Human cortical folding across regions within individual brains follows universal scaling law

Neuro-evolutionary evidence for a universal fractal primate brain shape

The cerebral cortex displays a bewildering diversity of shapes and sizes across and within species. Despite this diversity, we present a universal multi-scale description of primate cortices. We show that all cortical shapes can be described as a set of nested folds of different sizes. As neighbouring folds are gradually merged, the cortices of 11 primate species follow a common scale-free morphometric trajectory, that also overlaps with over 70 other mammalian species. Our results indicate that all cerebral cortices are approximations of the same archetypal fractal shape with a fractal dimension of df = 2.5. Importantly, this new understanding enables a more precise quantification of brain morphology as a function of scale. To demonstrate the importance of this new understanding, we show a scale-dependent effect of ageing on brain morphology. We observe a more than fourfold increase in effect size (from two standard deviations to eight standard deviations) at a spatial scale of approximately 2 mm compared to standard morphological analyses. Our new understanding may, therefore, generate superior biomarkers for a range of conditions in the future.

Folding of the cerebellar cortex is clade-specific in form but universal in degree

Like the cerebralcortex, the surface of the cerebellum is repeatedly folded. Unlike the cerebralcortex, however, cerebellar folds are much thinner and more numerous; repeatthemselves largely along a single direction, forming accordion-like folds transverseto the mid-sagittal plane; and occur in all but the smallest cerebella. We haveshown previously that while the location of folds in mammalian cerebral cortex isclade-specific, the overall degree of folding strictly follows a universalpower law relating cortical thickness and the exposed and total surface areas predictedfrom the minimization of the effective free energy of an expanding, self-avoidingsurface of a certain thickness. Here we show that this scaling law extends tothe folding of the mid-sagittal sections of the cerebellum of 53 speciesbelonging to six mammalian clades. Simultaneously, we show that each clade hasa previously unsuspected distinctive spatial pattern of folding evident at themid-sagittal surface of the cerebellum. We note, however, that the mammaliancerebellum folds as a multi-fractal object, because of the difference betweenthe outside-in development of the cerebellar cortex around a preexisting coreof already connected white matter, compared to the inside-out development ofthe cerebral cortex with a white matter volume that develops as the cerebralcortex itself gains neurons. We conclude that repeated folding, one of the mostrecognizable features of biology, can arise simply from the interplay betweenthe universal applicability of the physics of self-organization and biological,phylogenetical clade-specific contingency, without the need for invokingselective pressures in evolution.

Cortical folding correlates to aging and Alzheimer's Disease's cognitive and CSF biomarkers

This manuscript presents the quantification and correlation of three aspects of Alzheimer's Disease evolution, including structural, biochemical, and cognitive assessments. We aimed to test a novel structural biomarker for neurodegeneration based on a cortical folding model for mammals. Our central hypothesis is that the cortical folding variable, representative of axonal tension in white matter, is an optimal discriminator of pathological aging and correlates with altered loadings in Cerebrospinal Fluid samples and a decline in cognition and memory. We extracted morphological features from T1w 3T MRI acquisitions using FreeSurfer from 77 Healthy Controls (age = 66 ± 8.4, 69% females), 31 Mild Cognitive Impairment (age = 72 ± 4.8, 61% females), and 13 Alzheimer's Disease patients (age = 77 ± 6.1, 62% females) of recruited volunteers in Brazil to test its discriminative power using optimal cut-point analysis. Cortical folding distinguishes the groups with reasonable accuracy (Healthy Control-Alzheimer's Disease, accuracy = 0.82; Healthy Control-Mild Cognitive Impairment, accuracy = 0.56). Moreover, Cerebrospinal Fluid biomarkers (total Tau, A[Formula: see text]1-40, A[Formula: see text]1-42, and Lipoxin) and cognitive scores (Cognitive Index, Rey's Auditory Verbal Learning Test, Trail Making Test, Digit Span Backward) were correlated with the global neurodegeneration in MRI aiming to describe health, disease, and the transition between the two states using morphology.

