Drug Absorption Simulator: Plasma Concentration-Time Curves

simulator intermediate ~10 min
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Cmax = 7.2 mg/L at t = 1.9 h

A 500 mg oral dose with ka=1.2/h and ke=0.15/h in a 50 L volume yields a peak plasma concentration of 7.2 mg/L at approximately 1.9 hours post-dose.

Formula

C(t) = (F·D·ka) / (Vd·(ka - ke)) × (e^(-ke·t) - e^(-ka·t))
tmax = ln(ka / ke) / (ka - ke)
AUC = F·D / (Vd·ke)

From Gut to Bloodstream

When you swallow a tablet, the drug must dissolve, cross the intestinal membrane, and survive first-pass metabolism before reaching systemic circulation. The absorption rate constant ka captures this complex process as a single first-order parameter. Faster absorption (higher ka) means a sharper, earlier peak — critical for analgesics where rapid pain relief matters, but potentially dangerous for drugs with narrow therapeutic windows.

The Bateman Curve

The plasma concentration-time profile after oral dosing follows the Bateman equation — a difference of two exponentials. The ascending limb reflects net absorption exceeding elimination; the descending limb reflects the opposite. The peak (Cmax) occurs at tmax, the moment absorption and elimination rates are exactly equal. This curve is the foundation of therapeutic drug monitoring.

Volume of Distribution

Vd is a proportionality constant linking the amount of drug in the body to its plasma concentration. A drug confined to plasma (like warfarin, Vd ~ 8 L) has a small Vd; one that accumulates in fat or muscle (like chloroquine, Vd ~ 15,000 L) has an enormous Vd. This parameter directly affects peak concentration: doubling Vd halves Cmax for the same dose.

Clinical Implications

Understanding absorption kinetics guides dosing decisions. Extended-release formulations deliberately lower ka to flatten the curve, keeping drug levels within the therapeutic window for longer. Conversely, sublingual or inhaled routes bypass the gut entirely, achieving near-instantaneous absorption. These simulations help visualize why the same drug molecule can behave so differently depending on how it enters the body.

FAQ

What determines how fast a drug is absorbed?

Oral drug absorption rate depends on dissolution rate, gastrointestinal motility, membrane permeability, and formulation (immediate vs. extended release). The absorption rate constant ka quantifies how quickly the drug moves from the gut lumen into systemic circulation, typically ranging from 0.5 to 3 per hour for oral drugs.

What is the Bateman equation?

The Bateman equation describes plasma concentration after oral dosing in a one-compartment model: C(t) = (F·D·ka)/(Vd·(ka-ke)) × (e^(-ke·t) - e^(-ka·t)). It captures the rise (absorption) and fall (elimination) of drug levels, producing the characteristic peak-and-decline curve.

What is volume of distribution?

Volume of distribution (Vd) is a theoretical volume that relates total drug in the body to plasma concentration. A Vd of 50 L means the drug distributes beyond plasma into tissues. Highly lipophilic drugs can have Vd exceeding 1000 L, meaning very little remains in plasma.

Why does tmax not depend on dose?

In linear (first-order) kinetics, tmax = ln(ka/ke)/(ka-ke), which contains only rate constants — not dose. Doubling the dose doubles Cmax but does not change when the peak occurs. This is a key feature of first-order pharmacokinetics.

Sources

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