The Heritability of Cortical Folding: Evidence from the Human Connectome Project

Abstract

The mechanisms underlying cortical folding are incompletely understood. Prior studies have suggested that individual differences in sulcal depth are genetically mediated, with deeper and ontologically older sulci more heritable than others. In this study, we examine FreeSurfer-derived estimates of average convexity and mean curvature as proxy measures of cortical folding patterns using a large (N = 1096) genetically informative young adult subsample of the Human Connectome Project. Both measures were significantly heritable near major sulci and primary fissures, where approximately half of individual differences could be attributed to genetic factors. Genetic influences near higher order gyri and sulci were substantially lower and largely nonsignificant. Spatial permutation analysis found that heritability patterns were significantly anticorrelated to maps of evolutionary and neurodevelopmental expansion. We also found strong phenotypic correlations between average convexity, curvature, and several common surface metrics (cortical thickness, surface area, and cortical myelination). However, quantitative genetic models suggest that correlations between these metrics are largely driven by nongenetic factors. These findings not only further our understanding of the neurobiology of gyrification, but have pragmatic implications for the interpretation of heritability maps based on automated surface-based measurements.

Introduction

The intricate wrinkly outer layer of the human cerebrum produced by cortical gyrification is one of the most iconic images in the neurosciences. Increased gyrification in mammals has generally paralleled evolutionary increases in cerebral surface area (SA) (Geschwind and Rakic 2013; Albert and Huttner 2015; Garcia, Kroenke, et al. 2018a; Strike et al. 2018); mammals with larger brains tend to have more cortical folding compared with those with smaller brains (Fernández et al. 2016). Traditionally, increased gyral complexity has been attributed to the simple necessity of fitting an evolutionarily expanded 2D cortical manifold into a reasonably sized calvarium (Welker 1990; Kroenke and Bayly 2018). However, greater cerebral gyrification also correlates with increased regional specificity of brain function (Changizi 2001); in addition to being a simple space-saving measure, gyrification may also facilitate regional differentiation, functional organization, and optimization of neural wiring (Van Essen 1997; Klyachko and Stevens 2003; Fischl et al. 2008).

The biological mechanisms underlying cortical gyrification are quite complex, and are currently under active investigation via cellular, genetic, evolutionary, molecular, and biomechanical perspectives (Fernández et al. 2016; Borrell 2018; Kroenke and Bayly 2018). Gyrification begins near the conclusion of neurogenesis (Bystron et al. 2008) following the migration of most cortical neurons (Neal et al. 2007). Gyrencephalic species have a greater abundance of neural stem neuroepithelial cells and radial glial cells compared with their lissencephalic counterparts, as well as a greater diversity of neural progenitors and larger, more complicated subventricular zones (Smart et al. 2002). The phylogenetic emergence of gyrencephaly is associated with the development of an outer subventricular zone during neurogenesis (Reillo et al. 2011). The combination of an increased number of progenitors and a prolonged period of neurogenesis results in a dramatically increased gray matter volume (Fernández et al. 2016).

Despite the coincidence of cortical folding with several key neurodevelopmental milestones, the mechanisms underlying folding itself are incompletely understood (Garcia, Kroenke, et al. 2018a; Kroenke and Bayly 2018). Gyrification does not appear to be directly caused by increases in neuronal volume. The completion of neurogenesis proceeds the onset of gyral folding (Zilles et al. 2013; Garcia, Kroenke, et al. 2018a); the development of cortical folds more closely correlates with gliogenesis in the outer subventricular zone (Rash et al. 2019). Biomechanical models have theorized that the process of gyrification may be related to 1) cerebral expansion within a rigid calvarium resulting in crumpling (Welker 1990), 2) differential cortical growth relative to deeper layers leading to cortical buckling (Richman et al. 1975; Tallinen et al. 2016), 3) differential regional growth of progenitor cells (Reillo et al. 2011), 4) heterogeneous radial expansion of subcortical layers (Smart and McSherry 1986), 5) development of intracortical connections (Rakic 1988), and 6) increased axonal tension (Van Essen 1997), among others.

Furthermore, the reasons for why cerebral folds form precisely where they do are yet to be established. Phylogenetically similar species have similarities in folding patterns (Zilles et al. 2013), suggesting that genetics plays a role, albeit a potentially indirect one. Cortical folding occurs in a partially organized fashion, with the larger primary sulci more consistent in location, and the smaller secondary and tertiary sulci appearing more random (Garcia, Kroenke, et al. 2018a). Nevertheless, there is some consistency in human folding patterns, enabling replicable neuroanatomic definitions of the larger gyri and sulci and standardized neuroanatomic parcellation (Destrieux et al. 2010). Certain convolutions, such as the central sulcus and Sylvian fissure, are more consistent in position and morphology. In general, there is reduced individual variation in sulcation patterns with increasing sulcal depth (Lohmann et al. 2008). Sulcal depth (most notably the central sulcus) is heritable in primates, and cerebral shape tends to be more heritable in the more rudimentary regions of the primate brain (Kochunov et al. 2010; McKay et al. 2013). During human brain development, gyrification also proceeds in a temporally stereotyped sequence, with the deeper primary sulci arising midgestation in relatively predictable locations, and smaller secondary and tertiary sulci forming later, even during childhood and adolescence (Welker 1990; Dubois et al. 2008; Tallinen et al. 2016).

