OpenDose-PopPK 🔬💊

A modular, open-source Python framework for Population Pharmacokinetic-Pharmacodynamic (PopPK/PD) modeling.

The library bridges classical compartmental pharmacology and modern control theory by integrating state-space representation, stochastic Monte Carlo simulations, and Bayesian individual parameter estimation.

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✨ Features

• 1-compartment PK model — first-order analytical solution with state-space formalism
• Multiple-dose regimen support — repeated dosing at fixed intervals
• IV bolus and infusion simulation — dedicated intravenous input modes
• Steady-state metrics — Cmax/trough/AUCτ estimation after repeated dosing
• Nonlinear PK simulation (Michaelis-Menten) — saturable elimination profiles
• Emax Hill PD model — sigmoidal pharmacodynamic effects
• Monte Carlo simulation — inter-individual variability with 90% prediction intervals
• Covariate modeling — weight, renal function (CrCl), age, hepatic markers (Power Model)
• MAP estimation — individual Bayesian fitting from sparse observed samples
• Clinical TDM input validation — robust CSV cleaning with alias mapping and automatic unit normalization
• Drug dataset validation — schema and value checks for drug parameter CSV
• Batch TDM fitting — MAP estimation per patient from real-world monitoring tables
• TDM prediction diagnostics — per-observation predictions and residual error tables
• Observed-vs-predicted diagnostic plot — quick visual goodness-of-fit check
• Population PK fitting (naive pooled) — estimate typical PK parameters from TDM datasets
• Population PK mixed-effects fitting — estimate fixed effects (theta) and random effects (omega/eta)
• Bootstrap uncertainty for population fit — confidence intervals for F/ka/ke/Vd
• External validation toolkit — compare model predictions with observed and reference-software concentrations (direct NONMEM/Monolix/Pumas benchmarking requires paid licenses)
• Web app baseline — lightweight local browser interface for quick PK profile exploration
• Reproducible validation report — protocol + metrics + limitations in JSON/Markdown
• Release readiness checks — strict semver/version alignment and asset checks before publishing
• End-to-end TDM workflow command — run full clinical pipeline in one execution
• Multi-drug regimen benchmarking — compare Cmax/trough/AUC across selected compounds
• Mixed-drug TDM fitting — run MAP fits when a single CSV contains multiple drugs
• Dose recommendation engine — suggest dose for target Cmax/AUC (with covariate adjustment)
• Regimen dose recommendation — suggest repeated-dose amount for target Cmax/trough
• Therapeutic-window regimen recommendation — suggest repeated-dose amount for trough/Cmax window
• Local sensitivity analysis — quantify how PK parameters impact Cmax/AUC
• Project health report — generate JSON/Markdown diagnostics (dataset + smoke + sensitivity)
• Dose sweep analysis — evaluate dose-response trends for Cmax/AUC
• Cohort simulation from CSV — compute patient-level Cmax/AUC with covariate adjustment
• DrugDatabase — loads and manages parameters from CSV
• Publication-ready figures — all plots from the companion paper

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📊 Results

Population Simulation with Covariates

Monte Carlo — Paracetamol 1000mg (N=1000)

MAP Estimation — Individual Patient

Multi-Drug Comparison

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🛠️ Installation

git clone https://github.com/redkk123/OpenDose-PopPK.git
cd OpenDose-PopPK
# Recommended: install the package for local development
pip install -e .
# or install the package (non-editable)
pip install .
# runtime-only dependencies (optional explicit install)
pip install -r requirements.txt
# development tooling (tests/lint/type-check)
pip install -e ".[dev]"

Running tests

python -m pytest -q

On Windows: make.bat test or python -m pytest -q

With coverage: pip install .[dev] then pytest --cov=opendose_poppk --cov-report=term-missing

Latest local validation: March 5, 2026 (Python 3.14.2), python -m pytest -q -> 199 passed.

PyPI publishing (maintainers)

The release pipeline publishes to PyPI via Trusted Publishing (OIDC) when a tag v* is pushed.

1. In PyPI, create (or open) project opendose-poppk.
2. Add a Trusted Publisher with:
   • Owner: redkk123
   • Repository: OpenDose-PopPK
   • Workflow: release.yml
   • Environment: pypi
3. Bump version in pyproject.toml and opendose_poppk/__init__.py.
4. Create and push a tag, e.g. git tag v1.0.1 && git push origin v1.0.1.

