The connectivity of the brain: multi-level quantitative analysis

The meso-connectomes of mouse, marmoset, and macaque: network organization and the emergence of higher cognition

The recent publications of the inter-areal connectomes for mouse, marmoset, and macaque cortex have allowed deeper comparisons across rodent vs. primate cortical organization. In general, these show that the mouse has very widespread, "all-to-all" inter-areal connectivity (i.e. a "highly dense" connectome in a graph theoretical framework), while primates have a more modular organization. In this review, we highlight the relevance of these differences to function, including the example of primary visual cortex (V1) which, in the mouse, is interconnected with all other areas, therefore including other primary sensory and frontal areas. We argue that this dense inter-areal connectivity benefits multimodal associations, at the cost of reduced functional segregation. Conversely, primates have expanded cortices with a modular connectivity structure, where V1 is almost exclusively interconnected with other visual cortices, themselves organized in relatively segregated streams, and hierarchically higher cortical areas such as prefrontal cortex provide top-down regulation for specifying precise information for working memory storage and manipulation. Increased complexity in cytoarchitecture, connectivity, dendritic spine density, and receptor expression additionally reveal a sharper hierarchical organization in primate cortex. Together, we argue that these primate specializations permit separable deconstruction and selective reconstruction of representations, which is essential to higher cognition.

Single-subject cortical morphological brain networks: Phenotypic associations and neurobiological substrates

Although single-subject morphological brain networks provide an important way for human connectome studies, their roles and origins are poorly understood. Combining cross-sectional and repeated structural magnetic resonance imaging scans from adults, children and twins with behavioral and cognitive measures and brain-wide transcriptomic, cytoarchitectonic and chemoarchitectonic data, this study examined phenotypic associations and neurobiological substrates of single-subject morphological brain networks. We found that single-subject morphological brain networks explained inter-individual variance and predicted individual outcomes in Motor and Cognition domains, and distinguished individuals from each other. The performance can be further improved by integrating different morphological indices for network construction. Low-moderate heritability was observed for single-subject morphological brain networks with the highest heritability for sulcal depth-derived networks and higher heritability for inter-module connections. Furthermore, differential roles of genetic, cytoarchitectonic and chemoarchitectonic factors were observed for single-subject morphological brain networks. Cortical thickness-derived networks were related to the three factors with contributions from genes enriched in membrane and transport related functions, genes preferentially located in supragranular and granular layers, overall thickness in the molecular layer and thickness of wall in the infragranular layers, and metabotropic glutamate receptor 5 and dopamine transporter; fractal dimension-, gyrification index- and sulcal depth-derived networks were only associated with the chemoarchitectonic factor with contributions from different sets of neurotransmitter receptors. Most results were reproducible across different parcellation schemes and datasets. Altogether, this study demonstrates phenotypic associations and neurobiological substrates of single-subject morphological brain networks, which provide intermediate endophenotypes to link molecular and cellular architecture and behavior and cognition.

Hybrid statistical and machine learning modeling of cognitive neuroscience data

The nested data structure is prevalent for cognitive measure experiments due to repeatedly taken observations from different brain locations within subjects. The analysis methods used for this data type should consider the dependency structure among the repeated measurements. However, the dependency assumption is mainly ignored in the cognitive neuroscience data analysis literature. We consider both statistical, and machine learning methods extended to repeated data analysis and compare distinct algorithms in terms of their advantage and disadvantages. Unlike basic algorithm comparison studies, this article analyzes novel neuroscience data considering the dependency structure for the first time with several statistical and machine learning methods and their hybrid forms. In addition, the fitting performances of different algorithms are compared using contaminated data sets, and the cross-validation approach. One of our findings suggests that the GLMM tree, including random term indices indicating the location of functional near-infrared spectroscopy optodes nested within experimental units, shows the best predictive performance with the lowest MSE, RMSE, and MAE model performance metrics. However, there is a trade-off between accuracy and speed since this algorithm is required the highest computational time.

Using connectomics for predictive assessment of brain parcellations

The organization of the human brain remains elusive, yet is of great importance to the mechanisms of integrative brain function. At the macroscale, its structural and functional interpretation is conventionally assessed at the level of cortical units. However, the definition and validation of such cortical parcellations are problematic due to the absence of a true gold standard. We propose a framework for quantitative evaluation of brain parcellations via statistical prediction of connectomics data. Specifically, we evaluate the extent in which the network representation at the level of cortical units (defined as parcels) accounts for high-resolution brain connectivity. Herein, we assess the pertinence and comparative ranking of ten existing parcellation atlases to account for functional (FC) and structural connectivity (SC) data based on data from the Human Connectome Project (HCP), and compare them to data-driven as well as spatially-homogeneous geometric parcellations including geodesic parcellations with similar size distributions as the atlases. We find substantial discrepancy in parcellation structures that well characterize FC and SC and differences in what well represents an individual's functional connectome when compared against the FC structure that is preserved across individuals. Surprisingly, simple spatial homogenous parcellations generally provide good representations of both FC and SC, but are inferior when their within-parcellation distribution of individual parcel sizes is matched to that of a valid atlas. This suggests that the choice of fine grained and coarse representations used by existing atlases are important. However, we find that resolution is more critical than the exact border location of parcels.

Multiparametric and multilevel characterization of morphological alterations in patients with transient ischemic attack

Transient ischemic attack (TIA), an important risk factor for stroke, is associated with widespread disruptions of functional brain architecture. However, TIA-related structural alterations are not well established. By analyzing structural MRI data from 50 TIA patients versus 40 healthy controls (HCs), here we systematically investigated TIA-related morphological alterations in multiple cortical surface-based indices (cortical thickness [CT], fractal dimension [FD], gyrification index [GI], and sulcal depth [SD]) at multiple levels (local topography, interregional connectivity and whole-brain network topology). For the observed alterations, their associations with clinical risk factors and abilities as diagnostic and prognostic biomarkers were further examined. We found that compared with the HCs, the TIA patients showed widespread morphological alterations and the alterations depended on choices of morphological index and analytical level. Specifically, the patients exhibited: (a) regional CT decreases in the transverse temporal gyrus and lateral sulcus; (b) impaired FD- and GI-based connectivity mainly involving visual, somatomotor and ventral attention networks and interhemispheric connections; and (c) altered GI-based whole-brain network efficiency and decreased FD-based nodal centrality in the middle frontal gyrus. Moreover, the impaired morphological connectivity showed high sensitivities and specificities for distinguishing the patients from HCs. Altogether, these findings demonstrate the emergence of morphological index-dependent and analytical level-specific alterations in TIA, which provide novel insights into neurobiological mechanisms underlying TIA and may serve as potential biomarkers to help diagnosis of the disease. Meanwhile, our findings highlight the necessity of using multiparametric and multilevel approaches for a complete mapping of cerebral morphology in health and disease.

