Infusions, Bioavailability, and Lag Times in Four Tools

Why these event features need careful translation

The same dose can produce different predictions depending on how its input is represented. An infusion delivers drug over a duration; bioavailability determines what fraction of an extravascular dose reaches systemic circulation; and an absorption lag delays the start of that input. Each can be represented partly in a dose record and partly in a model specification, and the division differs across software.

Cross-tool translation therefore means more than copying a parameter name. The event must have the same dose amount, route, start time, duration or rate, bioavailability, and lag-time meaning. This tutorial uses a one-compartment model with linear elimination to make those meanings explicit. The examples are hypothetical and intended to illustrate implementation checks, not a real study.

The reference model and its checks

For an intravenous infusion into a one-compartment model, assume constant clearance \(CL\), volume \(V\), and elimination rate constant \(k=CL/V\). Drug enters the compartment at constant rate \(R_0\) from time zero to \(T_{\mathrm{inf}}\); after that, input is zero. Concentration is amount divided by \(V\). These assumptions exclude nonlinear elimination, time-varying parameters, and distribution into additional compartments.

During the infusion, the amount \(A\) satisfies \(dA/dt=R_0-kA\), with \(A(0)=0\). Dividing by \(V\) gives \(dC/dt=R_0/V-kC\). Multiplying by the integrating factor \(e^{kt}\) and integrating from 0 to \(t\) gives the concentration profile below.

At the end of the infusion, the concentration is \(C(T_{\mathrm{inf}})\). Thereafter the model has no input, so concentration declines exponentially from that value.

For a complete infusion with linear elimination, the total area under the concentration-time curve (AUC) is \(D/CL\). The duration changes the shape and peak concentration, but not this AUC when the entire dose is delivered and clearance is unchanged. This is a useful check, not a guarantee that two implementations are equivalent: profiles can differ even when their AUCs match.

Bioavailability and absorption lag

For an extravascular dose with first-order absorption, assume the dose enters an absorption compartment with rate constant \(k_a\), then reaches a one-compartment systemic model with \(CL\) and \(V\). A fraction \(F\) of the dose is available systemically. If the dose time is \(t_d\), absorption starts at \(t_d+T_{\mathrm{lag}}\). For time \(\tau=t-t_d-T_{\mathrm{lag}}\geq0\), the concentration after one dose is

Before the lag has elapsed, that dose contributes no absorbed input in this model. Its AUC over the complete profile is \(FD/CL\). Thus \(F\) scales exposure, while \(T_{\mathrm{lag}}\) shifts the input timing. Neither parameter is interchangeable with a change in clearance, dose time, or infusion duration.

Representing the same meaning in four tools

Before comparing software, specify the event independently of its syntax: dose amount and units; dose time; route and target compartment; infusion duration or rate when applicable; and whether \(F\) and \(T_{\mathrm{lag}}\) act on that route. Then inspect which parts are carried by the input data and which by model code. The names below refer to common conventions; verify the data-column and model-language requirements for the software version and model structure in use.

The table summarizes semantic mappings, not a claim that one text record can be copied unchanged between tools. In NONMEM, the selected compartment index determines which compartment-specific F and ALAG values apply. In Monolix, the event type and administration mapping are central: a data column that looks like a duration is not sufficient if the event is interpreted as a bolus. In nlmixr2 and mrgsolve, compartment-specific settings must match the event’s target; a correct value assigned to a different compartment has no intended effect.

For a NONMEM duration-coded infusion, a conceptual event record has a dose amount, a target compartment, RATE set to the duration convention, and D1 containing the duration in the required time units. The corresponding model setup must not inadvertently apply an unrelated rate or duration. For the extravascular example, assign the fraction and lag to the dose compartment, rather than the central compartment, unless the model specifically defines the input differently.

In Monolix, configure an infusion event and its duration in the event data or administration setup, and verify how that configuration is imported. For extravascular input, ensure the model’s absorption process, fraction, lag, and administration identifier all refer to the same route. In nlmixr2, use event data with a dose and infusion information for the infusion case; for a depot dose, the model’s compartment-specific fraction and lag statements must match the depot name. In mrgsolve, likewise pair the dose event’s infusion information with the named compartment receiving the dose; set the compartment’s fraction and lag in the model where appropriate. These are implementation patterns: exact field requirements depend on the selected event format and model interface, so validate them with a small deterministic simulation before fitting.

A reproducible cross-tool verification workflow

A reliable comparison separates event semantics from model predictions. Begin with fixed parameter values and one subject, without random effects or residual error. Use the same units, dose time, compartment structure, and output times in all implementations. Then test the route features separately: first a single infusion, then a single extravascular dose with fraction and lag, and only after those agree combine them or add repeated dosing.

This verification is especially important when an event table is generated in one tool and imported into another. The same numeric value can have different meanings if one system expects a duration and another a rate, or if an event code identifies an infusion in one format but a bolus in another. Check event interpretation, not just whether the files load.

Diagnostics, alternatives, and limitations

Three checks are particularly informative. First, the amount check asks whether rate times duration equals the intended dose. Second, the timing check asks whether input begins and ends when intended, including the lag. Third, the exposure check compares AUC with \(D/CL\) for intravenous input or \(FD/CL\) for a completely absorbed extravascular profile under linear, time-invariant clearance. These checks address different errors; none substitutes for comparing the full concentration-time profile.

The main alternatives are not simply different spellings. Infusion duration and infusion rate are two equivalent ways to specify constant-rate delivery if their values satisfy \(R_0=D/T_{\mathrm{inf}}\). A bolus is not equivalent to an infusion, even if the same amount is delivered. Similarly, a lag can be implemented as a model input delay or by changing event time, but only if all downstream timing and observation conventions are shifted consistently. Changing a dose time in the data may also alter the relation between dose records and observations, so it is not automatically equivalent to a compartment-specific lag.

Bioavailability may be represented as a model-level multiplier or incorporated into a dose amount before simulation. Those approaches agree only when the multiplier is applied exactly once to the correct route and dose. If dose amounts are already expressed as systemic amounts, applying F again will reduce input twice. Conversely, omitting F from a nominal administered dose overstates systemic exposure when \(F<1\).

The reference equations rely on linear one-compartment kinetics. With nonlinear elimination, the simple AUC ratios need not hold. Multiple compartments change the concentration profile; repeated doses require accounting for prior doses; and software may implement numerical event handling differently. A close match at a few selected times is evidence of agreement for the tested case, not proof of equivalence for every model or data set.