Translating an Oral Two-Compartment Model End to End

Why an End-to-End Translation Needs More Than Matching Parameter Names

A population-estimation implementation and a simulation engine can use different names, code structures, and event conventions for the same pharmacokinetic model. Translating an oral two-compartment model therefore requires more than copying a parameter table. The translated model must preserve the state definitions, rate equations, parameter meanings, dose routing, bioavailability, and observation calculation. If any of those differ, the two implementations can produce different concentrations even when several parameter values appear to match.

Here the target is a linear, first-order absorption model with a depot, a central compartment, and a peripheral compartment. The purpose is to implement the same individual parameter vector in mrgsolve and verify its predictions against the source implementation. This is a prediction-equivalence exercise: it does not re-estimate the population parameters or compare estimation objectives.

Map the Source Model Before Writing Target Code

First identify what each source parameter means, not just how it is spelled. A source model may use \(V_1\) for central volume and \(V_2\) for peripheral volume, while another uses \(V_c\) and \(V_p\). These are equivalent only if their definitions and units agree. Similarly, \(Q\) must be an intercompartmental clearance, not a rate constant. The model equations divide clearances by volumes to obtain rates with units of inverse time.

For an individual prediction, use the same individual parameter values in both implementations. If the estimation model defines an individual parameter from a typical value and an individual effect, evaluate that relationship first and transfer the resulting individual value. Transferring a typical value to one implementation and an individual value to the other is not a test of translation equivalence.

Implement and Check the Prediction

In mrgsolve, the compartment declarations define the state amounts, the ODE block defines their rates of change, and the table block can calculate the observation from the central amount. For example, the concentration calculation is “capture CP = CENT/VC”. The dose record must be an oral event to GUT, with the same dose amount, time, and bioavailability convention as the source. An oral dose is not an intravenous bolus into CENT: those inputs generate different concentration-time profiles.

A useful independent check comes from deriving the expected concentration under the stated model. Define \(k_{10}=CL/V_c\), \(k_{12}=Q/V_c\), and \(k_{21}=Q/V_p\). The two disposition rates \(\alpha\) and \(\beta\), with \(\alpha>\beta>0\), are the roots of

For a dose \(D\) given orally at time zero, with no lag time and no prior drug in the system, the central concentration is

This expression assumes the rates are distinct, including \(k_a\ne\alpha\) and \(k_a\ne\beta\). If rates coincide, the corresponding limiting expression must be used rather than dividing by zero. The equation provides a numerical reference for the implementation; it does not replace checking event records and units.

Verify the Dose Semantics and Event Schedule

Prediction equivalence requires equivalent events as well as equivalent equations. Check the dose amount and units, dose time, route or target compartment, bioavailability, any lag time, and the observation times. For repeated dosing, also verify the interval and whether the records represent doses at the same boundaries in both tools. If the source model applies \(F\) within its absorption input, do not apply it a second time to the dose amount in mrgsolve.

Diagnose Mismatches Systematically

The earlier material on testing cross-software prediction equivalence and event equivalence motivates comparing predictions at matched times, but a mismatch is easiest to diagnose by checking the model in layers. First confirm parameter values and units, then the model equations, then the dose events and output calculation. Compare the earliest time points as well as the later profile: an early discrepancy often points to input or absorption, while a discrepancy that develops during the terminal phase can indicate a disposition parameter or state-equation mismatch.

A few common failures have recognizable signatures. A dose mistakenly placed into CENT creates an immediate central amount instead of gradual absorption from GUT. Omitting \(F\) increases exposure when \(F<1\); applying it twice decreases exposure. Confusing \(Q\) with \(Q/V_c\) gives a dimensional inconsistency and can radically change distribution. A concentration reported as CENT without division by \(V_c\) has units of amount, not concentration. Finally, different solver tolerances can cause small numerical differences, but they do not explain a consistent, substantial change in the profile.

What This Translation Does—and Does Not—Establish

There are two useful ways to verify the implementation. Comparing mrgsolve with the source implementation tests that their predictions agree under matched inputs. Comparing both with the analytical expression adds an independent check of the stated linear model. A direct ODE comparison is more flexible for models that lack a closed-form solution; the analytical calculation is valuable here because it can help distinguish an implementation error from a shared coding error.

Neither check establishes that the model is clinically adequate or that the estimated parameters are scientifically appropriate. Equivalence only means that the implementations reproduce the same specified model under the checked conditions. It also does not automatically verify residual-error calculations, likelihoods, random-effects distributions, covariate relationships, or estimation results. Those components require their own checks if they are part of the intended workflow. For this translation, keep the comparison focused on the structural prediction and dose semantics.