Proc. Natl. Acad. Sci. USA Vol. 91, pp. 5033-5037, May 1994 Neurobiology A measure for complexity: Relating functional segregation and integration in the GiULio TONONI, OLAF SPORNS, AND GERALD M. EDELMAN The Institute, 3377 North Torrey Pines Court, La , CA 92037 Contributed by Gerald M. Edelman, February 17, 1994

ABSTRACT In ofhigher , the functional the analysis of the specific deficits produced by localized segregation of local areas that differ in their and cortical lesions (8). contrasts sharply with their global ination dur- In contrast to such local specialization, brain activity is ing and . In this paper, we introduce a globally integrated at many levels ranging from the to measure, called neural complexity (CN), that captures the interareal interactions to overall behavioral output. The interplay between these two dental aspects of brain arrangement of cortical pathways guarantees that any two organization. We express functional segregation within a neu- , whatever their location, are separated from each ral system in terms of the relative statistical independence of otherby a small number ofsynaptic steps. Furthermore, most small subsets of the system and functional integration in terms of the pathways linking any two areas are reciprocal and, ofsignicant deviations from independence oflarge subsets. CN hence, provide a structural substrate for reentry-a process is then obtained from estimates of the average deviation from of ongoing recursive signaling among neuronal groups and statistical independence for subsets of increasing size. CN is areas across massively parallel paths (2, 3, 9-11). One of the shown to be high when functional segregation coexists with dynamic consequences of reentry is the emergence of wide- integration and to be low when the components of a system are spread patterns of correlations among neuronal groups (10- either completely independent (segregated) or completely de- 14). Accordingly, perceptual scenes appear unified and are pendent (integrated). We apply this complexity measure in globally coherent, a property essential for the unity of computer simulations of cortical areas to examine how some behavior. Disconnection of various cortical areas often leads basic principles of neuroanatomical organization constrain to specific disruptions of these integrative processes (8). brain dynamics. We show that the connectivity patterns of the We have shown (10, 11) that a balance between the cerebral cortex, such as a high density of connections, strong functional segregation of specialized areas and their func- local connectivity ornizing cells into neuronal groups, patch- tional integration arises naturally through the constructive iness in the connectivity am neuronal groups, and prevalent and correlative properties of reentry. Computer simulations reciprocal connections, are associated with hi values of CN. of the connectivity and physiological characteristics of the The approach outlined here may prove useful in analyzing visual system showed that neuronal activity in segregated complexity in other biological domains such as gene regulation areas simultaneously responding to different stimulus at- and embryogenesis. tributes can be integrated to achieve coherent perceptual performance and behavior even in the absence of a master A long-standing controversy in has set local- area (10, 11). These models provide a parsimonious th