Avoiding Dose and Bioavailability Double Counting

Why the Dose Must Be Counted Once

A PBPK model can have the right absorption rate constant and still predict the wrong exposure if its input function counts drug more than once. This often happens when a model starts with an already bioavailable dose in a depot and then multiplies depot release by bioavailability again. A related error occurs when eliminated drug is added to systemic input, even though it has already entered the body and is now leaving it. These mistakes distort the amount entering the model, so they can be difficult to repair by tuning absorption parameters.

The accounting begins by distinguishing four quantities: the administered dose is the amount placed at the dosing site; the depot amount is the amount still present in a modeled absorption site; the systemic input is the rate at which drug crosses into the systemic circulation; and systemic elimination is drug leaving the systemic circulation. Bioavailability is a fraction relating dose or absorption to systemic entry. It is not an additional dose.

The equation depends on the model’s definition of \(F\). It may represent the fraction of the administered dose that ultimately reaches systemic circulation, or a fraction applied to a specific absorption flux. State which interpretation is being used before implementing it. In either case, do not apply the same fraction twice.

Two Consistent Ways to Represent Bioavailability

For a simple first-order depot, suppose the administered dose is placed in the depot at time zero, and the depot loses drug by absorption at rate \(k_a A_{\mathrm{dep}}(t)\), where \(k_a\) has units of inverse time. Assume there are no competing depot losses and a constant fraction \(F\) of the absorption flux reaches systemic circulation. The depot and systemic input are then

The same total input can be represented with a bioavailable depot amount \(A_{\mathrm{bio}}(0)=F D_{\mathrm{admin}}\), if its release rate is \(k_a A_{\mathrm{bio}}(t)\). That alternative is valid only when \(F\) is not applied again to the release flux. The two representations are alternative bookkeeping conventions, not sequential steps.

This equivalence assumes that bioavailability is a constant fraction of the modeled absorption and that both representations use the same release kinetics. If loss competes with absorption, if the fraction varies over time, or if the depot contains multiple processes, the model must represent those processes explicitly. A single dose multiplier may not reproduce the resulting input profile.

Deriving the Input Total From Depot Mass Balance

A mass balance makes the bookkeeping rule explicit. Under the first-order assumptions above, the depot equation has solution \(A_{\mathrm{dep}}(t)=D_{\mathrm{admin}}e^{-k_a t}\). Integrating the absorption flux gives the amount leaving the depot by absorption:

Multiplying this absorption flux by the systemic fraction \(F\) therefore gives total systemic input \(F D_{\mathrm{admin}}\). The result relies on the depot eventually emptying through that absorption process. With an additional depot loss \(R_{\mathrm{loss}}(t)\), the balance is instead

Now the total absorption need not equal the administered dose, because some drug can leave by the competing loss pathway. The systemic input is \(F\int_0^\infty R_{\mathrm{abs}}(t)\,dt\), not automatically \(F D_{\mathrm{admin}}\). This distinction matters for processes such as local degradation or clearance from an absorption site. The depot’s loss terms and the meaning of \(F\) must be defined consistently; do not use \(F\) to represent a loss already included explicitly in the model.

Systemic Input Is Not Systemic Elimination

Once drug has entered the systemic circulation, it belongs to the systemic amount, whether it remains in the body or is later eliminated. For a systemic amount \(A_{\mathrm{sys}}(t)\), a general amount balance is

where \(R_{\mathrm{elim}}(t)\) is the rate of systemic elimination. In a linear model with clearance \(CL\) and systemic concentration \(C(t)\), one possible elimination expression is \(R_{\mathrm{elim}}(t)=CL\,C(t)\). Elimination is a sink from the systemic amount; it is not an additional systemic input. Integrating the balance from time zero to \(t\), with initial systemic amount \(A_{\mathrm{sys}}(0)\), gives

Thus, if cumulative input is reconstructed from systemic amount and elimination, elimination is added to the amount currently present to recover the input that has already occurred. It is not added to the dose as a second amount entering the body. This identity assumes the balance includes all systemic sources and sinks; distribution among modeled compartments does not itself count as elimination from the whole systemic model.

Practical Checks and Common Failure Modes

A reliable input function should pass both a local and a cumulative check. Locally, confirm that each rate has the intended units and corresponds to transfer across the intended boundary. For example, a depot absorption rate has units of amount per time, and multiplying it by a dimensionless fraction preserves those units. Cumulatively, integrate the systemic input and compare it with the amount that should reach systemic circulation under the model’s stated assumptions.

A common mistake is to say, “Only a fraction \(F\) is available, so I should multiply the input by \(F\),” without checking whether the depot was already initialized with \(F D_{\mathrm{admin}}\). The correction is to trace the mass from the model’s initial condition: either begin with \(D_{\mathrm{admin}}\) and apply \(F\) once to the relevant absorption flux, or begin with \(F D_{\mathrm{admin}}\) and do not apply \(F\) again.

Another failure is to infer systemic input as administered dose minus depot amount remaining. That difference is the amount that has left the depot, not necessarily the amount that reached systemic circulation. It may include presystemic loss, depending on the model. Separately, adding eliminated drug to an input function confuses a cumulative systemic balance with a source rate. Check both the pathway and the direction of every flux.

The main alternative implementations—scaling the initial depot or scaling its absorption flux—are equivalent only under the stated constant-fraction assumptions and when they encode the same kinetics. An explicit model with separate absorbed and lost fractions is more informative when local loss, incomplete absorption, or time-varying availability matters. Its additional states and parameters require evidence or justification, and each pathway must still be counted once. These bookkeeping checks establish consistent input; they do not by themselves determine the correct absorption mechanism or identify bioavailability uniquely from plasma concentrations.