Differences in cortical structure between cognitively normal East Asian and Caucasian older adults: a surface-based morphometry study

There is a growing literature on the impact of ethnicity on brain structure and function. Despite the regional heterogeneity in age-related changes and non-uniformity across brain morphometry measurements in the aging process, paucity of studies investigated the difference in cortical anatomy between the East Asian and Caucasian older adults. The present study aimed to compare cortical anatomy measurements, including cortical thickness, volume and surface area, between cognitively normal East Asian (n = 171) and Caucasian (n = 178) older adults, using surface-based morphometry and vertex-wise group analysis of high-dimensional structural magnetic resonance imaging (MRI) data. The East Asian group showed greater cortical thickness and larger cortical volume in the right superior temporal gyrus, postcentral gyrus, bilateral inferior temporal gyrus, and inferior parietal cortex. The Caucasian group showed thicker and larger cortex in the left transverse temporal cortex, lingual gyrus, right lateral occipital cortex, and precentral gyrus. Additionally, the difference in surface area was discordant with that in cortical thickness. Differences in brain structure between the East Asian and Caucasian might reflect differences in language and information processing, but further studies using standardized methods for assessing racial characteristics are needed. The research results represent a further step towards developing a comprehensive understanding of differences in brain structure between ethnicities of older adults, and this would enrich clinical research on aging and neurodegenerative diseases.

Association of Copy Number Variation of the 15q11.2 BP1-BP2 Region With Cortical and Subcortical Morphology and Cognition

Importance

Recurrent microdeletions and duplications in the genomic region 15q11.2 between breakpoints 1 (BP1) and 2 (BP2) are associated with neurodevelopmental disorders. These structural variants are present in 0.5% to 1.0% of the population, making 15q11.2 BP1-BP2 the site of the most prevalent known pathogenic copy number variation (CNV). It is unknown to what extent this CNV influences brain structure and affects cognitive abilities.

Objective

To determine the association of the 15q11.2 BP1-BP2 deletion and duplication CNVs with cortical and subcortical brain morphology and cognitive task performance.

Design, Setting, and Participants

In this genetic association study, T1-weighted brain magnetic resonance imaging were combined with genetic data from the ENIGMA-CNV consortium and the UK Biobank, with a replication cohort from Iceland. In total, 203 deletion carriers, 45 247 noncarriers, and 306 duplication carriers were included. Data were collected from August 2015 to April 2019, and data were analyzed from September 2018 to September 2019.

Main Outcomes and Measures

The associations of the CNV with global and regional measures of surface area and cortical thickness as well as subcortical volumes were investigated, correcting for age, age2, sex, scanner, and intracranial volume. Additionally, measures of cognitive ability were analyzed in the full UK Biobank cohort.

Results

Of 45 756 included individuals, the mean (SD) age was 55.8 (18.3) years, and 23 754 (51.9%) were female. Compared with noncarriers, deletion carriers had a lower surface area (Cohen d = -0.41; SE, 0.08; P = 4.9 × 10-8), thicker cortex (Cohen d = 0.36; SE, 0.07; P = 1.3 × 10-7), and a smaller nucleus accumbens (Cohen d = -0.27; SE, 0.07; P = 7.3 × 10-5). There was also a significant negative dose response on cortical thickness (β = -0.24; SE, 0.05; P = 6.8 × 10-7). Regional cortical analyses showed a localization of the effects to the frontal, cingulate, and parietal lobes. Further, cognitive ability was lower for deletion carriers compared with noncarriers on 5 of 7 tasks.

Conclusions and Relevance

These findings, from the largest CNV neuroimaging study to date, provide evidence that 15q11.2 BP1-BP2 structural variation is associated with brain morphology and cognition, with deletion carriers being particularly affected. The pattern of results fits with known molecular functions of genes in the 15q11.2 BP1-BP2 region and suggests involvement of these genes in neuronal plasticity. These neurobiological effects likely contribute to the association of this CNV with neurodevelopmental disorders.

The Netrin-1/DCC guidance system: dopamine pathway maturation and psychiatric disorders emerging in adolescence

Axon guidance molecules direct growing axons toward their targets, assembling the intricate wiring of the nervous system. One of these molecules, Netrin-1, and its receptor, DCC (deleted in colorectal cancer), has profound effects, in laboratory animals, on the adolescent expansion of mesocorticolimbic pathways, particularly dopamine. Now, a rapidly growing literature suggests that (1) these same alterations could occur in humans, and (2) genetic variants in Netrin-1 and DCC are associated with depression, schizophrenia, and substance use. Together, these findings provide compelling evidence that Netrin-1 and DCC influence mesocorticolimbic-related psychopathological states that emerge during adolescence.

The reductions in the subcallosal region cortical volume and surface area in major depressive disorder across the adult life span

BACKGROUND

Imaging studies have shown that the subcallosal region (SCR) volume was decreased in patients with major depressive disorder (MDD). However, whether the volumetric reductions in the SCR are due to thinning of the cortex or a loss of surface area (SA) remains unclear. In addition, the relationship between cortical measurements of the SCR and age through the adult life span in MDD remains unclear.

METHODS

We used a cross-sectional design from 114 individuals with MDD and 112 matched healthy control (HC) individuals across the adult life span (range: 18-74 years). The mean cortical volume (CV), SA and cortical thickness (CT) of the SCR were computed using cortical parcellation based on FreeSurfer software. Multivariate analyses of covariance models were performed to compare differences between the MDD and HC groups on cortical measurements of the SCR. Multiple linear regression models were used to test age-by-group interaction effects on these cortical measurements of the SCR.

RESULTS

The MDD had significant reductions in the CV and SA of the left SCR compared with HC individuals after controlling of other variables. The left SCR CV and SA reductions compared with matched controls were observed only in early adulthood patients. We also found a significant age-related CT reduction in the SCR both in the MDD and HC participants.

CONCLUSIONS

The SCR volume reduction was mainly driven by SA in MDD. The different trajectories between the CT and SA of the SCR with age may provide valuable information to distinguish pathological processes and normal ageing in MDD.

