Physiologically based pharmacokinetics: when it earns its cost

PBPK divides the body into anatomical compartments with literature blood flows and volumes, and represents the drug through physicochemical and in vitro properties. Nothing about the system is fitted; the drug parameters are.

When PBPK is the right tool

It earns its cost where the question requires extrapolating outside the observed data in a way a population model cannot:

• Drug interactions — the most common regulatory use by a wide margin. Predicting an untested combination, an untested dose of a perpetrator, or a staggered dosing schedule. ICH M12 points to PBPK when a basic model signals a possible interaction and a refined estimate is needed.
• Paediatric first-dose selection, where enzyme ontogeny and organ maturation are represented mechanistically instead of by an empirical maturation function.
• Organ impairment — predicting exposure in hepatic or renal impairment without a dedicated study.
• Food effect and formulation, using absorption models (ACAT, ADAM) that represent transit, dissolution and regional permeability.
• Tissue concentrations that cannot be measured — brain, tumour, lung.

It is the wrong tool when the question is "what is the exposure in the population I studied" — a population PK model answers that better, with the variability estimated rather than assumed.

Platforms

There is no mature open-source PBPK library in Python. PK-Sim/MoBi with the R toolchain is the realistic open route; the Python ecosystem is limited to building the ODE system yourself.

Structure

Perfusion-limited tissue (the default for most tissues and small molecules):

V_t * dC_t/dt = Q_t * (C_arterial - C_t / Kp_t)

Permeability-limited tissue splits into vascular and extravascular subcompartments and adds a permeability-surface-area product. Use it for tissues with tight barriers (brain), for large molecules, and for transporter-mediated distribution.

Tissue-to-plasma partition coefficients (Kp) are predicted from physicochemistry rather than measured, most often via:

• Rodgers & Rowland — accounts for ionisation and binding to acidic phospholipids; the usual choice for bases
• Poulin & Theil — lipophilicity- and composition-based; better for neutrals and acids
• Berezhkovskiy — a correction to Poulin & Theil's volume terms
• Schmitt

Different methods can give Kp values differing several-fold, which propagates directly into Vss. Choosing the method that reproduces the observed Vss is a legitimate calibration step, but it must be reported as such.

In vitro to in vivo extrapolation

Hepatic clearance is built up from intrinsic clearance measured in microsomes or hepatocytes:

CLint,in vivo = CLint,in vitro * MPPGL (or HPGL) * liver weight
CL_hepatic    = Q_h * fu_b * CLint / (Q_h + fu_b * CLint)      (well-stirred model)

Scaling factors: microsomal protein per gram of liver ≈ 40 mg/g; hepatocytes ≈ 99-120 × 10⁶ cells/g; liver weight ≈ 1500-1800 g in an adult. The well-stirred model is standard; parallel-tube and dispersion models give different answers for high-extraction drugs.

IVIVE routinely under-predicts clearance, often 2-5 fold, especially for low-clearance compounds. Empirical scaling factors are widely applied and must be declared. This is the weakest link in a PBPK model and the first place to look when predictions are off.

Verification and credibility

A PBPK model used for a regulatory decision must be verified against observed clinical data before being applied to the untested scenario, and the standard of verification scales with how much the decision rests on it:

• Predict the observed data first. A model that cannot reproduce single-dose and multiple-dose plasma profiles in healthy adults should not be used to predict a DDI.
• Verify the perpetrator model independently using a known index substrate before predicting a novel victim, and vice versa.
• Acceptance is usually judged on predicted-to-observed AUC and Cmax ratios within 2-fold, with a tighter criterion where the decision is more consequential.
• Sensitivity analysis on the uncertain inputs — fu, fm, Ki, CLint, Kp method — is expected, not optional. Report the range of predictions, not a single number.
• Software version, model file, and every parameter with its source must be reportable. Regulators ask for the model files.

Reporting

State: the platform and version, the population library used, every drug-specific parameter with its source (measured, predicted, or optimised — and if optimised, against what), the Kp prediction method, the absorption model, the verification datasets and their outcome, and the sensitivity analysis. A PBPK prediction whose inputs are not individually traceable cannot be evaluated by anyone else, and will not be accepted.