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The regional variation of laminar thickness in the human isocortex is related to cortical hierarchy and interregional connectivity [1]

['Amin Saberi', 'Otto Hahn Research Group For Cognitive Neurogenetics', 'Max Planck Institute For Human Cognitive', 'Brain Sciences', 'Leipzig', 'Institute Of Neurosciences', 'Medicine', 'Research Centre Jülich', 'Jülich', 'Institute Of Systems Neuroscience']

Date: 2023-11

The human isocortex consists of tangentially organized layers with unique cytoarchitectural properties. These layers show spatial variations in thickness and cytoarchitecture across the neocortex, which is thought to support function through enabling targeted corticocortical connections. Here, leveraging maps of the 6 cortical layers based on 3D human brain histology, we aimed to quantitatively characterize the systematic covariation of laminar structure in the cortex and its functional consequences. After correcting for the effect of cortical curvature, we identified a spatial pattern of changes in laminar thickness covariance from lateral frontal to posterior occipital regions, which differentiated the dominance of infra- versus supragranular layer thickness. Corresponding to the laminar regularities of cortical connections along cortical hierarchy, the infragranular-dominant pattern of laminar thickness was associated with higher hierarchical positions of regions, mapped based on resting-state effective connectivity in humans and tract-tracing of structural connections in macaques. Moreover, we show that regions with similar laminar thickness patterns have a higher likelihood of structural connections and strength of functional connections. In sum, here, we characterize the organization of laminar thickness in the human isocortex and its association with cortico-cortical connectivity, illustrating how laminar organization may provide a foundational principle of cortical function.

Funding: This work was funded in part by Helmholtz Association’s Initiative and Networking Fund under the Helmholtz International Lab grant agreement InterLabs-0015, and the Canada First Research Excellence Fund (CFREF Competition 2, 2015–2016) awarded to the Healthy Brains, Healthy Lives initiative at McGill University, through the Helmholtz International BigBrain Analytics and Learning Laboratory (HIBALL), supporting A.S., C.P., S.B.E., B.C.B. and S.L.V. S.L.V. and A.S. were additionally funded by the Max Planck Society (Otto Hahn award). K.W. was supported by the Wellcome Trust (215901/Z/19/Z). M.D.H. was funded by the German Federal Ministry of Education and Research (BMBF) and the Max Planck Society. B.C.B. acknowledges support from the SickKids Foundation (NI17-039), the National Sciences and Engineering Research Council of Canada (NSERC; Discovery-1304413), CIHR (FDN-154298), Azrieli Center for Autism Research (ACAR), an MNI-Cambridge collaboration grant, and the Canada Research Chairs program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Data Availability: All the code and data for this study are openly available at a Github repository ( https://github.com/amnsbr/laminar_organization ) which is archived in Zenodo ( https://zenodo.org/record/8410965 ). Our code, data and computing environment are published in a Docker image ( https://hub.docker.com/r/amnsbr/laminar_organization ), which can be used to reproduce our results and to perform additional analyses on the BigBrain data without having to install dependencies. The analyses in this project were performed predominantly using Python (version 3.9). BigBrain maps of cortical layers are available at https://ftp.bigbrainproject.org/ . Other data used were either openly available online or acquired by contacting the authors and can be accessed in the project Github repository and Docker image. We refer the reader to the text and the project Github repository for the description and source of this data.

Here, we aimed to study the organization of laminar profiles across the cortical mantle and its relevance to cortical hierarchy and interregional connectivity to further understand the relationship between human intracortical structure and function. To do so, we leveraged previously reported maps of the locations of cortical layers across isocortical regions of the BigBrain that were predicted using a convolutional neural network [ 42 ]. We extend previous work investigating the spatial arrangement of cortical profiles based on microstructure [ 10 ], through formally probing layer-profiles in this model, and describe a data-driven axis of laminar thickness covariance by quantifying the interregional covariation of laminar thickness in the BigBrain [ 9 , 42 ]. To do so, we employ dimensionality reduction techniques to identify the principal axis along which laminar thickness covaries. We next evaluate how laminar thickness covariation relates to hierarchical positioning of cortical regions based on resting-state effective connectivity in humans and anatomical layer-wise connections in macaques. We then investigate whether similarity of laminar structure relates to the likelihood and strength of structural and functional interregional connections and, last, explore its links to interregional structural covariance and maturational coupling.

