Invited reviewThe application of graph theoretical analysis to complex networks in the brain
Introduction
Traditionally, neuroscientists correlate ‘focal’ brain lesions, for instance brain tumors, with ‘focal’ clinical deficits. This approach gave important insights into the localization of brain functions; a classical example is the identification of the motor speech center in the lower left frontal cortex by the French neurologist Paul Broca at the end of the 19th century. Particularly during the last decades of the 20th century, this essentially reductionistic program led to significant progress in neuroscience in terms of molecular and genetic mechanisms.
Despite the impressive increase of knowledge in neuroscience, however, progress in true understanding of higher level brain processes has been disappointing. Evidence has accumulated that functional networks throughout the brain are necessary, particularly for higher cognitive functions such as memory, planning, and abstract reasoning. It is more and more acknowledged that the brain should be conceived as a complex network of dynamical systems, consisting of numerous functional interactions between closely related as well as more remote brain areas (Varela et al., 2001).
Evaluation of the strength and temporal and spatial patterns of interactions in the brain and the characteristics of the underlying functional and anatomical networks may contribute substantially to the understanding of brain function and dysfunction. A major advantage of this approach is that a lot can be learned from other fields of science, particularly the social sciences, that are also devoted to the study of complex systems. In the last decade of the 20th century, considerable progress has been made in the study of complex systems consisting of large numbers of weakly interacting elements. The modern theory of networks, which is derived from graph theory, has proven to be particularly valuable for this purpose (Amaral and Ottino, 2004, Boccaletti et al., 2006).
The aim of this paper is to review applications of network theories to neuroscience in general, and clinical neurophysiology in particular (a more technically oriented review can be found in Stam and Reijneveld (Stam and Reijneveld, 2007)). After a brief historical introduction, we will summarize the basic characteristics of networks in general, and some important results on the relation between network properties and dynamical processes in these networks. Subsequently we will discuss applications of network theories in experimental neuroscience, both neuro-anatomical and neurophysiological. In the last section of this review, we will determine the effect of interventions or brain disease on neural network properties, in the light of patients with disturbed brain function, e.g. cognitive disturbances, epilepsy, and psychiatric disorders.
Section snippets
Historical background
The modern theory of networks has its roots both in mathematics and sociology. In 1736 the mathematician Leonard Euler solved the problem of ‘the bridges of Konigsberg’. This problem involved the question whether it was possible to make a walk crossing exactly one time each of the seven bridges connecting the two islands in the river Pregel and its shores. Euler proved that this is not possible by representing the problem as an abstract network: a ‘graph’. This is often considered as the first
Basics of modern network theory
The discovery of small world networks and scale free networks set off a large body of theoretical and experimental research, which has led to increasing knowledge on various aspects of network properties in the last decade. Before we move on to the application of network theories to experimental neural networks, and healthy and diseased brain, we will provide some basic knowledge on several aspects of network properties. As mentioned before, more detailed mathematical descriptions can be found
Do biological neural networks display small world and scale free properties?
An important question is to what extent the abovementioned features are relevant for networks of neuron-like elements. It is thought that generally speaking the brain is faced with two opposing requirements: (i) segregation, which means local specialization for specific tasks and (ii) integration, combining all the information at a global level (Sporns et al., 2000a, Sporns et al., 2000b, McIntosh, 2000). The first key question is which kind of anatomical and functional architecture allows both
What is the effect of damage on network properties?
Considering functional connectivity and network properties to be a physiological substrate for segregated and distributed information processing (Salvador et al., 2005a, Salvador et al., 2005b, Achard et al., 2006, Achard and Bullmore, 2007), intervention, whether on purpose (e.g. medication) or accidentally (e.g. brain disease), would lead to changes in these parameters. In the next section, we will summarize existing evidence on the effect of intentional manipulation or disease-related
Conclusions and future prospects
In this review, we demonstrate that the modern network theories provide a very useful framework for the study of complex networks in the brain. They offer powerful realistic models and an increasing number of measures to study complex networks in the brain, thereby enabling better understanding of the correlation between network structure and the processes taking place in these networks, in particular synchronization processes, and providing scenarios how complex networks might respond to
Acknowledgement
Thanks to Els van Deventer who helped to retrieve many of the papers used in this review.
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