Common Parameterization Errors in Absorption Models

Why absorption inputs are easy to misparameterize

An absorption model can have the intended shape and still deliver the wrong amount of drug or deliver it at the wrong time. A rate entered where a duration was expected, a lag applied twice, or a pathway fraction multiplied into an already scaled dose can change the predicted input even when every parameter value looks plausible. These errors matter because disposition models respond to the input they are given; they cannot repair a wrongly specified absorption event.

A useful audit starts with four questions: What quantity does each parameter represent? What are its units? At what time does the input begin? How much of each administered dose is assigned to each pathway? The equations below use dose \(D\) in mg, bioavailability \(F\) as a dimensionless fraction, pathway fraction \(f_j\) as a dimensionless fraction, time in hours, first-order absorption rate constant \(k_a\) in \(\mathrm{h}^{-1}\), and lag time \(t_{\mathrm{lag},j}\) in hours.

Unit checks: rate is not duration

A zero-order pathway delivers its assigned amount at a constant rate over a specified duration. If the pathway receives fraction \(f_j\) of the bioavailable dose, then its rate and duration must obey

The units confirm the distinction: \(\mathrm{mg}/\mathrm{h}=\mathrm{mg/h}\), whereas \(T_j\) is measured in hours. If a model parameter expects a rate, entering a duration is not a harmless alternative notation; it changes both the dimensions and the implied amount. Conversely, entering a rate into a duration field changes the time over which the dose is delivered. The correct conversion depends on which quantity the model specifies.

For a first-order depot, the remaining amount declines exponentially after absorption begins. For one dose event at time \(t_d\), the pathway input rate is zero before \(t_d+t_{\mathrm{lag},j}\), and after that time it is

The exponent must be dimensionless: \(k_{a,j}\) is in \(\mathrm{h}^{-1}\), and the time difference is in hours. The rate has units \(\mathrm{h}^{-1}\times\mathrm{mg}=\mathrm{mg/h}\). A rate constant is not a duration; a larger \(k_a\) means faster first-order disappearance from the absorption depot, not a longer absorption time.

Lag times belong to pathways and dose events

A lag time shifts the onset of the specified absorption pathway relative to its dose event. It does not mean that the dose itself occurred later, and it does not automatically delay every parallel pathway. If one pathway is immediate and another has a lag, each has its own onset time. For repeated doses, the lag is applied to each event according to the model specification; it is not a one-time shift of the entire dosing history.

For a zero-order pathway, the corresponding input interval for one event is from \(t_d+t_{\mathrm{lag},j}\) to \(t_d+t_{\mathrm{lag},j}+T_j\). Its rate is \(Ff_jD/T_j\) during that interval and zero outside it. Shifting the dose time and also specifying the same lag would delay the input twice. Likewise, using elapsed time \(t-t_d\) in a lagged first-order expression instead of \(t-t_d-t_{\mathrm{lag},j}\) makes absorption begin too early.

Pathway fractions and dose scaling

Pathway fractions describe allocation, not additional doses. Under the convention used here, \(F\) is applied once to the administered dose and the fractions divide that bioavailable amount. Thus the pathway amounts are \(Ff_jD\), and when all modeled absorption pathways account for the bioavailable dose, their sum is

This mass-balance identity is a direct check on the parameterization. If the fractions sum to more than one, the model allocates more than the specified bioavailable dose. If they sum to less than one while they are intended to represent a complete allocation, some amount is unassigned. A different convention may define fractions of the administered dose or pathway-specific bioavailability; that convention can be valid, but it must be stated and used consistently rather than combined with this one.

Dose scaling should also be checked across occasions. \(D\) in these equations is the amount for one event, not the sum of all doses in a repeated-dose regimen. Each event contributes its own pathway amount at its own event time. Using a cumulative dose in place of the event dose and then applying the repeated events again counts dose more than once.

A practical audit and its limits

A compact audit can catch many errors before fitting or interpreting a model. First, write the units beside each input parameter and verify that every exponent is dimensionless. Next, calculate the amount assigned to each pathway for one event. Then check the pathway fractions and verify that rates multiplied by durations recover the corresponding zero-order amounts. Finally, list the dose time, lagged onset, and end of each finite-duration input on a single time line.

Common warning signs include an input rate with units of time, an exponential evaluated with a dimensional exponent, a pathway amount larger than the dose it is meant to allocate, or an onset that disagrees with the event time plus lag. In a fitted model, unexpectedly low or high predicted exposure can prompt an audit, but it does not identify a particular coding error on its own. Similar concentration patterns can arise from different absorption and disposition specifications, so a plausible fit is not proof that the inputs are correctly parameterized.

A dimensional and mass-balance audit is a check of implementation, not a model-selection procedure. It cannot establish that a first-order or zero-order pathway is biologically appropriate, nor can it resolve weak identification from sparse observations. Those questions require examination of the model assumptions, data, and predictions. The advantage of this audit is narrower and important: it verifies that the implemented input corresponds to the intended dose, timing, and pathway allocation.

Common mistake

Wrong reasoning: “The absorption lasts six hours, so I will enter 6 as the zero-order rate.” This confuses a duration with a rate and does not preserve the amount delivered. Correction: calculate the pathway amount first, then divide by the duration to obtain a rate in amount per time. Similarly, apply a lag to the pathway onset rather than shifting the dose event and applying the lag again. Always verify both units and mass balance.