Sampling During and After Intravenous Infusions

Why Infusion Timing Matters

An intravenous infusion has a known start and stop time, but a measured concentration still depends on when the sample was collected relative to those times. During an ongoing infusion, drug is entering the circulation while elimination and distribution are occurring. After the infusion stops, there is no further input from that infusion, and the measured concentration changes as drug distributes and is eliminated. Consequently, two accurately measured samples from the same patient can differ simply because they were collected at different phases.

Sampling plans should therefore begin with the clinical question. A sample during a continuous infusion may be intended to assess whether the concentration is approaching a target during ongoing delivery. A sample after an intermittent infusion may be intended to represent a concentration after an early distribution phase or at a specified time in the dosing interval. There is no universal “post-infusion” time that suits every drug or purpose. The intended phase, infusion duration, and relevant pharmacokinetics must be specified.

Concentration During and After a Continuous Infusion

First consider a one-compartment model with linear elimination, constant clearance \(CL\), and a constant infusion rate \(R_0\). Assume the drug is initially absent, the infusion rate and clearance remain constant, and no other dose contributes to the concentration. Let \(k=CL/V\), where \(V\) is the model’s apparent volume of distribution. Under these assumptions, the concentration rises toward a limiting value while the infusion continues.

If the infusion continues indefinitely in this model, the limiting concentration is \(R_0/CL\). It is approached asymptotically rather than reached at a finite time. After the infusion stops at \(T\), the one-compartment concentration declines exponentially:

These equations make the timing distinction explicit: the first uses time since infusion began, while the second uses time since it ended. The post-infusion equation applies to this one-compartment model. If distribution between compartments is important, a single exponential may not describe the early decline well.

Intermittent Infusions: End-of-Infusion and Pre-Infusion Samples

An intermittent infusion is given over a finite duration \(T\), then stopped until the next infusion begins. In the one-compartment, linear model, assume the same infusion rate \(R_0\) and duration \(T\) recur every interval \(\tau\), with \(T\leq\tau\). At steady state, the concentration at the end of an infusion is the sum of contributions from the current infusion and all earlier infusions. Each previous contribution has undergone additional elimination.

Under these assumptions, the steady-state concentration at the end of an infusion and immediately before the next infusion are:

The second equation uses the drug-free interval \(\tau-T\) between the end of one infusion and the start of the next. Thus, a pre-infusion sample is not the concentration at \(\tau\) hours after the end of an infusion; it is taken \(\tau-T\) hours after that end. This distinction prevents a common timing error.

Post-Infusion Distribution Can Produce More Than One Decline Phase

Some drugs distribute between a central compartment and other tissues on a timescale that is visible in measured concentrations. After an infusion ends, the concentration may fall rapidly at first as distribution occurs, then decline more slowly as elimination becomes the dominant visible process. A one-compartment exponential cannot represent both phases. For a linear multicompartment model, a post-infusion concentration can instead be represented as a sum of exponential terms. For two phases, write \(C(T+u)=A e^{-\alpha u}+B e^{-\beta u}\), where \(A\) and \(B\) are the contributions at infusion end, and \(\alpha>\beta>0\) are rate constants. The fast component has rate \(\alpha\); the slower component has rate \(\beta\).

A useful justification for why infusion duration changes the coefficients follows from the linear model’s response to a bolus. Suppose a bolus dose produces a concentration response \(c_b(t)=\sum_j a_j e^{-\lambda_j t}\), where \(a_j\) is the coefficient per unit dose for component \(j\), and \(\lambda_j>0\). A constant infusion adds the responses to small inputs delivered throughout the infusion. At post-infusion time \(u\), the contribution of component \(j\) is:

To see the equality, factor \(e^{-\lambda_j u}\) outside the integral and integrate \(e^{-\lambda_j(T-s)}\) from \(s=0\) to \(T\). The resulting factor \((1-e^{-\lambda_jT})/\lambda_j\) depends on infusion duration. Therefore, a finite infusion does not generally have the same post-infusion component weights as an instantaneous bolus with the same total dose. This derivation assumes linear, time-invariant pharmacokinetics and an infusion into the model’s central input compartment.

Practical Sampling Choices, Diagnostics, and Limitations

The main alternatives are not competing formulas so much as sampling strategies designed for different questions. An end-of-infusion sample documents a concentration at a clearly defined point, but may reflect ongoing distribution. A later post-infusion sample allows more time for distribution, but its value depends on the elapsed time and the model’s decline phases. During a continuous infusion, a sample taken after a long duration may be closer to the limiting concentration than one taken early, but “long” must be judged relative to the drug’s kinetics. Model-based correction can account for timing under stated assumptions; it cannot repair inaccurate dose or sample timestamps.

Check the actual infusion start and stop times, the time of blood collection, the infusion rate and duration, and the timing of prior doses. Confirm whether the patient was at steady state before using a steady-state equation. For a sample intended to represent circulating drug rather than infused solution, avoid drawing from the infusion line or a site that may be contaminated by it; follow the relevant collection procedure. If measured concentrations do not behave as expected, review timing and sample location before concluding that the pharmacokinetic model or the patient’s clearance has changed.

A visible early decline that is steeper than a later decline can be evidence that a single exponential is inadequate, but it does not by itself identify the correct model. Sparse samples, uncertain timestamps, assay variation, changing physiology, and nonlinear pharmacokinetics can also explain discrepancies. The formulas here assume linear pharmacokinetics and stable model parameters; they are not a substitute for a drug-specific monitoring protocol or clinical assessment.

Common Mistake

Wrong reasoning: “The infusion lasted one hour, so any sample taken one hour later is the trough.” This confuses time since infusion start with time since infusion end and ignores the dosing interval. In repeated dosing, the pre-infusion sample is taken immediately before the next infusion begins; after an infusion of duration \(T\) in an interval \(\tau\), it occurs \(\tau-T\) hours after the previous infusion ended. A sample at another time can still be useful, but it must be interpreted at its actual elapsed time, with distribution and accumulation considered as appropriate.