VCell Finite-Volume 3D Reaction-Diffusion Report

Three 3D reaction-diffusion simulations wrapped as process-bigraph Processes, with the native VCell pyvcell-fvsolver finite volume PDE kernel producing the spatial fields. The 3D viewers embedded below are PyVista + vtk.js scenes — the same rendering stack used by pyvcell's built-in trame widget — exported as self-contained interactive HTML.

Gaussian Pulse DiffusionReaction-Diffusion CascadeTwo-Source Mixing
1

Gaussian Pulse Diffusion

Single-species diffusion from a point source

A Gaussian concentration pulse of species A centered at the middle of the cubic domain diffuses outward under Fick's law. No reactions — a pure diffusion benchmark of the VCell finite volume PDE solver. The peak concentration decays while the distribution spreads uniformly over the domain.

Mesh22×22×22
Species1
Peak [A]44.6
Final [A]0.506from 0.445
Duration8.0 s
Snapshots12
Runtime1.0s

Model & Geometry

Antimony source
compartment ec;
compartment cell;
species A in cell;
A = 0
Species mapping
SpeciesInitial concentration (µM)Diff. coef. (µm²/s)
A50 * exp(-((x-5)^2 + (y-5)^2 + (z-5)^2) / 1.5)1
Geometry & solver
Domain extent10 × 10 × 10 µm
Voxel grid22 × 22 × 22 (10,648 cells)
Voxel size0.455 × 0.455 × 0.455 µm
Duration8.0 s
Output step0.4 s
Compartmentcell

3D Volume Viewer — species A (early / middle / late — drag to rotate, scroll to zoom)

Early — t = 0s
Middle — t = 4s
Late — t = 8s

Mid-plane z-slice strip — all tracked species

mid-plane z-slices

Species Time Series

Bigraph Architecture

Bigraph architecture diagram

Composite Document

2

Reaction-Diffusion Cascade

A → B → C with distinct diffusion coefficients

A linear reaction cascade: A decays into B, which decays into C. All three species diffuse but with very different coefficients (A slow, B medium, C fast). The wrapper drives VCell's finite volume PDE solver to couple first-order kinetics with Fickian transport across a 3D Cartesian mesh, producing three distinct spatial profiles that emerge and decay in sequence.

Mesh22×22×22
Species3
Peak [B]1.54e-05
Final [B]2.59e-06from 0
Duration6.0 s
Snapshots12
Runtime0.6s

Model & Geometry

Antimony source
compartment ec;
compartment cell;
species A in cell;
species B in cell;
species C in cell;
J1: A -> B; k1*A
J2: B -> C; k2*B
k1 = 0.6
k2 = 0.3
A = 0
B = 0
C = 0
Species mapping
SpeciesInitial concentration (µM)Diff. coef. (µm²/s)
A30 * exp(-((x-5)^2 + (y-5)^2 + (z-5)^2) / 2.0)0.2
B0.00.6
C0.01.2
Geometry & solver
Domain extent10 × 10 × 10 µm
Voxel grid22 × 22 × 22 (10,648 cells)
Voxel size0.455 × 0.455 × 0.455 µm
Duration6.0 s
Output step0.3 s
Compartmentcell

3D Volume Viewer — species B (early / middle / late — drag to rotate, scroll to zoom)

Early — t = 0s
Middle — t = 3s
Late — t = 6s

Mid-plane z-slice strip — all tracked species

mid-plane z-slices

Species Time Series

Bigraph Architecture

Bigraph architecture diagram

Composite Document

3

Two-Source Mixing

Opposing diffusion fronts with a binding reaction

Two Gaussian sources of species A and species B sit on opposite corners of the cubic domain. As both diffuse inward they collide in the middle where a bimolecular association reaction A + B -> C traps product along the interface. The VCell finite volume solver handles the coupled transport and nonlinear reaction across the 3D mesh.

Mesh22×22×22
Species3
Peak [C]2.97e-07
Final [C]3.43e-08from 0
Duration6.0 s
Snapshots12
Runtime0.7s

Model & Geometry

Antimony source
compartment ec;
compartment cell;
species A in cell;
species B in cell;
species C in cell;
J1: A + B -> C; k1*A*B
k1 = 1.5
A = 0
B = 0
C = 0
Species mapping
SpeciesInitial concentration (µM)Diff. coef. (µm²/s)
A40 * exp(-((x-2)^2 + (y-2)^2 + (z-2)^2) / 1.5)0.6
B40 * exp(-((x-8)^2 + (y-8)^2 + (z-8)^2) / 1.5)0.6
C0.00.1
Geometry & solver
Domain extent10 × 10 × 10 µm
Voxel grid22 × 22 × 22 (10,648 cells)
Voxel size0.455 × 0.455 × 0.455 µm
Duration6.0 s
Output step0.3 s
Compartmentcell

3D Volume Viewer — species C (early / middle / late — drag to rotate, scroll to zoom)

Early — t = 0s
Middle — t = 3s
Late — t = 6s

Mid-plane z-slice strip — all tracked species

mid-plane z-slices

Species Time Series

Bigraph Architecture

Bigraph architecture diagram

Composite Document

Generated by pbg-vcell-fvsolver — pyvcell + pyvcell-fvsolver + process-bigraph — Finite-volume PDE solver on a 3D Cartesian mesh