How Big Data and High-performance Computing Drive Brain Science

Brain science accelerates the study of intelligence and behavior, contributes fundamental insights into human cognition, and offers prospective treatments for brain disease. Faced with the challenges posed by imaging technologies and deep learning computational models, big data and high-performance computing (HPC) play essential roles in studying brain function, brain diseases, and large-scale brain models or connectomes. We review the driving forces behind big data and HPC methods applied to brain science, including deep learning, powerful data analysis capabilities, and computational performance solutions, each of which can be used to improve diagnostic accuracy and research output. This work reinforces predictions that big data and HPC will continue to improve brain science by making ultrahigh-performance analysis possible, by improving data standardization and sharing, and by providing new neuromorphic insights.

State-independent and -dependent structural alterations in limbic-cortical regions in patients with current and remitted depression

BACKGROUND

The high recurrence of major depressive disorder (MDD) may derive from underlying state-independent structural alterations.

METHODS

First-episode drug-naïve currently depressed (cMDD) patients (N = 97), remitted depressed (RD) patients (N = 72), and healthy controls (HCs, N = 100) underwent structural magnetic resonance imaging (MRI). Group differences in cortical thickness (CT), surface area (SA), and local gyrification index (lGI) were analyzed in FreeSurfer.

RESULTS

Both groups of depressed patients had significantly decreased CT, relative to HCs, in the left precentral gyrus and significantly increased lGI values in the left superior frontal gyrus (SFG) indicative of state-independent alterations. Relative to HCs, the cMDD group had decreased CT of the SFG, caudal middle frontal gyrus (MFG), posterior cingulate cortex (PCC), and lateral occipital regions as well as increased SA or lGI of the superior temporal gyrus, precuneus, and pericalcarine, whereas the RD group had increased SA or lGI of the SFG, caudal MFG, and supramarginal gyrus; these alterations appeared to be state-dependent. SA or lGI values of the fusiform gyrus, inferior temporal gyrus, and superior parietal lobule differed between the cMDD and RD groups, consistent with state-dependent alterations. Beck depression inventory scores correlated with CT or lGI values of the caudal MFG, lateral occipital cortex in depressed patients.

LIMITATIONS

The structural features of several subcortical limbic regions were not analyzed.

CONCLUSIONS

Left precentral gyrus CT and left SFG gyrification alterations may represent state-independent alterations in MDD.

Age-Related Differences in Brain Morphology and the Modifiers in Middle-Aged and Older Adults

Brain structural morphology differs with age. This study examined age-differences in surface-based morphometric measures of cortical thickness, volume, and surface area in a well-defined sample of 8137 generally healthy UK Biobank participants aged 45-79 years. We illustrate that the complexity of age-related brain morphological differences may be related to the laminar organization and regional evolutionary history of the cortex, and age of about 60 is a break point for increasing negative associations between age and brain morphology in Alzheimer's disease (AD)-prone areas. We also report novel relationships of age-related cortical differences with individual factors of sex, cognitive functions of fluid intelligence, reaction time and prospective memory, cigarette smoking, alcohol consumption, sleep disruption, genetic markers of apolipoprotein E, brain-derived neurotrophic factor, catechol-O-methyltransferase, and several genome-wide association study loci for AD and further reveal joint effects of cognitive functions, lifestyle behaviors, and education on age-related cortical differences. These findings provide one of the most extensive characterizations of age associations with major brain morphological measures and improve our understanding of normal structural brain aging and its potential modifiers.

Cortical morphometry of the five-factor model of personality: findings from the Human Connectome Project full sample

This study is a replication of an existing large study (N = 507) on the surface-based morphometric correlates of five-factor model (FFM) personality traits. The same methods were used as the original study in another large sample drawn from the same population (N = 597) with results then being aggregated from both samples (N = 1104), providing the largest investigation into the neuroanatomical correlates of FFM personality traits to date. Clusters of association between brain morphometry and each FFM trait are reported. For neuroticism, agreeableness, openness and conscientiousness clusters of association were found in the dorsolateral prefrontal cortex for at least one morphometric index. Morphometry in various other regions was also associated with each personality trait. While some regions found in the original study were confirmed in the replication and full samples, others were not, highlighting the importance of replicating even high-quality, well-powered studies. Effect sizes were very similar in the replication and whole samples as those found in the original study. As a whole, the current results provide the strongest evidence to date on the neuroanatomical correlates of personality and highlights challenges in using this approach to understanding the neural correlates of personality.

The Relationship Between General Intelligence and Cortical Structure in Healthy Individuals

Considerable work in recent years has examined the relationship between cortical thickness (CT) and general intelligence (IQ) in healthy individuals. It is not known whether specific IQ variables (i.e., perceptual reasoning [PIQ], verbal comprehension IQ [VIQ], and full-scale IQ [FSIQ]) are associated with multiple cortical measures (i.e., CT, cortical volume (CV), cortical surface area (CSA) and cortical gyrification (CG)) within the same individuals. Here we examined the association between these neuroimaging metrics and IQ in 56 healthy adults. At a cluster-forming threshold (CFT) of p < 0.05, we observed significant positive relationships between CT and all three IQ variables in regions within the posterior frontal and superior parietal lobes. Regions within the temporal and posterior frontal lobes exhibited positive relationships between CV and two IQ variables (PIQ and FSIQ) and regions within the inferior parietal lobe exhibited positive relationships between CV and PIQ. Additionally, CV was positively associated with VIQ in the left insula and with FSIQ within the inferior frontal gyrus. At a more stringent CFT (p < 0.01), the CT-PIQ, CT-VIQ, CT-FSIQ, and CV-PIQ relationships remained significant within the posterior frontal lobe, as did the CV-PIQ relationship within the temporal and inferior parietal lobes. We did not observe statistically significant relationships between IQ and either CSA or CG. Our findings suggest that the neural basis of IQ extends beyond previously observed relationships with fronto-parietal regions. We also conclude that CT and CV may be more useful metrics than CSA or CG in the study of intellectual abilities.

Abnormal age-related cortical folding and neurite morphology in children with developmental dyslexia

There is increasing recognition of a relationship between regional variability in cerebral gyrification and neurodevelopment. Recent work in morphometric MRI has shown that the local gyrification index (lGI), a measure of regional brain folding, may be altered in certain neurodevelopmental disorders. Other studies report that the lGI generally decreases with age in adolescence and young adulthood; however, little is known about how these age-dependent differences in brain maturation occur in atypical neurodevelopment and mechanisms underlying gyrification, such as synaptic pruning. Organization and optimization of dendrites and axons connections across the brain might be driving gyrification and folding processes. In this study, we first assessed lGI differences in the left hemisphere in a cohort of 39 children with developmental dyslexia (DD) between the ages of 7 and 15 years in comparison to 56 typically developing controls (TDC). To better understand the microstructural basis of these changes, we next explored the relationship between lGI differences and cortical thickness and neurite morphology by applying neurite orientation dispersion and density imaging (NODDI). We identified significant differences in lGI between children with DD and TDC in left lateral temporal and middle frontal regions. Further, DD failed to show the expected age-related decreases in lGI in the same regions. Age-related differences in lGI in DD were not explained by differences in cortical thickness, but did correlate with NODDI neurite density and orientation dispersion index. Our findings suggest that gyrification changes in DD are related to abnormal neurite morphology, and are possibly an expression of differences in synaptic pruning.

