= Drug distribution
{title2=$V_d$}
<Drug distribution> is movement of a <drug> between <blood> and other body compartments. Perfusion, membrane permeability, <tissue> binding and plasma-protein binding jointly affect it. The apparent distribution <volume> is
$$
V_d=\frac{A}{C_p},
$$
where $A$ is the amount in the body and $C_p$ the plasma concentration. If $A=100$ mg and $C_p=2$ mg/L, $V_d=50$ L. <Population Pharmacokinetics Guidance for Industry by the FDA>[2022, pharmacokinetic parameters and concentration-time models]{ref}
The result is a proportionality quantity, not an anatomical cavity that must contain that many litres. Extensive <tissue> binding can lower $C_p$ and make $V_d$ large. A rapid fall in plasma concentration immediately after administration can therefore reflect distribution as well as <drug elimination>; distinguishing them requires a model and a suitable sampling schedule.
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