The laminar pattern and likelihood of cortico-cortical connections are suggested to relate to the interregional variation of cortical cytoarchitecture [ 3 , 17 , 18 ]. Connectivity is shown to be more likely between regions with similar cytoarchitecture [ 19 – 24 ]. In addition, the gradation of cytoarchitecture is suggested to predict the laminar pattern of cortico-cortical connections [ 3 , 17 , 18 , 25 , 26 ], categorized as "feedback" (FB), "feedforward" (FF), or "lateral" based on tract-tracing data [ 27 – 29 ]. These laminar projections have, in turn, been used to describe an ordering of regions along a cortical hierarchy, in which FF projections are suggested to carry high-dimensional sensory information from lower to higher regions and are reciprocated by FB projections transmitting context and modulatory signals from higher to lower regions [ 29 , 30 ]. Recently, it was shown that a marker of cortical myelination (T1/T2w) was associated with the map of laminar-based hierarchy [ 27 ]. Together with findings on the association of cortical cytoarchitecture and laminar projections [ 3 , 17 , 25 , 26 ], this suggests a potential link between cortical microstructure and hierarchy. Yet, it is unclear how laminar thickness may scaffold connections within the cortical hierarchy. Notably, in neuroscience, the term "hierarchy" has been used to describe different phenomena [ 31 ], such as gradients of structural and functional features [ 27 , 32 ], topological sequence of connections [ 33 ], asymmetry of directional connections indicating interregional control or dominance [ 34 , 35 ], or, as described above, the sorting of laminar projection patterns and their physiological correlates [ 28 , 29 , 36 – 41 ]. Throughout this paper, we will focus on the latter 2 definitions of hierarchy, that is, laminar-based and asymmetry-based hierarchy.

Quantitative studies of cortical profiles have helped improve our understanding of cytoarchitectural variability of the human cerebral cortex. However, the cerebral cortex is a layered structure, and models of cortical profiles are, at least explicitly, agnostic to cortical layering. The layers in the neocortex are generally described as 6 horizontally superimposed stripes of gray matter with characteristic features such as size, type, and density of the neurons, which can again be differentiated into multiple sublayers [ 1 , 4 ]. From the pial to the gray-white matter interface, they include layer I, which contains mostly dendrites and axon terminals and has a low cellular density; layers II and III, which mainly contain pyramidal cells, with a size gradient in neurons of layer III that become larger towards its lower extent; layer IV, which consists of densely packed small pyramidal and non-pyramidal neurons; layer V, which is composed of pyramidal neurons that are small and intratelencephalic (layer Va) or large and sparse (layer Vb); and layer VI with corticothalamic pyramidal cells and heterogeneously shaped neurons [ 2 , 4 , 12 , 13 ]. One of the prominent cytoarchitectural features that vary across the cerebral cortex is its laminar structure, with respect to laminar thickness, as well as neuronal size and density of each layer. Indeed, laminar features have been an important focus of many qualitative studies of human cytoarchitectural variation [ 3 , 4 , 14 ]. For example, agranular and dysgranular cortical types are defined based on the absence or thinness of layer IV, relative to eulaminate and koniocortical regions [ 4 , 14 ]. However, studies on quantitative analysis of cortical cytoarchitecture with respect to its laminar features in humans are limited. Yet, understanding layered organization of the human neocortex may provide further insights into how intracortical circuits ultimately support function [ 15 , 16 ].

Cortical cytoarchitecture, that is, the organization and characteristics of neurons across the depth of the cerebral cortex, varies markedly across the cortical mantle [ 1 – 4 ]. Characterizing this variation has been an important focus of histological studies over the past century. Early studies were largely based on visual inspection and qualitative descriptions of cytoarchitectural features across the cerebral cortex to identify local borders between regions [ 2 ] or to describe more global cytoarchitectural variations [ 4 , 5 ]. With methodological advances of recent decades, there has been a shift towards more quantitative investigations of cortical cytoarchitecture based on statistical analysis on 2D histological sections [ 6 – 8 ]. The central idea of these studies has been to quantify the variation of cell body–stained image intensity across the cortical depth, i.e., "cortical profile." This is followed by observer-independent analysis of how cortical profiles vary across the cerebral cortex and define borders of regions, particularly with respect to the central moments, i.e., mean, standard deviation, kurtosis, and skewness [ 1 , 6 , 7 ]. The release of BigBrain, a whole-brain ultrahigh-resolution postmortem histological atlas of a 65-year-old male [ 9 ], enables such quantitative investigations at a much larger scale, for example, to quantify large-scale microstructural gradients at a neocortical [ 10 ] and mesiotemporal level [ 11 ].