Cell division angle predicts the level of tissue mechanics that tune the amount of cerebellar folding

Modeling has led to proposals that the amount of neural tissue folding is set by the level of differential expansion between tissue layers and that the wavelength is set by the thickness of the outer layer. Here, we used inbred mouse strains with distinct amounts of cerebellar folding to investigate these predictions. We identified a distinct critical period during which the folding amount diverges between the two strains. In this period, regional changes in the level of differential expansion between the external granule layer (EGL) and underlying core correlate with the folding amount in each strain. Additionally, the thickness of the EGL varies regionally during the critical period alongside corresponding changes in wavelength. The number of SHH-expressing Purkinje cells predicts the folding amount, but the proliferation rate in the EGL is the same between the strains. However, regional changes in the cell division angle within the EGL predicts both the tangential expansion and the thickness of the EGL. Cell division angle is likely a tunable mechanism whereby both the level of differential expansion along the perimeter and the thickness of the EGL are regionally tuned to set the amount and wavelength of folding.

Systematic cortical thickness and curvature patterns in primates

Humans are known to have significant and consistent differences in thickness throughout the cortex, with thick outer gyral folds and thin inner sulcal folds. Our previous work has suggested a mechanical basis for this thickness pattern, with the forces generated during cortical folding leading to thick gyri and thin sulci, and shown that cortical thickness varies along a gyral-sulcal spectrum in humans. While other primate species are expected to exhibit similar patterns of cortical thickness, it is currently unknown how these patterns scale across different sizes, forms, and foldedness. Among primates, brains vary enormously from roughly the size of a grape to the size of a grapefruit, and from nearly smooth to dramatically folded; of these, human brains are the largest and most folded. These variations in size and form make comparative neuroanatomy a rich resource for investigating common trends that transcend differences between species. In this study, we examine 12 primate species in order to cover a wide range of sizes and forms, and investigate the scaling of their cortical thickness relative to the surface geometry. The 12 species were selected due to the public availability of either reconstructed surfaces and/or population templates. After obtaining or reconstructing 3D surfaces from publicly available neuroimaging data, we used our surface-based computational pipeline (https://github.com/mholla/curveball) to analyze patterns of cortical thickness and folding with respect to size (total surface area), geometry (i.e. curvature, shape, and sulcal depth), and foldedness (gyrification). In all 12 species, we found consistent cortical thickness variations along a gyral-sulcal spectrum, with convex shapes thicker than concave shapes and saddle shapes in between. Furthermore, we saw an increasing thickness difference between gyri and sulci as brain size increases. Our results suggest a systematic folding mechanism relating local cortical thickness to geometry. Finally, all of our reconstructed surfaces and morphometry data are available for future research in comparative neuroanatomy.

Effects of anterior temporal lobe resection on cortical morphology

Neuroimaging can capture brain restructuring after anterior temporal lobe resection (ATLR), a surgical procedure to treat drug-resistant temporal lobe epilepsy (TLE). Here, we examine the effects of this surgery on brain morphology measured in recently-proposed independent variables. We studied 101 individuals with TLE (55 left, 46 right onset) who underwent ATLR. For each individual we considered one pre-surgical MRI and one follow-up MRI 2-13 months after surgery. We used a surface-based method to locally compute traditional morphological variables, and the independent measures K, I, and S, where K measures white matter tension, I captures isometric scaling, and S contains the remaining information about cortical shape. A normative model trained on data from 924 healthy controls was used to debias the data and account for healthy ageing effects occurring during scans. A SurfStat random field theory clustering approach assessed changes across the cortex caused by ATLR. Compared to preoperative data, surgery had marked effects on all morphological measures. Ipsilateral effects were located in the orbitofrontal and inferior frontal gyri, the pre- and postcentral gyri and supramarginal gyrus, and the lateral occipital gyrus and lingual cortex. Contralateral effects were in the lateral occipital gyrus, and inferior frontal gyrus and frontal pole. The restructuring following ATLR is reflected in widespread morphological changes, mainly in regions near the resection, but also remotely in regions that are structurally connected to the anterior temporal lobe. The causes could include mechanical effects, Wallerian degeneration, or compensatory plasticity. The study of independent measures revealed additional effects compared to traditional measures.

