Quality Meshing of a Forest of Branching Structures

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, inter-neuron 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.