CLI

opendose list-drugs
opendose validate-dataset --output-clean output/tables/drugs_parameters_clean.csv
opendose simulate --drug Paracetamol --n-subjects 200 --t-max 12 --output output/tables/paracetamol_cli.csv
opendose simulate-iv --drug Paracetamol --mode bolus --dose 1000 --output-csv output/tables/paracetamol_iv_bolus.csv
opendose simulate-nonlinear --drug Paracetamol --dose 1000 --vmax 200 --km 15 --output-csv output/tables/paracetamol_nonlinear.csv
opendose steady-state --drug Paracetamol --interval-h 12 --n-doses 20 --output-csv output/tables/paracetamol_steady_state.csv
opendose init-cohort-template --output data/cohort_template.csv
opendose simulate-cohort --drug Paracetamol --input data/cohort.csv --output-csv output/tables/cohort_simulation.csv
opendose sensitivity --drug Paracetamol --dose 1000 --rel-step 0.1 --output-csv output/tables/sensitivity_paracetamol.csv
opendose dose-sweep --drug Paracetamol --doses 250,500,750,1000 --output-csv output/tables/dose_sweep_paracetamol.csv
opendose simulate-regimen --drug Paracetamol --interval-h 12 --n-doses 4 --output-csv output/tables/paracetamol_regimen.csv --plot-png output/figures/paracetamol_regimen.png
opendose fit --drug Paracetamol --times 0.5,1,2,4 --obs 4.2,6.8,7.5,5.9 --weight 80 --crcl 70 --age 55
opendose validate-tdm --input data/tdm.csv --output-clean output/tables/tdm_clean.csv
opendose validate-tdm --input data/tdm_raw.csv --time-unit min --conc-unit ng/mL --dose-unit g --output-clean output/tables/tdm_clean.csv
opendose fit-tdm --drug Paracetamol --input data/tdm.csv --output output/tables/tdm_fit.csv --predictions-csv output/tables/tdm_predictions.csv --plot-png output/figures/tdm_obs_vs_pred.png --report-md output/reports/tdm_fit_report.md
opendose fit-population --input data/tdm.csv --maxiter 2000 --bootstrap-n 200 --output-json output/reports/pop_fit.json
opendose fit-population-mixed --drug Paracetamol --input data/tdm.csv --maxiter 1200 --eta-csv output/tables/pop_mixed_eta.csv --output-json output/reports/pop_mixed_fit.json
opendose init-external-template --output data/external_validation_template.csv
opendose validate-external --drug Paracetamol --input data/external_validation.csv --predictions-csv output/tables/external_predictions.csv --output-json output/reports/external_validation.json
opendose web-app --drug Paracetamol --dose 750 --t-end 12 --output-html output/web/web_app.html --dry-run
opendose validation-report --drug Paracetamol --output-md output/reports/validation_report.md --output-json output/reports/validation_report.json
opendose release-readiness --repo-root . --output-md output/reports/release_readiness.md --strict
opendose init-tdm-template --output data/tdm_template.csv
opendose init-tdm-template --format clinical --output data/tdm_template_clinical.csv
opendose run-tdm-workflow --drug Paracetamol --input data/tdm.csv --outdir output/workflows/tdm_paracetamol
opendose benchmark-regimen --drugs Paracetamol,Ibuprofen,Diazepam --interval-h 12 --n-doses 4 --output-csv output/tables/regimen_benchmark.csv
opendose fit-tdm-mixed --input data/tdm_mixed.csv --output output/tables/tdm_mixed_fit.csv
opendose doctor --strict
opendose project-report --drug Paracetamol --output-md output/reports/project_report.md
opendose recommend-dose --drug Paracetamol --target-cmax 10 --weight 80 --crcl 70 --age 55 --output-json output/reports/dose_recommendation.json
opendose recommend-regimen-dose --drug Paracetamol --target-trough 1.0 --interval-h 12 --n-doses 4 --output-json output/reports/regimen_dose_recommendation.json
opendose recommend-regimen-window --drug Paracetamol --target-trough-min 0.05 --target-cmax-max 12.0 --interval-h 12 --n-doses 4 --strategy midpoint --output-json output/reports/regimen_window_recommendation.json

Drug-specific runnable examples are available in examples/drugs/ (for example, paracetamol.py and ibuprofen.py).

