A transparent, reproducible, open-source Python toolkit for dissolution, NCA, PK/PD simulation, and pharmacometric reporting. Every formula is cross-validated against published references and the output is regulatory-ready.
OpenPKFlow gives formulation scientists, PK/PD researchers, and CRO/CDMO teams a clean Python workflow for:
- Dissolution similarity: f1, f2, bootstrap f2, maximum deviation, MSD (Mahalanobis Statistical Distance), model fitting (Weibull, Higuchi, first-order, zero-order, Korsmeyer-Peppas), model-dependent comparison via 90% CI
- NCA: AUClast, AUCinf, Cmax, Tmax, lambda_z, half-life, CL/F, Vz/F; three AUC methods, explicit BLQ handling, %AUCextrap flag, dose-normalised parameters, CDISC PP output; sparse NCA from 3-5 samples
- Bayesian PK (v2.0.0): MAP individual PK estimation (scipy, no extra deps) plus full posterior via PyMC (
[bayes]extra); Bayesian 2x2 crossover BE with P(GMR in 80-125) decision quantity alongside frequentist 90% CI - Bioequivalence: paired 2x2 TOST (80-125% FDA/EMA limits), GMR + 90% CI, intra-subject CV; research-grade replicate-design screening with CVwR and scaled-limit summaries
- Report generation: Markdown, HTML, PDF, Word
- PK simulation: 1- and 2-compartment models, oral/IV bolus/IV infusion, repeated dosing
- Population PK diagnostics: 4-panel GOF plots (OBS vs PRED, IWRES vs TIME/IPRED), simulation-based VPC with percentile bands, NONMEM-style dataset helpers
- Population PK estimation (v2.3.0): FOCE-I (scipy, zero extra deps) and SAEM (PyMC
[bayes]extra) for 1- and 2-compartment oral/IV models; diagonal or full Omega block matrix;PopPKResultwith.summary(),.plot()(6-panel),.report()(research-grade; FOCE-I sanity-checked against thenlmeTheophylline reference) - Theory guide: Full LaTeX formula derivations for every module (NCA, simulation, dissolution, IVIVC, BE, pop PK, Bayesian PK) for regulatory review support and teaching
- ML surrogate (experimental): torch MLP that approximates 1-cmt oral profiles
It does not replace expert regulatory judgement or validated commercial platforms. It makes routine analysis faster, cleaner, and more reproducible.
pip install openpkflowFor PDF and Word reports:
pip install openpkflow[reports]For full Bayesian PK (PyMC MCMC):
pip install openpkflow[bayes]from openpkflow.dissolution import f1, f2
reference = [20.0, 40.0, 60.0, 80.0, 90.0]
test = [21.0, 39.0, 61.0, 79.0, 88.0]
print(f"f1 = {f1(reference, test):.2f}")
print(f"f2 = {f2(reference, test):.2f}")from openpkflow.dissolution import DissolutionStudy
study = DissolutionStudy.from_csv("dissolution.csv")
# or load directly from Excel (requires pip install openpkflow[reports]):
# study = DissolutionStudy.from_excel("dissolution.xlsx", sheet_name="Data")
result = study.compare(reference="reference", test="test")
result.summary()
result.report("dissolution_report.html")
result.report("dissolution_report.pdf", format="pdf") # requires [reports]CSV format: formulation,batch,time,percent_released
openpkflow version
openpkflow similarity --reference "20,40,60,80" --test "21,39,61,79"from openpkflow.nca import NCAStudy
study = NCAStudy.from_csv(
"pk_data.csv",
auc_method="linear_up_log_down", # required: "linear", "log", or "linear_up_log_down"
blq_method="none", # required: "none", "drop", "zero", "half_lloq", "lloq"
)
summary = study.analyze()
print(summary.summary()) # tabular ASCII output
# Per-subject results
result = summary.results[0]
print(f"Subject: {result.subject}")
print(f"AUClast: {result.AUClast:.2f} h*mg/L")
print(f"Cmax: {result.Cmax:.2f} mg/L")
print(f"Tmax: {result.Tmax:.2f} h")
print(f"t1/2: {result.half_life:.2f} h")
print(f"CL/F: {result.CL_F:.2f} L/h")
# Reports
result.report("nca_subject1.html")
summary.report("nca_summary.html")subject,time,conc,dose,route
1,0.0,0.0,320.0,oral
1,0.5,4.2,320.0,oral
1,1.0,8.1,320.0,oral
1,2.0,6.8,320.0,oral
1,4.0,3.5,320.0,oral
1,8.0,1.7,320.0,oral
1,12.0,0.9,320.0,oral
1,24.0,0.2,320.0,oralRequired columns: subject, time, conc, dose, route.
