Coordinate-independent mapping of structural and functional data by objective relational transformation (ORT)

Neuroscience has produced an enormous amount of structural and functional data. Powerful database systems are required to make these data accessible for computational approaches such as higher-order analyses and simulations. Available databases for key data such as anatomical and functional connectivity between cortical areas, however, are still hampered by methodological problems. These problems arise predominantly from the parcellation problem, the use of incongruent parcellation schemes by different authors. We here present a coordinate-independent mathematical method to overcome this problem: objective relational transformation (ORT). Based on new classifications for brain data and on methods from theoretical computer science, ORT represents a formally defined, transparent transformation method for reproducible, coordinate-independent mapping of brain data to freely chosen parcellation schemes. We describe the methodology of ORT and discuss its strengths and limitations. Using two practical examples, we show that ORT in conjunction with connectivity databases like CoCoMac (http://www.cocomac.org) is an important tool for analyses of cortical organization and structure-function relationships.     

Mapping brains without coordinates

Brain mapping has evolved considerably over the last century. While most emphasis has been placed on coordinate-based spatial atlases, coordinate-independent parcellation-based mapping is an important technique for accessing the multitude of structural and functional data that have been reported from invasive experiments, and provides for flexible and efficient representations of information. Here. we provide an introduction to motivations, concepts, techniques and implications of coordinate-independent mapping of microstructurally or functionally defined brain structures. In particular, we explain the problems of constructing mapping paths and finding adequate heuristics for their evaluation. We then introduce the three auxiliary concepts of acronym-based mapping (AM), of a generalized hierarchy (GM ontology), and of a topographically oriented regional map (RM) with adequate granularity for mapping between individual brains with different cortical folding and between humans and non-human primates. Examples from the CoCoMac database of primate brain connectivity demonstrate how these concepts enhance coordinate-independent mapping based on published relational statements. Finally, we discuss the strengths and weaknesses of spatial coordinate-based versus coordinate-independent microstructural brain mapping and show perspectives for a wider application of parcellation-based approaches in the integration of multi-model structural, functional, and clinical data.     

Emergent functional properties of neuronal networks with controlled topology

The interplay between anatomical connectivity and dynamics in neural networks plays a key role in the functional properties of the brain and in the associated connectivity changes induced by neural diseases. However, a detailed experimental investigation of this interplay at both cellular and population scales in the living brain is limited by accessibility. Alternatively, to investigate the basic operational principles with morphological, electrophysiological and computational methods, the activity emerging from large in vitro networks of primary neurons organized with imposed topologies can be studied. Here, we validated the use of a new bio-printing approach, which effectively maintains the topology of hippocampal cultures in vitro and investigated, by patch-clamp and MEA electrophysiology, the emerging functional properties of these grid-confined networks. In spite of differences in the organization of physical connectivity, our bio-patterned grid networks retained the key properties of synaptic transmission, short-term plasticity and overall network activity with respect to random networks. Interestingly, the imposed grid topology resulted in a reinforcement of functional connections along orthogonal directions, shorter connectivity links and a greatly increased spiking probability in response to focal stimulation. These results clearly demonstrate that reliable functional studies can nowadays be performed on large neuronal networks in the presence of sustained changes in the physical network connectivity.     

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.     

Functional connectivity analyses in imaging genetics: considerations on methods and data interpretation

Functional magnetic resonance imaging (fMRI) can be combined with genotype assessment to identify brain systems that mediate genetic vulnerability to mental disorders ("imaging genetics"). A data analysis approach that is widely applied is "functional connectivity". In this approach, the temporal correlation between the fMRI signal from a pre-defined brain region (the so-called "seed point") and other brain voxels is determined. In this technical note, we show how the choice of freely selectable data analysis parameters strongly influences the assessment of the genetic modulation of connectivity features. In our data analysis we exemplarily focus on three methodological parameters: (i) seed voxel selection, (ii) noise reduction algorithms, and (iii) use of additional second level covariates. Our results show that even small variations in the implementation of a functional connectivity analysis can have an impact on the connectivity pattern that is as strong as the potential modulation by genetic allele variants. Some effects of genetic variation can only be found for one specific implementation of the connectivity analysis. A reoccurring difficulty in the field of psychiatric genetics is the non-replication of initially promising findings, partly caused by the small effects of single genes. The replication of imaging genetic results is therefore crucial for the long-term assessment of genetic effects on neural connectivity parameters. For a meaningful comparison of imaging genetics studies however, it is therefore necessary to provide more details on specific methodological parameters (e.g., seed voxel distribution) and to give information how robust effects are across the choice of methodological parameters.     