Energy-efficient neural information processing in individual neurons and neuronal networks

Brains are composed of networks of an enormous number of neurons interconnected with synapses. Neural information is carried by the electrical signals within neurons and the chemical signals among neurons. Generating these electrical and chemical signals is metabolically expensive. The fundamental issue raised here is whether brains have evolved efficient ways of developing an energy-efficient neural code from the molecular level to the circuit level. Here, we summarize the factors and biophysical mechanisms that could contribute to the energy-efficient neural code for processing input signals. The factors range from ion channel kinetics, body temperature, axonal propagation of action potentials, low-probability release of synaptic neurotransmitters, optimal input and noise, the size of neurons and neuronal clusters, excitation/inhibition balance, coding strategy, cortical wiring, and the organization of functional connectivity. Both experimental and computational evidence suggests that neural systems may use these factors to maximize the efficiency of energy consumption in processing neural signals. Studies indicate that efficient energy utilization may be universal in neuronal systems as an evolutionary consequence of the pressure of limited energy. As a result, neuronal connections may be wired in a highly economical manner to lower energy costs and space. Individual neurons within a network may encode independent stimulus components to allow a minimal number of neurons to represent whole stimulus characteristics efficiently. This basic principle may fundamentally change our view of how billions of neurons organize themselves into complex circuits to operate and generate the most powerful intelligent cognition in nature. © 2017 Wiley Periodicals, Inc.

The Lateral Temporal Lobe in Early Human Life

Abnormalities of lateral temporal lobe development are associated with a spectrum of genetic and environmental pathologic processes, but more normative data are needed for a better understanding of gyrification in this brain region. Here, we begin to establish guidelines for the analysis of the lateral temporal lobe in humans in early life. We present quantitative methods for measuring gyrification at autopsy using photographs of the gross brain and simple computer-based quantitative tools in a cohort of 28 brains ranging in age from 27 to 70 postconceptional weeks (end of infancy). We provide normative ranges for different indices of gyrification and identify a constellation of qualitative features that should also be considered in these analyses. The ratio of the temporal area to the whole brain area increased dramatically in the second half of gestation, but then decelerated after birth before increasing linearly around 50 postconceptional weeks. Tertiary gyrification continued beyond birth in a linear process through infancy with considerable variation in patterns. Analysis of 2 brains with gyral disorders of the lateral temporal lobe demonstrated proof-of-principle that the proposed methods are of diagnostic value. These guidelines are proposed for assessments of temporal lobe pathology in pediatric brains in early life.

After over 200 years, 7 T magnetic resonance imaging reveals the foliate structure of the human corpus callosum in vivo

Objective:

A fine structure of the corpus callosum (CC), consisting of radial lines, is seen in historical anatomical atlases as far back as that of Vicq d'Azyr (1786). This study examines a similar pattern observed in vivo using high-resolution MR images at 7 T.

Methods:

8 healthy subjects were examined with 7.0-T MRI. Anatomical images were collected with a gradient echo scan with 0.5-mm isotropic resolution, which were rated for visibility of the radial pattern. In addition, the second eigenvector of the diffusion tensor images was examined.

Results:

The fine radial lines are detected not only in the sagittal view but also in the axial view of the in vivo MR images. From this, it is likely that these structures are two-dimensional ribbons. Interestingly, and confirming the structural nature of these stripes, the second eigenvector of the diffusion tensor imaging data shows an extremely similar pattern of oriented foliate structure. A similar modular structure involving transient septa has been observed previously in histological sections of human fetal CC.

Conclusion:

The separate sets of data—the atlas of Klingler, anatomical images and second eigenvector images—all indicate a ribbon-like arrangement of the fibres in the CC. As such, they closely match the structures shown in the drawn atlases of as old as 1786.

Advances in knowledge:

This ribbon arrangement of fibres in the CC, previously unseen in CT or lower field MRI, can now be observed in vivo. This appears to match over two centuries of ex vivo observations.

Quantification of degeneracy in Hodgkin-Huxley neurons on Newman-Watts small world network

Degeneracy is a fundamental source of biological robustness, complexity and evolvability in many biological systems. However, degeneracy is often confused with redundancy. Furthermore, the quantification of degeneracy has not been addressed for realistic neuronal networks. The objective of this paper is to characterize degeneracy in neuronal network models via quantitative mathematic measures. Firstly, we establish Hodgkin-Huxley neuronal networks with Newman-Watts small world network architectures. Secondly, in order to calculate the degeneracy, redundancy and complexity in the ensuing networks, we use information entropy to quantify the information a neuronal response carries about the stimulus - and mutual information to measure the contribution of each subset of the neuronal network. Finally, we analyze the interdependency of degeneracy, redundancy and complexity - and how these three measures depend upon network architectures. Our results suggest that degeneracy can be applied to any neuronal network as a formal measure, and degeneracy is distinct from redundancy. Qualitatively degeneracy and complexity are more highly correlated over different network architectures, in comparison to redundancy. Quantitatively, the relationship between both degeneracy and redundancy depends on network coupling strength: both degeneracy and redundancy increase with complexity for small coupling strengths; however, as coupling strength increases, redundancy decreases with complexity (in contrast to degeneracy, which is relatively invariant). These results suggest that the degeneracy is a general topologic characteristic of neuronal networks, which could be applied quantitatively in neuroscience and connectomics.

Spatial Embedding and Wiring Cost Constrain the Functional Layout of the Cortical Network of Rodents and Primates

Mammals show a wide range of brain sizes, reflecting adaptation to diverse habitats. Comparing interareal cortical networks across brains of different sizes and mammalian orders provides robust information on evolutionarily preserved features and species-specific processing modalities. However, these networks are spatially embedded, directed, and weighted, making comparisons challenging. Using tract tracing data from macaque and mouse, we show the existence of a general organizational principle based on an exponential distance rule (EDR) and cortical geometry, enabling network comparisons within the same model framework. These comparisons reveal the existence of network invariants between mouse and macaque, exemplified in graph motif profiles and connection similarity indices, but also significant differences, such as fractionally smaller and much weaker long-distance connections in the macaque than in mouse. The latter lends credence to the prediction that long-distance cortico-cortical connections could be very weak in the much-expanded human cortex, implying an increased susceptibility to disconnection syndromes such as Alzheimer disease and schizophrenia. Finally, our data from tracer experiments involving only gray matter connections in the primary visual areas of both species show that an EDR holds at local scales as well (within 1.5 mm), supporting the hypothesis that it is a universally valid property across all scales and, possibly, across the mammalian class.

