In brains ofhigher vertebrates, the functional segregation of local areas that differ in their anatomy and physiology contrasts sharply with their global ination during perception and behavior. In this paper, we introduce a measure, called neural complexity (CN), that captures the interplay between these two dental aspects of brain organization. We express functional segregation within a neural system in terms of the relative statistical independence of small subsets of the system and functional integration in terms of signicant deviations from independence of large subsets. CN is then obtained from estimates of the average deviation from statistical independence for subsets of increasing size. CN is shown to be high when functional segregation coexists with integration and to be low when the components of a system are either completely independent (segregated) or completely dependent (integrated). We apply this complexity measure in computer simulations of cortical areas to examine how some basic principles of neuroanatomical organization constrain brain dynamics. We show that the connectivity patterns of the cerebral cortex, such as a high density of connections, strong local connectivity ornizing cells into neuronal groups, patchiness in the connectivity am neuronal groups, and prevalent reciprocal connections, are associated with hi values of CN. The approach outlined here may prove useful in analyzing complexity in other biological domains such as gene regulation and embryogenesis. A long-standing controversy in neuroscience has set localizationist views of brain function against holist views. The former emphasize the specificity and modularity of brain organization, whereas the latter stress global functions, mass action, and Gestalt phenomena (1). This controversy mirrors two contrasting properties that coexist in the brains of higher vertebrates: the functional segregation of different brain regions and their integration in perception and behavior. In this paper, we attempt to provide a measure that reflects their interaction. The understanding of these two aspects of brain organization is central to any theoretical description of brain function (2-4). Evidence that the brain is functionally segregated at multiple levels of organization is overwhelming. Developmental events and activity-dependent selection result in the formation of neuronal groups-local collectives of strongly interconnected cells sharing inputs, outputs, and response properties (2). Each group tends to be connected to a specific subset of other groups and, directly or indirectly, to specific sensory afferents. Different groups within a given brain area (e.g., a primary visual area) can show preferential responses for different stimulus orientations or retinotopic positions. Moreover, at the level of areas or subdivisions of areas, there is functional segregation for different stimulus attributes such as color, motion, and form (5-7). Further evidence for functional segregation in a variety of systems is provided by the analysis of the specific deficits produced by localized cortical lesions (8). In contrast to such local specialization, brain activity is globally integrated at many levels ranging from the neuron to interareal interactions to overall behavioral output. The arrangement of cortical pathways guarantees that any two neurons, whatever their location, are separated from each otherby a small number of synaptic steps. Furthermore, most of the pathways linking any two areas are reciprocal and, hence, provide a structural substrate for reentry-a process of ongoing recursive signaling among neuronal groups and areas across massively parallel paths (2, 3, 9-11). One of the dynamic consequences of reentry is the emergence of widespread patterns of correlations among neuronal groups (10-14). Accordingly, perceptual scenes appear unified and are globally coherent, a property essential for the unity of behavior. Disconnection of various cortical areas often leads to specific disruptions of these integrative processes (8). We have shown (10, 11) that a balance between the functional segregation of specialized areas and their functional integration arises naturally through the constructive and correlative properties of reentry. Computer simulations of the connectivity and physiological characteristics of the visual system showed that neuronal activity in segregated areas simultaneously responding to different stimulus attributes can be integrated to achieve coherent perceptual performance and behavior even in the absence of a master area (10, 11). These models provide a parsimonious theoretical solution to the so-called "binding problem" (15). In the present paper, we consider the relationship between functional segregation and integration in the brain from a more general theoretical perspective. By making certain simplifying assumptions, we show that these two organizational aspects can be formulated within a unified framework. We consider neural systems consisting of a number of elementary components that can be brain areas, groups of neurons, or individual cells. In this initial analysis, we choose the level of neuronal groups (2) and study their dynamic interactions as determined by the topology of their interconnections. We assume that the statistical properties of these interactions do not change with time (stationarity) and that the anatomical connectivity is fixed. Moreover, we concentrate on the intrinsic properties ofa neural system and, hence, do not consider extrinsic inputs from the environment. By following these assumptions, functional segregation and integration are characterized in terms of deviations from statistical independence among the components of a neural system, measured using the concepts of statistical entropy and mutual information (16) . Different neuronal groups are functionally segregated if their activities tend to be statistically independent when these groups are considered a few at a time. Conversely, groups are functionally integrated if they show a high degree of statistical dependence when considered many at a time. This leads to the formulation of a measure, called neural complexity (CN), that reflects the interplay between functional segregation and integration within a neural system. In accord with recent attempts in 5033 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
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A measure for brain complexity: relating functional segregation and integration in the nervous system
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Biology Medicine