Epidemiological studies based on medical and administrative databases : a potential strength in France

Population-based epidemiological cohorts may include nowadays hundreds of thousands of subjects, followed-up during decades. France has a major potential strength: nationwide medical and social databases set up for administrative purposes. The main databases useful for epidemiology are the social security database which contains individual medical data from different sources, and the retirement fund database on employment and social benefits. These databases have several advantages: they cover the whole French population, with no lost to follow-up, data are often of good quality and it is possible to link them with individual surveys. However medical data are not always ascertained and an important methodological and practical work has to be done, and some legal and practical problems have to be solved for an optimal use.     

Global relationship between anatomical connectivity and activity propagation in the cerebral cortex

Anatomical connectivity is a prerequisite for cooperative interactions between cortical areas, but it has yet to be demonstrated that association fibre networks determine the macroscopical flow of activity in the cerebral cortex. To test this notion, we constructed a large-scale model of cortical areas whose interconnections were based on published anatomical data from tracing studies. Using this model we simulated the propagation of activity in response to activation of individual cortical areas and compared the resulting topographic activation patterns to electrophysiological observations on the global spread of epileptic activity following intracortical stimulation. Here we show that a neural network with connectivity derived from experimental data reproduces cortical propagation of activity significantly better than networks with different types of neighbourhood-based connectivity or random connections. Our results indicate that association fibres and their relative connection strengths are useful predictors of global topographic activation patterns in the cerebral cortex. This global structure-function relationship may open a door to explicit interpretation of cortical activation data in terms of underlying anatomical connectivity.     

Investigating the neural basis for functional and effective connectivity. Application to fMRI

Viewing cognitive functions as mediated by networks has begun to play a central role in interpreting neuroscientific data, and studies evaluating interregional functional and effective connectivity have become staples of the neuroimaging literature. The neurobiological substrates of functional and effective connectivity are, however, uncertain. We have constructed neurobiologically realistic models for visual and auditory object processing with multiple interconnected brain regions that perform delayed match-to-sample (DMS) tasks. We used these models to investigate how neurobiological parameters affect the interregional functional connectivity between functional magnetic resonance imaging (fMRI) time-series. Variability is included in the models as subject-to-subject differences in the strengths of anatomical connections, scan-to-scan changes in the level of attention, and trial-to-trial interactions with non-specific neurons processing noise stimuli. We find that time-series correlations between integrated synaptic activities between the anterior temporal and the prefrontal cortex were larger during the DMS task than during a control task. These results were less clear when the integrated synaptic activity was haemodynamically convolved to generate simulated fMRI activity. As the strength of the model anatomical connectivity between temporal and frontal cortex was weakened, so too was the strength of the corresponding functional connectivity. These results provide a partial validation for using fMRI functional connectivity to assess brain interregional relations.     

Factor structure of regional cerebral blood flow and glucose metabolism rate as a tool to study the default mode of the brain

The functional connectivity of anatomical and functional brain structures in the state of operational rest was assessed on the basis of positron emission tomography (PET) data to study the so-called default mode of the brain, i.e., the brain’s spontaneous activity at rest. It is concluded that the possibility of identifying neuroanatomical systems of the default mode (default mode network) in routine clinical PET studies of the cerebral blood flow and glucose metabolism is important for studying the functional organization of the brain in the normal state and its rearrangements in pathologies.     

Combining structural connectivity and response latencies to model the structure of the visual system

Several approaches exist to ascertain the connectivity of the brain, and these approaches lead to markedly different topologies, often incompatible with each other. Specifically, recent single-cell recording results seem incompatible with current structural connectivity models. We present a novel method that combines anatomical and temporal constraints to generate biologically plausible connectivity patterns of the visual system of the macaque monkey. Our method takes structural connectivity data from the CoCoMac database and recent single-cell recording data as input and employs an optimization technique to arrive at a new connectivity pattern of the visual system that is in agreement with both types of experimental data. The new connectivity pattern yields a revised model that has fewer levels than current models. In addition, it introduces subcortical-cortical connections. We show that these connections are essential for explaining latency data, are consistent with our current knowledge of the structural connectivity of the visual system, and might explain recent functional imaging results in humans. Furthermore we show that the revised model is not underconstrained like previous models and can be extended to include newer data and other kinds of data. We conclude that the revised model of the connectivity of the visual system reflects current knowledge on the structure and function of the visual system and addresses some of the limitations of previous models.     