Despite some predictable neurodevelopmental patterns, there remain nontrivial individual differences in human sulcation (Ono et al. 1990). Even the central sulcus can vary up to 2 cm in anterior–posterior position (Talairach and Tournoux 1988), and the morphology of smaller sulci can be highly variable (Lohmann et al. 2008). This variability is not only of interest in understanding the neurodevelopmental processes that underlie gyrification itself, but also has pragmatic implications for automated brain parcellation algorithms. These algorithms typically rely on the appropriate registration of individual subject images to standardized templates; this in turn depends in part on gyral patterns. Thus, individual differences in cerebral shape have the potential to impact the ability to perform group comparisons of other structural metrics (e.g., cortical thickness [CT]), as well as the appropriate anatomic localization of functional imaging results.

There is some evidence that cortical folding is partly under genetic control. The heritability (i.e., the proportion of the phenotypic variance attributable to additive genetic factors) of related structural metrics such as SA, CT, and myelination have been shown to be both statistically significant and regionally variable (Peper et al. 2007; Lenroot et al. 2009; Rimol et al. 2010; Eyler et al. 2011; Schmitt, Neale, et al. 2019a; Schmitt, Raznahan, Liu, et al. 2019c). In humans, genetic variants associated with individual differences in cerebral SA are enriched in regulatory elements of outer radial glial cells (Grasby et al. 2020), and some of these genes may also influence gyrification. Early imaging genetic studies on shape noted that sulcal patterns were more similar in related individuals, but nevertheless with individual-specific variability (Bartley et al. 1997; Baaré 2001); like fingerprints, gyral patterns are unique even between monozygotic (MZ) twins. In a landmark paper, Lohmann (1999).examined gyrification quantitatively via structural magnetic resonance imaging (MRI) in 19 pairs of MZ twins and found statistically significant familial relationships in sulcal patterns that were more pronounced for deeper, ontologically earlier sulci. More recently, genetically informative analyses of the deepest portions of cerebral sulci (“sulcal pits”) have found significant genetic influences on sulcal pit depth in the cingulate, collateral, occipitotemporal, and superior temporal sulci (Le Guen et al. 2017, 2018).

In the current study, we take an alternative approach to the genetics of gyrification by examining cortical folding via FreeSurfer’s vertex-level average convexity and mean curvature maps; to our knowledge we are the first to perform a systematic quantitative genetic analysis of these 2 phenotypes. We chose these maps as potential heritable phenotypes for several reasons. First, both maps include uniform vertex-level measures across the entire cortical sheet (i.e., include measures over both gyri and sulci), enabling spatially fine-grained comparisons between individuals. Second, they are both readily constructed using a widely-available, popular image processing pipeline. Third, these maps are central to FreeSurfer’s registration and parcellation algorithms, and understanding the potential impact of genetics on these processes was a core goal. Finally, these maps spatially correspond to other vertex-level measures derived from FreeSurfer’s surface pipeline, facilitating direct comparisons with other high-resolution phenotypic measures (e.g., SA), as well as maps of evolutionary and neurodevelopmental expansion.

Materials and Methods

Data were obtained from the Human Connectome Project (HCP) S1200 release (Van Essen et al. 2012). This dataset includes high-resolution MRI structural neuroimaging on 1113 adults. The image acquisition protocol included T1 weighted MP-RAGE (TR 2400 ms, TE 2.14 ms, flip angle = 8°, FOV 224 × 224 mm², voxel size = 0.7 mm isotropic, scan time = 7:40 min) and T2 weighted T2-SPACE (TR = 3200 ms, TE = 565 ms, FOV 224 × 224 mm², voxel size = 0.7 mm isotropic, scan time = 8:24 min). All data were acquired on the same 3T scanner. Raw images were postprocessed using standard HCP pipelines; these pipelines have been described in detail elsewhere (Glasser et al. 2013). The initial pipeline (“PreFreesurfer”) aims to correct image distortion, isolate brain parenchyma from other tissues, and register images to a shared space. Vertex-level measures were then calculated via FreeSurfer 5.3.0 (Fischl 2012).

Our principal metric of interest was average convexity (SULC), a vertex-level measure of displacement (Fischl et al. 1999). After construction of a tessellated surface, the FreeSurfer pipeline inflates the cortex to form a spherical model. During the process of unfolding the model, vertices within sulci are displaced outward, whereas those on gyri are displaced inward (Destrieux et al. 2010). Average convexity represents a scalar measure of this displacement, which generally is positive for vertices originally in gyri, and negative for vertices within sulci. We also examined the related mean curvature (CURV) measure. Vertices along sharper cortical curves have higher absolute values; vertices in concavities have negative values and those on convexities have positive values. In general, average convexity identifies primary sulcal folds and large geometric features of the cerebral surface, but mean curvature more efficiently delineates secondary and tertiary gyri and sulci (Fischl et al. 1999; Destrieux et al. 2010).

We also examined the relationships between these 2 folding metrics and several more commonly-investigated structural measures, specifically CT, SA, and cortical myelination (CM). We have described the genetic relationships between these measures in a prior study on a similar HCP sample (Schmitt, Raznahan, Liu, et al. 2019c). CT was estimated as the distance between the pial surface and the gray–white matter junction (Fischl and Dale 2000). SA was calculated by measuring the average triangular size surrounding the tessellated cortical vertices, following deformation of individual subject vertices (Fischl et al. 1999). Cortical myelin content was estimated by calculating the ratio of T1-weighted to T2-weighted images; this ratio accentuates the inherent myelin contrast in both sequences while simultaneously attenuating the effects of magnetic field inhomogeneity (Glasser and Van Essen 2011).

