Solid and Liquid Gastric Emptying Time Courses

Why the Shape of Emptying Matters

Gastric emptying is not always well represented by a single number. Two meals can have the same total amount emptied by a particular time yet differ substantially earlier: one may begin emptying promptly, while another shows a delay followed by faster emptying. These differences matter when interpreting how quickly material becomes available to the intestine. A PBPK description should therefore be informed by the time course, not just by an average or endpoint.

Solids and liquids often have different time courses. Solid particles generally need to be reduced to sufficiently small sizes before they can pass through the pylorus; this processing can produce an initial delay and changing emptying rates. Many noncaloric liquids can begin leaving the stomach relatively quickly, but their rate can change as the stomach empties. These are common patterns, not universal rules. Meal composition, volume, energy content, physical properties, and physiological state can alter them. The fed-state physiological context is important, as discussed in the earlier material on fed-state physiological changes relevant to gastric emptying.

The goal here is descriptive: learn to read observed trajectories and determine whether a single emptying rate is a defensible summary. This does not require assuming a particular mathematical model for the curve.

Representing an Emptying Time Course

Let \(M_0\) be the amount of a tracked meal component in the stomach at the start of observation, and let \(M_g(t)\) be the amount still in the stomach at time \(t\). If the tracked material is neither added to nor lost from the measured system except by emptying, the amount that has left the stomach is \(M_0-M_g(t)\). Normalizing by the starting amount gives a fraction that can be compared across meals of different sizes.

These quantities describe different aspects of the curve. The retained fraction shows how much remains; the cumulative emptied fraction shows how much has left; and an interval rate summarizes the average change over a specified interval. An interval rate is not necessarily the instantaneous rate at every time within that interval. The more rapidly a curve changes, the more a coarse sampling interval can conceal what happened between observations.

Interpreting these quantities requires care. The measured tracer or marker must reasonably track the material whose emptying is being described, the starting amount and times must be defined consistently, and the measurement method must distinguish gastric retention from material elsewhere. A meal marker does not automatically track a drug dissolved in the meal or a drug particle with different physical properties.

How to Read Solid and Liquid Curves

A representative solid-meal curve may show little early loss, followed by a period of more substantial emptying and then a slower late phase. The early interval can reflect processing and retention of particles that are not yet ready to pass. The middle portion need not have a constant slope: the amount leaving per minute may rise or fall over successive intervals. A late tail can occur when only a residual portion remains or when the remaining contents empty more slowly.

A representative noncaloric-liquid curve often shows appreciable early emptying. Its later slope may become shallower as the volume remaining falls. Caloric liquids do not necessarily follow the same pattern as noncaloric liquids; energy content and the surrounding meal can slow or otherwise change emptying. “Liquid” is therefore not a sufficient description for predicting a curve.

For a given observation method, the most useful comparison is often the normalized curve \(R(t)\) or \(E(t)\), rather than the raw amount alone. Normalization allows comparison of the proportions retained or emptied, but does not eliminate differences in meal conditions or measurement. When comparing curves, examine the initial phase, intermediate slopes, and late residual together. A single endpoint can hide a meaningful difference in timing.

Why One Rate Can Fail: A Simple Justification

A rate is a compact summary, but it imposes a simplification. For a constant absolute emptying rate \(q\), the expected amount emptied over any interval of length \(\Delta t\) would be \(q\Delta t\). Thus, if the amount remaining is observed directly, the expected decrease over equal-length intervals would be equal. Large, systematic differences among successive interval rates indicate that this assumption is a poor description over the observation window.

This conclusion follows directly from the rate definition. If \(M_g(t_1)-M_g(t_2)=q(t_2-t_1)\), then dividing both sides by \(t_2-t_1\) gives \([M_g(t_1)-M_g(t_2)]/(t_2-t_1)=q\). Therefore, when computed interval rates differ beyond what measurement variability plausibly explains, no one value of \(q\) describes all those intervals. A short interval may still be summarized by one rate, but that does not justify applying it to the whole time course.

This check concerns a constant absolute amount-per-time rate. Other mathematical descriptions use different assumptions, including rates that change with the amount remaining or explicit delays. Choosing and parameterizing those models is a separate task. Here, the practical point is to inspect the observed curve before compressing it into a single rate.

Diagnostics, Comparisons, and Limitations

Several features should prompt caution about a single-rate summary:

• A clear early lag: little apparent emptying initially followed by a marked decline later is not well captured by an average across the full period.
• Changing interval slopes: substantially different rates across comparable intervals suggest that the process changes over time, although noisy measurements can also produce variation.
• A late tail: a substantial residual remains after rapid early emptying, so an early rate would overstate later loss.
• Different conclusions at different endpoints: curves may differ markedly early and converge later. Reporting only a late measurement obscures the timing difference.
• Insufficient sampling: widely spaced measurements cannot determine whether a change was gradual, abrupt, or composed of multiple phases.

A direct gastric-content time course is more informative about emptying than a downstream drug concentration alone. Plasma concentrations also reflect dissolution, intestinal absorption, first-pass processes, and systemic disposition. A change in concentration timing therefore cannot, by itself, identify a change in gastric emptying. Likewise, a meal tracer is an indirect stand-in for drug movement unless it has been shown to track the drug-relevant material.

Different measurement approaches answer related but not identical questions. Imaging or other direct retention measurements can describe the meal or a labeled component over time. A marker-based proxy can be easier to collect but depends on the proxy tracking the contents of interest. Drug pharmacokinetic data capture the combined consequences of gastric delivery and later processes. None should be treated as interchangeable without justification.

A single rate can remain useful when the question is deliberately limited to a short interval, when data show little meaningful change in slope, or when a coarse summary is adequate for the decision at hand. Its limitation is not that it is always wrong, but that it can conceal delay, changing speed, and residual emptying. Interpretation also depends on measurement precision, observation times, meal composition, and the population or physiological condition represented.

Common Mistakes

• Assuming every liquid empties faster than every solid. Noncaloric liquids often empty rapidly, but caloric content and meal context can alter the trajectory. Compare like with like and describe the tested conditions.
• Treating an endpoint as the entire time course. Similar fractions emptied at 120 minutes do not imply similar emptying at 15 or 30 minutes. Inspect intermediate observations.
• Calling an interval average an instantaneous rate. A rate computed from two measurements averages change over that interval; it does not reveal the exact rate at every moment.
• Inferring gastric emptying directly from plasma concentration. Concentrations combine gastric delivery with absorption and disposition. Use direct evidence or a justified proxy when the question concerns emptying itself.
• Assuming the meal marker represents the drug. Dissolved drug, suspended particles, and labeled meal components may not move identically. State what the measurement actually tracks.