Relating Structure and Function in the Human Brain: Relative Contributions of Anatomy,Stationary Dynamics,and Non-stationarities

Investigating the relationship between brain structure and function is a central endeavor for neuroscience research. Yet, the mechanisms shaping this relationship largely remain to be elucidated and are highly debated. In particular, the existence and relative contributions of anatomical constraints and dynamical physiological mechanisms of different types remain to be established. We addressed this issue by systematically comparing functional connectivity (FC) from resting-state functional magnetic resonance imaging data with simulations from increasingly complex computational models, and by manipulating anatomical connectivity obtained from fiber tractography based on diffusion-weighted imaging. We hypothesized that FC reflects the interplay of at least three types of components: (i) a backbone of anatomical connectivity, (ii) a stationary dynamical regime directly driven by the underlying anatomy, and (iii) other stationary and non-stationary dynamics not directly related to the anatomy. We showed that anatomical connectivity alone accounts for up to 15% of FC variance; that there is a stationary regime accounting for up to an additional 20% of variance and that this regime can be associated to a stationary FC; that a simple stationary model of FC better explains FC than more complex models; and that there is a large remaining variance (around 65%), which must contain the non-stationarities of FC evidenced in the literature. We also show that homotopic connections across cerebral hemispheres, which are typically improperly estimated, play a strong role in shaping all aspects of FC, notably indirect connections and the topographic organization of brain networks.     

Functional Connectivity in the Brain Estimated by Analysis of Gamma Events

It is known that gamma activity is generated by local networks. In this paper we introduced a new approach for estimation of functional connectivity between neuronal networks by measuring temporal relations between peaks of gamma event amplitudes. We have shown in freely moving rats that gamma events recorded between electrodes 1.5 mm apart in the majority of cases, are generated by different neuronal modules interfering with each other. The map of functional connectivity between brain areas during the resting state, created based on gamma event temporal relationships is in agreement with anatomical connections and with maps described by fMRI methods during the resting state. The transition from the resting state to exploratory activity is accompanied by decreased functional connectivity between most brain areas. Our data suggest that functional connectivity between interhemispheric areas depends on GABAergic transmission, while intrahemispheric functional connectivity is kainate receptor dependent. This approach presents opportunities for merging electrographic and fMRI data on brain functional connectivity in normal and pathological conditions.     

ViBE-Z: a framework for 3D virtual colocalization analysis in zebrafish larval brains

Precise three-dimensional (3D) mapping of a large number of gene expression patterns, neuronal types and connections to an anatomical reference helps us to understand the vertebrate brain and its development. We developed the Virtual Brain Explorer (ViBE-Z), a software that automatically maps gene expression data with cellular resolution to a 3D standard larval zebrafish (Danio rerio) brain. ViBE-Z enhances the data quality through fusion and attenuation correction of multiple confocal microscope stacks per specimen and uses a fluorescent stain of cell nuclei for image registration. It automatically detects 14 predefined anatomical landmarks for aligning new data with the reference brain. ViBE-Z performs colocalization analysis in expression databases for anatomical domains or subdomains defined by any specific pattern; here we demonstrate its utility for mapping neurons of the dopaminergic system. The ViBE-Z database, atlas and software are provided via a web interface.     

Assessing the influence of different ROI selection strategies on functional connectivity analyses of fMRI data acquired during steady-state conditions

In blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI), assessing functional connectivity between and within brain networks from datasets acquired during steady-state conditions has become increasingly common. However, in contrast to connectivity analyses based on task-evoked signal changes, selecting the optimal spatial location of the regions of interest (ROIs) whose timecourses will be extracted and used in subsequent analyses is not straightforward. Moreover, it is also unknown how different choices of the precise anatomical locations within given brain regions influence the estimates of functional connectivity under steady-state conditions. The objective of the present study was to assess the variability in estimates of functional connectivity induced by different anatomical choices of ROI locations for a given brain network. We here targeted the default mode network (DMN) sampled during both resting-state and a continuous verbal 2-back working memory task to compare four different methods to extract ROIs in terms of ROI features (spatial overlap, spatial functional heterogeneity), signal features (signal distribution, mean, variance, correlation) as well as strength of functional connectivity as a function of condition. We show that, while different ROI selection methods produced quantitatively different results, all tested ROI selection methods agreed on the final conclusion that functional connectivity within the DMN decreased during the continuous working memory task compared to rest.     

