Connectivity and complexity: the relationship between neuroanatomy and brain dynamics

Abstract

Nervous systems facing complex environments have to balance two seemingly opposing requirements. First, there is a need quickly and reliably to extract important features from sensory inputs. This is accomplished by functionally segregated (specialized) sets of neurons, e.g. those found in different cortical areas. Second, there is a need to generate coherent perceptual and cognitive states allowing an organism to respond to objects and events, which represent conjunctions of numerous individual features. This need is accomplished by functional integration of the activity of specialized neurons through their dynamic interactions. These interactions produce patterns of temporal correlations or functional connectivity involving distributed neuronal populations, both within and across cortical areas. Empirical and computational studies suggest that changes in functional connectivity may underlie specific perceptual and cognitive states and involve the integration of information across specialized areas of the brain. The interplay between functional segregation and integration can be quantitatively captured using concepts from statistical information theory, in particular by defining a measure of neural complexity. Complexity measures the extent to which a pattern of functional connectivity produced by units or areas within a neural system combines the dual requirements of functional segregation and integration. We find that specific neuroanatomical motifs are uniquely associated with high levels of complexity and that such motifs are embedded in the pattern of long-range cortico-cortical pathways linking segregated areas of the mammalian cerebral cortex. Our theoretical findings offer new insight into the intricate relationship between connectivity and complexity in the nervous system.

Introduction

Humans experience the world as composed of coherent objects and events, arranged in an ever-changing multi-modal mental scene (Edelman & Tononi, 2000). The coherency of perceptual and cognitive states is achieved rapidly and effortlessly, and it is of critical importance for the ability to execute behavior and motor action that depends on multiple sources of information. How is this remarkable capacity to integrate information rooted in the anatomy and physiology of the nervous system? Integration must occur across vast numbers of specialized neuronal groups and segregated areas of the brain, involving changing subsets of components depending upon the functional state of the organism, its current sensory inputs, and motor behavior. Functional integration accompanying cognitive or behavioral states is associated with patterns of functional connectivity, expressed as deviations from statistical independence (e.g. temporal correlations) across distributed neuronal groups and areas. There is an increasing amount of empirical evidence for the importance of functional connectivity in perception and cognition (reviewed below). Over recent years, neurophysiological and neuroimaging experiments as well as detailed computer simulations of neuronal networks have contributed to our understanding of the neural mechanisms generating functional connectivity.

Several multivariate statistical methods such as multidimensional scaling, path analysis or cluster analysis (Büchel and Friston, 1997, Friston et al., 1996, McIntosh et al., 1994) can be used to characterize patterns of functional connectivity, but none of these methods directly addresses the issue of integrating neural activity across segregated groups and areas. Because we consider functional integration to be central for an understanding of perceptual and cognitive states, we have pursued an approach based on concepts of statistical information theory to measuring integration among elements of a neural system. This approach led to the development of a series of quantitative measures all aiming at how well a given functional architecture balances the dual requirements of functional segregation and integration (Tononi, Edelman, & Sporns, 1998). One measure, called complexity (Tononi, Sporns, & Edelman, 1994), captures deviations from statistical independence (e.g. temporal correlations) across all hierarchical levels within a system and quantifies to what extent specialized local units are globally integrated, participating in coherent states. Another measure, called functional cluster index (Tononi, McIntosh, Russell, & Edelman, 1998), can be used to identify specific subsets of units or areas that interact more strongly with each other than with the rest of the neural system, thus forming a functional cluster. These measures can be applied to multidimensional data sets from computer simulations as well as from neurophysiology or neuroimaging.

It is obvious that functional integration must occur within a structural substrate, defined by the anatomy of the underlying neuronal network. Some computational approaches such as covariance structural equation modeling (e.g. McIntosh et al., 1994, Taylor et al., 2000) aim at inferring causal relations between brain areas from their pattern of covariance, by extracting networks of effective connectivity (Friston, 1994) from functional data sets. We have asked a different, but related, question. In computer simulations, it is easy to observe that different kinds of anatomical structures give rise to different patterns of functional connectivity. This basic observation raises the question of whether distinct neuroanatomical motifs are consistently associated with particular classes of functional connectivity, e.g. those having high levels of complexity. In other words, can high levels of complexity (indicating that specialized information is integrated across a distributed network) be achieved in many qualitatively different ways that are structurally unrelated, or are there unique categories of connectivity or anatomical motifs that favor the emergence of complexity? What selectional processes can drive the emergence of high complexity as networks interact with an environment through inputs and outputs? Answers to these questions may shed light not only on how different neuroanatomical patterns give rise to complex dynamical states, but may also point to factors that have driven the selection of particular anatomies in the course of development and evolution.