Synthesis of geometrically realistic and watertight neuronal ultrastructure manifolds for in silico modeling

Abstract

Understanding the intracellular dynamics of brain cells entails performing three-dimensional molecular simulations incorporating ultrastructural models that can capture cellular membrane geometries at nanometer scales. While there is an abundance of neuronal morphologies available online, e.g. from NeuroMorpho.Org, converting those fairly abstract point-and-diameter representations into geometrically realistic and simulation-ready, i.e. watertight, manifolds is challenging. Many neuronal mesh reconstruction methods have been proposed; however, their resulting meshes are either biologically unplausible or non-watertight. We present an effective and unconditionally robust method capable of generating geometrically realistic and watertight surface manifolds of spiny cortical neurons from their morphological descriptions. The robustness of our method is assessed based on a mixed dataset of cortical neurons with a wide variety of morphological classes. The implementation is seamlessly extended and applied to synthetic astrocytic morphologies that are also plausibly biological in detail. Resulting meshes are ultimately used to create volumetric meshes with tetrahedral domains to perform scalable in silico reaction-diffusion simulations for revealing cellular structure-function relationships. Availability and implementation: Our method is implemented in NeuroMorphoVis, a neuroscience-specific open source Blender add-on, making it freely accessible for neuroscience researchers.

Keywords: in silico; mesh reconstruction; molecular simulations; reaction-diffusion simulations; surface and solid voxelization; ultrasturcture; watertight.

Figure 1

The structure of a neuronal morphology in three formats: (A) individual samples, where each sample has a unique identifier, position and diameter, (B) segments, in which each pair of connected samples form conical segments, and (C) sections, where adjacent segments between two branching points construct an individual section. The arbors are composed of a set of connected sections and stored in acyclic graphs. Dendritic spines are not shown.

Figure 2

The neuronal morphology (A) is initially used to create a set of corresponding proxy meshes of every individual component of the morphology, which are then combined into a single mesh object with overlapping geometries using a joint operation (B). The Voxel remesher is applied to this mesh object to create a volumetric representation of the membrane (C) with which all the overlapping structures are eliminated. This remesher creates a watertight manifold with a continuous and smooth surface (D), which can be used to synthesize a volumetric mesh (E), for example, using TetGen, to perform a stochastic reaction-diffusion simulation in steps (F). Dendritic spines are not shown.

Figure 3

Two approaches are used to construct the proxies of the arbors: node-to-leaf path constructions (A) and articulated sections, where an icosphere (or geodesic polyhedra) is added at every branching point along the arbor (B).

Figure 4

Creation of somatic profiles using implicit surfaces (A) and soft body simulations (B). The realism of the resulting profile using the soft body approach requires tuning the stiffness of the soft body object—indicated on the side of every simulation—and the initial radius of the icosphere used to build the mesh (C).

Figure 5

Integration of spines models with realistic geometries along the dendrites of a pyramidal neuron (A). The mesh in light red is created using union operators [30], while that in blue is created with our proposed method. The closeups in (B1–3) demonstrate the smooth connectivity between the spines and the dendrites. Wireframe visualizations are shown in Fig. 8. (B4) The union operator fails to weld the spine meshes with the dendritic mesh resulting in a fragmented mesh.

Figure 6

(A) A closeup on a dendritic segment of a spiny neuron showing the resulting meshes with different voxelization resolutions: 0.07 and 0.1 m for the red and blue meshes, respectively. Using lower resolution without taking into consideration the dimensions of the spine meshes results in fragmented mesh partitions as demonstrated by the magnifications in (B).

Figure 7

The neuronal mesh generated from the Voxel remesher (left) is typically highly tessellated (100k triangles). This mesh is re-tessellated using coarsening to create an adaptively optimized clone (right)—with 68k triangles, where local regions with high frequency contain more facets than flat regions. Complete analysis of both meshes is illustrated Fig. 9.

Figure 8

While adaptive optimization eliminates unnecessary vertices of flat regions of the manifold—mainly across the somatic region as shown in Fig. 7, the topology of the mesh around spines still have sufficient number of vertices to capture their geometric details.

Figure 9

Comparative quantitative and qualitative analyses of the meshes generated from the Voxel remesher (in light red) and the mesh optimizer (in light blue) shown in Fig. 7. Note that the volume of the mesh is preserved.

Figure 10

Performance benchmarks (in seconds) for our implementation based on a data set consisting of 60 various morphological types of cortical neurons [6, 40]. The timing of the Proxy Mesh Reconstruction stage comprises the soma simulation time, arbors reconstruction, and the integration of the spines along the dendritic arbors. The mesh optimization time comprises the mesh coarsening and smoothing. Axons of the shown neurons are limited to second-order branching only.

Figure 11

Our algorithm is applied to a synthetic astroglial cell [34] (A) to create a corresponding watertight mesh with a single manifold (B). Perisynaptic processes, perivascular processes, and endfeet are colored in red, blue, and green, respectively. The wireframe closeup highlights the topology of the mesh around the astrocytic soma.

Figure 12

A tetrahedral mesh of a pyramidal neuron visualizing random simulation reports at multiple time steps, mimicking the variations of the Ca signals across the cellular membrane. The watertight mesh created with our implementation is used to synthesize the tetrahedral counterpart relying on TetGen.

Figure 13

A side-by-side comparison between a neuronal mesh reconstructed with AnaMorph [33] (left) and our method (right). While AnaMorph approximates the soma with a symbolic sphere (A), our method is capable of reconstructing a faithful 3D profile of the soma based on mass-spring modeling and soft body dynamics (B). The meshing algorithm of AnaMorph cannot integrate any realistic spines along the dendritic branches of the neuron (C). Our implementation can seamlessly integrate detailed and highly realistic spine geometries that emanate smoothly from the neuronal membrane (D).