Postprocessing of brain measures involved image downsampling (we used HCP’s 32k vertex Conte 69 data), multimodal surface matching which incorporates both structural and functional data for registration (Robinson et al. 2014), and conversion to the GIFTI file format. Image acquisition and image processing was performed using standard HCP guidelines (Marcus et al. 2013). Each subject’s average convexity, mean curvature, myelination, SA, and CT maps were then smoothed with a 5 mm kernel via the “cifti-smoothing” command from the Connectome Workbench (Van Essen et al. 2012). We additionally generated global and region of interest (ROI) based measures of SULC and CURV by determining mean values over all vertices per subject, or regions of interest from the Desikan–Killaney parcellation (Desikan et al. 2006).

Structural measures were available for a total of 1096 subjects (500 males, 596 females); Table 1 summarizes characteristics of the sample. The final sample had a mean age of 28.8 years and included 229 subjects ages 22–25 years, 478 from 26–30, 376 ages 31–35, and 13 subjects over 35 years. Data from 442 families with up to 6 individuals per family were available, including families with twin-pairs. Genotype-derived zygosity information were available for 283 MZ and 168 dizygotic (DZ) twins. An additional 66 self-reported MZ and 65 DZ twins also were included; we preferentially used genomic data to assign zygosity if available, but also included subjects with self-reported zygosity in order to maximize power. Three hundred and forty-three MZ twins (168 complete pairs), 228 DZ twins (104 complete pairs), and 525 singletons were included in total. The study was approved by the Institutional Review Board of the Hospital of the University of Pennsylvania.

Table 1.

Summary statistics for demographic and global brain measures

	MZ	DZ	Singletons
N	343	228	525
Age	29.4 (3.3)	29.1 (3.5)	28.3 (3.9)
Gender	134 M	92 M	274 M
	209 F	136 F	251 F
Total cognition	120.6 (14.9)	122.0 (14.9)	121.3 (14.6)
Average convexity	−0.039 (0.009)	−0.038 (0.009)	−0.039 (0.010)
Mean curvature	0.036 (0.002)	0.036 (0.002)	0.036 (0.003)
Cortical thickness	2.67 (0.08)	2.67 (0.09)	2.66 (0.09)
Surface area	1589.0 (416.7)	1581.5 (458.6)	1518.3 (404.7)
Cortical myelination	1.85 (0.10)	1.86 (0.09)	1.84 (0.09)

Statistical Analysis

Each subject’s scalar neuroanatomic measures were imported into the R statistical environment for analysis (R Core Team, 2020) using the “cifti” package. The data were reformatted such that each record represented family-wise (rather than individual-wise) data. Genetic modeling was performed in OpenMx, a structural equation modeling (SEM) package fully integrated into the R environment (Boker et al. 2011; Neale et al. 2016). SEM, and its mathematically equivalent visual analog path analysis, represent techniques to model causal and correlational influences between observed and unobserved (i.e., latent) traits. Based on the observed correlational patterns in family members and known kinships between individuals, the relative contributions of genetic and nongenetic influences on phenotypic variance and covariance can be estimated. Although MZ twins are genetically identical, both DZ twins and siblings are expected to (on average) share only half of their genes identical by descent.

Univariate analyses of SULC and CURV were performed at each vertex using an extended twin design (ETD) model (Posthuma and Boomsma 2000). This model used all available pedigree data in HCP, including nontwin families and siblings of twins. We first used an ACET model, which decomposes the observed phenotypic variance into latent components attributable to additive genetic (A), shared environmental (C), unique environmental (E), and twin-specific (T) environmental factors (Neale and Cardon 1992; Neale and Schmitt 2005). In these models, variance due to measurement error is included as part of E. Due to differences observed phenotypic variance and cross-twin or cross-sibling covariances and known degrees of kinship, it is possible to obtain estimates of multiple variance components by solving multiple linear equations:

where V_P represents the observed phenotypic variance, the MZ twin–twin phenotypic covariance, the DZ phenotypic covariance, and the observed covariance between siblings. Proportional variance estimates were subsequently calculated by dividing each variance component by the total variance; for example the heritability (A/V_P, also known as â²) represents the proportion of the total phenotypic variance that is attributable to additive genetic effects. Since the role of the twin-specific environment was minimal, it was subsequently removed from the analysis without significantly worsening model fit. As an alternative analytic approach, we used the twins-only subset of the S1200 HCP data (N = 571) and the classical ACE model; results from both ACET-ETD and twins-only ACE models were similar to the ACE-ETD model, and are presented as supplementary data.

All models contained parameters to control for the effects of sex, age, age², and sex × age interactions on vertex-mean phenotypic values. Optimum model fit was determined via numeric optimization using maximum likelihood (Edwards 1972). In order to test for statistical significance of individual variance components, fit of the full models were compared with nested submodels in which specific variance components were removed; differences in model fit generally follow χ² distributions asymptotically, with df equal to the difference in number of free parameters. However, because of boundary constraints inherent to the classic ACE parameterization (variance cannot be negative), tests of individual variance components actually follow a 50:50 mixture distribution of χ² with 0 and 1 degree of freedom (Dominicus et al. 2006). Control for multiple testing was performed with the false discovery rate (Genovese et al. 2002). The effects of age and sex on folding measures were derived from ACE-ETD models; unlike a standard linear regression, these analysis account for the collinearity inherent to family-wise data (i.e., nonindependent subjects).

