Human non-olfactory cognition phase-locked with inhalation

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.

How rich functionality emerges from the invariant structural architecture of the brain remains a major mystery in neuroscience. Recent applications of network theory and theoretical neuroscience to large-scale brain networks have started to dissolve this mystery. Network analyses suggest that hierarchical modular brain networks are particularly suited to facilitate local (segregated) neuronal operations and the global integration of segregated functions. Although functional networks are constrained by structural connections, context-sensitive integration during cognition tasks necessarily entails a divergence between structural and functional networks. This degenerate (many-to-one) function-structure mapping is crucial for understanding the nature of brain networks. The emergence of dynamic functional networks from static structural connections calls for a formal (computational) approach to neuronal information processing that may resolve this dialectic between structure and function.

This paper presents a new method for localizing the electric activity in the brain based on multichannel surface EEG recordings. In contrast to the models presented up to now the new method does not assume a limited number of dipolar point sources nor a distribution on a given known surface, but directly computes a current distribution throughout the full brain volume. In order to find a unique solution for the 3-dimensional distribution among the infinite set of different possible solutions, the method assumes that neighboring neurons are simultaneously and synchronously activated. The basic assumption rests on evidence from single cell recordings in the brain that demonstrates strong synchronization of adjacent neurons. In view of this physiological consideration the computational task is to select the smoothest of all possible 3-dimensional current distributions, a task that is a common procedure in generalized signal processing. The result is a true 3-dimensional tomography with the characteristic that localization is preserved with a certain amount of dispersion, i.e., it has a relatively low spatial resolution. The new method, which we call Low Resolution Electromagnetic Tomography (LORETA) is illustrated with two different sets of evoked potential data, the first showing the tomography of the P100 component to checkerboard stimulation of the left, right, upper and lower hemiretina, and the second showing the results for the auditory N100 component and the two cognitive components CNV and P300. A direct comparison of the tomography results with those obtained from fitting one and two dipoles illustrates that the new method provides physiologically meaningful results while dipolar solutions fail in many situations. In the case of the cognitive components, the method offers new hypotheses on the location of higher cognitive functions in the brain.