Thus far, we described how the laminar structure varies across the isocortex and evaluated its relevance to cortical hierarchy and connectivity. Lastly, we sought to study potential links of individual-level LTC to population-level interregional covariance and maturational coupling of cortical thickness. Structural covariance matrix reflects the pattern of covariation in cortical morphology (e.g., cortical thickness) across a population, which provides a model of shared maturational and genetic effects between cortical regions [ 60 – 62 ]. We obtained the structural covariance matrix based on the HCP dataset (N = 1,113) from our previous work [ 62 ] and observed that it was significantly correlated with the LTC at the level of matrices (r = 0.33, p spin < 0.001) and their principal axes (r = -0.57, p variogram < 0.001). This may indicate shared maturational and genetic effects between regions with similar laminar thickness ( S16A Fig ). Next, we studied the association of LTC with the interregional maturational coupling matrix (MCM), obtained from a previous study by Khundrakpam and colleagues [ 61 ]. This matrix shows the similarity of regions in longitudinal cortical thickness changes over development in a dataset of children and adolescents (N = 140, baseline age = 11.9 ± 3.6, followed up for approximately 2 years) and was weakly correlated with the LTC matrix (r = 0.10, p spin < 0.001) ( S17 Fig ).

Having observed alignment of asymmetry- and laminar-based hierarchy with laminar thickness variation, we next studied whether the similarity of regions in laminar thickness relates to interregional connectivity in humans ( Fig 4 ). We used the structural and functional connectivity (SC and FC) matrices (400 regions) averaged across a subgroup of the HCP dataset (N = 207) [ 52 , 54 ], which was obtained from the ENIGMA (Enhancing NeuroImaging Genetics through Meta-Analysis) Toolbox [ 55 ]. Using logistic regression, we observed higher LTC was associated with the increased likelihood of SC (R 2 = 0.082, p spin < 0.00). In addition, LTC was correlated with the increased strength of FC (r = 0.15, p spin < 0.001). Neighboring regions in the cerebral cortex are more likely to connect [ 56 , 57 ] and also tend to have similar structural and functional features [ 58 , 59 ]. Here, we also observed this effect, with physically proximal regions showing higher likelihood of SC (R 2 = 0.400, p spin < 0.001) and strength of FC (R 2 = 0.150, p spin < 0.001) on one hand, and higher LTC (R 2 = 0.164, p spin < 0.001) on the other hand. To understand whether LTC was associated with connectivity independent of distance effects, we studied the association of LTC with long-range connectivity. We observed that LTC was not significantly associated with the likelihood of long-range SC (R 2 = 0.006, p spin = 0.310) or strength of long-range FC (r = 0.023, p spin = 0.331). This finding suggested interregional distance as an important covariate in the association of LTC with connectivity.

In addition, we obtained the laminar-based hierarchy map of the macaque cerebral cortex from a previous study [ 27 ]. Laminar-based hierarchy assumes higher hierarchical positions for regions projecting FB and receiving FF connections, as quantified in tract-tracing studies [ 28 , 29 ]. After aligning the LTC G1 map of the human cerebral cortex to the macaque’s cerebral cortex in the left hemisphere [ 53 ], we observed that it was significantly correlated with the map of macaque’s laminar-based hierarchy (r = −0.54, p variogram < 0.001; Fig 3C ). In addition, the laminar-based hierarchy showed significant positive correlations with the relative thickness of layers III and IV, and negative correlations with the relative thickness of layers V and VI ( S13 Fig ). These findings indicated association of laminar thickness variation to 2 alternative maps of cortical hierarchy based on the asymmetry of effective functional connectivity and the laminar pattern of structural connections.

Asymmetry-based hierarchy was defined based on the group-averaged effective (directed) connectivity of cortical regions based on resting-state fMRI. The effective connectivity matrix ( Fig 3A ) shows the influence of each brain region on the activity of other regions during resting state, and was previously estimated using regression dynamical causal modelling (rDCM), based on the data from 40 healthy adults [ 48 – 51 ]. Using the effective connectivity matrix, we calculated the asymmetry-based hierarchy of each region as the difference between its weighted out-degree (efferent strength) and in-degree (afferent strength). The asymmetry-based hierarchy map was significantly correlated with LTC G1 (r = −0.40, p variogram < 0.001), indicating higher asymmetry-based hierarchy of infragranular-dominant regions ( Fig 3B ). Accordingly, the asymmetry-based hierarchy map was significantly correlated with the relative thickness of layers III and IV negatively, and layers V and VI positively ( S13 Fig ). Of note, decomposing the asymmetry-based hierarchy into its components, we observed a significant correlation of LTC G1 with the weighted in-degree (r = 0.61, p variogram < 0.001) but not out-degree (r = −0.01, p variogram = 0.868) ( S14 Fig ). The asymmetry-based hierarchy map of a replication sample from the Human Connectome Project (HCP) dataset (N = 100) [ 50 , 52 ] was similarly correlated with LTC G1 (r = −0.49, p variogram < 0.001; S15 Fig ). Note that for the above analyses, we recalculated LTC and LTC G1 in the Schaefer-400 parcellation, as the effective connectivity matrices obtained from the previous work by Paquola and colleagues [ 50 ] were available in this parcellation.

