Bayesian Identification of Interspecies Interaction Parameters in a 5-Species Oral Biofilm Model and Propagation of Posterior Uncertainty to 3D Finite Element Stress Analysis

5種口腔バイオフィルム Hamilton ODE モデルにおける種間相互作用パラメータの TMCMC ベイズ同定と、事後分布の 3D FEM 応力解析への伝播

日本語要約

歯周病は、口腔バイオフィルム内の菌叢遷移（dysbiosis）— 健康関連菌から病原性菌への群集レベルの移行 — によって駆動される。本研究では、Heine et al. (2025) の 5 種バイオフィルム in vitro 実験データ（4 条件 × 5 時間点）に対して、以下の 2 段階パイプラインを構築・実行する。

Stage 1 — TMCMC ベイズ推定: Klempt et al. (2024) の Hamilton 変分 ODE（20 パラメータ）に TMCMC を適用し、相互作用強度 $a_{ij}$ の事後分布を 1000 サンプルとして取得。Hill ゲート関数により bridge organism → Pg の非線形促進をモデル化。
Stage 2 — FEM 応力解析: Shannon エントロピーベースの Dysbiotic Index (DI) を経由して空間変動ヤング率 $E(\mathbf{x})$ にマッピングし、Abaqus 3D FEM で von Mises 応力場と 90% 信用区間を算出。

主要結果: commensal vs dysbiotic で弾性率 28 倍差 (909 Pa vs 33 Pa)、Pg RMSE 76% 改善、Pseudo Bayes Factor 1.35×10⁹（DI モデルが decisive に優位）。

Overview

Scientific Motivation

Periodontal disease is driven by dysbiosis — a community-level shift from a health-associated (commensal) microbiome to one dominated by the keystone pathogen Porphyromonas gingivalis (Pg). This shift is enabled by bridge organisms: Veillonella dispar (Vd) facilitates Pg via lactate cross-feeding, and Fusobacterium nucleatum (Fn) provides coaggregation scaffolding.

This project addresses two coupled questions:

Ecology: How do species interaction strengths $a_{ij}$ differ between commensal and dysbiotic communities?
Mechanics: How does the inferred community composition alter the effective stiffness and stress in periodontal tissue?

Pipeline

%%{init: {"theme": "base", "themeVariables": {"primaryColor": "#f0f9ff", "edgeLabelBackground": "#ffffff", "fontSize": "14px"}}}%%
flowchart LR
    classDef inp    fill:#dbeafe,stroke:#3b82f6,stroke-width:2px,color:#1e3a5f
    classDef tmcmc  fill:#dcfce7,stroke:#16a34a,stroke-width:2px,color:#14532d
    classDef eq     fill:#bbf7d0,stroke:#16a34a,stroke-width:1px,color:#14532d
    classDef fem    fill:#fef9c3,stroke:#ca8a04,stroke-width:2px,color:#713f12
    classDef feq    fill:#fef3c7,stroke:#ca8a04,stroke-width:1px,color:#713f12
    classDef jax    fill:#f3e8ff,stroke:#9333ea,stroke-width:2px,color:#4a1d96
    classDef out    fill:#ffe4e6,stroke:#e11d48,stroke-width:2px,color:#881337,font-weight:bold

    subgraph INPUT["Input: Heine et al. 2025"]
        direction TB
        I1["4 conditions:\nCommensal / Dysbiotic\n× Static / HOBIC"]:::inp
        I2["5 species × 5 time points\nIn vitro CFU/mL"]:::inp
    end

    subgraph TMCMC["Stage 1: TMCMC Bayesian Inference"]
        direction TB
        T1["Hamilton variational ODE\n20 free parameters"]:::tmcmc
        T1eq["dφi/dt = φi(ri − di·φi + Σj aij·H(φj))"]:::eq
        T1hill["H(φ) = φⁿ/(Kⁿ+φⁿ), K=0.05, n=4"]:::eq
        T2["Sequential tempering β: 0→1\nMH-MCMC sampling"]:::tmcmc
        T3["θ_MAP, θ_MEAN\nN=1000 posterior samples"]:::tmcmc
        T1 --- T1eq --- T1hill --> T2 --> T3
    end