Shared genetic and nongenetic factors between SULC and CURV were then tested using genetically informative bivariate AE Cholesky decomposition and an ETD; given the negligible role of the shared environment in univariate models, it was not included in bivariate analyses. Cholesky decomposition factors any symmetric positive definite matrix into a lower triangular matrix postmultiplied by its transpose (Neale and Cardon 1992). In these bivariate models, 2 latent factors are defined for both genetic (A) and environmental (E) variance components. Path coefficients are expressed as 2 × 2 lower triangular matrices, each with 3 free parameters:

Subscripts represent which variables are connected by each path coefficient (e.g., a₂₁ is the path between the first latent genetic factor and second phenotype). If the off-diagonal paths (, were not included, this parameterization would effectively perform univariate analysis on 2 phenotypes in parallel; the presence of these off-diagonal paths allows for the additional estimation of the genetic and environmental contributions to phenotypic “covariance”. Based on a similar pattern to the univariate case above, the expected phenotypic variance–covariance matrix (P) and cross-twin covariance matrices (T_MZ, T_DZ) can be expressed as:

Based on the rules of path analysis, the expected genetic variance for each observed variable (V1, V2) and genetic covariance are estimated thus:

,,

Mathematically identical to converting a phenotypic covariance to a correlation, genetic ( correlations between SULC and CURV can similarly be obtained from their respective covariance matrices. For example:

where represents the genetic covariance between SULC and CURV at the ith, vertex and and the vertex-level genetic variances in SULC and CURV, respectively. The environmental correlation ( that is, the standardized environmental covariance matrix, can be estimated similarly. As a secondary metric of CURV–SULC relationships, we also calculated the contribution of phenotypic variance attributable to genetic factors (sometimes called the “bivariate heritability” when all components of covariance have the same sign), which standardizes the genetic correlation by the heritabilities of the 2 phenotypes of interest:

Relationships between Cortical Folding and Other Measures of Brain Structure

We were also interested in the relationships between cortical folding and common surface-based structural measures. We therefore performed a series of vertex-based bivariate models of SULC with: CT, cerebral SA, and CM. A similar series of bivariate models comparing CURV to these measures (i.e., CURV-CT, CURV-SA, CURV-CM) was also performed.

Comparisons of Brain Maps via Spatial Permutation

We tested for the statistical significance of intermap spatial correspondence via spatial permutation, also referred to as the “spin” test (Alexander-Bloch et al. 2018). This test is useful as it controls for both spatial autocorrelations and multiple testing. Briefly, spherical projections are constructed for any 2 coregistered vertex-level brain maps. The cross-vertex Pearson’s correlation can then be calculated between these 2 maps, generating a simple estimate of global pattern similarity. In order to determine statistical significance of this correlation, the observed measure is plotted against a null distribution of spatially permuted values in which 1 of the 2 spherical projections is randomly rotated and its cross-correlation subsequently calculated; 1000 permutations were used to generate the null distribution. Using this method, we compared pairwise combinations of mean SULC, mean CURV, SULC, and CURV. We also used spin tests to compare our cortical folding heritability to 2 maps of cortical expansion described by Hill et al. (Hill et al. 2010; Reardon et al. 2018; Schmitt, Neale, et al. 2019a). These maps estimate regional variability in primate evolutionary expansion (EVO) based on macaque and human subjects, and typical human neurodevelopmental expansion (DEVO) based on 12 healthy term infants compared with 12 healthy young adult controls.

Relationships with Cognition

Finally, we investigated the relationships between cognition and cortical folding patterns. Cognition was assessed via the NIH Toolbox’s “Total Cognition” composite score (NTC); this score correlates highly (r = 0.95) with traditional constructs of cognition in adults (Heaton et al. 2014) and is heritable in the HCP dataset (Schmitt, Raznahan, Clasen, et al. 2019b). In these bivariate models, NTC remained fixed to a scalar value for each subject, but average convexity was iterated at every vertex over the cerebrum. CURV-NTC covariances were assessed similarly.

Results

Relationships to Age and Sex

Results of regression analyses on folding measures are summarized in Figure S1. Neither age  sex interactions nor nonlinear age effects were statistically significant for either folding measure. However, there were strong effects of sex on average convexity (SULC). Females generally had more positive average convexity measures over gyri and more negative measures within sulci over most of the cerebrum, suggesting deeper sulcation relative to males. A similar pattern was observed for mean curvature, although effects were not statistically significant after correction for multiple testing. For the relatively narrow age range studied, linear effects of age on average convexity were weak for both metrics, with strongest effects in perisylvian regions. Age effects on average convexity were statistically significant for only a few vertices after multiple testing correction; neither age nor sex effects were statistically significant for mean curvature.