Microstructural profile covariance (MPC) is based on the image intensity profiles in the BigBrain cerebral cortex, reflecting variation of grey-matter density across cortical depth, and is a data-driven model of cytoarchitecture that is explicitly agnostic to layer boundaries [ 10 ]. MPC was significantly correlated with our model of laminar thickness covariation, at the level of matrices (r = 0.34, p spin < 0.001) and their principal axes (r = 0.55, p variogram < 0.001) ( S10 Fig ). Extending this approach to the individual layers, we calculated layer-wise intensity profiles of the BigBrain cerebral cortex as the image intensity sampled at 10 equivolumetric surfaces across each layer’s depth, which we then averaged across the samples. Next, we calculated laminar intensity covariance (LIC) and applied principal component analysis on the fused matrices of LTC and LIC, as a model of laminar structure covariation that took both laminar thickness and laminar grey-matter density into account. The principal axis of the laminar thickness and intensity covariance (LTIC G1) was significantly correlated with LTC G1 and showed a similar pattern (r = 0.84, p variogram < 0.001) ( Fig 2A ). Along the LTIC G1, from rostral to caudal regions, we observed significantly increased grey-matter density of all the layers with layer IV showing the strongest effect (r = 0.74, p variogram < 0.001) ( Fig 2B ). The image intensity in the cell body–stained BigBrain atlas reflects an aggregate of neuronal size and density, and at a resolution of 20 μm, as individual neurons cannot be readily distinguished, these components cannot be disentangled. To further explore variations of neuronal size and density separately, we leveraged on a preliminary dataset of layer-wise neuron segmentations based on higher-resolution (1 μm) 2D patches from selected cortical regions of the BigBrain ( S11A Fig ). We observed variation of laminar neuronal features along LTIC G1, which was most prominent in layer IV, showing increase of neuronal density (rho = 0.57, p < 0.001) and decrease of neuronal size (rho = −0.62, p < 0.001) ( Fig 2C ). In addition, the ratio of average neuronal size in layer III to layer V, as a proxy for externopyramidization, was increased along LTIC G1 (rho = 0.27, p = 0.01; Fig 2D ). Last, we compared our data-driven model of laminar thickness covariation with the map of cortical types, a theory-driven model of laminar structural variation [ 14 ], and observed no significant association of the maps (F = 6.41, p spin = 0.633) but significantly higher within- than between-type average LTC in koniocortex ( S12 Fig ).

The spatial map of LTC G1 was mostly robust to analytical choices, i.e., using unparcelled data (17,386 vertices) as well as alternative parcellation schemes, covariance metrics, dimensionality reduction techniques, sparsity ratios, and the inclusion of a-/dysgranular regions ( S4 Fig ). In addition, evaluating the left and right hemispheres separately, we observed high similarity of hemisphere-specific LTC G1 maps (r = 0.74, p variogram < 0.001; S5 Fig ). While LTC was higher between physically proximal regions in an exponential regression model (R 2 = 0.16, p spin < 0.001), the spatial map of LTC G1 was robust to the effects of geodesic distance (r = 0.97, p variogram < 0.001) ( S6 Fig ). We also showed that LTC G1 created based on a 3-layer model with supragranular, granular, and infragranular layers was similar to the original 6-layer model ( S7 Fig ). Moreover, as an alternative data-driven approach of quantifying organization of laminar thickness variability, we used K-means clustering, which revealed 4 optimal clusters of the regional laminar thickness profiles that were largely aligned with the LTC G1 (F = 813.1, p spin < 0.001) ( S8 Fig ).

Principal component analysis was then applied to the LTC matrix to identify the axes or gradients along which differences in the loadings indicates regional dissimilarity in the laminar thickness pattern [ 47 ]. Here, we focused on the principal axis, LTC G1, which explained approximately 28.1% of the variance in LTC (see the second and third axes in S3 Fig ). LTC G1 spanned from the lateral frontal regions, towards medial frontal, temporal, and primary visual areas, ending in the parietal and occipital regions ( Fig 1E ). This axis was correlated with the relative thickness of layers II (r = 0.42, p variogram < 0.001), III (r = 0.73, p variogram < 0.001), and IV (r = 0.16, p variogram < 0.001) positively, and layers V (r = -0.35, p variogram < 0.001) and VI (r = -0.82, p variogram < 0.001) negatively, characterizing a shift from the dominance of infra- to supragranular layers ( Fig 1G ).