Dose units must match concentration x time (mg when conc is mg/L and time is h).
Route values: "oral", "iv_bolus", "iv_infusion".
Oral route yields apparent clearance and volume: CL_F, Vz_F.
IV routes yield absolute clearance and volume: CL, Vz.
import numpy as np
from openpkflow.sim import simulate
from openpkflow.sim.models import OneCompartmentModel
from openpkflow.sim.dosing import DoseRegimen
model = OneCompartmentModel(route="oral", CL_F=5.0, Vz_F=50.0, ka=1.2)
regimen = DoseRegimen.from_repeated(amount=100.0, route="oral", tau=24.0, n_doses=3)
times = np.linspace(0, 72, 500)
result = simulate(model, regimen, times)
print(result.summary())
result.report("sim_report.html")
result.report("sim_report.pdf", format="pdf") # requires [reports]from openpkflow.bayes import map_individual_pk, PKPrior
import math
# Noiseless 1-cmt oral data (CL_F=5, Vz_F=50, ka=1.2, dose=100)
times = [0.5, 1.0, 2.0, 4.0, 8.0, 12.0]
concs = [1.23, 1.85, 1.97, 1.61, 0.89, 0.49]
result = map_individual_pk(times, concs, dose=100.0, route="oral", subject="S01")
print(result.summary()) # MAP estimates, SEs, diagnostics, disclaimer
result.report("map_pk_report.html")For full posterior sampling (requires pip install openpkflow[bayes]):
from openpkflow.bayes.bayes_pk import bayes_individual_pk
result = bayes_individual_pk(times, concs, dose=100.0, route="oral",
n_samples=1000, tune=1000, chains=2)
print(f"CL_F = {result.cl_mean:.3g} [95% CrI: {result.cl_95ci[0]:.3g}, {result.cl_95ci[1]:.3g}]")
print(f"P(shrinkage) = {result.shrinkage_cl:.1%}")import pandas as pd
from openpkflow.bayes.bayes_be import bayes_be
# Long-format 2x2 crossover data
data = pd.DataFrame({
"subject": ["S01","S01","S02","S02","S03","S03","S04","S04"],
"sequence": ["RT", "RT", "TR", "TR", "RT", "RT", "TR", "TR"],
"period": [1, 2, 1, 2, 1, 2, 1, 2 ],
"treatment": ["R", "T", "T", "R", "R", "T", "T", "R" ],
"value": [98.0, 103.0, 95.0, 91.0, 107.0, 112.0, 99.0, 94.0],
})
result = bayes_be(data, metric="AUC", n_samples=2000, tune=1000, chains=2)
print(f"P(BE) = {result.p_be:.3f}")
print(f"GMR = {result.gmr_mean:.4g} [95% CrI: {result.gmr_95ci[0]:.4g}, {result.gmr_95ci[1]:.4g}]")
print(f"Frequentist 90% CI: [{result.freq_90ci[0]:.4g}, {result.freq_90ci[1]:.4g}]")
result.report("bayes_be_report.html")import pandas as pd
from openpkflow.be import BEStudy
# Wide-format DataFrame: one row per subject, reference and test PK parameter values
be_df = pd.DataFrame({
"subject": ["S01", "S02", "S03", "S04", "S05", "S06"],
"sequence": ["RT", "RT", "RT", "TR", "TR", "TR"],
"reference": [100.2, 98.7, 105.1, 97.3, 102.8, 99.5],
"test": [95.1, 94.0, 99.8, 92.9, 97.4, 94.8],
})
study = BEStudy(be_df, parameter="AUCinf")
result = study.analyze() # default: 80-125%, alpha=0.05
print(result.summary())
result.report("be_report.html")
# NTI products: pass narrower limits
result_nti = study.analyze(be_lower=0.90, be_upper=1.1111)from openpkflow.be import BEStudy
# Run NCA separately on each formulation's PK data
# reference_nca_summary = NCAStudy.from_csv("ref_pk.csv", ...).analyze()
# test_nca_summary = NCAStudy.from_csv("test_pk.csv", ...).analyze()
study = BEStudy.from_nca_results(
reference_nca_summary, test_nca_summary, parameter="AUCinf"
)
result = study.analyze()OpenPKFlow deliberately keeps openpkflow.be as a lightweight convenience layer.
