Selecting Dose Amount and Interval for Children

Why Dose Amount and Interval Must Be Chosen Together

A pediatric dose should reflect how the child handles the drug, not simply a mechanical fraction of an adult dose. Clearance determines the rate at which drug is eliminated, while volume of distribution influences the concentration produced by a given amount in the body. Together they determine the elimination half-life and, with the dosing interval, the concentration fluctuation between doses. The earlier material on a framework for model-based pediatric dosing and pediatric clearance maturation provides the background for obtaining age-appropriate pharmacokinetic parameters. Here the task is to use clearance and volume to choose a dose amount and interval for a specified concentration profile.

The calculations below use a deliberately simple model and hypothetical concentration targets. Such targets must come from appropriate clinical and pharmacological evidence for a particular drug and indication; the equations do not establish which concentrations are safe or effective. The aim is to make the relationship between a target profile and a regimen explicit.

Assumptions and Steady-State Equations

The equations require a one-compartment model with instantaneous intravenous bolus input, first-order elimination, and constant \(CL\) and \(V\) over the interval. They also assume repeated dosing has continued long enough to reach steady state: the concentration-time profile then repeats from one interval to the next. The dose and interval are expressed in compatible units, and the child’s parameters are appropriate to the child and clinical circumstances being considered. If a drug is given orally, absorbed slowly, infused, or described by a more complex or nonlinear model, these bolus equations do not directly describe its peak and trough.

Between bolus doses, concentration falls exponentially. Thus, over one interval, the trough is the peak multiplied by the fraction remaining after \(\tau\) hours:

At steady state, each new dose adds \(D/V\) to the concentration. Earlier doses contribute less because they have undergone more elimination. Summing those contributions gives the peak equation:

The terms in parentheses form a geometric series with ratio \(e^{-k\tau}\), which is between zero and one when \(k>0\) and \(\tau>0\). Its sum is \(1/(1-e^{-k\tau})\), giving the displayed result. The average steady-state concentration over the interval is also useful. The area under the concentration-time curve during one steady-state interval is \(D/CL\) for this linear model, so:

This average describes overall concentration across the interval, but it does not describe fluctuation. Two regimens can have the same \(D/\tau\), and therefore the same average concentration under unchanged clearance, while producing different peaks and troughs.

Turning Profile Bounds Into a Regimen

Suppose a regimen is being designed to keep the steady-state concentration between a specified lower bound \(L\) and upper bound \(U\), where \(0<L<U\). For a fixed interval, the trough must be at least \(L\), and the peak must be no more than \(U\). The relationship between peak and trough implies that their ratio is determined by the interval and elimination rate:

If the desired peak and trough are specified exactly, solve for the interval and dose:

The dose expression follows by rearranging the peak equation and using \(C_{\min,ss}=C_{\max,ss}e^{-k\tau}\): \(D=VC_{\max,ss}(1-e^{-k\tau})=V(C_{\max,ss}-C_{\min,ss})\). For bounds rather than exact targets, a candidate interval is feasible only if a dose exists that meets both bounds. At that interval, dosing to the lower bound requires \(D=VL(e^{k\tau}-1)\); dosing at the upper bound permits at most \(D=VU(1-e^{-k\tau})\). Feasibility therefore requires:

This check is useful before choosing a dose: if the interval is too long relative to the child’s elimination rate and the allowed peak-to-trough range, no dose amount can satisfy both bounds.

Choosing Among Candidate Intervals

Clinical schedules generally use candidate intervals rather than any mathematically possible interval. A useful approach is to test each candidate against both concentration bounds. If an interval passes the feasibility check, calculate the dose required to meet the lower bound and verify that the resulting peak remains below the upper bound. Choosing a shorter interval usually reduces fluctuation, but may require more frequent administration. Choosing a longer interval increases fluctuation and can make a lower-bound trough incompatible with an upper-bound peak.

Average Exposure Is Not the Whole Profile

A dose rate chosen to match an average concentration may still produce an unacceptable trough or peak. This matters when the desired profile includes concentration limits, or when the pharmacological effect is sensitive to the duration spent above or below a concentration. Average concentration is a useful summary, but it cannot substitute for checking the profile if the profile itself is the design goal.

Checks, Alternatives, and Limitations

The calculations are only as reliable as their assumptions and inputs. Before using them to support a decision, check that the modeled route and input pattern are appropriate, that the pharmacokinetics are reasonably linear over the dose range, and that \(CL\) and \(V\) represent the child at the relevant age, size, and clinical state. A one-compartment bolus model may not capture delayed absorption, distribution into multiple compartments, time-varying clearance, or nonlinear elimination. For those cases, the corresponding model should be used to simulate the candidate regimens rather than treating bolus equations as universal.

Model predictions should also be checked against available concentration-time data when such data are relevant. Confirm that sample times are measured relative to the dose, that the predicted accumulation and profile are plausible, and that the model does not systematically miss observed peaks or troughs. A mismatch can reflect incorrect parameter estimates, a misspecified model, changing physiology, or inaccurate dosing or sampling times. A precise arithmetic result does not remove uncertainty in the parameters or in the clinical target.

Dose amount and interval are the main alternatives to compare within this design task. Reducing the amount while keeping the interval fixed lowers both peak and trough; extending the interval while adjusting dose can preserve an average dose rate but generally increases peak-to-trough fluctuation. A regimen selected to match average concentration is therefore not equivalent to one selected to satisfy peak and trough bounds. More detailed pharmacokinetic simulation may be preferable when the input is not a bolus or when the model has more than one compartment. The equations here provide a transparent starting point, not a replacement for a suitable model or clinical judgment.

• Common mistake: treating the half-life as the dosing interval. A half-life describes the time for concentration to fall by half during elimination; it does not, by itself, specify an appropriate interval. The interval must be judged against the desired profile and the value of \(k\).
• Common mistake: changing the dose to fix every trough problem. Increasing the dose raises both peak and trough. If the interval makes the peak-to-trough ratio too large, increasing the dose enough to meet a trough bound may violate the peak bound. Check feasibility before settling on a dose.
• Common mistake: assuming the same mg/kg dose gives the same profile in every child. The modeled profile depends on clearance and volume, which may vary with development and body size. A dose expressed per kilogram does not by itself guarantee the intended concentrations.