3D Real Biofilm
Zenodo TIFF (PA single + SAPA dual) → 3D Voronoi → polyhedral VEM
3D confocal z-stack (TIFF) から直接 3D Voronoi polyhedral mesh を生成し、VEM で弾性解析。
Data: Zenodo — PA single-species + SAPA dual-species (Drescher lab)
3D TIFF (Z×2ch×Y×X)
↓ load_tiff_3d()
Channel separation (SA/PA)
↓ segment_colonies_3d()
Colony centroids + species fractions
↓ build_voronoi_mesh_3d()
3D Voronoi polyhedra
↓ vertex cleanup ← CRITICAL!
Compact mesh (used vertices only)
↓ assign_material_properties()
DI, E(DI), ν per cell
↓ vem_3d_solve()
Displacement, stress
↓ export_vtk()
VTK for ParaView + PNG
scipy.spatial.Voronoi は ~2200 頂点を返すが実際に使うのは ~350。浮遊頂点を除去しないと剛性行列が特異 (|u| → 10⁸)。
used_verts = set()
for cv in cells:
used_verts.update(cv.tolist())
used_sorted = sorted(used_verts)
old_to_new = {old: new for new, old in enumerate(used_sorted)}
vertices = vertices_raw[used_sorted] # 2196 → 352 vertices
- (a) 3D colony positions
- (b) DI = 0 (単種 → 多様性なし)
- (c) E field: 42–237 Pa
- (d) Displacement: max |u| = 0.0023 µm
SA (Staphylococcus aureus) + PA (Pseudomonas aeruginosa)
- (a) 3D colony positions (2 channels)
- (b) DI: 0.18–0.79 (空間的に不均一)
- (c) E field: 74–682 Pa
- (d) Displacement: max |u| = 0.0037 µm
| Metric | PA Single | SAPA Dual |
|---|---|---|
| Cells | 65 | 131 |
| DI range | 0.00 | 0.18–0.79 |
| E range [Pa] | 42–237 | 74–682 |
| Max | u | [µm] |
| Solve time | 11s | 37s |
Dual-species は:
- DI が 0 → 0.18–0.79 に増加（多様性 → 構造に反映）
- E の range が広がる (SA 高剛性 + PA 低剛性)
- 変位 1.6× 大きい
同一 real biofilm geometry で VEM (Voronoi) vs FEM (Delaunay tet C3D4) を比較。
| Method | Elements | DOFs | Max |u| [µm] | Time | |--------|----------|------|----------------|------| | VEM Voronoi | 80 | 1290 | 0.0037 | 0.9s | | FEM C3D4 | 482 | 282 | 0.0002 | 0.3s |
- 1 colony = 1 VEM 要素 → DI/E がセル単位で自然定義
- 材料プロパティの割り当てが trivial
- DOF 数が少ない（頂点共有の効率）
- 高速ソルバ
合成 confocal z-stack (64×64×20, 5 channels) での結果。
2D 断面に phase-field fracture を適用。詳細は Phase-Field Fracture を参照。
69 VEM elements, DI 0.18–0.76, d_max = 0.85, 57/82 nodes cracked。
世界初: 3D polyhedral VEM × phase-field fracture × バイオフィルム。
- 30 polyhedral VEM 要素, 165 頂点
- DI gradient: center=dysbiotic → edge=commensal
- Progressive damage 0→0.34 → catastrophic failure at step 28 (d=1.0)
- Phase transition: step 27 (d=0.34) → step 28 (d=1.0) — 脆性破壊
- 208 polyhedral VEM elements, 1195 vertices (cleaned from 7959)
- DI: [0.18, 0.79], E: [74, 682] Pa, G_c: [0.032, 0.340] J/m²
- Progressive damage → catastrophic at step 14
- Pre-catastrophic: d_max = 0.56, PA-dominant regions initiate damage
- PA 領域 (低 G_c, 低 E) から亀裂開始 → 全体崩壊
| Metric | Synthetic | Real SAPA |
|---|---|---|
| Cells | 30 | 208 |
| Vertices | 165 | 1195 |
| DI range | 0.16–0.68 | 0.18–0.79 |
| G_c range [J/m²] | 0.06–0.36 | 0.032–0.340 |
| Catastrophic step | 28/30 | 14/30 |
| Pre-catastrophic d_max | 0.345 | 0.562 |
| Solve time | 51s | 328s |
3D phase-field では 3×3 ひずみテンソルの固有値分解 で引張/圧縮を分離:
- ε⁺ = Σ max(ε_i, 0) · n_i ⊗ n_i (引張成分 → 亀裂駆動)
- ε⁻ = ε - ε⁺ (圧縮成分 → 亀裂に影響しない)
-
vem_phase_field_3d.py— 3D phase-field solver + demo + real pipeline
PDF から抽出した FISH 画像 → Voronoi → VEM。
| Script | Purpose |
|---|---|
pipeline_3d_real.py |
Full pipeline: TIFF → VEM → VTK |
benchmark_3d_vem_vs_tet.py |
VEM vs FEM benchmark |
phase_field_real_3d.py |
Phase-field on real SAPA |
vem_3d_confocal.py |
3D synthetic confocal |
process_heine_fish.py |
Heine FISH → VEM |
vem_confocal_pipeline.py |
2D synthetic confocal |
- Home — Overview
- Phase-Field Fracture — 破壊力学
- Growth-Coupled VEM — 成長連成
- Results Gallery — 全結果画像集