Geometry and meshes

A simulation starts from a geometry recipe (a "setup"), which create_geometry turns into a finite element mesh in three steps:

1. a configuration of cells (positions and radii), random by default (SpinDoctor.create_cells);

2. the surfaces of the cells and of the extracellular space (ECS) (SpinDoctor.create_surfaces);

3. a mesh of triangles (2D, with Triangle) or tetrahedra (3D, with TetGen), split into compartments (SpinDoctor.create_mesh, SpinDoctor.split_mesh).

setup = CylinderSetup(; ncell = 3, layersizes = [0.6, 1.0], ecs = BoxECS(; margin = 1.0))
mesh, surfaces, cells = create_geometry(setup; rng = Xoshiro(1))

See Geometry recipes for pictures of all of them.

Recipes

Recipe	Dimension	Cells
PlateSetup	2D	stacked plates
SlabSetup	3D	stacked slabs (extruded plates)
DiskSetup	2D	disks, with layers
CylinderSetup	3D	cylinders (extruded disks), with layers
SphereSetup	3D	spheres, with layers
VoronoiSetup	3D	polyhedral cells filling a periodic box
NeuronSetup	3D	a neuron from a volume mesh (Gmsh format)

Disks, cylinders and spheres may have several layers (layersizes, relative radii), for example an axon in a myelin sheath, or a nucleus in a cell. Extruded setups (slabs and cylinders) may be bent and twisted (ExtrusionSetup).

Extracellular space

The cells of disks, cylinders, spheres and neurons may be immersed in an ECS:

• NoECS: no ECS;

• BoxECS: a box around the cells, with a margin;

• ConvexHullECS: the convex hull of the cells, with a margin;

• PeriodicBoxECS: a sample of periodic tissue (disks and cylinders).

Samples of periodic tissue

For dense tissue, PeriodicBoxECS and VoronoiSetup fill a box with cells, cut by its faces, with their periodic images entering on the opposite faces:

• periodic_packing packs disks or spheres with gaps between them, up to about 80 % of the area or 60 % of the volume (counting the gaps);

• VoronoiSetup creates polyhedral cells for any volume fraction.

The meshes are periodic (the opposite faces of the box have the same points), so that the solvers can use periodic boundary conditions (see Solvers). Then the sample represents a larger piece of tissue, without walls.

Cell configurations

The cell configuration cells returned by create_geometry may be given back to create the same cells with other parameters (e.g. a finer mesh), or replaced by a configuration of your own, for example from another packing algorithm:

mesh, = create_geometry(setup; cells)

The random configurations are drawn from the random number generator rng.

Compartments and boundaries

The mesh is split into compartments, numbered as follows:

• plates and slabs: one per plate;

• disks, cylinders and spheres: the inner layers of all the cells, then the next layers, ..., then the ECS (e.g. with two layers and three cells: the axons 1-3, the myelin 4-6, the ECS 7);

• neurons: the neuron, then the ECS.

The boundaries are the interfaces between pairs of compartments, followed by the outer boundaries of each compartment. The coefficients of the recipes (coefficients) follow this numbering. compartment_mesh extracts one compartment as a mesh of its own, and box_faces finds the facets of a box-shaped compartment on each face.

Files

By default, create_geometry writes no files. With using JLD2, the geometry can be stored in a file and loaded again when it was created for the same setup:

using JLD2
mesh, surfaces, cells = create_geometry(setup; cache = "geometry.jld2")

With savedir, the geometry is written as text files in the TetGen format of the MATLAB version of SpinDoctor.