Genetic Influences on Cortical Folding

Global average convexity (â² = 0.49 ± 95%CI [0.27–0.69], P value <0.0001) was highly heritable, with approximately half of the phenotypic variance attributable to genetic effects. Maximum likelihood estimates and probability maps from vertex-level and ROI-based univariate models are presented in Figure 1, Supplementary Figures S2–S6, and Supplementary Tables S1 and S2. The vertex heritability of average convexity (SULC) varied widely over the cerebral surface (mean â² = 0.28, SD = 0.15, range 0.00–0.78) and was highest in the parasagittal occipital lobe as well as the peri-Rolandic, peri-Sylvian, and pericallossal cortex. Heritability estimates tended to be slightly higher in sulci relative to gyri (r = −0.16; p_spin = 0.004, Supplementary Fig. S7). In these regions, genetic influences were identified for vertices within both sulci and gyri. Variance components attributable to shared and twin-specific environmental effects were generally smaller and more uniform across the cortex. The principal exception was within the insula, where there were clear familial effects (i.e., genetic and/or shared environmental effects), but the relative importance of genetic versus shared environmental influences were less certain. Unique or individual-specific variance (including measurement error) was the dominant variance component, accounting for more than half of the phenotypic variance for the majority of vertices.

Figure 1.

Brain maps for average convexity (SULC) and mean curvature (CURV) estimate the proportion of phenotypic variance owed to genetic (a²), shared environmental (c²), and unique environmental (e²) components. FDR-corrected probability maps are also provided, testing the significance of genetic (Gen), shared environmental (S. Env), or both (Fam) effects on phenotypic variance. For reference, the vertex-level mean value for each metric (μ) is also shown at the top of the figure. On the right, heritability maps are also presented as flatmaps. Additional univariate results are provided in Supplementary Figures S1–S6 and in Tables S1 and S2.

Global mean curvature also was a highly heritable phenotype (â² = 0.61 95% C [0.42–0.72], P value <0.0001). The heritability for vertex measures of mean curvature were generally lower than for average convexity (mean â² = 0.15, SD = 0.13, range 0.00–0.72), but had a similar pattern with the strongest genetic effects observed in the parasagittal occipital lobe and peri-Rolandic cortex. Similar to average convexity, increased genetic signal was regionally localized and involved vertices in both sulci and gyri. The correlation between SULC and CURV heritability maps was high and statistically significant (r = 0.72, p_spin < 0.001).

Strong Shared Genetic Influences between Average Convexity and Mean Curvature

Bivariate models identified very strong relationships between average convexity and mean curvature (Fig. 2). When vertices were considered as separate data points, there was a strong correlation between the mean values of SULC and CURV (r = 0.86, p_spin < 0.0001). Genetic correlations between the 2 measures were exceedingly high throughout the brain. The contribution of genetic factors to the phenotypic covariance was substantial, particularly in the perisagittal occipital lobe, frontal operculum, insula, and within the central sulcus. Genetic covariance was statistically significant throughout most of the brain, with the exception of regions of the inferior parietal lobes, anterior cingulate, dorsolateral frontal cortex, and middle temporal gyrus. Covariance associated with environmental factors was also very high and statistically significant throughout the entire cerebrum. Because of the strong similarities between folding measures, subsequent analyses on mean curvature are presented as supplementary data.

Figure 2.

Bivariate relationships between average convexity (SULC) and mean curvature (CURV). On left, brain maps display mean values for each metric, with a scatterplot showing the relationship between means at the vertex level. On the top right, regional variability in phenotypic (r^P), genetic (r^G), and environmental (r^E) correlations are shown. As an alternative metric of the results from variance decomposition, the proportion of the phenotypic variance attributable to genetic (pcor) and environmental (ecor) variance is shown. At bottom, FDR-corrected probability maps for genetic (p_A) and environmental (p_E) covariance are provided.

Phenotypic Correlations with Other Structural Metrics

The phenotypic relationships between our principle vertex metrics (SULC, CURV) and common structural brain measures (CT, SA, and CM) are summarized in Figures 3 and S8. Correlations between CT and both SULC and CURV were generally positive for most vertices, suggesting that the cerebral cortex is, on average, thicker in gyri relative to sulci. Correlations were particularly strong in the supramarginal gyrus and superior and middle temporal gyri bilaterally. There were notable exceptions, with negative correlations in insular and parasagittal occipital cortex. Correlational patterns appeared to be largely independent of mean CT; for example, insular cortex is among the thickest in the human brain, and primary visual cortex is relatively thin. SULC-CT phenotypic correlations were statistically significant for the majority of the brain and involved both sulcal and gyral vertices; regions near the gyral-sulcal boundaries (i.e., where average convexity approximated zero) did not reach statistical significance. Overall, the correlational patterns between CURV and CT were very similar, although the strength of the correlations were somewhat weaker compared with SULC-CT.

Figure 3.

Phenotypic correlations between average convexity (SULC) and common structural brain metrics of cortical thickness (CT), surface area (SA) and cortical myelination (CM). The corresponding FDR-corrected P values testing significance of the correlation (H₀: r = 0) are also provided below. Probability maps are color coded based on whether the corresponding mean value of the folding measure is positive or negative at that vertex.

Correlations between SULC and SA were largely positive, indicating that gyral regions tend to be associated with increased area. The associations were overall weaker and more uniform compared with SULC-CT. Nevertheless, statistically significant relationships between these measures were observed for the majority of the cerebral surface, regardless of whether vertices were (on average) within gyri or sulci. Correlational patterns were similar between CURV and SA, as were the associated probability maps.