External validation licensing note

Direct one-to-one benchmarking against licensed software (NONMEM/Monolix/Pumas) requires paid licenses. Without licenses, external validation remains limited to public datasets and/or precomputed reference columns (ref_conc).

Cloud CI/CD billing note

If cloud CI/CD billing or credits are unavailable, cloud pipelines may be blocked/intermittent. In this scenario, local test execution (pytest) is the primary validation path until billing is enabled.

Generating figures

python main.py

Figures are saved to figures/. On Windows: make.bat figures

---

🚀 Quick Start

from opendose_poppk import DrugDatabase, PKModel, PDModel
import numpy as np

# Load parameters from CSV
db   = DrugDatabase("datasets/drugs_parameters.csv")
drug = db.get_drug("Paracetamol")

# Build PK/PD models
pk = PKModel(**drug.pk_kwargs)
pd = PDModel(drug.EC50, drug.n_hill)

# Simulate
t = np.linspace(0, 12, 300)
C = pk.concentration(t, D=drug.dose)
E = pd.effect(C)

# Analytical metrics
cmax, tmax = pk.cmax(D=drug.dose)
auc        = pk.auc(D=drug.dose)
print(f"Cmax = {cmax:.2f} µg/mL at Tmax = {tmax:.2f} h")
print(f"AUC₀→∞ = {auc:.1f} µg·h/mL")

---

Radioactive Isotope Modeling (Physical Decay)

OpenDose-PopPK supports pharmacokinetic modeling of radioactive pharmaceuticals (e.g., Lu-177, I-131, Y-90) by incorporating physical decay of the isotope.

Theory

For radioactive drugs, the activity (MBq) decays due to both biological elimination and physical decay of the isotope:

$$\frac{dA}{dt} = -\left(k_e + \lambda_{\text{phys}}\right)A(t)$$

where:

• $k_e$ — biological elimination rate constant (h⁻¹)
• $\lambda_{\text{phys}}$ — physical decay constant (h⁻¹) = $\frac{\ln(2)}{t_{1/2}}$
• $t_{1/2}$ — physical half-life of the isotope (hours)

The overall clearance is the sum of biological and physical elimination.

Example: Lu-177 (Lutetium-177)

from opendose_poppk import PKModel
import numpy as np

# Lu-177 half-life: 6.647 days = 159.528 hours
pk = PKModel(
    F=1.0,                      # 100% bioavailability (IV injection)
    ka=0.0,                     # no absorption (IV)
    ke=0.01,                    # biological clearance (h⁻¹)
    Vd=5.0,                     # volume of distribution (L)
    Q=0.5,                      # inter-compartment flow (L/h)
    V2=2.0,                     # peripheral volume (L)
    phys_half_life_h=159.528    # Lu-177 physical half-life in hours
)

# Dose: 7400 MBq (typical therapeutic activity)
t = np.linspace(0, 168, 500)  # 7 days
A = pk.concentration(t, D=7400.0)  # Activity profile (MBq)

# AUC accounts for both biological and physical elimination
auc = pk.auc(D=7400.0)
print(f"AUC₀→∞ = {auc:.1f} MBq·h")

Key Parameters (Unit Consistency)

Parameter	Unit	Description
D	MBq (or Bq)	Initial activity dose
t	h (hours)	Time post-injection
C or A1	MBq or MBq/L	Activity in compartment (central, peripheral)
CL	L/h	Biological clearance rate
V1, V2	L	Central and peripheral volumes
Q	L/h	Inter-compartmental flow
phys_half_life_h	h (hours)	Physical half-life of isotope
lambda_phys	h⁻¹	Physical decay constant = ln(2) / t_1/2

Decay Impact on PK Metrics

Without decay: AUC = F·D / CL
With decay: AUC is reduced; computed numerically: $$\text{AUC}{0→\infty} = \int_0^∞ C(t) , dt \quad \text{(includes} , \lambda{\text{phys}})$$

# Compare models with/without decay
pk_no_decay = PKModel(F=1.0, ka=0.0, ke=0.01, Vd=5.0)
pk_with_decay = PKModel(F=1.0, ka=0.0, ke=0.01, Vd=5.0,
                        phys_half_life_h=159.528)

auc_no_decay = pk_no_decay.auc(D=7400.0)
auc_with_decay = pk_with_decay.auc(D=7400.0)

print(f"AUC without decay: {auc_no_decay:.1f} MBq·h")
print(f"AUC with decay:    {auc_with_decay:.1f} MBq·h")
print(f"Reduction: {100*(auc_no_decay - auc_with_decay)/auc_no_decay:.1f}%")