    subgraph FEM["Stage 2: 3D FEM Stress Analysis"]
        direction TB
        F1["Posterior ODE ensemble\n→ spatial composition fields"]:::fem
        F2eq["DI(x) = 1 − H(x)/ln5"]:::feq
        F3eq["E(x) = Emax·(1−r)ⁿ + Emin·r"]:::feq
        F4["Abaqus 3D · NLGEOM\nOpen-Full-Jaw"]:::fem
        F4out["σ_Mises, U_max, 90% CI"]:::feq
        F1 --> F2eq --> F3eq --> F4 --- F4out
    end

    subgraph JAXFEM["JAX-FEM Benchmark"]
        direction TB
        J1["Klempt 2024\nNutrient PDE"]:::jax
        J2["Newton solver\nc_min ≈ 0.31"]:::jax
        J1 --> J2
    end

    RFEM["E_commensal ≈ 909 Pa\nE_dysbiotic ≈ 33 Pa\n28× difference"]:::out

    INPUT  --> TMCMC
    TMCMC  --> FEM
    TMCMC  --> JAXFEM
    FEM    --> RFEM

Four Experimental Conditions

Condition	Role	Biological Interpretation
Commensal Static	Negative control	Health-associated community; Pg suppressed
Commensal HOBIC	Negative control	Health-associated + fluid shear
Dysbiotic Static	Partial control	Pg present but no HOBIC-driven surge
Dysbiotic HOBIC	Target	Pg "surge" via bridge organism facilitation

HOBIC (High-flow Open Biofilm Incubation Chamber) mimics oral shear forces that accelerate pathogen colonisation.

Five Species

%%{init: {"theme": "base", "themeVariables": {"fontSize": "13px"}}}%%
flowchart TB
    classDef comm fill:#dcfce7,stroke:#16a34a,stroke-width:2px,color:#14532d
    classDef bridge fill:#fef9c3,stroke:#ca8a04,stroke-width:2px,color:#713f12
    classDef path fill:#ffe4e6,stroke:#e11d48,stroke-width:2px,color:#881337

    So["So: S. oralis\nEarly coloniser"]:::comm
    An["An: A. naeslundii\nEarly coloniser"]:::comm
    Vd["Vd: V. dispar\nBridge (pH modulation)"]:::bridge
    Fn["Fn: F. nucleatum\nBridge (coaggregation)"]:::bridge
    Pg["Pg: P. gingivalis\nKeystone pathogen"]:::path

    So -->|"cross-feeding"| An
    So -->|"lactate"| Vd
    Vd -->|"a₃₅ facilitation"| Pg
    Fn -->|"a₄₅ scaffold"| Pg
    An -.->|"weak"| Fn

Novelty & Contribution

1. Hamilton ODE + TMCMC による種間相互作用の確率的同定

Klempt et al. (2024) の Hamilton 原理 ODE に対し TMCMC ベイズ推定を適用。Hill ゲート $H(\varphi) = \varphi^n/(K^n + \varphi^n)$ で bridge organism → Pg の非線形促進をモデル化し、20 パラメータの同時事後分布を取得する。

2. 微生物生態 → 組織力学のエンドツーエンドパイプライン

$$ \underbrace{\text{In vitro CFU}}_{\text{Heine 2025}} ;\xrightarrow{\text{TMCMC}}; \hat{\boldsymbol{\theta}}_{\text{MAP}},;{\boldsymbol{\theta}^{(i)}} ;\xrightarrow{\text{ODE}}; \varphi_i(\mathbf{x}) ;\xrightarrow{\text{DI}}; E(\mathbf{x}) ;\xrightarrow{\text{FEM}}; \sigma_{\text{Mises}} \pm \text{90% CI} $$

3. 事後分布の FEM への完全伝播

TMCMC 事後サンプルを ODE → DI → $E(\mathbf{x})$ → FEM に順伝播し、応力場の 90% credible interval を構成。決定論的最適化では不可能な定量的不確かさ評価を実現。

