Bringing Anatomical Information into Neuronal Network Models.

For constructing neuronal network models computational neuroscientists have access to wide-ranging anatomical data that nevertheless tend to cover only a fraction of the parameters to be determined. Finding and interpreting the most relevant data, estimating missing values, and combining the data and estimates from various sources into a coherent whole is a daunting task. With this chapter we aim to provide guidance to modelers by describing the main types of anatomical data that may be useful for informing neuronal network models. We further discuss aspects of the underlying experimental techniques relevant to the interpretation of the data, list particularly comprehensive data sets, and describe methods for filling in the gaps in the experimental data. Such methods of "predictive connectomics" estimate connectivity where the data are lacking based on statistical relationships with known quantities. Exploiting organizational principles that link the plethora of data in a unifying framework can be useful for informing computational models. Besides overarching principles, we touch upon the most prominent features of brain organization that are likely to influence predicted neuronal network dynamics, with a focus on the mammalian cerebral cortex. Given the still existing need for modelers to navigate a complex data landscape full of holes and stumbling blocks, it is vital that the field of neuroanatomy is moving toward increasingly systematic data collection, representation, and publication.

Spatiotemporal ontogeny of brain wiring.

The wiring of vertebrate and invertebrate brains provides the anatomical skeleton for cognition and behavior. Connections among brain regions are characterized by heterogeneous strength that is parsimoniously described by the wiring cost and homophily principles. Moreover, brains exhibit a characteristic global network topology, including modules and hubs. However, the mechanisms resulting in the observed interregional wiring principles and network topology of brains are unknown. Here, with the aid of computational modeling, we demonstrate that a mechanism based on heterochronous and spatially ordered neurodevelopmental gradients, without the involvement of activity-dependent plasticity or axonal guidance cues, can reconstruct a large part of the wiring principles (on average, 83%) and global network topology (on average, 80%) of diverse adult brain connectomes, including fly and human connectomes. In sum, space and time are key components of a parsimonious, plausible neurodevelopmental mechanism of brain wiring with a potential universal scope, encompassing vertebrate and invertebrate brains.

Neural correlates of visuospatial bias in patients with left hemisphere stroke: a causal functional contribution analysis based on game theory.

Stroke patients frequently display spatial neglect, an inability to report, or respond to, relevant stimuli in the contralesional space. Although this syndrome is widely considered to result from the dysfunction of a large-scale attention network, the individual contributions of damaged grey and white matter regions to neglect are still being disputed. Moreover, while the neuroanatomy of neglect in right hemispheric lesions is well studied, the contributions of left hemispheric brain regions to visuospatial processing are less well understood. To address this question, 128 left hemisphere acute stroke patients were investigated with respect to left- and rightward spatial biases measured as severity of deviation in the line bisection test and as Center of Cancellation (CoC) in the Bells Test. Causal functional contributions and interactions of nine predefined grey and white matter regions of interest in visuospatial processing were assessed using Multi-perturbation Shapley value Analysis (MSA). MSA, an inference approach based on game theory, constitutes a robust and exact multivariate mathematical method for inferring functional contributions from multi-lesion patterns. According to the analysis of performance in the Bells test, leftward attentional bias (contralesional deficit) was associated with contributions of the left superior temporal gyrus and rightward attentional bias with contributions of the left inferior parietal lobe, whereas the arcuate fascicle was contributed to both contra- and ipsilesional bias. Leftward and rightward deviations in the line bisection test were related to contributions of the superior longitudinal fascicle and the inferior parietal lobe, correspondingly. Thus, Bells test and line bisection tests, as well as ipsi- and contralesional attentional biases in these tests, have distinct neural correlates. Our findings demonstrate the contribution of different grey and white matter structures to contra- and ipsilesional spatial biases as revealed by left hemisphere stroke. The results provide new insights into the role of the left hemisphere in visuospatial processing.

Sequence of information processing for emotions based on the anatomic dialogue between prefrontal cortex and amygdala.