The relationships between cortical folding and myelination were very different to those for thickness and SA. Phenotypic correlations were negative between CM and both SULC and CURV, particularly in the lateral posterior cerebrum near the parietotemporal junction (i.e., more myelinated regions tended to be in sulci). The principal exception was along the inferior temporal lobe including parahippocampal and lingual gyri where there were strong and statistically significant positive correlations. Similar patterns were observed between CURV and CM.

The observed phenotypic correlations with all structural measures were primarily driven by environmental effects (Supplementary Fig. S9). Environmental correlations largely followed the phenotypic correlation maps. Relatively low correlations with CT were observed at transition points between gyri and sulci. Correlations with SA were more uniform and generally weaker. Distinct correlational patterns with CM were observed, with generally negative, posterior-predominant environmental correlations.

Shared Genetic Influences between Cortical Folding and Other Structural Measures

Results from genetic variance decomposition are provided in Figures 4 and S10. In general, there were moderate genetic correlations between average convexity and structural measures. Genetic correlations between average convexity and CT were largely positive and strongest in the lateral temporal and inferior parietal cortex; primary visual cortex had strong negative genetic correlations. Genetic correlations with SA also were also generally positive and strongest in peri-Sylvian and pericalcarine regions. Similar to phenotypic relationships, genetic correlations between average convexity and CM were mostly negative, with the exception of the inferior temporal lobes. Similar patterns were seen for bivariate models between mean convexity and other measures.

Figure 4.

Shared genetic relationships between average convexity (SULC) and cortical thickness (CT), surface area (SA) and cortical myelination (CM). Genetic correlations (r^G), the proportion of phenotypic variance attributable to the genetic factors (pcor), and FDR-corrected probability maps testing the significance of vertex-level genetic covariance (p_A) are shown. Probability maps are color coded based on whether the mean value at that vertex was positive (red) or negative (blue).

Although genetic correlations between cortical folding and thickness, SA or myelination were reasonably high (>0.7) over most of the brain, estimates of the genetic contributions to the phenotypic covariance (pcor) were lower than those for environmental effects for both folding measures. In other words, although there was reasonable genetic correlation between measures, the relative contributions of genetic factors to phenotypic covariance were small. This was particularly true for mean convexity, where the genetic contributions to covariation were weak throughout the cerebrum. There was substantial regional variation in the relative strength of pcor for models including average convexity. After correction for multiple testing, statistically significant genetic covariance was confined to a relatively small number of vertices, primarily in the peri-Sylvian cortex, inferior peri-Rolandic cortex, and medial occipital lobe.

Relationships to Evolutionary and Neurodevelopmental Expansion

Both cortical folding heritability maps subjectively resembled the inverse of those for evolutionary and neurodevelopmental expansion (Hill et al. 2010). In order to test this observation objectively, we performed post hoc spin tests between â² and these maps (Fig. S11). Heritability maps for both average convexity and mean curvature were significantly anticorrelated with neurodevelopmental expansion (r < = −0.30; p_spin < 0.0001). Similar weak negative correlations were observed for evolutionary expansion, although only mean convexity reached statistical significance (r = −0.28; p_spin = 0.007).

Relationships to Cognition

Phenotypic correlations between total cognition and both folding measures were weak and not statistically significant. Genetic correlations were stronger and most pronounced in the temporal lobes, orbitofrontal cortex, and cingulate (Fig. S12). Correlations tended to be positive in gyri and negative in sulci. However, most genetic correlations were not statistically significant after correction for multiple testing. Environmentally mediated correlations were very week and none reached statistical significance.

Discussion

The complex convolutions of the human cerebral cortex represent one of its most defining characteristics, yet the mechanisms responsible for its gyrencephalic morphology remain largely enigmatic. There is strong evidence that genetic mutations are responsible for several pathological abnormalities in cortical folding via disruptions in neuronal migration or cortical organization (Guerrini et al. 2008; Barkovich et al. 2012). For example, mutations in several genes (e.g., LIS1, ARX, DCX, and RELN) have well-established roles in the development of lissensephaly; specific gene mutations have also been associated with polymicrogyria and pachygyria (Guerrini et al. 2008). Aberrant gyrification has also been found in neurogenetic syndromes with distinct subchromosal copy number variations (Schmitt et al. 2002; Gaser et al. 2006; Schaer et al. 2006, 2008). However, the importance of genetic factors on individual differences in gyrification within typically-developing populations is much less well-established.

The current analysis finds that average convexity is most heritable near primary sulci and fissures. These sulci form earlier relative to secondary and tertiary sulci, both on evolutionarily and neurodevelopmental timescales (Armstrong et al. 1995). We observed similar heritability patterns for mean curvature, although they generally were weaker compared with average convexity. Given that mean curvature better isolates higher order sulci (Destrieux et al. 2010), the overall lower heritability of this measure may also support the hypothesis that genetic factors are dominant in patterning the major sulci and fissures of the human brain, whereas individual-specific environmental factors predominate in explaining the variation of smaller gyri and sulci that form later in development. It is noteworthy that we found strong genetic correlations between these 2 metrics, although environmental influences were dominant in explaining the phenotypic covariation between them. Heritability patterns for folding metrics were distinct compared with prior estimates for CT, SA, and myelination (Schmitt, Raznahan, Liu, et al. 2019c), suggesting that familial similarities in brain shape are not driving the observed heritability of these endophenotypes. Similar to studies on other structural measures, we found little evidence of shared environmental influences on cortical folding. In contrast, individual-specific environmental factors explained the majority of variation in most regions, noting that this may be in part owed to measurement error, particularly at the vertex level.