Balance of Mass (Mass Balance Check)

The model enforces conservation of mass across compartments:

$$\frac{d(A_1 + A_2)}{dt} = -\text{CL} \frac{A_1}{V_1} - \lambda_{\text{phys}}(A_1 + A_2)$$

This ensures:

• Biological clearance acts only on central concentration
• Physical decay acts on activity in all compartments
• Total activity decreases exponentially when no input

Common Radioisotopes

Isotope	Half-Life	Application
Lu-177	6.647 days	Peptide receptor radionuclide therapy (PRRT)
I-131	8.0 days	Thyroid cancer, hyperthyroidism
Y-90	64.1 hours	Radioembolization, monoclonal antibody therapy
Tc-99m	6.0 hours	Diagnostic imaging
F-18	110 minutes	PET imaging

---

Covariate-Adjusted Simulation

from opendose_poppk import CovariateModel, PopulationSimulator

cov = CovariateModel(pk)
sim = PopulationSimulator(pk, pd, cov, dose=drug.dose)

result = sim.run(
    n_subjects=1000,
    t_max=12.0,
    covariates={
        "weight": ("normal", 70.0, 15.0),   # kg
        "crcl":   ("normal", 90.0, 30.0),   # mL/min — renal function
        "age":    ("normal", 45.0, 15.0),   # years
    }
)

---

🧑‍⚕️ Individual MAP Estimation

from opendose_poppk import MAPEstimator
import numpy as np

t_obs = np.array([0.5, 1.0, 2.0, 4.0, 6.0, 8.0])
c_obs = np.array([4.2, 6.8, 7.5, 5.9, 4.1, 2.8])

est = MAPEstimator(pk, covariate_model=cov, sigma_obs=0.8)
res = est.fit(
    times=t_obs, obs=c_obs,
    patient_covariates={"weight": 95.0, "crcl": 45.0, "age": 68.0},
    dose=drug.dose
)

print(res["params_map"])

---

📐 Mathematical Background

PK Model (Eq. 1)

$$C(t) = \frac{F \cdot D \cdot k_a}{V_d(k_a - k_e)}\left(e^{-k_e t} - e^{-k_a t}\right)$$

State-Space Representation (Section 3)

$$\dot{\mathbf{x}} = \mathbf{A}\mathbf{x} + \mathbf{B}u, \quad \mathbf{A} = \begin{bmatrix}-k_a & 0 \ k_a & -k_e\end{bmatrix}$$

Eigenvalues $\lambda = {-k_a, -k_e}$ guarantee asymptotic stability.

Covariate Power Model

$$\theta_i = \theta_{pop} \cdot \prod_k\left(\frac{COV_k}{ref_k}\right)^{\beta_k} \cdot e^{\eta_i}, \quad \eta_i \sim \mathcal{N}(0, \omega^2)$$

---

📁 Project Structure

OpenDose-PopPK/
├── opendose_poppk/         ← Core package (PK, PD, covariate, population, bayesian)
├── main.py                 ← Full pipeline (generates all figures)
├── docs/                   ← Sphinx documentation
├── notebooks/
│   └── demo_paracetamol.ipynb
├── datasets/
│   └── drugs_parameters.csv
└── figures/
    ├── monte_carlo_paracetamol.png
    ├── drug_comparison_panel.png
    ├── covariate_simulation.png
    └── map_estimation.png

---

📚 Documentation

Full documentation is available at opendose-poppk.readthedocs.io, GitHub Pages, or build locally:

pip install -e ".[docs]"
sphinx-build -b html docs docs/_build/html

---

📜 Citation

If you use this framework in your research, please cite: GitHub citation metadata is available in CITATION.cff.

@article{gomes2026opendose,
  title  = {OpenDose-PopPK: A Modular Open-Source Framework for
             Population Pharmacokinetic-Pharmacodynamic Modeling},
  author = {Gomes, Angelo Gabriel C. Silva},
  year   = {2026},
  note   = {arXiv preprint}
}

---

🤝 Contributing

See CONTRIBUTING.md for guidelines. CHANGELOG.md lists version history.

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👤 Author

Angelo Gabriel C. Silva Gomes
Federal Institute of Brasília (IFB)
angelogabriel860@gmail.com