Sampling at Steady State

Why Steady State Matters for Monitoring

A concentration measured after repeated doses reflects more than the most recent dose. Drug from previous doses may still be present, and each new dose adds to that residual amount. As a result, a concentration measured early in a regimen can differ from the value expected under the same regimen after accumulation has stabilized. For therapeutic drug monitoring, it matters whether a sample represents a repeating, stable dosing pattern or an evolving one.

Steady state does not mean that concentration is constant throughout each dosing interval. With intermittent dosing, concentration generally rises and falls after each dose. At steady state, that rise-and-fall pattern repeats from one interval to the next. A trough is therefore a recurring low point at a specified time relative to the next dose; a peak is a recurring high point or a concentration at a specified postdose time. The interpretation also depends on recording sample time relative to dosing, as covered in the earlier material on Recording Sample Time Relative to Dosing.

How Repeated Doses Approach Steady State

A useful estimate of the time to approach steady state follows from first-order elimination. Let \(k\) be the elimination rate constant and \(t_{1/2}\) the elimination half-life. Under first-order elimination, the fraction of a concentration remaining after elapsed time \(t\) is \(e^{-kt}\). Since \(t_{1/2}=\ln(2)/k\), this fraction can also be written \(2^{-t/t_{1/2}}\).

The following result applies when pharmacokinetics are linear and time-invariant, the regimen repeats at a fixed interval \(\tau\), the patient begins with no residual drug from earlier dosing, and the dose response at a matched phase is multiplied by \(e^{-k\tau}\) for each preceding interval. This holds, for example, with instantaneous bolus dosing in a one-compartment model with mono-exponential elimination. Doses and relevant conditions must remain unchanged during the approach. With delayed or first-order absorption, the approach fraction generally depends on the full dose-response model and its absorption and disposition rates.

One way to justify the result is to compare the accumulated dose contributions at a fixed phase. If each dose produces the same concentration-time contribution shifted by one interval, the contributions from the latest dose, the preceding dose, and earlier doses form a geometric series. The contribution from a dose one interval earlier is multiplied by \(r=e^{-k\tau}\); from two intervals earlier it is multiplied by \(r^2\), and so on. After \(n\) doses, the relative sum is \(1+r+\cdots+r^{n-1}\), while the steady-state sum is \(1+r+r^2+\cdots=1/(1-r)\). Their ratio is $$ \frac{1-r^n}{1-r}\,(1-r)=1-r^n=1-e^{-kn\tau}. $$ This explains why the fraction reached is the same at a matched phase in this mono-exponential bolus model, even though the absolute concentration at a peak and at a trough differs.

The result also gives a practical time estimate. To reach at least a chosen fraction \(q\) of steady state, require $$ 1-2^{-n\tau/t_{1/2}}\ge q \quad\Longleftrightarrow\quad n\tau\ge \frac{-\ln(1-q)}{k}. $$ Thus, reaching 90% takes about 3.322 half-lives; reaching 95% takes about 4.322 half-lives; and reaching 99% takes about 6.644 half-lives. These are approximate thresholds, not a sudden transition. Accumulation approaches steady state asymptotically, so the exact steady-state profile is not attained after a finite number of doses in this model.

What the Estimate Means for Peak and Trough Samples

At steady state, a concentration measured at a consistent postdose time can be compared with the expected concentration at that same time under the repeating profile. A trough sample is typically drawn just before the next scheduled dose. A postdose sample should be described by its actual time after dosing; for an oral drug, a sample at a selected postdose time is not automatically the maximum concentration. The earlier material on trough concentrations and peak concentrations distinguishes these monitoring targets.

Steady-state status and sample timing are separate requirements. A sample may be collected at the correct time for a trough but before accumulation is sufficiently close to steady state. Conversely, a patient may be at steady state while a sample drawn several hours away from the intended trough cannot be treated as that trough. Even a small timing difference can matter when concentration changes rapidly.

Checking Assumptions and Recognizing Failure Modes

The half-life calculation is a planning estimate, not proof that a patient is at steady state. It assumes the relevant elimination process is adequately represented by a stable half-life and that the dose, interval, and pharmacokinetic conditions have not changed. It also assumes proportional accumulation: each dose contributes a concentration profile that can be added to those from earlier doses. Under these conditions the approach fraction is independent of dose size, although the absolute steady-state concentrations depend on dose and disposition.

Check the estimate against the clinical and dosing record. A recent dose change resets the approach to the new regimen; a missed or delayed dose disrupts the repeating pattern. A half-life estimated for a different patient or condition may not describe the current patient. Multiple disposition phases, delayed absorption, or a terminal process slower than the half-life used for the calculation can make a simple estimate misleading. For a complex profile, model-based predictions or repeated measurements at matched dose-relative times may be more informative than a single half-life rule. A value that varies across matched samples can signal a changed regimen, changing conditions, timing errors, or measurement variability; it should prompt review rather than an automatic declaration of steady state.

A common shortcut is to say that steady state is reached after exactly five half-lives. Under the stated first-order model, five half-lives correspond to \(1-2^{-5}=0.96875\), or 96.875% of steady state—not 100%. Whether that is close enough depends on the purpose and the clinical context. Another mistake is to count dosing intervals without considering their length relative to the half-life: 13 short intervals can represent fewer half-lives of elapsed time than five longer intervals.

A calendar rule is convenient when the kinetic assumptions are reasonable and an approximate threshold is sufficient. A model-based estimate can account for the actual interval and a specified fraction threshold more explicitly, but depends on the model and its parameter estimates. Repeated, consistently timed concentrations can provide evidence of a stable pattern, though apparent similarity across a small number of samples does not prove that all assumptions hold. No approach removes the need to verify the dosing history and sample timing.