Physiologically-Based Pharmacokinetic modeling with GUM-compliant uncertainty propagation.
Part of the Sounio ecosystem — the L0 systems + scientific programming language for epistemic computing.
A PBPK modeling framework where every value carries its uncertainty, confidence, and provenance as intrinsic properties — not as an afterthought.
Three capabilities that no existing PK/PD tool offers:
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GUM-through-ODE — First application of the ISO metrology standard (JCGM 100:2008) to PBPK. Linearized uncertainty propagation through ODE integration via finite-difference Jacobian. 100-1000× faster than Monte Carlo with equivalent accuracy for CV < 40-50%.
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Compile-time confidence gates — The type system enforces minimum epistemic confidence thresholds. If a computation chain erodes confidence below the threshold, the program refuses to compile.
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Biomaterial → PBPK → uncertainty pipeline — Controlled-release kinetics (Higuchi, zero-order, first-order) integrated with full 14-compartment PBPK via operator splitting, with uncertainty tracked at every step.
The framework is validated with rapamycin (sirolimus) — the canonical biomaterial+drug combination (Cypher coronary stent, Cordis 2003):
| Metric | Value | Interpretation |
|---|---|---|
| AUC(0-168h) | 3.26 ± 0.88 mg·h/L | CV=27% — CYP3A4 variability propagated |
| Brain/blood ratio | 0.137 | < 0.15 — P-gp efflux at BBB confirmed |
| s_CL (sensitivity) | 0.84 (84%) | CL dominates AUC uncertainty |
| DES/IV AUC ratio | 1:103 | Implant release correctly orders of magnitude below IV |
| Mass conservation | 5.0 → 3.07 mg | 39% eliminated in 7 days |
stdlib/
├── darwin_pbpk/
│ ├── tsit5_pbpk14.sio # 14-compartment PBPK, adaptive Tsit5 solver
│ ├── epistemic_pbpk14.sio # GUM uncertainty bridge (finite-difference Jacobian)
│ ├── epistemic_sim.sio # 4-compartment epistemic PBPK (analytical GUM)
│ ├── release/
│ │ └── biomaterial_release.sio # Higuchi, zero-order, first-order release models
│ ├── drugs/
│ │ └── rapamycin.sio # Sirolimus parameters (Ferron 1997, Lampen 1998)
│ ├── core/
│ │ ├── rodgers_rowland.sio # Tissue partition coefficient prediction
│ │ └── fractal_blood.sio # CTRW anomalous transport
│ └── validation/
│ └── metrics.sio # FDA/EMA metrics (GMFE, AAFE, percent-within-2-fold)
├── epistemic/
│ ├── knowledge.sio # Knowledge<T> type
│ ├── gum.sio # GUM Type A/B, Welch-Satterthwaite
│ ├── propagate.sio # Variance propagation rules (GUM §13.3)
│ └── ... # ODE, PDE, MCMC, Sobol, optimization
tests/
└── run-pass/
└── rapamycin_epistemic_pbpk.sio # 3-compartment rapamycin validation (6/6 PASS)
Requires the Sounio JIT compiler:
SOUC=./artifacts/omega/souc-bin/souc-linux-x86_64-jit
# Epistemic 14-compartment PBPK (8 tests)
$SOUC run stdlib/darwin_pbpk/epistemic_pbpk14.sio
# Biomaterial release models (8 tests)
$SOUC run stdlib/darwin_pbpk/release/biomaterial_release.sio
# Rapamycin 3-compartment epistemic test (6 tests)
$SOUC run tests/run-pass/rapamycin_epistemic_pbpk.sio- JCGM 100:2008 — Guide to the Expression of Uncertainty in Measurement (GUM)
- Ferron GM et al. (1997) Clin Pharmacol Ther 61:696-708 — Sirolimus population PK
- Lampen A et al. (1998) Biochem Pharmacol — P-gp substrate, BBB transport
- Higuchi T (1963) J Pharm Sci 52:1145 — Matrix diffusion release model
- Sousa JE et al. (2003) Circulation 107:2274 — Cypher stent clinical data
- FDA (2018) — Physiologically Based Pharmacokinetic Analyses Guidance
- Tsitouras Ch (2011) Comput Math Appl 62:770 — RK 5(4) pairs
MIT
Demetrios Chiuratto Agourakis — ORCID 0009-0001-8671-8878