Project Personnel:Nancy Amato
The brain has extraordinary computational power to represent and interpret complex natural environments. The topology and geometry of the structures in the brain have a decissive role in these natural computations. NeuronPRM is a framework to construct a 3D model of a cortical network, using probabilistic roadmap methods. Although not the usual motion planning problem, our objective of building a network that encodes the pathways of the cortical network is analogous to the PRM objective of constructing roadmaps that contain a representative sample of feasible paths. We represent the network as a large-scale directed graph and use L-systems and statistics data to `grow' neurons that are morphologically indistinguishable from real neurons. Our ultimate goal is to map and understand the connectivity and geometry of the cortical network.
Neuron-PRM (N-PRM) samples graph nodes and connects nodes using local information. Each vertex in the graph defines a configuration of a neuron and each directed edge represents an abstract connection or synapse between neurons. Here, we define an abstract synpase as a set of real synapses from segments of one neuron to another. Since actual synapses can be quite complex, these abstract synapses help us not only maintain data more easily but also provide a hierarchical representation for searching the cortical network. Following figure shows the result of N-PRM in abstract level.
Statistically each neuron has thousands of synapses. An adult human being has more than one hundred billion neurons and even the cortex of the mouse has more than seventeen billion neurons. Based on current technology, it is not feasible to compute and store such a huge amount of synaptic connections between all possible pairs of neurons. The tradition PRM connection strategy of computing all pairwise distances and attempting to connect the k-closet nodes is not feasible for roadmaps with millions or billions of nodes, each of which consists of thousands of segments. To deal with such large numbers of complex nodes, we define simple dustnace metrics to reject neuron pairs and find potentioal synapses very quickly. Most neuron pairs are quickly rejected by a filtering test, which checks for intersection of their bounding volumes. Thus, detailed distance computations between the neuronal segmetns will only be performed for those neuron pairs that pass the bounding volume test. Three bounding columes tests are implemented. They are bounding sphere, boudning box, bounding convex hull.
After constructing the roadmaps with abstract synaptic connections, we applied the simple synapse discovery algorithm to identify real synapses. The running time for discovery is linear in the number of edges of the input roadmap, so the convex hull is the fastest.
We determined that the approximate convex hull bounding volume was the fastest overall (considering both the cost of the abstract and the actual synapse discovery phases); its drawback is the increased storage requirements for the convex hull as compared to the bounding sphere or box.
Neuron PRM: A Framework for Constructing Cortical Networks, Jyh-Ming Lien, Marco Morales, Nancy M. Amato, Neurocomputing, 52-54(28):191-197, Jun 2003. Also, Technical Report, TR01-002, Parasol Laboratory, Department of Computer Science, Texas A&M University, Oct 2001.
Journal(ps, pdf, abstract) Technical Report(ps, pdf, abstract)
Supported by NSF, Dept. of Education, Texas Higher Education Coordinating Board
Project Alumni:Jyh-Ming Lien,Marco Morales
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