Structural PK models and identifiability

Parameters and units

Clearance/volume parameterization is convenient for interpretation: CL and Q are volume/time, V is volume, and ka is 1/time. Microconstants (CL/V, Q/V) and exponential coefficients can also be valid estimation parameterizations; none guarantees identifiability. Physiological plausibility and covariate relationships depend on the drug, population and estimand.

_models.disposition() constructs a linear mammillary rate matrix and obtains exponential components by eigendecomposition. The library supports any number of peripheral compartments; the individual fitting CLI offers one through three. Positive finite CL, volumes and Q are required.

For an IV dose D, the central concentration is D*sum(coef_i*exp(lambda_i*t)). The infusion response convolves this with a finite constant input; oral first-order input adds ka and F. At ka=-lambda_i, evaluate the removable limit t*exp(lambda_i*t) within the convolution. The library includes that branch. Analytical checks include:

AUC_iv(0,inf) = D/CL
Vss = Vcentral + sum(Vperipheral)
MRT_iv_bolus = Vss/CL
AUC_ss(0,tau) = D/CL

Multicompartment accumulation depends on the metric. The terminal half-life alone does not give the peak, trough or interval-AUC accumulation ratio. Closed-form metrics in the simulation CLI are restricted to IV bolus; oral or infusion inputs require their actual input model.

Oral and nonlinear models

Oral data alone generally identify apparent CL/F and V/F. For a one-compartment first-order model, interchanging absorption and elimination rates with an adjusted apparent volume can reproduce the same curve. A slow observed terminal phase can therefore reflect absorption. Do not interpret Vz/F as an independently identified physiological volume without supporting absorption information.

The transit helper convolves a gamma-shaped input with disposition on a numerical grid. It uses lgamma to avoid factorial overflow; this does not make the convolution exact. Check grid/horizon sensitivity for narrow absorption distributions. An additional post-transit ka is not implemented and is rejected. Lag and transit can both be justified in some models, but require data that identify their distinct roles.

Michaelis-Menten elimination uses Vmax*C/(Km+C): Vmax is amount/time, Km concentration. At low C its approximate clearance is Vmax/Km. Superposition does not hold. Nonlinear dose proportionality has other possible causes (bioavailability, binding, absorption, assay), so it does not by itself identify a saturable elimination mechanism.

The ODE library splits at dose starts and infusion boundaries and checks solver success. Select tolerances by sensitivity of the requested exposure/effect output, not by a solver-success flag. SciPy solve_ivp documentation.

Fitting and model choice

fit_compartmental.py performs separate individual fits on log-positive parameters. Fixed observed weights are supported. Prediction-dependent weights are rejected because the implemented WLS objective lacks the variance-normalization term of their likelihood. Observed 1/y² weights can strongly bias noisy low concentrations; justify the residual model.

Inspect dose/time accuracy, residual dependence, multiple starts, boundary estimates, sensitivity rank and parameter profiles. Local Gauss-Newton covariance is not a profile likelihood; singular information does not support finite uncertainty. AIC/BIC comparisons require identical records and weight conventions. Extra-compartment parameters lie on boundaries under the simpler model, so the nominal F comparison is exploratory. Residual runs do not uniquely diagnose the cause of misfit. SciPy least_squares documentation.

For NONMEM translation, choose and verify the ADVAN/TRANS combination in the installed vendor manual, including compartment numbering, F, scaling and input. ADVAN16/17 address delay equations; they are not interchangeable with ordinary ODE ADVANs. No NONMEM execution was performed here. ICON NONMEM platform.