The prefrontal cortex and the amygdala have synergistic roles in regulating purposive behavior, effected through bidirectional pathways. Here we investigated the largely unknown extent and laminar relationship of prefrontal input-output zones linked with the amygdala using neural tracers injected in the amygdala in rhesus monkeys. Prefrontal areas varied vastly in their connections with the amygdala, with the densest connections found in posterior orbitofrontal and posterior medial cortices, and the sparsest in anterior lateral prefrontal areas, especially area 10. Prefrontal projection neurons directed to the amygdala originated in layer 5, but significant numbers were also found in layers 2 and 3 in posterior medial and orbitofrontal cortices. Amygdalar axonal terminations in prefrontal cortex were most frequently distributed in bilaminar bands in the superficial and deep layers, by columns spanning the entire cortical depth, and less frequently as small patches centered in the superficial or deep layers. Heavy terminations in layers 1-2 overlapped with calbindin-positive inhibitory neurons. A comparison of the relationship of input to output projections revealed that among the most heavily connected cortices, cingulate areas 25 and 24 issued comparatively more projections to the amygdala than they received, whereas caudal orbitofrontal areas were more receivers than senders. Further, there was a significant relationship between the proportion of 'feedforward' cortical projections from layers 2-3 to 'feedback' terminations innervating the superficial layers of prefrontal cortices. These findings indicate that the connections between prefrontal cortices and the amygdala follow similar patterns as corticocortical connections, and by analogy suggest pathways underlying the sequence of information processing for emotions.

The portable UNIX programming system (PUPS) and CANTOR: a computational environment for dynamical representation and analysis of complex neurobiological data.

Many problems in analytical biology, such as the classification of organisms, the modelling of macromolecules, or the structural analysis of metabolic or neural networks, involve complex relational data. Here, we describe a software environment, the portable UNIX programming system (PUPS), which has been developed to allow efficient computational representation and analysis of such data. The system can also be used as a general development tool for database and classification applications. As the complexity of analytical biology problems may lead to computation times of several days or weeks even on powerful computer hardware, the PUPS environment gives support for persistent computations by providing mechanisms for dynamic interaction and homeostatic protection of processes. Biological objects and their interrelations are also represented in a homeostatic way in PUPS. Object relationships are maintained and updated by the objects themselves, thus providing a flexible, scalable and current data representation. Based on the PUPS environment, we have developed an optimization package, CANTOR, which can be applied to a wide range of relational data and which has been employed in different analyses of neuroanatomical connectivity. The CANTOR package makes use of the PUPS system features by modifying candidate arrangements of objects within the system's database. This restructuring is carried out via optimization algorithms that are based on user-defined cost functions, thus providing flexible and powerful tools for the structural analysis of the database content. The use of stochastic optimization also enables the CANTOR system to deal effectively with incomplete and inconsistent data. Prototypical forms of PUPS and CANTOR have been coded and used successfully in the analysis of anatomical and functional mammalian brain connectivity, involving complex and inconsistent experimental data. In addition, PUPS has been used for solving multivariate engineering optimization problems and to implement the digital identification system (DAISY), a system for the automated classification of biological objects. PUPS is implemented in ANSI-C under the POSIX.1 standard and is to a great extent architecture- and operating-system independent. The software is supported by systems libraries that allow multi-threading (the concurrent processing of several database operations), as well as the distribution of the dynamic data objects and library operations over clusters of computers. These attributes make the system easily scalable, and in principle allow the representation and analysis of arbitrarily large sets of relational data. PUPS and CANTOR are freely distributed (http://www.pups.org.uk) as open-source software under the GNU license agreement.

Quantitative architecture distinguishes prefrontal cortical systems in the rhesus monkey.

