PBPK Drug Distribution Under Measurement Noise
An 11-compartment physiologically based pharmacokinetic model — drug distribution across organs — that survives noisy bioanalytical measurements.
- 30/30
- SolvSRK seeds survived
- 0/30
- BDF seeds survived
- 34ms
- SolvSRK median wall time
- 11
- Organ compartments
The scenario
Set the picture
Physiologically based pharmacokinetic (PBPK) models predict how a drug distributes across organs — liver, kidney, brain, gut, muscle, fat, and more. The Jones & Rowland-Yeo (2013) 11-compartment model captures inter-compartmental transfer with stiff rate constants spanning several orders of magnitude (stiffness class S2).
In drug development, PBPK models are used for dose selection, DDI prediction, and pediatric extrapolation. Bioanalytical noise from plasma assays, tissue sampling, and metabolite quantification introduces stochastic perturbations into the ODE system. The solver must produce stable predictions despite this noise.
Cost today
Standard implicit solvers fail on the noisy 11-compartment PBPK system. BDF achieved 0% survival, timing out at 15 seconds per seed with 455K–905K function evaluations. Radau also achieved 0%, hitting the nfev cap near 1M evaluations at 14–15 seconds each.
When the solver fails, pharmacokineticists must clean the data, smooth the inputs, and re-run — introducing manual preprocessing that is difficult to validate and impossible to reproduce exactly. For regulatory submissions, this undermines traceability.
What changes with SolvSRK
SolvSRK integrates the 11-compartment PBPK model through bioanalytical noise without preprocessing or smoothing. 30/30 seeds survived. Median wall time: 34ms. Median function evaluations: 1,195.
For drug development teams, this means PBPK simulations can run directly on noisy bioanalytical data — no manual data cleaning, no smoothing artifacts, no reproducibility gaps. Every simulation run produces the same result from the same input, with a single SHA-256 hash for regulatory traceability.
Measurable outcome
What we claim — and how it survives review
Each line below maps to a captured number in the demo section. Every number is reproducible from the benchmark suite.
- SolvSRK: 30/30 seeds survived (100% survival rate).
- BDF: 0/30 survived — timeout at 15s, 455K–905K nfev.
- Radau: 0/30 survived — nfev cap ~1M, 14–15s per seed.
- SolvSRK median wall time: 34ms.
- SolvSRK median function evaluations: 1,195.
- Stiffness class S2, 11 compartments — representative of production PBPK models.
The demo
What was tested. How. What the simulation printed.
Benchmark: 11-compartment PBPK model (Jones & Rowland-Yeo 2013). Stiffness class S2, dimension 11, t_span [0, 72.0]. Simulates 72-hour drug distribution across organ compartments. Gaussian noise at sigma=0.001.
Three solver arms: SolvSRK, scipy BDF, scipy Radau. 30 seeds per solver, 90 total runs. Reference solution computed with ||y_ref|| = 2.48.
Both BDF and Radau spent the full timeout budget attempting Newton convergence on the noisy 11-dimensional Jacobian. SolvSRK avoids these failure modes entirely, completing 72-hour simulations in 34ms.
Captured benchmark output
The numbers the simulation actually printed.
| Solver | Survived | Survival % | Median nfev | Median wall (s) | Failure mode |
|---|---|---|---|---|---|
| SolvSRK | 30/30 | 100% | 1,195 | 0.034 | — |
| BDF | 0/30 | 0% | — | 15.0 (cap) | Timeout |
| Radau | 0/30 | 0% | — | 14–15 | nfev cap (~1M) |
Claim ID: MEDTECH-PBPK. Topic: solvsrk-reval-medtech. 30 seeds, Gaussian noise sigma=0.001.
Composes with
Where this POC sits in the validation suite
Evidence pointers
Where the claims live in the evidence register
These are the validation sources a reviewer should trace to verify every number on this page.
- Claim MEDTECH-PBPK — Grade A CONFIRMED. Topic: solvsrk-reval-medtech.
- Sub-finding SF-MEDTECH-1: SolvSRK stiffness-invariant survival (S0–S2).
- Problem: pbpk_11cpt (Jones & Rowland-Yeo 2013). Stiffness: S2. Dim: 11.
- 90 runs total (30 SolvSRK + 30 BDF + 30 Radau). Noise: Gaussian sigma=0.001.
- Triage date: 2026-05-08. Phase verdict: CLOSED.
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