Open Issues in Evolutionary Robotics

One of the long-term goals in evolutionary robotics is to be able to automatically synthesize controllers for real autonomous robots based only on a task specification. While a number of studies have shown the applicability of evolutionary robotics techniques for the synthesis of behavioral control, researchers have consistently been faced with a number of issues preventing the widespread adoption of evolutionary robotics for engineering purposes. In this article, we review and discuss the open issues in evolutionary robotics. First, we analyze the benefits and challenges of simulation-based evolution and subsequent deployment of controllers versus evolution on real robotic hardware. Second, we discuss specific evolutionary computation issues that have plagued evolutionary robotics: (1) the bootstrap problem, (2) deception, and (3) the role of genomic encoding and genotype-phenotype mapping in the evolution of controllers for complex tasks. Finally, we address the absence of standard research practices in the field. We also discuss promising avenues of research. Our underlying motivation is the reduction of the current gap between evolutionary robotics and mainstream robotics, and the establishment of evolutionary robotics as a canonical approach for the engineering of autonomous robots.

Does degree of gyrification underlie the phenotypic and genetic associations between cortical surface area and cognitive ability?

The phenotypic and genetic relationship between global cortical size and general cognitive ability (GCA) appears to be driven by surface area (SA) and not cortical thickness (CT). Gyrification (cortical folding) is an important property of the cortex that helps to increase SA within a finite space, and may also improve connectivity by reducing distance between regions. Hence, gyrification may be what underlies the SA-GCA relationship. In previous phenotypic studies, a 3-dimensional gyrification index (3DGI) has been positively associated with cognitive ability and negatively associated with mild cognitive impairment, Alzheimer's disease, and psychiatric disorders affecting cognition. However, the differential genetic associations of 3DGI and SA with GCA are still unclear. We examined the heritability of 3DGI, and the phenotypic, genetic, and environmental associations of 3DGI with SA and GCA in a large sample of adult male twins (N = 512). Nearly 85% of the variance in 3DGI was due to genes, and 3DGI had a strong phenotypic and genetic association with SA. Both 3DGI and total SA had positive phenotypic correlations with GCA. However, the SA-GCA correlation remained significant after controlling for 3DGI, but not the other way around. There was also significant genetic covariance between SA and GCA, but not between 3DGI and GCA. Thus, despite the phenotypic and genetic associations between 3DGI and SA, our results do not support the hypothesis that gyrification underlies the association between SA and GCA.

Differential longitudinal changes in cortical thickness, surface area and volume across the adult life span: regions of accelerating and decelerating change

Human cortical thickness and surface area are genetically independent, emerge through different neurobiological events during development, and are sensitive to different clinical conditions. However, the relationship between changes in the two over time is unknown. Additionally, longitudinal studies have almost invariably been restricted to older adults, precluding the delineation of adult life span trajectories of change in cortical structure. In this longitudinal study, we investigated changes in cortical thickness, surface area, and volume after an average interval of 3.6 years in 207 well screened healthy adults aged 23-87 years. We hypothesized that the relationships among metrics are dynamic across the life span, that the primary contributor to cortical volume reductions in aging is cortical thinning, and that magnitude of change varies with age and region. Changes over time were seen in cortical area (mean annual percentage change [APC], -0.19), thickness (APC, -0.35), and volume (APC, -0.51) in most regions. Volume changes were primarily explained by changes in thickness rather than area. A negative relationship between change in thickness and surface area was found across several regions, where more thinning was associated with less decrease in area, and vice versa. Accelerating changes with increasing age was seen in temporal and occipital cortices. In contrast, decelerating changes were seen in prefrontal and anterior cingulate cortices. In conclusion, a dynamic relationship between cortical thickness and surface area changes exists throughout the adult life span. The mixture of accelerating and decelerating changes further demonstrates the importance of studying these metrics across the entire adult life span.

Constancy and trade-offs in the neuroanatomical and metabolic design of the cerebral cortex

Mammalian brains span about four orders of magnitude in cortical volume and have to operate in different environments that require diverse behavioral skills. Despite these geometric and behavioral diversities, the examination of cerebral cortex across species reveals that it contains a substantial number of conserved characteristics that are associated with neuroanatomy and metabolism, i.e., with neuronal connectivity and function. Some of these cortical constants or invariants have been known for a long time but not sufficiently appreciated, and others were only recently discovered. The focus of this review is to present the cortical invariants and discuss their role in the efficient information processing. Global conservation in neuroanatomy and metabolism, as well as their correlated regional and developmental variability suggest that these two parallel systems are mutually coupled. It is argued that energetic constraint on cortical organization can be strong if cerebral blood supplied is either below or above a certain level, and it is rather soft otherwise. Moreover, because maximization or minimization of parameters associated with cortical connectivity, function and cost often leads to conflicts in design, it is argued that the architecture of the cerebral cortex is a result of structural and functional compromises.

A tree-like model for brain growth and structure

The Flory-Stockmayer theory for the polycondensation of branched polymers, modified for finite systems beyond the gel point, is applied to the connection (synapses) of neurons, which can be considered highly branched "monomeric" units. Initially, the process is a linear growth and tree-like branching between dendrites and axons of nonself-neurons. After the gel point and at the maximum "tree" size, the tree-like model prescribes, on average, one pair of twin synapses per neuron. About 13% of neurons, "unconnected" to the maximum tree, migrate to the surface to form cortical layers. The number of synapses in each neuron may reach 10000, indicating a tremendous amount of flexible, redundant, and neuroplastic loop-forming linkages which can be preserved or pruned by experience and learning.

A scalable neural chip with synaptic electronics using CMOS integrated memristors

The design and simulation of a scalable neural chip with synaptic electronics using nanoscale memristors fully integrated with complementary metal-oxide-semiconductor (CMOS) is presented. The circuit consists of integrate-and-fire neurons and synapses with spike-timing dependent plasticity (STDP). The synaptic conductance values can be stored in memristors with eight levels, and the topology of connections between neurons is reconfigurable. The circuit has been designed using a 90 nm CMOS process with via connections to on-chip post-processed memristor arrays. The design has about 16 million CMOS transistors and 73 728 integrated memristors. We provide circuit level simulations of the entire chip performing neuronal and synaptic computations that result in biologically realistic functional behavior.