For regulator-facing BE analysis with long-format crossover data, ANOVA source
tables, NTI, ABEL/RSABE, and validation fixtures, export a BioEqPy-ready table:
from openpkflow.be import BEStudy
from bioeqpy import analyze
study = BEStudy(be_df, parameter="AUCinf")
bioeqpy_input = study.to_bioeqpy_dataframe()
formal_results = analyze(bioeqpy_input, parameters=["AUCinf"])openpkflow be compare be_data.csv --parameter AUCinf --report be_report.htmlCSV format: subject, sequence, reference, test
import pandas as pd
from openpkflow.pop import GOFResult, simulate_vpc
from openpkflow.sim.models import OneCompartmentModel
from openpkflow.sim.dosing import DoseRegimen
# GOF: supply your own PRED/IPRED from NONMEM or nlmixr2
gof = GOFResult(
dv=[5.2, 8.1, 6.4, 3.2],
pred=[4.9, 7.8, 6.0, 3.0],
ipred=[5.1, 8.0, 6.3, 3.1],
time=[1.0, 2.0, 4.0, 8.0],
id=["S1", "S1", "S1", "S1"],
sigma=0.15,
study_label="Phase 1 Study",
)
print(gof.summary())
gof.report("gof_report.html")
# Simulation-based VPC
model = OneCompartmentModel(route="oral", CL_F=5.0, Vz_F=50.0, ka=1.2)
regimen = DoseRegimen.from_repeated(amount=100.0, route="oral", tau=24.0, n_doses=1)
observed = pd.DataFrame({"TIME": [1, 2, 4, 8, 12], "DV": [5.1, 8.2, 6.5, 3.8, 2.1]})
vpc = simulate_vpc(model, regimen, observed, n_replicates=500, seed=42)
vpc.report("vpc_report.html")| Capability | OpenPKFlow | PKNCA (R) | WinNonlin | Pharmpy |
|---|---|---|---|---|
| Dissolution f1 / f2 | ✅ | ❌ | ✅ | ❌ |
| Bootstrap f2 | ✅ | ❌ | ❌ | ❌ |
| Dissolution model fitting (5 models + AICc) | ✅ | ❌ | ❌ | ❌ |
| MSD / max deviation / model-dependent comparison | ✅ | ❌ | ✅ | ❌ |
| NCA (AUClast, AUCinf, CL/F, lambda_z), cross-validated vs Phoenix WinNonlin | ✅ | ✅ | ✅ | ❌ |
| C0 back-extrapolation for IV bolus (matches WinNonlin within 2%) | ✅ | ✅ | ✅ | ❌ |
| %AUCextrap flag, dose-normalised params | ✅ | ✅ | ✅ | ❌ |
| CDISC PP output (SDTM, PPTESTCD codes) | ✅ | ❌ | ✅ | ❌ |
| Bioequivalence convenience (paired 2x2 TOST) | ✅ | ❌ | ✅ | ❌ |
| PK simulation (1/2-cmt, oral/IV) | ✅ | ❌ | ✅ | ✅ |
| Population PK diagnostics (GOF, VPC) | ✅ | ❌ | ❌ | ✅ |
| Multi-format reports (HTML, PDF, DOCX) | ✅ | ❌ | ✅ | ❌ |
| Open-source and free | ✅ | ✅ | ❌ | ✅ |
| Python-native API | ✅ | ❌ | ❌ | ✅ |
| Regulatory reference validation (citations) | ✅ | ✅ | ✅ | ❌ |
| IVIVC (Level A) | ✅ (v1.2.0) | ❌ | ✅ | ❌ |
| Multi-media dissolution | ✅ (v1.4.0) | ❌ | ✅ | ❌ |
| Sparse-sampling NCA | ✅ (v1.5.0) | ✅ | ❌ | ❌ |
| Steady-state NCA + urinary excretion | ✅ (v1.3.0) | ✅ | ✅ | ❌ |
| MAP individual PK (scipy, no extra deps) | ✅ (v2.0.0) | ❌ | ✅ | ❌ |
| Full Bayesian PK + Bayesian BE (PyMC) | ✅ (v2.0.0) | ❌ | ❌ | ❌ |
| Population PK estimation: FOCE-I + SAEM (1/2-cmt, full Omega) | ✅ (v2.3.0)* | ❌ | ❌ | ❌ |
| Replicate BE screening (CVwR/scaled-limit summaries) | ✅ (v2.4.0)** | ❌ | ✅ | ❌ |
| Formal BE ANOVA / validated RSABE decision | ❌ | ❌ | ✅ | ❌ |
* Research-grade; FOCE-I typical values are sanity-checked against nlme Theophylline reference values. nlmixr2 rerun is waiting on local Rtools/C compiler support. See HANDOFF.md.