The prefrontal cortex encompasses a large and heterogeneous set of areas, whose borders have been variously mapped in different architectonic studies. Differences in cortical maps present a formidable problem in comparing data across studies and in constructing databanks on the connections and functional attributes of cortical areas. Here we used quantitative approaches to cortical mapping to investigate (i) if architectonic areas of the prefrontal cortex in adult rhesus monkeys have unique profiles and (ii) if groups of architectonic areas belonging to distinct cortical types, ranging from agranular to eulaminate, have similar features. In addition, we used multidimensional analyses to see if, and how, prefrontal areas form clusters when multiple features are considered simultaneously. We used quantitative unbiased sampling procedures to estimate the areal and laminar density of neurons, glia and neurons positive for the calcium binding proteins parvalbumin (PV), calbindin (CB) and calretinin (CR) among 21 prefrontal areas or subdivisions of areas. Neuronal density varied among the prefrontal cortices (range: 38 569 +/- 4078 to 58 708 +/- 2327 neurons/mm(3)); it was lowest in caudal orbitofrontal and medial areas (OPAll, OPro, 13, 24a, 32, M25) and highest in lateral prefrontal areas (subdivisions of areas 46 and 8). Neurons positive for PV were most prevalent in lateral prefrontal areas and least prevalent in caudal orbitofrontal and medial pre-frontal areas, whereas the opposite trend was noted for neurons that expressed CB. Neurons positive for CR did not show regional differences, and the density of glia showed small variations among prefrontal cortices. The differences among areas, along with differences in the thickness of individual areas and layers, were used to establish a quantitative profile for each area. The results showed that differences in the density of neurons, and the preponderance of neurons positive for PV and CB, were related to different architectonic types of areas found within the prefrontal cortex. Conventional as well as multiparameter statistical analyses distinguished at one extreme the agranular and dysgranular (limbic) cortices, which were characterized by prominent deep layers (V-VI), the lowest neuronal density, the highest ratio of glia/neurons, and the lowest density of PV and the highest for CB. At the other extreme, lateral eulaminate cortices were characterized by the highest density of neurons, a prominent granular layer IV, denser supragranular (II-III) than infragranular (V-VI) layers, and a balanced distribution of neurons positive for PV and CB. The results provide insights into potentially different rates of development or maturation of limbic and eulaminate prefrontal areas, and their differential vulnerability in neurological and psychiatric diseases. The quantitative methods used provide an objective approach to construct maps, address differences in nomenclature across studies, establish homologies in different species and provide a baseline to identify changes in pathologic conditions.

Enhanced visual spatial attention ipsilateral to rTMS-induced 'virtual lesions' of human parietal cortex.

The breakdown of attentional mechanisms after brain damage can have drastic behavioral consequences, as in patients suffering from spatial neglect. While much research has concentrated on impaired attention to targets contralateral to sites of brain damage, here we report the ipsilateral enhancement of visual attention after repetitive transcranial magnetic stimulation (rTMS) of parietal cortex at parameters known to reduce cortical excitability. Normal healthy subjects received rTMS (1 Hz, 10 mins) over right or left parietal cortex. Subsequently, detection of visual stimuli contralateral to the stimulated hemisphere was consistently impaired when stimuli were also present in the opposite hemifield, mirroring the extinction phenomenon commonly observed in neglect patients. Additionally, subjects' attention to ipsilateral targets improved significantly over normal levels. These results underline the potential of focal brain dysfunction to produce behavioral improvement and give experimental support to models of interhemispheric competition in the distributed brain network for spatial attention.

Simultaneity of responses in a hierarchical visual network.

The pattern of anatomical connections between areas of the primate visual system is organized hierarchically. However, onset latencies in parietal and occipital stations are often simultaneous, and this seems to contradict hierarchical organization in its simplest interpretation, as serial organization. To understand the reasons for this contradiction, we simulated the cortical network for which there is onset data, including the network's hierarchical structure. The network's dynamics reproduced the simultaneous onset latencies reported in several dorsal areas. These results show that a strictly hierarchical visual system is compatible with much more complex dynamics than serial processing, and that hodological and biophysical properties, are more closely related to onset dynamics than is hierarchical organisation.