(a) The laminar thickness maps based on the postmortem histological atlas of BigBrain. ( b , c ) For each cortical layer, the a-/dysgranular regions were excluded, the thickness map was smoothed using a disc, normalized by the total thickness, and parcellated. (d) The LTC matrix was created by calculating the pairwise partial correlation of relative thickness across layers and between regions. ( e) The main axis of laminar thickness covariance (LTC G1) was calculated by principal component analysis. ( f) LTC G1 reorders the LTC such that closer regions on this axis have similar LTC patterns. ( g) LTC G1 characterized a shift of infra- to supragranular dominance. The data and code needed to generate this figure can be found in https://zenodo.org/record/8410965 .

We used the maps of cortical layers based on the BigBrain, an ultrahigh-resolution postmortem histological atlas of a 65-year-old male [ 9 , 42 ], to study laminar thickness covariation across the cerebral cortex ( Fig 1A ). We first excluded agranular and dysgranular regions, such as cingulate, anterior insula, temporal pole, and parahippocampal cortices, in addition to allocortex, given their lack of a clear 6-layer structure [ 14 ]. Cortical folding impacts the laminar structure, such that layers inside of the fold are compressed and thicker, whereas layers outside of the fold are stretched and thinner [ 43 – 46 ]. Accordingly, in the BigBrain, we observed that from the sulci to the gyri, the relative thickness of superficial layers decreases (r = −0.27, p spin < 0.001) ( S1A Fig ). To reduce the local effects of curvature on laminar thickness, we smoothed laminar thickness maps using a moving disk, which reduced this effect remarkably, as the correlation of curvature with the relative thickness of superficial layers dropped to r = −0.12 (p spin < 0.001) (S1A). Following, the laminar thickness maps were normalized by the total cortical thickness at each cortical location to get the relative thickness. The maps of relative laminar thickness were then parcellated using the Schaefer-1000 parcellation ( Fig 1B and 1C ). We next calculated the laminar thickness covariance (LTC) matrix, showing the similarity of laminar thickness patterns between cortical areas. The LTC matrix was created by calculating the pairwise partial correlation of relative laminar thickness between cortical locations (controlled for the average laminar thickness across the isocortex), which was subsequently z-transformed (Figs 1D and S2 ).

Discussion

In the current study, we sought to extend previous quantitative studies on cytoarchitectural variability of the cerebral cortex [1,10], by focusing on the layered structure of the cerebral cortex, and evaluated its links to cortical connectivity. We used the map of cortical layers [42] based on the ultrahigh-resolution atlas of BigBrain [9] to identify a principal axis of laminar thickness covariation in the isocortex. We observed an axis of LTC showing a shift from the dominance of supragranular towards infragranular layers thickness from the occipital to lateral frontal areas. This shift was coaligned with the cortical hierarchy, defined based on either the asymmetry of afferent and efferent connections in the human cerebral cortex or the laminar pattern of connections in the macaque cerebral cortex. We also found a higher likelihood of structural and strength of functional connections between regions with similar patterns of laminar thickness, supporting the principle of "similar prefers similar" in cortical wiring and the structural model of connectivity [3,17,22,26]. Finally, we showed that laminar thickness covariation was linked to the population-level interregional covariance of total-depth cortical thickness, suggesting potential shared maturational and genetic effects between regions with similar laminar thickness.

The principal axis of laminar thickness covariation characterized an overall increase in the relative thickness of supragranular layers from the lateral frontal to posterior occipital regions. This was in line with a previous animal study that illustrated relative increase in the implied column height of the upper layers along the rostro-caudal axis of the cerebral cortex in several rodent and nonhuman primate species [63]. The same study also reported that from rostral to caudal regions the density of neurons increases, as had been shown in a few other studies [64–66], but additionally reported the increase to be more prominent in layers II to IV rather than layers V to VI (without differentiating the individual layers in each layer group). In an integrated model of combined laminar thickness and intensity variations, we observed a rostral to caudal principal axis, similar to LTC G1, characterizing increased grey-matter density in all the layers, most prominently in layer IV. Using a preliminary dataset of laminar neuronal features in a few cortical regions of the BigBrain and based on automated labeling of 1-μm resolution images [67], we also observed increased neuronal density and decreased soma size along the integrated axis of laminar thickness and intensity, with the most prominent association found in layer IV. In addition, we observed an increased ratio of layer III to layer V average neuronal size, which may indicate externopyramidization along this axis. Of note, our cellular-level results should be interpreted with caution as they were limited to a small number of available samples located primarily at the two ends of LTC G1. Overall, from the lateral frontal towards parietal and occipital regions, there is an increase in the prominence of the granular and supragranular cortical layers relative to the infragranular layers, with respect to thickness, and potentially neuronal density and soma size.