Heterogeneous growth of the insula shapes the human brain

The human cerebrum consists of a precise and stereotyped arrangement of lobes, primary gyri, and connectivity that underlies human cognition [P. Rakic, Nat. Rev. Neurosci. 10, 724-735 (2009)]. The development of this arrangement is less clear. Current models explain individual primary gyrification but largely do not account for the global configuration of the cerebral lobes [T. Tallinen, J. Y. Chung, J. S. Biggins, L. Mahadevan, Proc. Natl. Acad. Sci. U.S.A. 111, 12667-12672 (2014) and D. C. Van Essen, Nature 385, 313-318 (1997)]. The insula, buried in the depths of the Sylvian fissure, is unique in terms of gyral anatomy and size. Here, we quantitatively show that the insula has unique morphology and location in the cerebrum and that these key differences emerge during fetal development. Finally, we identify quantitative differences in developmental migration patterns to the insula that may underlie these differences. We calculated morphologic data in the insula and other lobes in adults (N = 107) and in an in utero fetal brain atlas (N = 81 healthy fetuses). In utero, the insula grows an order of magnitude slower than the other lobes and demonstrates shallower sulci, less curvature, and less surface complexity both in adults and progressively throughout fetal development. Spherical projection analysis demonstrates that the lenticular nuclei obstruct 60 to 70% of radial pathways from the ventricular zone (VZ) to the insula, forcing a curved migration to the insula in contrast to a direct radial pathway. Using fetal diffusion tractography, we identify radial glial fascicles that originate from the VZ and curve around the lenticular nuclei to form the insula. These results confirm existing models of radial migration to the cortex and illustrate findings that suggest differential insular and cerebral development, laying the groundwork to understand cerebral malformations and insular function and pathologies.

Aberrant allometric scaling of cortical folding in preterm-born adults

A universal allometric scaling law has been proposed to describe cortical folding of the mammalian brain as a function of the product of cortical surface area and the square root of cortical thickness across different mammalian species, including humans. Since these cortical properties are vulnerable to developmental disturbances caused by preterm birth in humans and since these alterations are related to cognitive impairments, we tested (i) whether cortical folding in preterm-born adults follows this cortical scaling law and (ii) the functional relevance of potential scaling aberrances. We analysed the cortical scaling relationship in a large and prospectively collected cohort of 91 very premature-born adults (<32 weeks of gestation and/or birthweight <1500 g, very preterm and/or very low birth weight) and 105 full-term controls at 26 years of age based on the total surface area, exposed surface area and average cortical thickness measured with structural magnetic resonance imaging and surface-based morphometry. We found that the slope of the log-transformed cortical scaling relationship was significantly altered in adults (very preterm and/or very low birth weight: 1.24, full-term: 1.14, P = 0.018). More specifically, the slope was significantly altered in male adults (very preterm and/or very low birth weight: 1.24, full-term: 1.00, P = 0.031), while there was no significant difference in the slope of female adults (very preterm and/or very low birth weight: 1.27, full-term: 1.12, P = 0.225). Furthermore, offset was significantly lower compared with full-term controls in both male (very preterm and/or very low birth weight: -0.546, full-term: -0.538, P = 0.001) and female adults (very preterm and/or very low birth weight: -0.545, full-term: -0.538, P = 0.023), indicating a systematic shift of the regression line after preterm birth. Gestational age had a significant effect on the slope in very preterm and/or very low birth weight adults and more specifically in male very preterm and/or very low birth weight adults, indicating that the difference in slope is specifically related to preterm birth. The shape or tension term of the scaling law had no significant effect on cognitive performance, while the size of the cortex did. Results demonstrate altered scaling of cortical surface and cortical thickness in very premature-born adults. Data suggest altered mechanical forces acting on the cortex after preterm birth.