4. DI (エントロピー) vs $\varphi_\text{Pg}$

Hamilton ODE では全条件で $\varphi_\text{Pg} < 0.10$ → 条件間の区別不可。DI は多様性の喪失を検出し、commensal (DI ≈ 0.05) と dysbiotic (DI ≈ 0.84) を明確に分離。Pseudo BF = 1.35×10⁹ で DI モデルが decisive に優位。

%%{init: {"theme": "base"}}%%
block-beta
    columns 3
    block:header:3
        columns 3
        h1["Aspect"] h2["Previous Work"] h3["This Work"]
    end
    block:row1:3
        columns 3
        r1a["Interaction\nestimation"] r1b["Correlation analysis\n(qualitative)"] r1c["Hamilton ODE\n+ TMCMC posterior"]
    end
    block:row2:3
        columns 3
        r2a["Dysbiosis\nindicator"] r2b["φ_Pg\n(pathogen fraction)"] r2c["DI\n(Shannon entropy)"]
    end
    block:row3:3
        columns 3
        r3a["FEM material\ninput"] r3b["Uniform constants\n(literature)"] r3c["DI(x)-based\nspatial mapping"]
    end
    block:row4:3
        columns 3
        r4a["Uncertainty"] r4b["Point estimate\n(sensitivity only)"] r4c["Full posterior\n→ σ credible interval"]
    end
    block:row5:3
        columns 3
        r5a["Scale\ncoupling"] r5b["Single scale"] r5c["ODE → PDE → FEM"]
    end

    style header fill:#dbeafe,stroke:#3b82f6
    style row1 fill:#f0fdf4,stroke:#bbf7d0
    style row2 fill:#f0fdf4,stroke:#bbf7d0
    style row3 fill:#f0fdf4,stroke:#bbf7d0
    style row4 fill:#f0fdf4,stroke:#bbf7d0
    style row5 fill:#f0fdf4,stroke:#bbf7d0

Repository Structure

Tmcmc202601/
├── data_5species/             # Stage 1: TMCMC estimation
│   ├── core/                  #   TMCMC engine, evaluator, Hamilton ODE
│   ├── main/                  #   Entry point: estimate_reduced_nishioka.py
│   ├── model_config/          #   Prior bounds (JSON)
│   ├── experiment_data/       #   Raw CFU/mL data (Heine et al. 2025)
│   └── _runs/                 #   θ_MAP, posterior samples per condition
│
├── FEM/                       # Stage 2: FEM stress analysis
│   ├── biofilm_conformal_tet.py       # Conformal tet mesh generator
│   ├── generate_paper_figures.py      # Paper figures (Fig 8–15)
│   ├── multiscale_coupling_{1,2}d.py  # 0D+1D/2D multiscale pipeline
│   ├── generate_abaqus_eigenstrain.py # Abaqus INP with thermal eigenstrain
│   ├── material_models.py            # DI → E(x) constitutive mapping
│   ├── JAXFEM/                        # JAX-FEM modules
│   └── external_tooth_models/         # Open-Full-Jaw STL (Git LFS)
│
├── deeponet/                  # DeepONet surrogate (~80× per-sample, ~29× E2E TMCMC)
│   ├── deeponet_hamilton.py   #   Equinox-based DeepONet
│   ├── generate_training_data.py  # Importance sampling data gen
│   └── checkpoints_*/         #   Trained models
│
├── tmcmc/                     # Core TMCMC library
├── docs/                      # LaTeX reports & slides
├── _tests/                    # Test suite
└── Makefile                   # Build targets (make help)

TMCMC: Bayesian Parameter Estimation

Governing Equations

$$ \frac{d\varphi_i}{dt} = \varphi_i \left( r_i - d_i \varphi_i + \sum_{j \neq i} a_{ij} H(\varphi_j) \right), \quad H(\varphi) = \frac{\varphi^n}{K^n + \varphi^n} $$

20 free parameters: growth rates $r_i$, self-inhibition $d_i$, interaction coefficients $a_{ij}$ (selected pairs). Hill gate fixed at $K = 0.05$, $n = 4$.