Previous theory-based approaches based on visual inspection of histological samples have additionally described a sensory-fugal axis of laminar structure variation transitioning from sensory to paralimbic regions [4,14]. This sensory-fugal axis, which was mapped qualitatively, is overall different from the quantitative axis of laminar thickness covariation that we described. This divergence may be attributed to the different approaches and the laminar features studied. Here, we benefited from using a data-driven approach on more extensive and denser histological data, but in doing so, we focused on the gross laminar features including thickness and the average grey-matter density. On the other hand, theory-driven maps of laminar structure such as cortical types are determined based on a variety of different laminar features [14], yet some of the finer features such as the properties of individual neurons were invisible to our model. This highlights the importance of future work on higher-resolution images of BigBrain, enabling a data-driven model of laminar structure that incorporates both gross and fine laminar features. Nevertheless, we observed that regions belonging to the same cortical type may have variable laminar thickness patterns. This may indicate differential processes underlying different features of laminar structure and, more broadly, cytoarchitecture. In fact, a previous data-driven model of MPC in the BigBrain revealed 2 main axes of cytoarchitectural variability: a rostro-caudal and a sensory-fugal axis [10]. Beyond cytoarchitecture, additional features such as myeloarchitecture and receptor architecture vary across regions and such changes may be distinct from cytoarchitectural variation of laminar structure [68]. A recent study on the large-scale variation of layer-wise receptor densities in the human cerebral cortex based on autoradiography [69] reported a "natural axis" of receptor distribution [70]. This axis spanned from association areas with higher infragranular AMPA density towards sensory areas with pronounced supragranular NMDA density as well as a higher diversity of receptor densities, which was more prominent in infragranular layers. The different axes that we highlighted here may reflect diverging neurobiological routes organizing the human cerebral cortex. Indeed, in our previous work on group-level cortical thickness covariance and genetic correlations, we observed a rostral-caudal axis, which was suggested to reflect differentiation between cortical hierarchy and maturational effect, and a ventral-dorsal axis reflecting microstructural pattern associated with the theory of dual origin [62,71].

Over the past century, there has been a debate over the optimal approach and level of granularity to study cytoarchitectural variability of the cerebral cortex [1,72]. Previous studies have ranged from focusing on fine cytoarchitectural details and identification of sharp borders between regions [2,4] to classification of the cerebral cortex into broader categories with grossly comparable cytoarchitecture [4,14]. On the other hand, some authors have argued against cortex-wide existence of sharp boundaries and rather focused on the gradual variations across the cerebral cortex [5,72]. We should note that, here, we refrained from making any assumptions on the (non)existence of sharp borders or a level of granularity as we aimed to provide a whole-cortex layer covariance organizational axis. We argue that the topology of cytoarchitectural variability of the cerebral cortex ranges from abrupt to more gradual changes [1,72]. Accordingly, the LTC G1 map consisted of a combination of sharp borders and gradual transitions but was more dominated by gradual changes. We observed the LTC G1 map was consistent regardless of whether laminar thickness data were averaged into parcels or were analyzed at the level of vertices. This highlights that LTC G1 captures broader variations of laminar thickness across regions, in contrast to the finer local and intraregional variations. Focusing on the local variations, we observed a varying level of intraregional heterogeneity of laminar thickness across regions, as quantified by the average within- versus between-regional LTC. Specifically, primary visual area and orbital parts of inferior frontal gyrus were most homogeneous structures, whereas regions in temporal and parietal lobes showed high heterogeneity of laminar thickness. Indeed, recent work is increasingly showing patterns of intraregional cortical heterogeneity such as stripes of differential myelination in V2 [73], inter-effector areas in M1 [74] or differential gene expression in V1 associated with cortical layout of eccentricity [75]. Future work may uncover the spatial pattern and nature of such intraregional heterogeneities in laminar structure and use data-driven approaches to study the organization of borders and abrupt alterations of layer thickness and associated cytoarchitecture variation.