Despite numerous methodological differences in image processing, our findings are generally consistent with prior studies investigating the genetics of typical human gyrification (Lohmann 1999; Potkin et al. 2009; Im, Pienaar, et al. 2011b; McKay et al. 2013, 2015; Le Guen et al. 2017, 2018; Pizzagalli et al. 2019). For example, focusing on the central sulcus, McKay et al. (2013). measured its depth in a genetically informative adult sample (N = 467). They found that central sulcal depth was not only significantly heritable, but there was regional variability; strongest genetic effects were observed near hand and oral motor regions. Lohmann (1999) measured sulcal patterns in 19 MZ twin pairs and found increased similarity to one’s cotwin relative to unrelated individuals. Using HCP’s S900 sample and quantitative genetic modeling, Le Guen et al. (2018), systematically classified sulcal pits into small regions of interest, finding evidence of significant genetic effects in central, cingulate, superior temporal, occipitotemporal, parietooccipital, and collateral areas. Using a graph theory approach in a sample of 48 MZ twins, Im et al. (2011b) found that networks of sulcal pits were more similar between twin pairs than between unrelated subjects. A recent study combining data from HCP, the Queensland Twin Imaging Study, the Genetics of Brain Structure and Function study, and the UK Biobank (with over 30 000 total participants) examined ROI-level measures of sulcal width, length, depth, and SA. This study found that regions of interest near areas of early brain development (e.g., central sulcus, Sylvian fissure, superior temporal sulcus, and parietooccipital sulci) were the most heritable for sulcal metrics (Pizzagalli et al. 2019). The current study differs from these prior studies in its use of somewhat different folding metrics measured at high-resolution over the entire cortical sheet (i.e., within both in gyri and sulci). Given these methodological differences, the current study presents complimentary evidence that genetic influences on shape are strongest in these regions.

Gyrification is largely a neurodevelopmental process, with the vast majority of cortical folding occurring prior to birth (White et al. 2010; Fernández et al. 2016). In humans, gyrification begins at 10–15 weeks of life and peaks during the period of rapid cerebral growth during the third trimester (White et al. 2010). Cortical folding can first be identified in occipital, parietal, and superior temporal regions before becoming apparent elsewhere later during development (Zilles et al. 2013). Numerous hypotheses have been proposed to explain the emergence of cortical folds early in ontogeny, broadly classified into genetic, activity-dependent, and mechanical processes (Foubet et al. 2019). In 1874, His (1874) suggested that differential growth rates between brain regions (and the subsequent tension produced) could explain the observed sulcal patterns. Regional variability in folding may be owed to the initial geometry prior to gyrification (Tallinen et al. 2016). Regional differences in cellular proliferation within the outer subventricular zone prior to gyrification may also play a critical role (Reillo et al. 2011; Rash et al. 2019). Differential cortical expansion has emerged as a leading theory, although in its simplest form it would not explain the observed consistency of within-species gyral/sulcal patterns. A recent study by Garcia et al. (2018b) found that in the third trimester (from 36 to 40 weeks of gestation), the regions of most active cortical folding mirror regions of fastest cortical expansion; regionally variable cortical expansion could potentially help explain species-specific gyral patterns. The regions of the brain with the lowest rates of folding during the third trimester largely corresponded to primary sulci and are the most heritable regions in the current study. We additionally find significant anticorrelations between maps of neurodevelopmental expansion and the heritability of cortical folds. These findings provide further evidence of distinct mechanisms for the formation of primary sulci and fissures versus higher order sulci, with individual differences in the latter largely determined via nongenetic influences.

We observed pronounced gender effects on cortical folding. In general, females tended to have higher values for both metrics over gyri, and lower values in sulci; gender differences in average convexity were highly significant. These observed gender differences may be owed to relatively deeper sulci in females relative to males. The extant literature on gender differences in gyrification is both sparse and conflicting (Zilles et al. 1988; Nopoulos et al. 2000; Luders et al. 2004; Luders, Narr, et al. 2006a). However, Luders et al. (2004) found that in a healthy young adult sample (N = 60), females had significantly higher gyral complexity in superior frontal and parietal regions compared with males. Using the same sample, Luders et al. (2006b) subsequently examined mean curvature at a comparable level of spatial resolution to the current study and found increased gyrification in females, particularly anterior frontal lobes, posterior temporal lobes, and lateral occipital lobes. We find somewhat similar patterns, although with much more regional variability; differences may be in part owed to differing smoothing kernels (5 mm vs. 25 mm). The etiology of observed differences in folding is uncertain, but may be due gender-specific differences in regional brain growth (Geschwind and Galaburda 1985; Luders, Thompson, et al. 2006b).

We also identified reasonably strong phenotypic correlations between several common structural metrics and cerebral shape. There were generally positive correlations between folding measures and CT; this finding is concordant with prior cytoarchitectural (von Economo 1929; Welker 1990; Hilgetag and Barbas 2005) and neuroimaging (Fischl and Dale 2000; Vandekar et al. 2015) studies. Increases in both thickness and SA are associated with increased gyrification both across and within species (Mota and Herculano-Houzel 2015), although CT more strongly scales with within-species folding, whereas cross-species associations tend to be stronger with areal expansion (Zilles et al. 2013). Regardless of underling cause, the observed phenotypic correlations serve as a reminder of the collinearity of many structural brain measures, and the subsequent difficulties in inferring causality.