Systematic, cross-cortex variation in neuron numbers in rodents and primates

Uniformity, local variability, and systematic variation in neuron numbers per unit of cortical surface area across species and cortical areas have been claimed to characterize the isocortex. Resolving these claims has been difficult, because species, techniques, and cortical areas vary across studies. We present a stereological assessment of neuron numbers in layers II-IV and V-VI per unit of cortical surface area across the isocortex in rodents (hamster, Mesocricetus auratus; agouti, Dasyprocta azarae; paca, Cuniculus paca) and primates (owl monkey, Aotus trivigratus; tamarin, Saguinus midas; capuchin, Cebus apella); these chosen to vary systematically in cortical size. The contributions of species, cortical areas, and techniques (stereology, "isotropic fractionator") to neuron estimates were assessed. Neurons per unit of cortical surface area increase across the rostro-caudal (RC) axis in primates (varying by a factor of 1.64-2.13 across the rostral and caudal poles) but less in rodents (varying by a factor of 1.15-1.54). Layer II-IV neurons account for most of this variation. When integrated into the context of species variation, and this RC gradient in neuron numbers, conflicts between studies can be accounted for. The RC variation in isocortical neurons in adulthood mirrors the gradients in neurogenesis duration in development.

Gyrification, cortical and subcortical morphometry in neurofibromatosis type 1: an uneven profile of developmental abnormalities

BACKGROUND

Neurofibromatosis type 1 (NF1) is a monogenic disorder associated with cognitive impairments. In order to understand how mutations in the NF1 gene impact brain structure it is essential to characterize in detail the brain structural abnormalities in patients with NF1. Previous studies have reported contradictory findings and have focused only on volumetric measurements. Here, we investigated the volumes of subcortical structures and the composite dimensions of the cortex through analysis of cortical volume, cortical thickness, cortical surface area and gyrification.

METHODS

We studied 14 children with NF1 and 14 typically developing children matched for age, gender, IQ and right/left-handedness. Regional subcortical volumes and cortical gyral measurements were obtained using the FreeSurfer software. Between-group differences were evaluated while controlling for the increase in total intracranial volume observed in NF1.

RESULTS

Subcortical analysis revealed disproportionately larger thalami, right caudate and middle corpus callosum in patients with NF1. Cortical analyses on volume, thickness and surface area were however not indicative of significant alterations in patients. Interestingly, patients with NF1 had significantly lower gyrification indices than typically developing children primarily in the frontal and temporal lobes, but also affecting the insula, cingulate cortex, parietal and occipital regions.

CONCLUSIONS

The neuroanatomic abnormalities observed were localized to specific brain regions, indicating that particular areas might constitute selective targets for NF1 gene mutations. Furthermore, the lower gyrification indices were accompanied by a disproportionate increase in brain size without the corresponding increase in folding in patients with NF1. Taken together these findings suggest that specific neurodevelopmental processes, such as gyrification, are more vulnerable to NF1 dysfunction than others. The identified changes in brain organization are consistent with the patterns of cognitive dysfunction in the NF1 phenotype.

Tracelink: A model of consolidation and amnesia

A connectionist model is presented, the TraceLink model, that implements an autonomous "off-line" consolidation process. The model consists of three subsystems: (1) a trace system (neocortex), (2) a link system (hippocampus and adjacent regions), and (3) a modulatory system (basal forebrain and other areas). The model is able to account for many of the characteristics of anterograde and retrograde amnesia, including Ribot gradients, transient global amnesia, patterns of shrinkage of retrograde amnesia, and correlations between anterograde and retrograde amnesia or the absence thereof (e.g., in isolated retrograde amnesia). In addition, it produces normal forgetting curves and can exhibit permastore. It also offers an explanation for the advantages of learning under high arousal for long-term retention.

Mental time travel and default-mode network functional connectivity in the developing brain

A core brain network is engaged in remembering the past and envisioning the future. This network overlaps with the so-called default-mode network, the activity of which increases when demands for focused attention are low. Because of their shared brain substrates, an intriguing hypothesis is that default-mode activity, measured at rest, is related to performance in separate attention-focused recall and imagination tasks. However, we do not know how functional connectivity of the default-mode network is related to individual differences in reconstruction of the past and imagination of the future. Here, we show that functional connectivity of the default-mode network in children and adolescents is related to the quality of past remembering and marginally to future imagination. These results corroborate previous findings of a common neuronal substrate for memory and imagination and provide evidence suggesting that mental time travel is modulated by the task-independent functional architecture of the default-mode network in the developing brain. A further analysis showed that local cortical arealization also contributed to explain recall of the past and imagination of the future, underscoring the benefits of studying both functional and structural properties to understand the brain basis for complex human cognition.

The structure of the cerebral cortex across adult life: age-related patterns of surface area, thickness, and gyrification

Older adults exhibit global reductions in cortical surface area, but little is known about the regional patterns of reductions or how these relate to other measures of brain structure. This knowledge is critical to understanding the dynamic relationship between different macrostructural properties of the cortex throughout adult life. Here, cortical arealization, local gyrification index (LGI), and cortical thickness were measured vertex wise across the brain surface in 322 healthy adults (20-85 years), with the aims of 1) characterizing age patterns of the three separate cortical measures and 2) testing the age-independent relationships among cortical surface area, gyrification, and thickness. Surface area showed strong age-related decreases, particularly pronounced in dorsomedial prefrontal, lateral temporal, and fusiform cortices, independently of total white matter volume. LGI decreased with age independently of regional surface area, with strongest effects laterally, extending from the angular gyrus in all directions. As expected, regional surface area and LGI were positively related. However, both measures correlated negatively with thickness, indicating increasing local arealization and gyrification with decreasing cortical thickness. We suggest that this pattern of regional "cortical stretching" reflects the well-established phylogenetic principle of maximizing surface area and gyrification rather than increase thickness to facilitate brain connectivity and functional development.

Fragmentation: loss of global coherence or breakdown of modularity in functional brain architecture?