TMCMC Algorithm

%%{init: {"theme": "base", "themeVariables": {"fontSize": "13px"}}}%%
flowchart TD
    classDef prior fill:#dbeafe,stroke:#3b82f6,stroke-width:2px,color:#1e3a5f
    classDef mcmc fill:#dcfce7,stroke:#16a34a,stroke-width:2px,color:#14532d
    classDef post fill:#ffe4e6,stroke:#e11d48,stroke-width:2px,color:#881337

    P0["Prior: θk ~ U(lk, uk)\nPhysically motivated bounds"]:::prior
    B0["β₀ = 0\nN = 1000 particles"]:::prior
    S1["Stage j: compute weights\nw(θ) = L(D|θ)^(βj − βj₋₁)"]:::mcmc
    S2["Resample proportional to w"]:::mcmc
    S3["MH-MCMC moves\n(component-wise, adaptive σ)"]:::mcmc
    S4{"βj = 1?"}:::mcmc
    POST["Posterior samples\nθ_MAP, θ_MEAN, ESS, R̂"]:::post

    P0 --> B0 --> S1 --> S2 --> S3 --> S4
    S4 -->|"No: βj < 1"| S1
    S4 -->|"Yes"| POST

Parameter Space (20 dims)

Category	Parameters	Count
Growth rates	$r_1, \ldots, r_5$	5
Self-inhibition	$d_1, \ldots, d_5$	5
Interactions	$a_{ij}$ (selected pairs)	10

Key interactions: $a_{35}$ (Vd→Pg, $\theta_{18}$), $a_{45}$ (Fn→Pg, $\theta_{19}$)

Results — All 4 Conditions (1000 particles, ~90 h)

MAP RMSE per species:

Species	Comm. Static	Comm. HOBIC	Dysb. Static	Dysb. HOBIC
S. oralis	0.094	0.104	0.026	0.042
A. naeslundii	0.042	0.081	0.057	0.071
V. dispar	0.060	0.046	0.075	0.107
F. nucleatum	0.021	0.014	0.029	0.081
P. gingivalis	0.019	0.017	0.065	0.056
Total	0.055	0.063	0.054	0.075

Mild-Weight Prior Improvement

$a_{35}$ bounds [0, 30] → [0, 5] + likelihood weighting ($\lambda_\text{Pg} = 2.0$, $\lambda_\text{late} = 1.5$):

Metric	Original	Mild-weight	Change
$a_{35}$ (MAP)	17.3 (non-physical)	3.56	Physical
Pg RMSE	0.413	0.103	−75%
Total RMSE	0.223	0.156	−30%

FEM: Stress Analysis Pipeline

Dysbiotic Index → Stiffness Mapping

$$ \mathrm{DI}(\mathbf{x}) = 1 - \frac{H(\mathbf{x})}{\ln 5}, \qquad E(\mathbf{x}) = E_{\max}(1 - r)^n + E_{\min} \cdot r, \quad r = \mathrm{clamp}(\mathrm{DI}/s,; 0,; 1) $$

DI = 0: equal diversity (healthy) → DI = 1: single-species dominance (dysbiotic)
$E_{\max} = 1000$ Pa (commensal), $E_{\min} = 10$ Pa (dysbiotic)

FEM Configuration

%%{init: {"theme": "base", "themeVariables": {"fontSize": "13px"}}}%%
flowchart LR
    classDef geo fill:#dbeafe,stroke:#3b82f6,stroke-width:2px,color:#1e3a5f
    classDef mesh fill:#dcfce7,stroke:#16a34a,stroke-width:2px,color:#14532d
    classDef mat fill:#fef9c3,stroke:#ca8a04,stroke-width:2px,color:#713f12
    classDef sol fill:#ffe4e6,stroke:#e11d48,stroke-width:2px,color:#881337

    G["Open-Full-Jaw\nPatient 1 mandible\n(Gholamalizadeh 2022)"]:::geo
    M["fTetWild C3D4\n17,970 nodes\nTie constraint"]:::mesh
    D["DI(x) → E(x)\nSpatial field mapping"]:::mat
    L["1 MPa compression\nNLGEOM enabled"]:::mat
    S["Abaqus 3D\nσ_Mises, U_max\n90% CI from posterior"]:::sol