Orchestrating human neocortex development across the scales; from micro to macro

How our brains have developed to perform the many complex functions that make us human has long remained a question of great interest. Over the last few decades, many scientists from a wide range of fields have tried to answer this question by aiming to uncover the mechanisms that regulate the development of the human neocortex. They have approached this on different scales, focusing microscopically on individual cells all the way up to macroscopically imaging entire brains within living patients. In this review we will summarise these key findings and how they fit together.

Establishing a Baseline for Human Cortical Folding Morphological Variables: A Multisite Study

Differences in the way human cerebral cortices fold have been correlated to health, disease, development, and aging. However, to obtain a deeper understanding of the mechanisms that generate such differences, it is useful to derive one's morphometric variables from the first principles. This study explores one such set of variables that arise naturally from a model for universal self-similar cortical folding that was validated on comparative neuroanatomical data. We aim to establish a baseline for these variables across the human lifespan using a heterogeneous compilation of cross-sectional datasets as the first step to extending the model to incorporate the time evolution of brain morphology. We extracted the morphological features from structural MRI of 3,650 subjects: 3,095 healthy controls (CTL) and 555 patients with Alzheimer's Disease (AD) from 9 datasets, which were harmonized with a straightforward procedure to reduce the uncertainty due to heterogeneous acquisition and processing. The unprecedented possibility of analyzing such a large number of subjects in this framework allowed us to compare CTL and AD subjects' lifespan trajectories, testing if AD is a form of accelerated aging at the brain structural level. After validating this baseline from development to aging, we estimate the variables' uncertainties and show that Alzheimer's Disease is similar to premature aging when measuring global and local degeneration. This new methodology may allow future studies to explore the structural transition between healthy and pathological aging and may be essential to generate data for the cortical folding process simulations.

Quantifying Age-Associated Cortical Complexity of Left Dorsolateral Prefrontal Cortex with Multiscale Measurements

BACKGROUND

Cortical complexity plays a central role in the diagnosis and prognosis of age-related diseases. However, little is known about the regional cortical complexity in the context of brain atrophy.

OBJECTIVE

We aimed to systematically examine the age-related changes of the cortical complexity of left dorsolateral prefrontal cortex (DLPFC) and its subregions.

METHODS

Two hundred and fourteen cognitively normal adults drawn from the Open Access Series of Imaging Studies (OASIS) were divided into four age groups: young, middle-aged, young-old, and old-old. Based on structural magnetic resonance imaging (sMRI) scans, the multiscale measures of cortical complexity included cortical thickness (mm), surface area (mm2), grey matter volume (mm3), density, gyrification index (GI), and fractal dimension (FD).

RESULTS

Advancing age was associated with reduced grey matter volume, pial surface area, density, and FD of left DLPFC, but correlated with increased cortical thickness and GI. Volumetric measures, cerebrospinal fluid volume in particular, showed better performance to discriminate young-old adults from old-old adults, while FD was more sensitive than the volumetric measures to discriminate young adults and middle-aged adults.

CONCLUSION

This is the first demonstration that chronological age has a pronounced and differential effect on the cortical complexity of left DLPFC. Our findings suggest that surface-based measures of cortical region, thickness, and gyrification in particular, could be considered as valuable imaging markers for the studies of aging brain and neurodegenerative diseases.