We also performed a systematic comparison of shape and CM patterns. We found strong regionally specific negative correlations with average convexity (e.g., gyri are less myelinated), with the exception of the inferior occipitotemporal regions where gyral cortex was more myelinated than that in sulci. In general, cerebral gyrification precedes myelination (Neal et al. 2007), although asserting a direct causal link based on the available data would be speculative. Since these results only report correlations, it is possible that shape merely represents is an indirect proxy for a different correlated metric (e.g., thickness). The precise etiology for these regional variations in myelination remains unknown, and warrants further investigation.

The contribution of genetic factors to phenotypic covariance between SULC/CURV and CT, SA, or CM was relatively small. Genetic covariances were largely nonsignificant. We did observe moderate genetic correlations for most pairs of measures throughout most of the brain, but these were largely due to low genetic variances. In other words, the genetic correlations between measures were reasonably high, but their importance in explaining phenotypic covariation was low. Alexander-Bloch et al. (2020) identified strong colocalization between the genetic influences on CT and sulcal patterns, suggesting that genetic influences may mediate gyrification through cortical development. In a prior study, we found that the pairwise genetic contributions to covariance between CT, SA, and CM themselves is relatively small (Schmitt, Raznahan, Liu, et al. 2019c), and similar genetic independence between CT and SA has been reported by the VETSA study (Panizzon et al. 2009). The current results do suggest that heritability maps of surface-based structural neuroimaging measures (e.g., thickness) are largely independent of familial similarities in cerebral shape (e.g., metrics used for subject coregistration). The principal exceptions localized to peri-Sylvian and calcarine cortex, where there was evidence that average convexity shares genetic factors with both CT and SA.

Finally, we found relatively weak associations between local folding metrics and global measures of cognition, with the strongest genetically mediated associations in the lateral temporal lobe, cingulate, and orbitofrontal cortex. The relationships between cortical gyrification and cognition in humans remains an area of active investigation, with mixed results to date (Fornito et al. 2004; Gautam et al. 2015; Gregory et al. 2016; Chung et al. 2017; Lamballais et al. 2020). The extant literature suggests that cognition is correlated with local gyral complexity in large regions of neocortex (specifically frontal, parietal, temporal, and cingulate cortex) in both pediatric and adult samples (Gregory et al. 2016). Global measures of gyrification are highly heritable, but do not share common genes with general cognitive ability (Docherty et al. 2015).

However, it is noteworthy that measures of gyral complexity represent a distinct (albeit related) phenotype to the cortical folding measures reported here. Investigations using similar metrics to the current study are more limited. Im et al. (2011a) found an increase likelihood of sulcal pits near language centers in individuals with higher intelligence. Luders et al. (2008) reported relatively weak associations between full scale IQ and mean curvature, with only a region of retrosplenial cingulate remaining statistically significant following multiple testing correction. Yang et al. (2013) found that in 78 typically developing subjects, there were weak but statistically significant associations between full scale IQ and both sulcal depth and mean curvature in peri-Rolandic operculum, supramarginal sulci, calcarine sulcus, and orbitofrontal sulci. We find somewhat similar patterns; our analyses additionally suggest that these weak associations are largely genetically mediated.

Our findings should be considered in light of certain caveats and study limitations. First, interindividual differences in sulcal typology (Ono et al. 1990) and presence/absence of smaller more variable tertiary sulci places a regionally variable limit on the possibility for perfect coregistration of the cortical sheet across individuals. Although our study attempts to better-understand the influences of cortical folding on other automated structural brain measures, it also is inexorably dependent on registration algorithms in order to generate its own spatially localized metrics. However, given that we observed that folding measures correlate within families, the current study does suggest an underlying biological basis for these relationships. Minimization of this technical challenge awaits development of new approaches to coregistration of cortical surfaces that are capable of incorporating information from fine-grained sulcal labeling and typology classification, while seeking to optimize vertex-to-vertex correspondence across individuals. Second, it is important to note that our analyses focus on genetically mediated individual differences rather than the genetics of cortical folding in their entirety; genetic effects that do not influence population variation would be undetectable with these methods. Third, when comparing brain regions, relatively uniform measurement errors are assumed, but this was not tested empirically. Fourth, the current study does not address questions regarding potential time-varying relationships of sulcal depth and average convexity with CT, SA and CM which will be an important area for future work. Finally, we have previously also reported variable and spatially patterned interrelationships between structural measures (Schmitt, Raznahan, Liu, et al. 2019c) and these data, together with our current study underlines the need for extended study designs that systematically probe a full series of possible pairwise intermetric relationships.

Notwithstanding these caveats and important areas for future work, the findings reported herein shed further light on relative contribution of genetic and environmental factors to variability in local measures of cortical folding and relationships between this fundamental property of the human cortical sheet and other anatomical metrics.

Notes

Conflict of Interest: None declared.

Funding

National Institute of Mental Health (grant MH-20030) and Big Data to Knowledge (BD2K) (grant K01-ES026840). Intramural program of the National Institutes of Health (Clinical trial NCT00001246, clinicaltrials.gov; NIH Annual Report Number, 1ZIAMH002949-03 to A.R. and S.L.). Data were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.