We observed that cortical hierarchy, defined using laminar pattern of connections in macaques and asymmetry of effective connections in humans, was aligned with the main axis of LTC. This finding extends previous observations on the link between laminar-based cortical hierarchy and microstructure [18,27]. The laminar pattern of corticocortical connections is suggested to relate to the gradation of cortical microstructure (the "structural model") [3,17,25,26] or the physical proximity of regions (the "distance rule model") [28,29]. These models suggest that the laminar connections of cytoarchitecturally similar or proximal regions are mostly lateral, but the pattern of connections that become increasingly FF/FB as regions are more dissimilar in cytoarchitecture or are more distant [3,17,25,28,29,76]. Here, we observed that LTC G1 was aligned with the laminar-based hierarchy map in macaques, and asymmetry-based hierarchy map of humans. Specifically, regions towards the infragranular-dominant end of the axis were positioned higher in the cortical hierarchy than the supragranular-dominant regions. This observation potentially relates to the laminar patterns of FF and FB connections along the laminar-based hierarchy, as observed in tract-tracing studies [27–29,77]. FF connections originate from the supragranular layers II and III and target layer IV of a higher-order region, whereas FB connections originate from infragranular layers V and VI and terminate outside layer IV of a lower-order region [28,29,36,38,41], which may reciprocate FF connections [78]. In addition, lateral connections originate from supra- and infragranular layers and terminate across all the layers, connecting regions at a similar level [38]. Of note, more detailed accounts of neuronal projections have revealed additional patterns of FF and FB connections [28,29,37,39,79], such as a FB projections originating from layer II and FF projections originating from layers V and VI [28,29], or FF and lateral projections targeting layer I [37]. The FF and FB projections are thought to have distinct physiological roles, that is, FF projections carry high-dimensional (sensory) information up the hierarchy, whereas FB projections propagate context and modulate the function of lower-order regions [29,30,80]. Interestingly, the FF and FB connections are, respectively, associated with gamma and alpha/beta rhythms [29,30,40,81–83], which, in turn, show regional and laminar specificity, with more prominent gamma rhythms in early visual areas and superficial layers and beta rhythms in fronto-parietal areas and infragranular layers [29]. In fact, the asymmetry of FF and FB projections inferred based on magnetoencephalography has been previously used to map the cortical hierarchy of visual areas in humans [40]. In our comparison of LTC G1 with the laminar-based hierarchy map, we performed a cross-species comparison, yet we should note the limitations of this approach given the differences of humans and nonhuman primates in cortical cytoarchitecture [84] and connectivity [53,85]. There is some evidence based on cortical oscillations (c.f. above) and the pattern of intralaminar connectivity estimated using layer-based functional magnetic resonance imaging [86], which indicate increased FB dominance towards rostral regions in humans as well. Moreover, the human map of cortical hierarchy that we defined based on the asymmetry of effective connections showed a similar association with LTC G1 as the macaque’s laminar-based hierarchy. However, the definitions of asymmetry-based and laminar-based hierarchy are different [31] and may result in different maps, as was previously shown in the frontal cortex of macaques [35]. Layer-wise functional imaging is a promising approach that can be used to further investigate the association of laminar structure with the pattern of laminar connections and their functional implications in humans [86]. For example, recent work using layer-based functional magnetic resonance imaging could show that specific cortical layers are involved in different aspects of memory processing in the dorsolateral prefrontal cortex [87]. Such differences in cognitive processing may be rooted in the connectivity profiles associated with different layer depths that are embedded in the laminar structure.

We found that the similarity of regions in their laminar thickness patterns was associated with an increased likelihood of structural and strength of functional connections. This finding supports a principle of the structural model for connectivity that relates cytoarchitectural similarity to connectivity [3,17,20]. Our finding was in line with studies showing higher likelihood or strength of connections between regions with similar microstructure, based on the complexity of pyramidal neurons [23], neuronal density [22,24], or cortical types [19–22]. In addition, and of particular relevance to our findings, interareal connectivity in the human cerebral cortex has been linked to the MPC of the BigBrain [88–90]. Specifically, connected regions were reported to have higher similarity in their microstructural profiles compared to nonconnected profiles, and MPC correlated with the connectivity strength [90]. Furthermore, a previous study used generative modeling of connectivity and showed that including both microstructural profiles covariance and wiring cost in the model, as opposed to including wiring cost alone, leads to a better fit [88]. In addition, a low-dimensional coordinate space of the human cerebral cortex calculated by incorporating interregional SC, physical proximity, and the BigBrain’s microstructural covariance was shown to predict FC with a high accuracy [89]. In our study, we extend these findings and show that the probability and strength of connectivity additionally relates to the laminar thickness profiles in the BigBrain. Using an alternative approach, another recent study focused on the interrelation between connectivity and the absolute thickness of individual layers in the BigBrain and showed that regions with thicker layer IV are less likely to connect to regions with higher thickness in layers III, V, and VI [91]. Overall, these findings are in line with the wiring principle of "similar prefers similar" [21,22,88,91], which has been observed not only with the similarity of microstructure but also in association to gene expression patterns [92–96], neurotransmitter receptor profiles [97], and macroscale morphometry [91,98]. An alternative model of connectivity is the "distance rule model," which proposes physical proximity as the main predictor of connectivity as a result of wiring cost minimization [56,57,99–101]. It can be argued that the increased connectivity of similar regions may be an epiphenomenon of the distance rule, as nearby cortical regions tend to be similar [58,59]. However, it has been shown that the distance rule alone does not fully account for the connectome architecture. For example, simulated connectomes were shown to better resemble the empirical connectomes when interregional similarity was considered in addition to the wiring cost reduction [88]. Recent studies on tract-tracing data have shown that both similarity of cortical types and physical proximity can predict likelihood of structural connections [25,76], though in most species, cytoarchitectonic similarity was related to connectivity, above and beyond physical proximity [76]. Nevertheless, in our study, long-range connections were not significantly associated with similarity of laminar thickness profiles, suggesting distance as an important covariate. A decreased association of microstructural similarity and connectivity among long-range connections has been also observed in previous studies [90]. This raises the question of how long distance connections are encoded in layer-based architecture of the human cerebral cortex. Possibly, the uncoupling of layer similarity and long-distance connections could be in part driven by an uncoupling through activity-dependent organization, linked to the tethering hypothesis [102]. Further work integrating connectivity with layer-based approaches may help to further understand the interrelationship between short- and long-distance connections and cortical architecture.