Psychiatric illnesses characterized by disorganized cognition, such as schizophrenia, have been described in terms of fragmentation and hence understood as reduction in functional brain connectivity, particularly in prefrontal and parietal areas. However, as graph theory shows, relatively small numbers of nonlocal connections are sufficient to ensure global coherence in the modular small-world network structure of the brain. We reconsider fragmentation in this perspective. Computational studies have shown that for a given level of connectivity in a model of coupled nonlinear oscillators, modular small-world networks evolve from an initially random organization. Here we demonstrate that with decreasing connectivity, the probability of evolving into a modular small-world network breaks down at a critical point, which scales to the percolation function of random networks with a universal exponent of α = 1.17. Thus, according to the model, local modularity systematically breaks down before there is loss of global coherence in network connectivity. We, therefore, propose that fragmentation may involve, at least in its initial stages, the inability of a dynamically evolving network to sustain a modular small-world structure. The result is in a shift in the balance in schizophrenia from local to global functional connectivity.

Self-organizing circuit assembly through spatiotemporally coordinated neuronal migration within geometric constraints

BACKGROUND

Neurons are dynamically coupled with each other through neurite-mediated adhesion during development. Understanding the collective behavior of neurons in circuits is important for understanding neural development. While a number of genetic and activity-dependent factors regulating neuronal migration have been discovered on single cell level, systematic study of collective neuronal migration has been lacking. Various biological systems are shown to be self-organized, and it is not known if neural circuit assembly is self-organized. Besides, many of the molecular factors take effect through spatial patterns, and coupled biological systems exhibit emergent property in response to geometric constraints. How geometric constraints of the patterns regulate neuronal migration and circuit assembly of neurons within the patterns remains unexplored.

METHODOLOGY/PRINCIPAL FINDINGS

We established a two-dimensional model for studying collective neuronal migration of a circuit, with hippocampal neurons from embryonic rats on Matrigel-coated self-assembled monolayers (SAMs). When the neural circuit is subject to geometric constraints of a critical scale, we found that the collective behavior of neuronal migration is spatiotemporally coordinated. Neuronal somata that are evenly distributed upon adhesion tend to aggregate at the geometric center of the circuit, forming mono-clusters. Clustering formation is geometry-dependent, within a critical scale from 200 µm to approximately 500 µm. Finally, somata clustering is neuron-type specific, and glutamatergic and GABAergic neurons tend to aggregate homo-philically.

CONCLUSIONS/SIGNIFICANCE

We demonstrate self-organization of neural circuits in response to geometric constraints through spatiotemporally coordinated neuronal migration, possibly via mechanical coupling. We found that such collective neuronal migration leads to somata clustering, and mono-cluster appears when the geometric constraints fall within a critical scale. The discovery of geometry-dependent collective neuronal migration and the formation of somata clustering in vitro shed light on neural development in vivo.

Gyrification and neural connectivity in schizophrenia

There is emerging evidence for a connection between the surface morphology of the brain and its underlying connectivity. The foundation for this relationship is thought to be established during brain development through the shaping influences of tension exerted by viscoelastic nerve fibers. The tension-based morphogenesis results in compact wiring that enhances efficient neural processing. Individuals with schizophrenia present with multiple symptoms that can include impaired thought, action, perception, and cognition. The global nature of these symptoms has led researchers to explore a more global disruption of neuronal connectivity as a theory to explain the vast array of clinical and cognitive symptoms in schizophrenia. If cerebral function and form are linked through the organization of neural connectivity, then a disruption in neural connectivity may also alter the surface morphology of the brain. This paper reviews developmental theories of gyrification and the potential interaction between gyrification and neuronal connectivity. Studies of gyrification abnormalities in children, adolescents, and adults with schizophrenia demonstrate a relationship between disrupted function and altered morphology in the surface patterns of the cerebral cortex. This altered form may provide helpful clues in understanding the neurobiological abnormalities associated with schizophrenia.

Network structure implied by initial axon outgrowth in rodent cortex: empirical measurement and models

The developmental mechanisms by which the network organization of the adult cortex is established are incompletely understood. Here we report on empirical data on the development of connections in hamster isocortex and use these data to parameterize a network model of early cortical connectivity. Using anterograde tracers at a series of postnatal ages, we investigate the growth of connections in the early cortical sheet and systematically map initial axon extension from sites in anterior (motor), middle (somatosensory) and posterior (visual) cortex. As a general rule, developing axons extend from all sites to cover relatively large portions of the cortical field that include multiple cortical areas. From all sites, outgrowth is anisotropic, covering a greater distance along the medial/lateral axis than along the anterior/posterior axis. These observations are summarized as 2-dimensional probability distributions of axon terminal sites over the cortical sheet. Our network model consists of nodes, representing parcels of cortex, embedded in 2-dimensional space. Network nodes are connected via directed edges, representing axons, drawn according to the empirically derived anisotropic probability distribution. The networks generated are described by a number of graph theoretic measurements including graph efficiency, node betweenness centrality and average shortest path length. To determine if connectional anisotropy helps reduce the total volume occupied by axons, we define and measure a simple metric for the extra volume required by axons crossing. We investigate the impact of different levels of anisotropy on network structure and volume. The empirically observed level of anisotropy suggests a good trade-off between volume reduction and maintenance of both network efficiency and robustness. Future work will test the model's predictions for connectivity in larger cortices to gain insight into how the regulation of axonal outgrowth may have evolved to achieve efficient and economical connectivity in larger brains.

The development of gyrification in childhood and adolescence

Gyrification is the process by which the brain undergoes changes in surface morphology to create sulcal and gyral regions. The period of greatest development of brain gyrification is during the third trimester of pregnancy, a period of time in which the brain undergoes considerable growth. Little is known about changes in gyrification during childhood and adolescence, although considering the changes in gray matter volume and thickness during this time period, it is conceivable that alterations in the brain surface morphology could also occur during this period of development. The formation of gyri and sulci in the brain allows for compact wiring that promotes and enhances efficient neural processing. If cerebral function and form are linked through the organization of neural connectivity, then alterations in neural connectivity, i.e., synaptic pruning, may also alter the gyral and sulcal patterns of the brain. This paper reviews developmental theories of gyrification, computational techniques for measuring gyrification, and the potential interaction between gyrification and neuronal connectivity. We also present recent findings involving alterations in gyrification during childhood and adolescence.