Finding Needles in a Haystack with Light: Resolving the Microcircuitry of the Brain with Fluorescence Microscopy

To understand the microcircuitry of the brain, the anatomical and functional connectivity among neurons must be resolved. One of the technical hurdles to achieving this goal is that the anatomical connections, or synapses, are often smaller than the diffraction limit of light and thus are difficult to resolve by conventional microscopy, while the microcircuitry of the brain is on the scale of 1 mm or larger. To date, the gold standard method for microcircuit reconstruction has been electron microscopy (EM). However, despite its rapid development, EM has clear shortcomings as a method for microcircuit reconstruction. The greatest weakness of this method is arguably its incompatibility with functional and molecular analysis. Fluorescence microscopy, on the other hand, is readily compatible with numerous physiological and molecular analyses. We believe that recent advances in various fluorescence microscopy techniques offer a new possibility for reliable synapse detection in large volumes of neural circuits. In this minireview, we summarize recent advances in fluorescence-based microcircuit reconstruction. In the same vein as these studies, we introduce our recent efforts to analyze the long-range connectivity among brain areas and the subcellular distribution of synapses of interest in relatively large volumes of cortical tissue with array tomography and superresolution microscopy.     

Estimation of Directed Effective Connectivity from fMRI Functional Connectivity Hints at Asymmetries of Cortical Connectome

The brain exhibits complex spatio-temporal patterns of activity. This phenomenon is governed by an interplay between the internal neural dynamics of cortical areas and their connectivity. Uncovering this complex relationship has raised much interest, both for theory and the interpretation of experimental data (e.g., fMRI recordings) using dynamical models. Here we focus on the so-called inverse problem: the inference of network parameters in a cortical model to reproduce empirically observed activity. Although it has received a lot of interest, recovering directed connectivity for large networks has been rather unsuccessful so far. The present study specifically addresses this point for a noise-diffusion network model. We develop a Lyapunov optimization that iteratively tunes the network connectivity in order to reproduce second-order moments of the node activity, or functional connectivity. We show theoretically and numerically that the use of covariances with both zero and non-zero time shifts is the key to infer directed connectivity. The first main theoretical finding is that an accurate estimation of the underlying network connectivity requires that the time shift for covariances is matched with the time constant of the dynamical system. In addition to the network connectivity, we also adjust the intrinsic noise received by each network node. The framework is applied to experimental fMRI data recorded for subjects at rest. Diffusion-weighted MRI data provide an estimate of anatomical connections, which is incorporated to constrain the cortical model. The empirical covariance structure is reproduced faithfully, especially its temporal component (i.e., time-shifted covariances) in addition to the spatial component that is usually the focus of studies. We find that the cortical interactions, referred to as effective connectivity, in the tuned model are not reciprocal. In particular, hubs are either receptors or feeders: they do not exhibit both strong incoming and outgoing connections. Our results sets a quantitative ground to explore the propagation of activity in the cortex.     

Rich Club Organization of Macaque Cerebral Cortex and Its Role in Network Communication

Graph-theoretical analysis of brain connectivity data has revealed significant features of brain network organization across a range of species. Consistently, large-scale anatomical networks exhibit highly nonrandom attributes including an efficient small world modular architecture, with distinct network communities that are interlinked by hub regions. The functional importance of hubs motivates a closer examination of their mutual interconnections, specifically to examine the hypothesis that hub regions are more densely linked than expected based on their degree alone, i.e. forming a central rich club. Extending recent findings of rich club topology in the cat and human brain, this report presents evidence for the existence of rich club organization in the cerebral cortex of a non-human primate, the macaque monkey, based on a connectivity data set representing a collation of numerous tract tracing studies. Rich club regions comprise portions of prefrontal, parietal, temporal and insular cortex and are widely distributed across network communities. An analysis of network motifs reveals that rich club regions tend to form star-like configurations, indicative of their central embedding within sets of nodes. In addition, rich club nodes and edges participate in a large number of short paths across the network, and thus contribute disproportionately to global communication. As rich club regions tend to attract and disperse communication paths, many of the paths follow a characteristic pattern of first increasing and then decreasing node degree. Finally, the existence of non-reciprocal projections imposes a net directional flow of paths into and out of the rich club, with some regions preferentially attracting and others dispersing signals. Overall, the demonstration of rich club organization in a non-human primate contributes to our understanding of the network principles underlying neural connectivity in the mammalian brain, and further supports the hypothesis that rich club regions and connections have a central role in global brain communication.