    G --> M --> D --> L --> S

Biofilm Mode Results

Condition	$\overline{\mathrm{DI}}$	$\bar{E}$ (Pa)	$U_{\max}$ (mm)
Dysbiotic HOBIC	0.00852	451	0.0267
Dysbiotic Static	0.00950	403	0.0286
Commensal Static	0.00971	392	0.0290
Commensal HOBIC	0.00990	383	0.0294

3-Model Comparison: DI vs $\varphi_\text{Pg}$ vs Virulence

%%{init: {"theme": "base", "themeVariables": {"fontSize": "13px"}}}%%
flowchart TB
    classDef good fill:#dcfce7,stroke:#16a34a,stroke-width:2px,color:#14532d
    classDef bad fill:#fee2e2,stroke:#ef4444,stroke-width:2px,color:#7f1d1d
    classDef neutral fill:#f3f4f6,stroke:#6b7280,stroke-width:2px,color:#374151

    subgraph DI["DI Model (Shannon Entropy)"]
        D1["E_commensal ≈ 909 Pa"]:::good
        D2["E_dysbiotic ≈ 33 Pa"]:::good
        D3["28× separation"]:::good
    end

    subgraph PHI["φ_Pg Model (Pathogen Fraction)"]
        P1["E ≈ 1000 Pa (all cond.)"]:::bad
        P2["φ_Pg < 0.10 everywhere"]:::bad
        P3["No separation"]:::bad
    end

    subgraph VIR["Virulence Model (Pg+Fn weighted)"]
        V1["E ≈ 990 Pa (all cond.)"]:::bad
        V2["Weak discrimination"]:::bad
        V3["Marginal separation"]:::bad
    end

    WINNER["DI Model: Pseudo BF = 1.35×10⁹\n(decisive)"]:::good

    DI --> WINNER
    PHI -.-> WINNER
    VIR -.-> WINNER

See FEM/FEM_README.md for detailed pipeline documentation.

Multiscale Micro→Macro Coupling

The TMCMC posterior gives a mean-field composition. The multiscale pipeline turns this into a spatially varying growth eigenstrain for FEM:

%%{init: {"theme": "base", "themeVariables": {"fontSize": "13px"}}}%%
flowchart TB
    classDef tmcmc  fill:#dcfce7,stroke:#16a34a,stroke-width:2px,color:#14532d
    classDef ode    fill:#dbeafe,stroke:#3b82f6,stroke-width:2px,color:#1e3a5f
    classDef oeq    fill:#bfdbfe,stroke:#3b82f6,stroke-width:1px,color:#1e3a5f
    classDef bridge fill:#fef9c3,stroke:#ca8a04,stroke-width:2px,color:#713f12
    classDef abaqus fill:#ffe4e6,stroke:#e11d48,stroke-width:2px,color:#881337

    A["θ_MAP (TMCMC posterior)"]:::tmcmc
    B["0D Hamilton ODE\nDI_0D: commensal ≈ 0.05\ndysbiotic ≈ 0.84"]:::ode
    C["1D/2D Hamilton + Nutrient PDE\nc(x,T), φi(x,T)"]:::ode
    D["α_Monod(x) = kα ∫ φ_total · c/(k+c) dt\nε_growth(x) = α/3"]:::bridge
    E["Abaqus INP\nSpatially non-uniform\nthermal eigenstrain"]:::abaqus

    A --> B
    A --> C
    C --> D --> E

$$ \alpha_{\text{Monod}}(\mathbf{x}) = k_\alpha \int_0^{T} \varphi_{\text{total}} \cdot \frac{c}{k + c},\mathrm{d}t, \qquad \varepsilon_{\text{growth}}(\mathbf{x}) = \frac{\alpha_{\text{Monod}}}{3} $$

Key Numerical Results

Quantity	Commensal	Dysbiotic	Ratio
DI (0D)	0.047	0.845	18×
$\varepsilon_{\text{growth}}$ (saliva side)	0.14 (14%)	0.14 (14%)	~1
Spatial gradient (saliva/tooth)	101×	101×	—
$E_{\text{eff}}$ (Pa)	~909	~33	28×

The spatial gradient in $\varepsilon_{\text{growth}}$ is driven by nutrient depletion: the biofilm interior (tooth surface) is nutrient-starved, while the saliva-exposed layer grows at 14% volumetric strain.