Having studied the what and why questions of LTC, we also explored the question of how the (adult) laminar structure variations may come about. A central hypothesis on the origins of laminar structure variability proposes that different developmental trajectories across regions may relate to the gradation of laminar structure [17,22,103]. There are regional differences in neurogenesis timing and cell cycle duration throughout fetal development [104–110], or region- and layer-specific neuronal death in early postnatal stages [111], which may result in the specification of regions and their cytoarchitectural variability. For example, outer subventricular zone, a germinal zone of the developing cortex that is thought to generate the expanded primate granular and supragranular layers, is denser and deeper in area 17 compared to area 18 and has an increased rate of cell cycles, leading to a marked expansion of the upper layers in this region [104,105,109,112]. In the current study, we observed that higher interregional LTC was linked to higher population-level interregional structural covariance, which potentially indicates shared genetic and maturational effects among regions [60,62]. In addition, we observed a significant but weak correlation of LTC with subject-level longitudinal maturational coupling of cortical regions during childhood and adolescence [61] and found distinct pre- and postnatal developmental trajectories of genes overexpressed at the two ends of LTC G1 (S1 Text). Importantly, our current findings only indirectly suggest developmental relevance of laminar thickness organization. For example, the transcriptomics analysis involves mere spatial colocalization of the LTC G1 with the gene expression maps and the developmental enrichment of those genes and, therefore, lacks mechanistic insights on the complex gene regulatory mechanisms underlying regional differences of laminar structure. We refer the interested reader to the rich literature on cortical arealization and its genetic regulation [113–116]. Consequently, further research will be needed to study the developmental relevance of laminar structure variability by investigating postmortem histology or in vivo markers of laminar structure [10,117,118] at different stages of development to shed light on the maturation of laminar structure and its regional variability.

Limitations and future directions In this study, we used the whole-brain map of cortical layers from a single individual, the BigBrain [9,42]. This is currently the only whole-brain and high-resolution map of cortical layers available, and until a similar atlas becomes available, it is unclear how much our findings would generalize to the other individuals. Of note, when we compared left and right hemispheres of the same individual, we observed similar principal axes, which hints at intraindividual interhemispheric consistency of the principal axis of LTC. In addition to generalizability, an intriguing question for the future research is the degree to which laminar structure varies across individuals, and how it might relate to behavior and function, and its changes through development. This highlights the importance of future studies on in vivo estimation of laminar structure based on high-resolution imaging. We studied LTC using a 6-layer model of the isocortex, previously created using a convolutional neural network [42]. However, it is well known that some isocortical areas have fewer or a greater number of layers, due to the individual layers being absent or being divided into sublayers [1,4,119]. For example, area V1 is characterized by a prominent layer IV that is divided into 3 sublayers, and on the other hand, layer IV is unclear in agranular regions [4,14,119]. To avoid forcing a 6-layer model in regions with fewer number of layers and less clear layer boundaries, we excluded a- and dysgranular regions from our analyses. Exclusion of these regions limits the generalizability of our findings to the whole extent of the isocortex, yet we showed that the LTC G1 map was consistent when these regions are included. In addition, to further explore the impact of a priori defined number of layers, we used a 3-layer model of supragranular, granular, and infragranular layers and observed a similar principal axis. This indicates that LTC G1 captures variations of thickness in the supragranular, granular, and infragranular layer groups rather than the individual layers within each group. Future research may account for the regional differences in the number of layers using more fine-grained models of intracortical structure where the number of layers in each location is determined based on the data rather than being fixed. This would enable formally testing the optimal architecture of cortical depth and enables inclusion of a-/dysgranular areas in a more comprehensive model of laminar structure in the cerebral cortex.

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[1] Url: https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3002365

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