Water-tight membranes from neuronal morphology files

Abstract

We present an algorithm to form watertight 3D surfaces consistent with the point-and-diameter based neuronal morphology descriptions widely used with spatial electrophysiology simulators. Such morphology descriptions are readily available online and may come from light-microscopy tracings or from an artificial cell grown algorithmically. These files contain only limited information about a neuron's full three-dimensional shape, as they consist mostly of a list of points and diameters with connectivity data. This representation is well-suited for electrophysiology simulations, where the space constants are larger than geometric ambiguities. However, the simple interpretations used for pure electrophysiological simulation produce geometries unsuitable for multi-scale models that also involve three-dimensional reaction-diffusion, as such models have smaller space constants. Although one cannot exactly reproduce an original neuron's full shape from point-and-diameter data, our new constructive tessellated neuronal geometry (CTNG) algorithm uses constructive solid geometry to define a plausible reconstruction without gaps or cul-de-sacs. CTNG then uses "constructive cubes" to produce a watertight triangular mesh of the neuron surface, suitable for use in reaction-diffusion simulations. CTNG provides the correspondence between internal voxels and surface triangles, needed to make connections between cytoplasmic and membrane mechanisms. Optimization of the underlying marching cubes algorithm and distance calculations enhanced the performance of constructive cubes for a neuronal geometry, where a large number of small objects sparsely occupy a large volume.

Keywords: Discretization; Membrane; Morphology; Reaction–diffusion; Reconstruction; Surface.