Quick Start

TMCMC Estimation

python data_5species/main/estimate_reduced_nishioka.py \
    --n-particles 150 --n-stages 8 \
    --lambda-pg 2.0 --lambda-late 1.5

Multiscale Coupling (JAX)

# Requires klempt_fem conda env (Python 3.11, JAX 0.9, jax-fem 0.0.11)
PYTHON=~/.pyenv/versions/miniconda3-latest/envs/klempt_fem/bin/python

$PYTHON FEM/multiscale_coupling_1d.py
# → FEM/_multiscale_results/macro_eigenstrain_{commensal,dysbiotic}.csv

$PYTHON FEM/generate_abaqus_eigenstrain.py
# → FEM/_abaqus_input/biofilm_1d_bar_{commensal,dysbiotic}.inp

FEM Stress Analysis

python FEM/run_posterior_abaqus_ensemble.py   # Posterior ensemble → Abaqus
python FEM/aggregate_di_credible.py           # 90% CI on DI fields

JAX-FEM Klempt 2024 Benchmark

$PYTHON FEM/jax_fem_reaction_diffusion_demo.py
# → Steady-state nutrient PDE: c_min ≈ 0.31, Newton 4 iterations

See REPRODUCIBILITY.md for the full reproduction guide.

Limitations & Known Constraints

Constraint	Detail
1D diffusion homogenisation	Fick diffusion homogenises composition → Hybrid approach (0D DI × 1D spatial α)
Low $\varphi_\text{Pg}$	Hamilton ODE + Hill gate → $\varphi_\text{Pg} < 0.10$ in all conditions → DI adopted
In vitro only	Data from 5-species in vitro biofilm (Heine 2025); no in vivo immune response
Single patient geometry	FEM uses Open-Full-Jaw Patient 1 only
Fixed Hill parameters	$K = 0.05$, $n = 4$ not estimated; uncertainty not propagated
Computation	TMCMC ~90 h (1000 particles); FEM ensemble ~4 h (Abaqus HPC)

Environment

Component	Version
Python (TMCMC)	3.x (system)
Python (JAX-FEM)	3.11 (`klempt_fem` conda)
JAX	0.9.0
jax-fem	0.0.11
Abaqus	2023 (HPC)

References

Klempt, Soleimani, Wriggers, Junker (2024) — A Hamilton principle-based model for diffusion-driven biofilm growth, Biomech Model Mechanobiol 23:2091–2113. DOI
Heine et al. (2025) — 5-species oral biofilm in vitro interaction data (source of CFU measurements)
Ching & Chen (2007) — Transitional Markov Chain Monte Carlo (TMCMC)
Hajishengallis & Lamont (2012) — Polymicrobial synergy and dysbiosis (PSD) model
Gholamalizadeh et al. (2022) — Open-Full-Jaw dataset. DOI
Junker & Balzani (2021) — Extended Hamilton principle for dissipative continua
Fritsch, Geisler et al. (2025) — Bayesian model updating for biofilm constitutive parameters

Citation

@software{nishioka2026tmcmc,
  author  = {Nishioka, Keisuke},
  title   = {Bayesian Identification of Interspecies Interaction Parameters
             in a 5-Species Oral Biofilm Model and Propagation of Posterior
             Uncertainty to 3D Finite Element Stress Analysis},
  year    = {2026},
  url     = {https://github.com/keisuke58/Tmcmc202601},
  note    = {Keio University / IKM Leibniz Universit\"at Hannover}
}

See CITATION.cff for machine-readable metadata.

