Assembling Connectivity Matrices

Interregional connectivity patterns of the brain are often represented as connectivity matrices of size n2, where n is the number of brain structures. While the matrix representation is a very concise notation and widely used it can be very differently interpreted. It is commonly assumed that every row or column entry is a single entity, which represents a unique part of the brain. The union of all entities would then be equivalent to a coherent part of the brain such as the visual cortex or the set of thalamo-cortical projections. While such sets of brain regions more often than not represent only a fraction of the brain system of interest, the designation of individual locations may not be unique, for example, when subdivisions are simultaneously listed with a supra-ordinate brain structure or when overlapping entities occur in the same matrix. Several such mapping issues, which are relevant to understanding the scope and reliability of structural and functional connectivity data have been discussed in detail by Kotter and Wanke (2005)

Analyses of connectivity matrices may be influenced by the resolution applied: At the level of lobes the cerebral cortex is a completely connected network, using area granularity the connection density declines to about 50%. Finer divisions produce sparser matrices because of the absence of detailed data but probably also in reality since long-range axons show locally clustered branching patterns leading to increasing sparseness until the resolution matches the branch cluster size. Therefore, when analyzing connectivity matrices it is relevant to note the absolute and relative size of the entities and to consider alternative partitioning schemes as controls.

Over the last 15 years tract tracing data have been collated in several nonhuman species: rats, cats, monkeys (mainly macaques). Some of these have become legacy data. In macaque monkeys, the first comprehensive review of connectivity within the visual system and within the sensorimotor system was published by Felleman and Van Essen (1991). Connectivity matrices resulting from this study have been published and analyzed by others numerous times (see e.g. Sporns and Tononi in this volume). Young added additional data from his reading of the literature and analyzed for the first time a matrix comprising almost the entire cerebral (neo-)cortex at the regional level (Young 1993). Improvements in databasing technology and coordinate-independent brain mapping have subsequently led to a systematic effort in collating tracing data from the entire forebrain in macaques with about 40,000 entries in many different parcellations schemes (; Stephan et al. 2001; Kotter et al. 2004). Several specialized regional matrices have been published and analyzed subsequently (e.g. Bozkurt et al. 2001, 2002; Kotter and Stephan 2003).

Related efforts were made to gain an overview of the regional cortical connectivity (Scannell et al. 1995) and thalamocortical connectivity (Scannell et al. 1999) in the cat. The cortical regions included a large extent of allocor-tex. Burns collected and analyzed regional connectivity of the allocortex and the hypothalamus of the rat (e.g. Burns and Young 2000).

All these efforts relied on data from published anatomical tracing studies. Although these have contributed much to our understanding of cortical organization they are lacking detail addressing important issues: Quantitative and laminar data are rare, and-where available-they do not cover much of the cortex. For example, many data on connections between visual areas in the macaque have been specified in terms of their laminar origin and termination, but they the anatomical density of fibres ("strength") has not received the same amount of attention. The situation is almost the opposite in the sensori-motor system where a group of researchers around Rizzolatti have performed extensive quantifications of connection density. But even fundamental data on the gender of the animals or on the identity of the investigated hemisphere are frequently missing even though they must have been known at the time of the experiments. Whether his shortcoming results from the opinion that such differences are not important or so small that they cannot be demonstrated in a single study or in a single laboratory, it now hampers the insights that could be gleaned from meta-analyses in large data collations. While there is still much information to be gained from investigating tracing data, this does require more detailed attention to the available data and suitable methods for analyzing them.

While macaques are a well investigated genus with particular relevance to the human brain, the wide availability of rodents has resulted in more detailed investigations at the columnar and cellular levels. This bears the promise to bridge levels and to understand the relationship between them. Unfortunately, not much corresponding efforts have been made to match investigations at the different levels.

Summaries of connectivity data suitable for generating matrices at the cellular or laminar levels are rare (see e.g. Hausler and Maass 2007; Bannister 2005; Thomson and Bannister 2003). Corresponding morphological studies often describe individual cases whereas connectivity matrices show cell types, which depend on the classificatory scheme applied. For example, whether every supragranular pyramidal cell has the same cellular or laminar targets or whether the correct number of fundamental inhibitory neuron types has been distinguished, such issues remain a matter of controversy.

There is some hope that characterizations at the molecular level could bring to light a fundamental underlying principle that would motivate a meaningful objective classification. So far, multivariate classifications of neurons based on mRNA or peptide expression (e.g. Markram et al. 2004; Sugino et al. 2006) or genetic constructs for visualizing cells expressing a specific gene product (Hatten and Heintz 2005) have provided exciting new ways of classifying neurons, but they have not resulted in a unified objective scheme.

Thus, the classification of individual cells, similar to the classification of brain structures, relies to a large degree on subjective experience and group consensus. Objective quantitative and universally recognized measures are still elusive.

Last not least, there are simpler animals where the whole nervous system has been targeted. Probably the simplest vertebrate whose motor behaviour has been extensively analyzed to the level of repetitive circuits is the lamprey (e.g., Grillner and Wallen 2002). Physiologically motivated studies that include the anatomy of cellular circuitry are being carried out in invertebrates, such as the leech (e.g., Zheng et al. 2007). Finally, there have been the electron microscopic studies of the whole organism in C. elegans mentioned in the section on neuronal connectivity above (White et al. 1986).

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