Features of brain networks: The spatial, modular, and hierarchical organisation
What constraints shape the spatial layout of neural networks? One influential idea in theoretical neuroscience has been that the overall wiring of neural networks should be as short as possible. Wire-saving could be achieved, for instance, through an optimal spatial arrangement of the connected network components. We evaluated this concept of component placement optimization in two representative systems, the neuronal network of the Caenorhabditis elegans worm and the long-range cortical connections of the primate brain. Contrary to previous results, we found many network layouts with substantially shorter total wiring than that of the original biological networks. This nonoptimal component placement arose from the existence of long-distance connections in the networks. Such connections may come at a developmental and metabolic cost; however, they also help to reduce the number of signal processing steps across the networks (Kaiser & Hilgetag, PLoS Computational Biology, 2006). Topological principles for neural systems include a small-world and scale-free architecture and a modular and hierarchical organisation in the form of multiple clusters at different levels (Kaiser, Neuroimage, 2011). Neural systems also show a hierarchical architecture with modules and sub-modules covering different levels of organization, from cortical columns to visual, auditory, and sensorimotor cortices (Kaiser et al. Frontiers in Neuroinformatics, 2011).
Recent work includes the characterization of the specific modular organisation of human structural connectivity (Kim et al. Phil. Trans. Roy. Soc. B, 2014) and an overview of network features across species (Kaiser, Current Biology, 2015).
Change of features during normal and pathological brain development
Neural systems as well as other biological networks show several organisational properties: they have a high clustering coefficient and a low characteristic path length thus resembling properties of small-world networks, they consists of multiple clusters (Hilgetag & Kaiser, Neuroinformatics, 2004) and they have a distinct spatial organisation (see previous project). How can networks with such properties arise? Which factors are necessary for getting each of these network properties? I could show that a simple model for the development of networks in space, spatial growth, can generate networks with small-world properties (Kaiser & Hilgetag, Physical Review E, 2004). The algorithm can generate networks with similar properties than cortical networks (Kaiser & Hilgetag, Neurocomputing, 2004). However, multiple clusters only arise in few cases. The existence of multiple clusters can be secured if there are time windows for connection establishment so that some parts of the network develops earlier than other parts and there is a higher probability to form connections if both regions have similar time windows for synaptogenesis (Kaiser & Hilgetag, Neurocomputing, 2007). Observing birth-times of neurons in C. elegans we could show that 70% of long-distance connections potentially arise early on during development, before hatching when the worm only has 20% of its final body size. In addition, hub nodes were also generated early on indicating that the time that neurons have available to receive connections from later neurons can explain the increased node degree (Varier & Kaiser, PLoS Computational Biology, 2011).
Recent work includes the characterization of changes in structural connectivity between the ages of 4-40 years showing a preferential detachment of intra-modular and short-distance fibres leaving the crucial long-distance connections intact (Lim et al. Cerebral Cortex, 2015).
Informing treatment options for brain network disorders
How does the effect of lesions and the probability of recovery relate to the structure of cortical networks? Why do some lesions cause more severe deficits than others? Among several measures to predict the effect of removing individual connections, edge betweenness was found to be the best measure for estimating the subsequent increase in characteristic path length after the removal. It turned out that the most important connections (connections whose removal led to the highest deficit) were found between network clusters (Kaiser & Hilgetag, Biological Cybernetics, 2004). In addition, cortical networks behave similar to scale-free networks after the removal of regions or connections. (Kaiser et al., European Journal of Neuroscience, 2007)
Can patterns of activity spreading during epileptic seizures be related to brain connectivity? An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable network activations within a limited critical range. In this range, the activity of neural populations in the network persists between the extremes of quickly dying out, or activating the whole network. Whereas standard explanations for balanced activity involve populations of inhibitory neurons for limiting activity, we observe the effect of network topology on limiting activity spreading. A cluster hierarchy at different levels, from cortical clusters such as the visual cortex at the highest level to individual columns at the lowest level, enables sustained activity in neural systems and prevents large-scale activation as observed during epileptic seizures. Such topological inhibition, in addition to neuronal inhibition, might help to maintain healthy levels of neural activity (Kaiser et al., New Journal of Physics, 2007). To maintain balanced activity it is crucial that the number of synapses per neuron remains comparable for different brain sizes across development and evolution (Kaiser & Hilgetag, Frontiers in Neuroinformatics, 2010).
Recent work includes the characterization of structural connectivity for temporal lobe epilepsy, the prediction of brain regions that are involved in the start of epileptic seizures (Hutchings et al. PLOS Computational Biology, 2015), and ongoing work on predicting the outcome of surgery in epilepsy patients.