Geometry recipes

SpinDoctor creates finite element meshes from geometry recipes ("setups"): a random configuration of cells, the surfaces of the cells and of the extracellular space (ECS), and a mesh of triangles (2D) or tetrahedra (3D). This example shows the available recipes.

using SpinDoctor
using Random
using WGLMakie # Or CairoMakie, GLMakie

Colors for the plots: the layers of the cells and the ECS.

axon, myelin, ecs = :steelblue, :orange, (:gray, 0.9)

Plates and slabs

Stacked plates in 2D (PlateSetup), with the given widths, and their extrusion to slabs in 3D (SlabSetup), here twisted around the vertical axis.

plates = PlateSetup(; depth = 20.0, widths = [3.0, 5.0, 4.0, 6.0], refinement = 2.0)
mesh_plates, = create_geometry(plates)
plot_mesh(mesh_plates)

slabs = SlabSetup(; depth = 10.0, widths = fill(2.5, 4), height = 30.0, twist = pi / 2)
mesh_slabs, = create_geometry(slabs)
plot_mesh(mesh_slabs; decorations = false)

Disks and cylinders

Disks in 2D (DiskSetup) with radii between rmin and rmax, possibly with several layers (here an axon and a myelin sheath), and an ECS: none (NoECS), a box (BoxECS) or the convex hull of the cells (ConvexHullECS), both with a margin.

disks = DiskSetup(;
    ncell = 6,
    rmin = 2.0,
    rmax = 5.0,
    nsidewall = 20,
    layersizes = [0.6, 1.0],
    ecs = BoxECS(; margin = 2.0),
)
mesh_disks, = create_geometry(disks; rng = Xoshiro(1))
plot_mesh(mesh_disks; colors = [fill(axon, 6); fill(myelin, 6); :lightgray])

Cylinders (CylinderSetup) are disks extruded in 3D, and may be bent and twisted.

cylinders = CylinderSetup(;
    ncell = 4,
    rmin = 2.0,
    rmax = 4.0,
    nsidewall = 20,
    ecs = ConvexHullECS(; margin = 1.5),
    height = 30.0,
    bend = 0.02,
    twist = pi / 3,
)
mesh_cylinders, = create_geometry(cylinders; rng = Xoshiro(2))
plot_mesh(mesh_cylinders; colors = [fill(axon, 4); :gray], alpha = [ones(4); 0.25])

Spheres

Spheres (SphereSetup) may also have layers, for example a nucleus.

spheres = SphereSetup(;
    ncell = 4,
    rmin = 3.0,
    rmax = 5.0,
    layersizes = [0.5, 1.0],
    ecs = ConvexHullECS(; margin = 1.0),
)
mesh_spheres, = create_geometry(spheres; rng = Xoshiro(3))
colors = [fill(:crimson, 4); fill(:steelblue, 4); :gray]
plot_mesh(mesh_spheres; colors, alpha = [fill(1.0, 4); fill(0.4, 4); 0.15])

Samples of dense tissue

For dense tissue, the cells fill a periodic box (PeriodicBoxECS): the cells are packed randomly with gaps between them (periodic_packing), cut by the faces of the box, and their periodic images enter on the opposite faces. Here, 20 disks fill 70 % of the area.

packed_disks = DiskSetup(;
    ncell = 20,
    rmin = 1.0,
    rmax = 2.5,
    nsidewall = 20,
    dmin = 0.15,
    ecs = PeriodicBoxECS(; fraction = 0.7),
)
mesh_packed_disks, = create_geometry(packed_disks; rng = Xoshiro(4))
plot_mesh(mesh_packed_disks; colors = [fill(axon, 20); :lightgray])

The same for 15 myelinated axons in 3D:

packed = CylinderSetup(;
    ncell = 15,
    rmin = 1.0,
    rmax = 2.5,
    nsidewall = 16,
    dmin = 0.15,
    layersizes = [0.7, 1.0],
    ecs = PeriodicBoxECS(; fraction = 0.65),
    height = 10.0,
)
mesh_packed, = create_geometry(packed; rng = Xoshiro(4))
plot_mesh(mesh_packed; colors = [fill(axon, 15); fill(myelin, 15); :lightgray])

Polyhedral cells (VoronoiSetup) are the shrunk Voronoi cells of random seeds, and fill any fraction of the volume, here 85 %.

voronoi = VoronoiSetup(; ncell = 12, boxsize = 12.0, fraction = 0.85)
mesh_voronoi, = create_geometry(voronoi; rng = Xoshiro(5))
plot_mesh(mesh_voronoi; colors = [fill(:seagreen, 12); :lightgray], decorations = false)

The meshes of these samples are periodic, for periodic boundary conditions (see Dense tissue with periodic boundary conditions).

Realistic neurons (NeuronSetup) are read from volume meshes, see Neurons.

Overview

All the recipes together:

fig = Figure(; size = (1200, 800))
panels = [
    (mesh_plates, "Plates", nothing),
    (
        mesh_disks,
        "Disks with layers and a box ECS",
        [fill(axon, 6); fill(myelin, 6); :lightgray],
    ),
    (mesh_slabs, "Twisted slabs", nothing),
    (mesh_cylinders, "Bent and twisted cylinders", [fill(axon, 4); (:gray, 0.25)]),
    (
        mesh_spheres,
        "Spheres with nuclei",
        [fill(:crimson, 4); fill((:steelblue, 0.4), 4); (:gray, 0.15)],
    ),
    (mesh_packed_disks, "Packed disks", [fill(axon, 20); :lightgray]),
    (
        mesh_packed,
        "Packed myelinated axons",
        [fill(axon, 15); fill(myelin, 15); :lightgray],
    ),
    (mesh_voronoi, "Polyhedral cells", [fill(:seagreen, 12); :lightgray]),
]
for (k, (mesh, title, colors)) in enumerate(panels)
    position = fig[div(k-1, 4)+1, mod1(k, 4)]
    dim = size(mesh.points[1], 1)
    ax =
        dim == 2 ? Axis(position; title, aspect = DataAspect()) :
        Axis3(position; title, aspect = :data)
    hidedecorations!(ax)
    hidespines!(ax)
    isnothing(colors) ? plot_mesh!(ax, mesh) : plot_mesh!(ax, mesh; colors)
end
fig

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