Uniformity, specificity and variability of corticocortical connectivity.

In many studies of the mammalian brain, subjective assessments of connectivity patterns and connection strengths have been used to subdivide the cortex into separate but linked areas and to make deductions about the flow of information through the cortical network. Here we describe the results of applying statistical analyses to quantitative corticocortical connection data, and the conclusions that can be drawn from such quantitative approaches. Injections of the tracer WGA-HRP were made into different visual areas either side of the middle suprasylvian sulcus (MSS) in 11 adult cats. Retrogradely labelled cells produced by these injections were counted in selected coronal sections taken at regularly spaced intervals (1 mm) through the entire visual cortex, and their cumulative sums and relative proportions in each of 16 recognized visual cortical areas were computed. The surface dimensions of these areas were measured in each cat, from contour lines made on enlarged drawings of the same sections. A total of 116,149 labelled neurons were assigned to all visual cortical areas in the 11 cats, with 5212 others excluded because of their uncertain location. The distribution of relative connection strengths, that is, the percentage of labelled cells per cortical area, was evaluated using non-parametric cluster analyses and Monte Carlo simulation, and relationships between connection strength and area size were examined by linear regression. The absolute size of each visual cortical area was uniform across individual cats, whereas the strengths of connections between the same area pairs were extremely variable for injections in different animals. The overall distribution of labelling strengths for corticocortical connections was continuous and monotonic, rather than inherently clustered, with the highest frequencies presented by the absent (zero density) and the very-low-density connections. These two categories could not, on analytical grounds, be separated from each other. Thus it seems that any subjective description of corticocortical connectivity strengths by ordinal classes (such as 'absent', 'weak', 'moderate' or 'strong') imposes a categorization on the data, rather than recognizes a structure inherent in the data themselves. Despite the great variability of connections, similarities in the distribution profiles for the relative strengths of labelled cells in all areas could be used to identify clusters of different injection sites in the MSS. This supported the conclusion that there are four connectionally distinct subdivisions of this cortex, corresponding to areas 21a, PMLS and AMLS (in the medial bank) and to area PLLS (in the lateral bank). Even for tracer deposits in the same cortical subdivision, however, the strength of connections projecting to the site from other cortical areas varied greatly across injection in different individual animals. We further demonstrated that, on average, the strength of connections originating from any given cortical area was positively and linearly correlated with the size of its surface dimensions. When analysed by specific injection site location, however, this relationship was shown to hold for the individual connections to the medial bank MSS areas, but not for connections leading to the lateral bank area. The data suggest that connectivity of the cat's visual cortex possesses a number of uniform global features, which are locally organized in such a way as to give each cortical area unique characteristics.

Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat.

The number of different cortical structures in mammalian brains and the number of extrinsic fibres linking these regions are both large. As with any complex system, systematic analysis is required to draw reliable conclusions about the organization of the complex neural networks comprising these numerous elements. One aspect of organization that has long been suspected is that cortical networks are organized into 'streams' or 'systems'. Here we report computational analyses capable of showing whether clusters of strongly interconnected areas are aspects of the global organization of cortical systems in macaque and cat. We used two different approaches to analyse compilations of corticocortical connection data from the macaque and the cat. The first approach, optimal set analysis, employed an explicit definition of a neural 'system' or 'stream', which was based on differential connectivity. We defined a two-component cost function that described the cost of the global cluster arrangement of areas in terms of the areas' connectivity within and between candidate clusters. Optimal cluster arrangements of cortical areas were then selected computationally from the very many possible arrangements, using an evolutionary optimization algorithm. The second approach, non-parametric cluster analysis (NPCA), grouped cortical areas on the basis of their proximity in multidimensional scaling representations. We used non-metric multidimensional scaling to represent the cortical connectivity structures metrically in two and five dimensions. NPCA then analysed these representations to determine the nature of the clusters for a wide range of different cluster shape parameters. The results from both approaches largely agreed. They showed that macaque and cat cortices are organized into densely intra-connected clusters of areas, and identified the constituent members of the clusters. These clusters reflected functionally specialized sets of cortical areas, suggesting that structure and function are closely linked at this gross, systems level.

