * ," "x," and "ns" if less than 0.001, less than 0.05 but higher than 0.001, and higher than 0.05, respectively (B).Pearson correlation coefficients for sex versus each asymmetry index across cortical measures (C).
When looking at raw cortical measures, correlation coefficients with sex did not differ between the left and the right hemisphere, suggesting that neither of them alone encodes cues for binary classification.In contrast, it is the combined magnitude of proportions between regions across hemispheres that appears to be a useful metric, which suggests that specific growth rules are at work ensuring cortical asymmetry differences in males and females.The fact that DI was a better biomarker of sexual dimorphism compared with LI or SI suggests that individual ROIs have different target sizes in non-random ways that is, they must be proportional to ROIs in the opposite hemisphere, which highlights a complex pattern of contralateral growth regulations across left and right side (Genikhovich and Technau 2017).In other words, asymmetry must have evolved in humans not as weighted pairwise differences between the left and the right hemisphere, which would simply involve scaling, but as globally coherent relationships relying on hemisphere target size, interactions among ROIs within each hemisphere, and inherent positional identity of each region to ensure effective signaling between ipsilateral and contralateral regions.
In the early mammalian cortex, neurogenesis ensures the growth of neural precursor cells (Eriksson et al. 1998) via contralateral signaling.Importantly, neurogenesis continues to ensure plasticity of selected regions in the adult brain (for reviews, see Kolb and Whishaw 1989;Plowman and Kleim 2010), especially following injury (Shohayeb 2018).Indeed, extensive changes in adult animals occur after brain damage that highlights the plasticity of uninjured networks.When stimulated, injury ipsilateral regions elicited both ipsilateral and contralateral motor responses (Murphy and Corbett 2009;Ueno et al. 2012), underscoring the importance of a continuous dialog between hemispheres.An important issue is whether contralateral signaling and neurogenesis are dependent on the properties of the corpus callosum, which links the two hemispheres.Early studies support the hypothesis that callosal axonal fibers mostly connect homotopic cortical areas, yet recent studies provide evidence that interhemispheric callosal connections are heterotopic for the most part, and are strongly involved in brain networks across hemispheres (Swanson et al. 2017;Szczupak et al. 2022).Even more remarkably, interhemispheric connectivity was found in mammals with or without a corpus callosum, which helps define a timeline of interhemispheric communications such that a gray matter connectome must precede callosal growth (Suarez et al. 2018).Nevertheless, abnormalities of gray as well as white matter have been reported in neurodevelopmental disorders including schizophrenia (Bilder et al. 1994;Honea et al. 2005;Steinmann et al. 2021), autism (Hazlett et al. 2005;Herbert et al. 2005), stuttering (Foundas et al. 2003), and Tourette syndrome (Hong et al. 2002), supporting a key role for the callosum in brain function.These findings lay bare the field of future conjectures on the origins of brain asymmetry, which develops both via signaling and across white matter bundles in the corpus callosum through global reorganization instead of pairwise connections across hemispheres.
Sexual dimorphism in the structure of gray and white matter is well documented in literature.Cerebral asymmetry patterns in neonates are opposite to that of older children and adults, suggesting that adult patterns arise before birth and persist throughout postnatal brain development, driven by genetics as well by experience (Gilmore et al. 2007).Cortical asymmetry can be observed as early as 22 weeks of gestation (Chi et al. 1977;Hering-Hanit et al. 2001), being more leftward in males (Kivilevitch et al. 2010) and predominantly rightward in premature males and females (Dubois et al. 2008;Lin et al. 2012).In the adult brain, asymmetries include the right hemisphere being larger than the left, mainly due to more white matter on the right, and frontooccipital asymmetry with larger right prefrontal cortex compared with the left and larger left occipital cortex compared with the right (Nopoulos et al. 2000;Toga and Thompson 2003).White matter continues to increase in volume throughout life (Lenroot et al. 2007;Giedd et al. 1999;Sowell et al. 2002), but gray matter reaches a peak around 10 years of age, slightly earlier in females for temporal and frontal lobes (Tanaka et al. 2012).Although males have larger brain volumes and surface areas compared with females, cortical thickness is greater in females (Ritchie et al. 2018).
There is greater variance in males compared with females for volume and surface area, suggesting that individual differences are more important in males (Giedd et al. 1996).However, asymmetry patterns appear to be systematic and predictable rather than random, as witness good DI performance, which suggests that mere variance or individual differences cannot explain away the sexual dimorphism of cortical asymmetries.Growth rates triggered by genetic and hormonal factors are more likely candidates, as they impact cortical growth across the lifespan (McEwen andMilner, 2017 Korol 2004;Sisk and Zehr 2005), have associated effects on cognition and mental illness, and account for increased variability of male brains via genomic imprinting (Dulac and Christopher 2013), mitochondrial DNA mutations passed on maternally (Gemmell et al. 2004), X chromosome effects (Craig et al. 2009)), and further mechanisms protecting females from damaging consequences of genetic mutations (Robinson et al. 2013).Moreover, testosterone and/or estradiol in males increase the number of calcium-binding proteins, which are known to prevent neuronal death, thus resulting in males having a greater number of neurons than females (Segovia et al. 1999).
To summarize, we found DI to be a robust biomarker of cortical asymmetry.Of the three indices, it captured best whole brain differences between the sexes, with female brains being structurally more coherent than male brains.Importantly, the whole brain size may remain unchanged, while degree of coherence may differ.Also, reduced lateralization does not entail higher coherence, and, conversely, highly lateralized structures need not be less coherent, since an interaction among ROIs within each hemisphere may or may not occur.Sexual dimorphism in brain structure appears to draw on the rules governing form and proportion, which are fundamental for the development of biological organisms (Harris et al. 2021).However, there are currently no advanced reports on the impact of genetic, epigenetic, and hormonal factors on distinct types of brain asymmetry in males versus females.Moreover, our findings cannot distinguish the effects of developmental processes from the effects of genetic hardwiring of proportion parameters as they converge toward global differences in brain asymmetry between young adult males and females.Further studies are needed, in the future, to explore the biological basis of various types of asymmetries in the human brain.

Fig. 1 .
Fig. 1.Performance of binary classification models.Each 2 × 2 confusion matrix corresponds to a specific measure (volume, area, thickness, or curvature) and index (DI, LI, or SI) with accuracy, p-value relative to no-information rate, and Cohen's Kappa given underneath.True positive, false positive, false negative, and true negative quadrants in each matrix include overall percentage and count in the middle.Column percentages are given at the bottom and row percentages to the right in each quadrant.Six regions of interest are displayed on lateral and medial cortical maps, ranking from most important (lightest) to least important (darkest) for each model.