Application of a “Staggered Walk” Algorithm for Generating Large-Scale Morphological Neuronal Networks

Large-scale models of neuronal structures are needed to explore emergent properties of mammalian brains. Because these models have trillions of synapses, a major problem in their creation is synapse placement. Here we present a novel method for exploiting consistent fiber orientation in a neural tissue to perform a highly efficient modified plane-sweep algorithm, which identifies all regions of 3D overlaps between dendritic and axonal projection fields. The first step in placing synapses in physiological models is neurite-overlap detection, at large scales a computationally intensive task. We have developed an efficient “Staggered Walk” algorithm that can find all 3D overlaps of neurites where trillions of synapses connect billions of neurons. 1. Introduction Simulating brain structures with large-scale neuronal models lets researchers precisely manipulate features of simulated neural tissues and observe both local and global properties of neural systems. During the last decade, large-scale brain modeling has risen in prominence, with a wide range of publications on brain-scale models[1–3]. Most large-scale modeling research groups focus either on networks that are highly realistic down to the individual axon collaterals and dendrite branches of each neuron [4] or on systems simplified enough to simulate in near real-time on massively parallel hardware [1, 2]. Rather than emphasizing details or simulation speed, our group is more interested in a balanced approach that capitalizes on general structural connectivity and data acquired through multiunit electrode experiments, diffusion tensor imaging, and connectomics studies with stacked slices of brain tissues stained for scanning [4–6]. To develop and test our model-creation code, we have derived parameters for cerebellar models from the detailed connection and density data for the cerebellar cortex in the compendium by Eccles et al. [7]. Large-scale neuronal models range in accuracy from simple, randomly probabilistic networks [8, 9] to realistic neuronal mappings [4]. The level of detail we need for our models is roughly at the tissue level [10], where probabilities of connectivity between distinct volumes of neural tissue and specified neuronal groups can be derived well enough to create alternative models for comparison. The resulting parameters allow for the generation of microcircuitry for particular areas of the brain. The microcircuits can be repeated, with small changes, up to millions of times in some brain regions [10, 11]. A critical and complex part of large-scale neuronal modeling is the