** Research-grade screening only; not a validated FDA/EMA RSABE submission engine.
Post-1.0.0 milestones: IVIVC Level A (done), multi-media dissolution (done), steady-state NCA (done), sparse NCA (done), Bayesian PK + BE (done v2.0.0), FOCE-I + SAEM pop PK (done v2.1.0), 2-cmt + full Omega (done v2.2.0), covariate skeleton removal + FOCE-I reference validation (v2.3.0), replicate BE screening + release credibility sprint (v2.4.0). See ROADMAP.md for the full plan.
| Module | Status |
|---|---|
| Dissolution f1 / f2 | Stable |
| MSD / max deviation / model-dependent comparison | Stable |
| Bootstrap f2 | Stable |
| Dissolution CSV loader | Stable |
| Dissolution model fitting (5 models, AICc) | Stable |
| IVIVC Level A (Wagner-Nelson, Loo-Riegelman, convolution, Levy plot, %PE) | Stable (v1.2.0) |
| Multi-media dissolution (f2 across pH, ethanol dose-dumping) | Stable (v1.4.0) |
| HTML, Markdown, PDF, Word reports | Stable |
| NCA (AUClast, AUCinf, lambda_z, CL/F, steady-state, urinary excretion) | Stable (v1.3.0) |
| Sparse NCA (model-informed 1-cmt oral from 3-5 samples) | Stable (v1.5.0) |
| PK simulation (1/2-comp, oral/IV bolus/IV infusion, repeated dosing) | Stable (v0.9.1) |
| Population PK diagnostics (GOF, VPC) | Stable (v0.6.0) |
| FOCE-I pop PK estimation (scipy tier, 1/2-cmt, full Omega)* | Stable (v2.3.0) |
| SAEM pop PK estimation ([bayes] extra, 1/2-cmt, full Omega)* | Stable (v2.3.0) |
| Covariate modeling | Removed (v2.3.0 breaking change) |
| Validation utilities (pct_bias, rmse, within_pct) | Stable (v0.9.1) |
| MAP individual PK (scipy, zero extra deps) | Stable (v2.0.0) |
| Full Bayesian PK posterior (PyMC, [bayes] extra) | Stable (v2.0.0) |
| Bayesian 2x2 BE with P(GMR in 80-125) (PyMC) | Stable (v2.0.0) |
| Bioequivalence convenience (paired TOST) | Stable (2x2 crossover TOST, GMR + 90% CI) |
| ML surrogate (torch MLP, EXPERIMENTAL) | Prototype (v0.9.0) |
| Stable public release | Done (v2.0.0) |
* Research-grade; FOCE-I typical values are sanity-checked against nlme Theophylline reference values. See HANDOFF.md.
| Stat | Value |
|---|---|
Lines of source code (src/) |
~19,600 |
Lines of tests (tests/) |
~15,200 |
| Total Python files | 141 (69 src + 72 tests) |
| Tests | 900 |
| Public functions / methods | 195 |
| Classes | 34 |
| HTML report templates | 12 |
| Bundled example datasets | 4 |
| Git commits | 100+ |
All formula implementations are validated against published FDA/EMA guidance examples. Each test case cites its source: paper DOI, FDA guidance ID, or R-package vignette.
NCA: four-way cross-validation against Phoenix WinNonlin:
NCA results are cross-validated against Phoenix WinNonlin (Certara), PKNCA 0.12.1, and NonCompart 0.8.0
on the standard R nlme::Theoph (12-subject oral theophylline) and nlme::Indometh (6-subject IV bolus
indomethacin) datasets. Key validated parameters: AUClast, AUCinf, CL/F, Vz/F, lambda_z, half-life.
C0 back-extrapolation for IV bolus data (WinNonlin's approach: OLS regression on the first 2 points,
linear trapezoid area added from t=0 to t_first) is implemented in c0_back_extrapolated() and verified
to match WinNonlin reference values within 2% for all 6 Indometh subjects.
See VALIDATION.md for the full regulatory test traceability matrix.
This software is for research and decision-support workflows. Final regulatory interpretation should be reviewed by qualified formulation, pharmacokinetic, and regulatory experts.
- Theory Guide - Full LaTeX formula derivations for every module: NCA, simulation, dissolution, IVIVC, BE, pop PK, Bayesian PK. Designed for regulatory review support and teaching.
- Migration Guide - Coming from WinNonlin, NONMEM, or R? Quick-reference mapping for every parameter and function.
- Tutorials - Step-by-step worked examples for all 7 modules.
- Validation Matrix - Every test mapped to its FDA/EMA/ICH guidance section or published DOI.
- API Reference - Full function and class reference for all 9 modules.
Issues and PRs welcome at https://github.com/priyamthakar/openpkflow/issues
If you use OpenPKFlow in research, please cite:
Thakar, P. (2026). OpenPKFlow: Python-first pharmacometrics and dissolution toolkit.
https://github.com/priyamthakar/openpkflow
MIT - see LICENSE