Hierarchical organization of macaque and cat cortical sensory systems explored with a novel network processor.

Neuroanatomists have described a large number of connections between the various structures of monkey and cat cortical sensory systems. Because of the complexity of the connection data, analysis is required to unravel what principles of organization they imply. To date, analysis of laminar origin and termination connection data to reveal hierarchical relationships between the cortical areas has been the most widely acknowledged approach. We programmed a network processor that searches for optimal hierarchical orderings of cortical areas given known hierarchical constraints and rules for their interpretation. For all cortical systems and all cost functions, the processor found a multitude of equally low-cost hierarchies. Laminar hierarchical constraints that are presently available in the anatomical literature were therefore insufficient to constrain a unique ordering for any of the sensory systems we analysed. Hierarchical orderings of the monkey visual system that have been widely reported, but which were derived by hand, were not among the optimal orderings. All the cortical systems we studied displayed a significant degree of hierarchical organization, and the anatomical constraints from the monkey visual and somato-motor systems were satisfied with very few constraint violations in the optimal hierarchies. The visual and somato-motor systems in that animal were therefore surprisingly strictly hierarchical. Most inconsistencies between the constraints and the hierarchical relationships in the optimal structures for the visual system were related to connections of area FST (fundus of superior temporal sulcus). We found that the hierarchical solutions could be further improved by assuming that FST consists of two areas, which differ in the nature of their projections. Indeed, we found that perfect hierarchical arrangements of the primate visual system, without any violation of anatomical constraints, could be obtained under two reasonable conditions, namely the subdivision of FST into two distinct areas, whose connectivity we predict, and the abolition of at least one of the less reliable rule constraints. Our analyses showed that the future collection of the same type of laminar constraints, or the inclusion of new hierarchical constraints from thalamocortical connections, will not resolve the problem of multiple optimal hierarchical representations for the primate visual system. Further data, however, may help to specify the relative ordering of some more areas. This indeterminacy of the visual hierarchy is in part due to the reported absence of some connections between cortical areas. These absences are consistent with limited cross-talk between differentiated processing streams in the system. Hence, hierarchical representation of the visual system is affected by, and must take into account, other organizational features, such as processing streams.

Computational analysis of functional connectivity between areas of primate cerebral cortex.

Recent analyses of association fibre networks in the primate cerebral cortex have revealed a small number of densely intra-connected and hierarchically organized structural systems. Corresponding analyses of data on functional connectivity are required to establish the significance of these structural systems. We therefore built up a relational database by systematically collating published data on the spread of activity after strychnine-induced disinhibition in the macaque cerebral cortex in vivo. After mapping these data to two different parcellation schemes, we used three independent methods of analysis which demonstrate that the cortical network of functional interactions is not homogeneous, but shows a clear segregation into functional assemblies of mutually interacting areas. The assemblies suggest a principal division of the cortex into visual, somatomotor and orbito-temporo-insular systems, while motor and somatosensory areas are inseparably interrelated. These results are largely compatible with corresponding analyses of structural data of mammalian cerebral cortex, and deliver the first functional evidence for 'small-world' architecture of primate cerebral cortex.

On imputing function to structure from the behavioural effects of brain lesions.