Documentation

Document	Description
ARCHITECTURE.md	Code design & module dependencies
REPRODUCIBILITY.md	Step-by-step reproduction guide
PAPER_OUTLINE.md	Manuscript figure strategy (Fig 8–18)
FEM/FEM_README.md	FEM pipeline details
CONTRIBUTING.md	Contribution guidelines
CHANGELOG.md	Version history
CODE_OF_CONDUCT.md	Contributor Covenant
SECURITY.md	Security policy

License

MIT — Keisuke Nishioka, 2026

Name		Name	Last commit message	Last commit date
Latest commit History 310 Commits
.dvc		.dvc
.github		.github
.wiki		.wiki
FEM		FEM
Tmcmc202601		Tmcmc202601
VirtualElementMethods		VirtualElementMethods
_runs/Dysbiotic_HOBIC_K0.05_n4.0_1k30		_runs/Dysbiotic_HOBIC_K0.05_n4.0_1k30
_sweeps		_sweeps
_tests		_tests
career		career
colab_package		colab_package
configs		configs
data_5species		data_5species
deeponet		deeponet
docs		docs
experimental_verification_DI		experimental_verification_DI
gnn		gnn
project_e		project_e
test_run		test_run
tmcmc		tmcmc
tools		tools
.cursorindexingignore		.cursorindexingignore
.cursorrules		.cursorrules
.dvcignore		.dvcignore
.env.example		.env.example
.gitattributes		.gitattributes
.gitignore		.gitignore
.pre-commit-config.yaml		.pre-commit-config.yaml
ARCHITECTURE.md		ARCHITECTURE.md
CHANGELOG.md		CHANGELOG.md
CITATION.cff		CITATION.cff
CODE_OF_CONDUCT.md		CODE_OF_CONDUCT.md
CONTRIBUTING.md		CONTRIBUTING.md
LICENSE		LICENSE
Makefile		Makefile
PAPER_OUTLINE.md		PAPER_OUTLINE.md
README.md		README.md
REPRODUCIBILITY.md		REPRODUCIBILITY.md
SECURITY.md		SECURITY.md
backup_to_gdrive.sh		backup_to_gdrive.sh
claude.md		claude.md
monitor_1000p.sh		monitor_1000p.sh
requirements-tools.txt		requirements-tools.txt
ruff.toml		ruff.toml
run_1000p_frontale.sh		run_1000p_frontale.sh
run_1000p_marinos.sh		run_1000p_marinos.sh
run_3conditions.sh		run_3conditions.sh
run_variants_frontale02.sh		run_variants_frontale02.sh
run_variants_frontale04.sh		run_variants_frontale04.sh
run_variants_marinos03.sh		run_variants_marinos03.sh
save_tmcmc_results.sh		save_tmcmc_results.sh
verify_dysbiotic_hobic_surge_comparison.png		verify_dysbiotic_hobic_surge_comparison.png

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Bayesian Identification of Interspecies Interaction Parameters in a 5-Species Oral Biofilm Model and Propagation of Posterior Uncertainty to 3D Finite Element Stress Analysis

Table of Contents

日本語要約

Overview

Scientific Motivation

Pipeline

Four Experimental Conditions

Five Species

Novelty & Contribution

1. Hamilton ODE + TMCMC による種間相互作用の確率的同定

2. 微生物生態 → 組織力学のエンドツーエンドパイプライン

3. 事後分布の FEM への完全伝播

4. DI (エントロピー) vs $\varphi_\text{Pg}$

Repository Structure

TMCMC: Bayesian Parameter Estimation

Governing Equations

TMCMC Algorithm

Parameter Space (20 dims)

Results — All 4 Conditions (1000 particles, ~90 h)

Mild-Weight Prior Improvement

FEM: Stress Analysis Pipeline

Dysbiotic Index → Stiffness Mapping

FEM Configuration

Biofilm Mode Results

3-Model Comparison: DI vs $\varphi_\text{Pg}$ vs Virulence

Multiscale Micro→Macro Coupling

Key Numerical Results

Quick Start

TMCMC Estimation

Multiscale Coupling (JAX)

FEM Stress Analysis

JAX-FEM Klempt 2024 Benchmark

Limitations & Known Constraints

Environment

References

Citation

Documentation

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