Modeling Pharmacokinetics in Preterm and Term Neonates

Why Neonatal PK Needs More Than One Age

A preterm infant’s pharmacokinetic profile cannot be described by body weight alone or by a single age label. Two infants with the same weight may differ in developmental maturity; two infants at the same postnatal age may differ in both maturity and size. Neonatal models therefore need to distinguish how mature the infant is from how long the infant has lived after birth, while representing how body size changes over time.

Gestational age (GA) is age at birth, conventionally counted from the last menstrual period. Postnatal age (PNA) is elapsed time since birth. Postmenstrual age (PMA) combines the two: \(PMA=GA+PNA\), using consistent units. For example, an infant born at 28 weeks’ GA and observed 4 weeks later has PMA 32 weeks. These quantities are related, but they are not interchangeable: at the same PNA, a preterm infant and a term infant usually have different PMAs.

The earlier material on body-size scaling and maturation functions provides the basic ingredients for pediatric PK. Here the central modeling task is to apply them coherently to preterm and term neonates, where age at birth, time after birth, and postnatal growth can contribute distinct information.

A Practical Clearance Model

A common starting point for clearance is a multiplicative model: a size term adjusts clearance for body weight, and a maturation term adjusts it for developmental status. The following equation is illustrative, not a universal neonatal model:

Here \(CL_i(t)\) is the typical clearance for infant \(i\) at time \(t\), \(WT_i(t)\) is current weight, \(WT_{\mathrm{ref}}\) is the weight at which the reference clearance is defined, and \(CL_{\mathrm{ref}}\) is the clearance at that reference weight when the maturation function equals one. The exponent 0.75 is a chosen allometric size exponent in this example; it is not a biological constant that must apply to every drug. The maturation multiplier \(M\) is dimensionless and lies between zero and one in the model below.

The parameter \(TM_{50}\) is the PMA at which \(M=0.5\); the exponent 3 controls the steepness of the rise. This saturating function is one possible representation of maturation. In an application, the maturity covariate and function should be selected based on the drug’s elimination pathways, available data, and biological rationale. Some processes may be better related to PNA, GA, or another measure than to PMA alone.

The model assumes, for the predictions shown here, that weight is measured accurately at the relevant time; the stated allometric exponent applies over the modeled size range; maturation follows the specified PMA function; and size and maturation effects combine multiplicatively. It also assumes the parameters are suitable for the population and drug being considered. Those are substantive assumptions, not consequences of writing down an equation.

Worked Comparison of Preterm and Term Predictions

The next example isolates the consequences of using both current weight and PMA. All values and parameters are hypothetical. Suppose \(CL_{\mathrm{ref}}=0.20\) L/h, \(WT_{\mathrm{ref}}=2.0\) kg, and \(TM_{50}=40\) weeks, with the allometric exponent and maturation function defined above.

Using Birth Weight and Postnatal Growth

Birth weight can be useful as a baseline descriptor, but it is not a substitute for current weight when the model is intended to predict clearance at a later time. An infant may gain weight substantially after birth. If the model uses a fixed birth weight throughout follow-up, it can miss the size-related change implied by its own scaling relationship. Conversely, replacing current weight with a growth prediction adds uncertainty if the growth trajectory is not well supported by measurements.

One approach is to use observed weight at each PK observation or dosing time. Another is to model the weight trajectory and use the resulting \(WT_i(t)\). In either case, age and weight should refer to the same time point. If observations are sparse, the analyst should be explicit about whether the input is measured, interpolated, or predicted weight.

Why the Multiplicative Structure Matters

The model’s combined effect follows directly from its definition. At fixed reference clearance, the ratio of clearances for two infants is the product of the ratio of their size multipliers and the ratio of their maturation multipliers:

This follows by substituting the model for each clearance and cancelling the shared \(CL_{\mathrm{ref}}\) and \(WT_{\mathrm{ref}}^{-0.75}\) terms. It clarifies why a comparison cannot be attributed to age alone when both weight and PMA differ. If the infants have the same PMA, their maturation multipliers cancel; if they have the same weight, their size multipliers cancel. When neither is equal, both contributions remain.

A PK model may also include volume of distribution, absorption, and other processes. Those should be specified separately rather than assuming that the clearance equation describes the whole concentration-time profile. For example, in a one-compartment model with constant clearance and volume after an intravenous bolus, concentration declines as \(C(t)=C(0)\exp[-(CL/V)t]\). If clearance or volume changes during follow-up, a constant-parameter exponential is generally not an adequate description over the entire period; the time-varying model must represent those changes.

Choosing Age Covariates and Checking the Model

PMA is a useful candidate when maturation is plausibly related to developmental age accumulated before and after birth. PNA may be more relevant when a process changes with extrauterine exposure or time since birth. GA can describe maturity at delivery and may be informative when infants with the same PMA but different durations outside the uterus are not expected to be equivalent. A model can consider more than one of these measures, but each added term needs a biological and data-based rationale. Using all age variables automatically can create redundant or poorly supported effects.

A practical model comparison asks whether the proposed age scale produces sensible predictions across the observed range, not merely whether it improves fit in the pooled data. Useful checks include:

• Compare observed and predicted concentrations across PMA, PNA, and gestational-age-at-birth groups, while accounting for dose and sampling time.
• Inspect whether prediction errors show a systematic trend with current weight or with time since birth.
• Check predictions at the boundaries of the data, especially the earliest PMAs and smallest weights, where extrapolation is most consequential.
• Verify age units and chronology: PMA should equal GA plus PNA after converting both to the same units, and the weight used should correspond to the stated observation time.
• Assess whether predicted clearance and related concentration profiles are physiologically plausible and consistent with the intended clinical use.

Patterns in these checks can reveal an inadequate maturation function, inaccurate weight histories, inappropriate age indexing, or omitted clinical factors. A model that fits the average concentration profile can still systematically overpredict or underpredict in one neonatal subgroup. Diagnostics should therefore be interpreted by subgroup and developmental range, not only in aggregate.

Alternatives and Limitations

A PMA-based maturation function with current-weight scaling is a compact option, but it is not the only defensible approach. A PNA-based function may be considered when postnatal exposure is central to the mechanism. A model may use a separate GA-at-birth effect if the biology and data support a distinct influence of prematurity. Mechanistic organ-specific models may be appropriate when the drug’s elimination pathways and neonatal physiology are sufficiently characterized. These alternatives answer different biological questions; their predictions should not be treated as interchangeable.

Birth weight alone is a simpler size covariate, but it does not track subsequent growth. Current weight is more time-specific, but can be measured with error and can vary with clinical fluid changes. A smooth growth model can provide weights between observations, but its predictions bring additional assumptions. Likewise, a smooth maturation function imposes a particular shape and may be weakly informed by data concentrated in a narrow age range.

The multiplicative model also assumes separable size and maturation effects. It may be inadequate if the size relationship changes with maturity, if important disease effects are omitted, or if a drug has multiple elimination pathways with different developmental patterns. A plausible model structure and carefully calculated predictions are necessary, but neither guarantees that the available data can support every parameter.

Common Pitfall