What is the link, if any, between the patterns of connections in the brain and the behavioural effects of localized brain lesions? We explored this question in four related ways. First, we investigated the distribution of activity decrements that followed simulated damage to elements of the thalamocortical network, using integrative mechanisms that have recently been used to successfully relate connection data to information on the spread of activation, and to account simultaneously for a variety of lesion effects. Second, we examined the consequences of the patterns of decrement seen in the simulation for each type of inference that has been employed to impute function to structure on the basis of the effects of brain lesions. Every variety of conventional inference, including double dissociation, readily misattributed function to structure. Third, we tried to derive a more reliable framework of inference for imputing function to structure, by clarifying concepts of function, and exploring a more formal framework, in which knowledge of connectivity is necessary but insufficient, based on concepts capable of mathematical specification. Fourth, we applied this framework to inferences about function relating to a simple network that reproduces intact, lesioned and paradoxically restored orientating behaviour. Lesion effects could be used to recover detailed and reliable information on which structures contributed to particular functions in this simple network. Finally, we explored how the effects of brain lesions and this formal approach could be used in conjunction with information from multiple neuroscience methodologies to develop a practical and reliable approach to inferring the functional roles of brain structures.

The connectional organization of the cortico-thalamic system of the cat.

Data on connections between the areas of the cerebral cortex and nuclei of the thalamus are too complicated to analyse with naked intuition. Indeed, the complexity of connection data is one of the major challenges facing neuroanatomy. Recently, systematic methods have been developed and applied to the analysis of the connectivity in the cerebral cortex. These approaches have shed light on the gross organization of the cortical network, have made it possible to test systematically theories of cortical organization, and have guided new electrophysiological studies. This paper extends the approach to investigate the organization of the entire cortico-thalamic network. An extensive collation of connection tracing studies revealed approximately 1500 extrinsic connections between the cortical areas and thalamic nuclei of the cat cerebral hemisphere. Around 850 connections linked 53 cortical areas with each other, and around 650 connections linked the cortical areas with 42 thalamic nuclei. Non-metric multidimensional scaling, optimal set analysis and non-parametric cluster analysis were used to study global connectivity and the 'place' of individual structures within the overall scheme. Thalamic nuclei and cortical areas were in intimate connectional association. Connectivity defined four major thalamo-cortical systems. These included three broadly hierarchical sensory or sensory/motor systems (visual and auditory systems and a single system containing both somatosensory and motor structures). The highest stations of these sensory/motor systems were associated with a fourth processing system composed of prefrontal, cingulate, insular and parahippocampal cortex and associated thalamic nuclei (the 'fronto-limbic system'). The association between fronto-limbic and somato-motor systems was particularly close.

A solution to the binding problem? Information processing.

The brain effortlessly recombines information about the shape, colour, motion and so on of objects in the visual scene, but how it does so is not known. Synchronous neuronal firing has seemed an attractive solution to this problem, but new results and theoretical insights cast doubt on its functional role.

Non-metric multidimensional scaling in the analysis of neuroanatomical connection data and the organization of the primate cortical visual system.

Neuroanatomists have established that the various gross structures of the brain are divided into a large number of different processing regions and have catalogued a large number of connections between these regions. The connectional data derived from neuroanatomical studies are complex, and reliable conclusions about the organization of brain systems cannot be drawn from considering them without some supporting analysis. Recognition of this problem has recently led to the application of a variety of techniques to the analysis of connection data. One of the techniques that we previously employed, non-metric multidimensional scaling (NMDS), appears to have revealed important aspects of the organization of the central nervous system, such as the gross organization of the whole cortical network in two species. We present here a detailed treatment of methodological aspects of the application of NMDS to connection data. We first examine in detail the particular properties of neuroanatomical connection data. Second, we consider the details of NMDS and discuss the propriety of different possible NMDS approaches. Third, we present results of the analyses of connection data from the primate visual system, and discuss their interpretation. Fourth, we study independent analyses of the organization of the visual system, and examine the relation between the results of these analyses and those from NMDS. Fifth, we investigate quantitatively the performance of a number of data transformation and conditioning procedures, as well as tied and untied NMDS analysis of untransformed low-level data, to determine how well NMDS can recover known metric parameters from artificial data. We then re-analyse real connectivity data with the most successful methods at removing the effects of sparsity, to ensure that this aspect of data structure does not obscure others. Finally, we summarize the evidence on the connectional organization of the primate visual system, and discuss the reliability of NMDS analyses of neuroanatomical connection data.