Developmental Sequences Predict Increased Connectivity in Brain Evolution: A Comparative Analysis of Developmental Timing, Gene Expression, Neuron Numbers, and Diffusion MR Tractography

Many complex networks have a small-world topology characterized by dense local clustering or cliquishness of connections between neighboring nodes yet a short path length between any (distant) pair of nodes due to the existence of relatively few long-range connections. This is an attractive model for the organization of brain anatomical and functional networks because a small-world topology can support both segregated/specialized and distributed/integrated information processing. Moreover, small-world networks are economical, tending to minimize wiring costs while supporting high dynamical complexity. The authors introduce some of the key mathematical concepts in graph theory required for small-world analysis and review how these methods have been applied to quantification of cortical connectivity matrices derived from anatomical tract-tracing studies in the macaque monkey and the cat. The evolution of small-world networks is discussed in terms of a selection pressure to deliver cost-effective information-processing systems. The authors illustrate how these techniques and concepts are increasingly being applied to the analysis of human brain functional networks derived from electroencephalography/magnetoencephalography and fMRI experiments. Finally, the authors consider the relevance of small-world models for understanding the emergence of complex behaviors and the resilience of brain systems to pathological attack by disease or aberrant development. They conclude that small-world models provide a powerful and versatile approach to understanding the structure and function of human brain systems.

While much information is available on the structural connectivity of the cerebral cortex, especially in the primate, the main organizational principles of the connection patterns linking brain areas, columns and individual cells have remained elusive. We attempt to characterize a wide variety of cortical connectivity data sets using a specific set of graph theory methods. We measure global aspects of cortical graphs including the abundance of small structural motifs such as cycles, the degree of local clustering of connections and the average path length. We examine large-scale cortical connection matrices obtained from neuroanatomical data bases, as well as probabilistic connection matrices at the level of small cortical neuronal populations linked by intra-areal and inter-areal connections. All cortical connection matrices examined in this study exhibit "small-world" attributes, characterized by the presence of abundant clustering of connections combined with short average distances between neuronal elements. We discuss the significance of these universal organizational features of cortex in light of functional brain anatomy. Supplementary materials are at www.indiana.edu/~cortex/lab.htm.

A general model of neural development is derived to fit 18 mammalian species, including humans, macaques, several rodent species, and six metatherian (marsupial) mammals. The goal of this work is to describe heterochronic changes in brain evolution within its basic developmental allometry, and provide an empirical basis to recognize equivalent maturational states across animals. The empirical data generating the model comprises 271 developmental events, including measures of initial neurogenesis, axon extension, establishment, and refinement of connectivity, as well as later events such as myelin formation, growth of brain volume, and early behavioral milestones, to the third year of human postnatal life. The progress of neural events across species is sufficiently predictable that a single model can be used to predict the timing of all events in all species, with a correlation of modeled values to empirical data of 0.9929. Each species' rate of progress through the event scale, described by a regression equation predicting duration of development in days, is highly correlated with adult brain size. Neural heterochrony can be seen in selective delay of retinogenesis in the cat, associated with greater numbers of rods in its retina, and delay of corticogenesis in all species but rodents and the rabbit, associated with relatively larger cortices in species with delay. Unexpectedly, precocial mammals (those unusually mature at birth) delay the onset of first neurogenesis but then progress rapidly through remaining developmental events.