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Quality Meshing of a Forest of BranchingStructures

Bajaj, Chandrajit Bajaj and Andrew Gillette

Proceedings, 17th International Meshing Roundtable, Springer-Verlag, pp.433-450, October 12-15 2008

IMR
PROCEEDINGS

17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 12-15, 2008

Department of Computer Sciences & Institute for Computational Engineering
and Sciences, University of Texas at Austin, USA
bajaj@cs.utexas.edu
Department of Mathematics & Institute for Computational Engineering and
Sciences, University of Texas at Austin, USA
agillette@math.utexas.edu

Abstract
Neurons are cellular compartments possessing branching morphologies, with information processing functionality, and the ability to communicate with each other via synaptic junctions (e.g. neurons come within less than a nano-meter of each other in a specialized way). A collection of neurons in each part of the brain form a dense forest of such branching structures, with myriad inter-twined branches, interneuron synaptic connections, and a packing density that leaves only 5% - 10% volume fraction of exterior-cellular space. Small-scale variations in branching morphology of neurons and inter-neuron spacing can exert dramatically different electrical effects that are overlooked by models that treat dendrites as cylindrical compartments in one dimension with lumped parameters. In this paper, we address the problems of generating topologically accurate and spatially realistic boundary element meshes of a forest of neuronal membranes for analyzing their collective electrodynamic properties through simulation. We provide a robust multi-surface reconstruction and quality meshing solution for the forest of densely packed multiple branched structures starting from a stack of segmented 2D serial sections from electron microscopy imaging. The entire 3D domain is about 8 cubic microns, with inter-neuron spacing down to sub-nanometers, adding additional complexity to the robust reconstruction and meshing problem.

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