Thermodynamic constraints on neural dimensions, firing rates, brain temperature and size

There have been suggestions that heat caused by cerebral metabolic activity may constrain mammalian brain evolution, architecture, and function. This article investigates physical limits on brain wiring and corresponding changes in brain temperature that are imposed by thermodynamics of heat balance determined mainly by Na(+)/K(+)-ATPase, cerebral blood flow, and heat conduction. It is found that even moderate firing rates cause significant intracellular Na(+) build-up, and the ATP consumption rate associated with pumping out these ions grows nonlinearly with frequency. Surprisingly, the power dissipated by the Na(+)/K(+) pump depends biphasically on frequency, which can lead to the biphasic dependence of brain temperature on frequency as well. Both the total power of sodium pumps and brain temperature diverge for very small fiber diameters, indicating that too thin fibers are not beneficial for thermal balance. For very small brains blood flow is not a sufficient cooling mechanism deep in the brain. The theoretical lower bound on fiber diameter above which brain temperature is in the operational regime is strongly frequency dependent but finite due to synaptic depression. For normal neurophysiological conditions this bound is at least an order of magnitude smaller than average values of empirical fiber diameters, suggesting that neuroanatomy of the mammalian brains operates in the thermodynamically safe regime. Analytical formulas presented can be used to estimate average firing rates in mammals, and relate their changes to changes in brain temperature, which can have important practical applications. In general, activity in larger brains is found to be slower than in smaller brains.

The scalable mammalian brain: emergent distributions of glia and neurons

In this paper, we demonstrate that two characteristic properties of mammalian brains emerge when scaling-up modular, cortical structures. Firstly, the glia-to-neuron ratio is not constant across brains of different sizes: large mammalian brains have more glia per neuron than smaller brains. Our analyses suggest that if one assumes that glia number is proportional to wiring, a particular quantitative relationship emerges between brain size and glia-to-neuron ratio that fits the empirical data. Secondly, many authors have reported that the number of neurons underlying one mm(2) of mammalian cortex is remarkably constant, across both areas and species. Here, we will show that such a constancy emerges when enlarging modular, cortical brain structures. Our analyses thus corroborate recent studies on the mammalian brain as a scalable architecture, providing a possible mechanism to explain some of the principles, constancies and rules that hold across brains of different size.

A cost-benefit analysis of neuronal morphology

Over hundreds of millions of years, evolution has optimized brain design to maximize its functionality while minimizing costs associated with building and maintenance. This observation suggests that one can use optimization theory to rationalize various features of brain design. Here, we attempt to explain the dimensions and branching structure of dendritic arbors by minimizing dendritic cost for given potential synaptic connectivity. Assuming only that dendritic cost increases with total dendritic length and path length from synapses to soma, we find that branching, planar, and compact dendritic arbors, such as those belonging to Purkinje cells in the cerebellum, are optimal. The theory predicts that adjacent Purkinje dendritic arbors should spatially segregate. In addition, we propose two explicit cost function expressions, falsifiable by measuring dendritic caliber near bifurcations.

Scaling of neuron number and volume of the pulvinar complex in New World primates: comparisons with humans, other primates, and mammals

The lateral posterior nucleus and pulvinar (LP-pulvinar complex) are the principal thalamic nuclei associated with the elaborate development of the dorsal and ventral streams of the parietal cortex in primates. In humans, a novel site of origin for a subpopulation of pulvinar neurons has been observed, the ganglionic eminence of the telencephalon. This additional site of neuron origin has been proposed to contribute to the pulvinar's evolutionary expansion (Letinic and Rakic [2001] Nat Neurosci 4:930-936). Studies of neuron number in the LP-pulvinar complex in gibbon, chimpanzee, and gorilla compared to humans, however, did not show that the human LP-pulvinar was unexpectedly large (Armstrong [1981] Am J Phys Anthropol 55:369-383). Here we enlarge the allometric basis for comparison by determining neuron number in the LP-pulvinar complex of six New World primates (Cebus apella, Saimiri ustius, Saguinus midas niger, Alouatta caraya, Aotus azarae, and Callicebus moloch) as well as measuring LP-pulvinar volume in a further set of 24 species including additional primates, carnivores, and rodents. The volume of the LP-pulvinar complex scaled with positive allometry with respect to brain volume across all species examined. The scaling of the number of neurons in the LP-pulvinar complex was extremely similar in New World primates and anthropoid apes, with the human LP-pulvinar value close to the regression line. Comparison of the relative volumes of the LP-pulvinar in the larger sample confirmed this observation, and further demonstrated that both primates and carnivores showed a "grade shift" in its size compared to rodents, with the pulvinar comprising a greater proportion of total brain volume across the board. Diurnal, nocturnal, or crepuscular niche did not discriminate LP-pulvinar size across taxa.

Optimally wired subnetwork determines neuroanatomy of Caenorhabditis elegans

Wiring cost minimization has successfully explained many structures of nervous systems. However, in the nematode Caenorhabditis elegans, for which anatomical data are most detailed, wiring economy is thought to play only a partial role and alone has failed to account for the grouping of neurons into ganglia [Chen BL, Hall DH, Chklovskii DB (2006) Proc Natl Acad Sci USA 103:4723-4728; Kaiser M, Hilgetag CC (2006) PLoS Comput Biol 2:e95; Ahn Y-Y, Jeong H, Kim BJ (2006) Physica A 367:531-537]. Here, we test the hypothesis that optimally wired subnetworks can exist within nonoptimal networks, thus allowing wiring economy to give an improved prediction of spatial structure. We show in C. elegans that the small subnetwork of wires connecting sensory and motor neurons with sensors and muscles, comprising only 15% of connections, is close to optimal and alone predicts the main features of the spatial segregation of neurons into ganglia and encephalization. Moreover, a method to dissect networks into optimal and nonoptimal components is shown to find a large near-optimal subnetwork of 84% of neurons with a very low position error of 5.4%, and that explains clustering of neurons into ganglia and encephalization to fine detail. In general, we expect realistic networks not to be globally optimal in wire cost. We thus propose the strategy of using near-optimal subnetworks to understand neuroanatomical structure.

Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems

It has been suggested that neural systems across several scales of organization show optimal component placement, in which any spatial rearrangement of the components would lead to an increase of total wiring. Using extensive connectivity datasets for diverse neural networks combined with spatial coordinates for network nodes, we applied an optimization algorithm to the network layouts, in order to search for wire-saving component rearrangements. We found that optimized component rearrangements could substantially reduce total wiring length in all tested neural networks. Specifically, total wiring among 95 primate (Macaque) cortical areas could be decreased by 32%, and wiring of neuronal networks in the nematode Caenorhabditis elegans could be reduced by 48% on the global level, and by 49% for neurons within frontal ganglia. Wiring length reductions were possible due to the existence of long-distance projections in neural networks. We explored the role of these projections by comparing the original networks with minimally rewired networks of the same size, which possessed only the shortest possible connections. In the minimally rewired networks, the number of processing steps along the shortest paths between components was significantly increased compared to the original networks. Additional benchmark comparisons also indicated that neural networks are more similar to network layouts that minimize the length of processing paths, rather than wiring length. These findings suggest that neural systems are not exclusively optimized for minimal global wiring, but for a variety of factors including the minimization of processing steps.