Neuroimaging Research on Dementia in Brazil in the Last Decade: Scientometric Analysis, Challenges, and Peculiarities

The last years have evinced a remarkable growth in neuroimaging studies around the world. All these studies have contributed to a better understanding of the cerebral outcomes of dementia, even in the earliest phases. In low- and middle-income countries, studies involving structural and functional neuroimaging are challenging due to low investments and heterogeneous populations. Outstanding the importance of diagnosing mild cognitive impairment and dementia, the purpose of this paper is to offer an overview of neuroimaging dementia research in Brazil. The review includes a brief scientometric analysis of quantitative information about the development of this field over the past 10 years. Besides, discusses some peculiarities and challenges that have limited neuroimaging dementia research in this big and heterogeneous country of Latin America. We systematically reviewed existing neuroimaging literature with Brazilian authors that presented outcomes related to a dementia syndrome, published from 2010 to 2020. Briefly, the main neuroimaging methods used were morphometrics, followed by fMRI, and DTI. The major diseases analyzed were Alzheimer's disease, mild cognitive impairment, and vascular dementia, respectively. Moreover, research activity in Brazil has been restricted almost entirely to a few centers in the Southeast region, and funding could be the main driver for publications. There was relative stability concerning the number of publications per year, the citation impact has historically been below the world average, and the author's gender inequalities are not relevant in this specific field. Neuroimaging research in Brazil is far from being developed and widespread across the country. Fortunately, increasingly collaborations with foreign partnerships contribute to the impact of Brazil's domestic research. Although the challenges, neuroimaging researches performed in the native population regarding regional peculiarities and adversities are of pivotal importance.

Independent components of human brain morphology

Quantification of brain morphology has become an important cornerstone in understanding brain structure. Measures of cortical morphology such as thickness and surface area are frequently used to compare groups of subjects or characterise longitudinal changes. However, such measures are often treated as independent from each other. A recently described scaling law, derived from a statistical physics model of cortical folding, demonstrates that there is a tight covariance between three commonly used cortical morphology measures: cortical thickness, total surface area, and exposed surface area. We show that assuming the independence of cortical morphology measures can hide features and potentially lead to misinterpretations. Using the scaling law, we account for the covariance between cortical morphology measures and derive novel independent measures of cortical morphology. By applying these new measures, we show that new information can be gained; in our example we show that distinct morphological alterations underlie healthy ageing compared to temporal lobe epilepsy, even on the coarse level of a whole hemisphere. We thus provide a conceptual framework for characterising cortical morphology in a statistically valid and interpretable manner, based on theoretical reasoning about the shape of the cortex.

Reliability and comparability of human brain structural covariance networks

Structural covariance analysis is a widely used structural MRI analysis method which characterises the co-relations of morphology between brain regions over a group of subjects. To our knowledge, little has been investigated in terms of the comparability of results between different data sets of healthy human subjects, as well as the reliability of results over the same subjects in different rescan sessions, image resolutions, or FreeSurfer versions. In terms of comparability, our results show substantial differences in the structural covariance matrix between data sets of age- and sex-matched healthy human adults. These differences persist after univariate site correction, they are exacerbated by low sample sizes, and they are most pronounced when using average cortical thickness as a morphological measure. Down-stream graph theoretic analyses further show statistically significant differences. In terms of reliability, substantial differences were also found when comparing repeated scan sessions of the same subjects, image resolutions, and even FreeSurfer versions of the same image. We could further estimate the relative measurement error and showed that it is largest when using cortical thickness as a morphological measure. Using simulated data, we argue that cortical thickness is least reliable because of larger relative measurement errors. Practically, we make the following recommendations (1) combining subjects across sites into one group should be avoided, particularly if sites differ in image resolutions, subject demographics, or preprocessing steps; (2) surface area and volume should be preferred as morphological measures over cortical thickness; (3) a large number of subjects (n≫30 for the Desikan-Killiany parcellation) should be used to estimate structural covariance; (4) measurement error should be assessed where repeated measurements are available; (5) if combining sites is critical, univariate (per ROI) site-correction is insufficient, but error covariance (between ROIs) should be explicitly measured and modelled.