Half Life

The elimination half-life fro a drug is the time required for the concentration of the drug to reach half of its original value usually expressed as

t_1/2

It is usually determined after intravenous administration of the drug, and the concentration of the drug in the plasma is measured at regular intervals. The concentration of the drug will reach a peak value in the plasma and will then fall as the drug is broken down and cleared from the blood.

It is often displayed as a semi log plot

Half-life can be expressed as

t_1/2=ln(2)Vd/Cl

Cl (mL/min/kg) = Total plasma clearance, the volume of plasma from which the drug is completely removed per unit time

Vd (L/kg) = Volume of distribution, the amount of drug in the body divided by the concentration in the blood.

Extending Half-life

The half-life of a drug has a major effect on both the size of the dose that is given and the frequency of dosing. For a short half-drug where the clinical efficacy is limited by the trough levels of the drug it may require multiple repeated dosing to maintain drug levels above the required levels, in addition it may require a high loading dose.

Whilst it may be possible to increase coverage by increasing the dose administered as the plot below shows the dose required increases very steeply for short half-life compounds. Thus for short half-life compounds increasing the half-life by even a small amount can have a significant effect on the dose required.

Since half-life is related to Volume of distribution (Vd) and Total plasma clearance (Cl) as shown below, either increasing Vd or decreasing Cl will increase the drug half-life, assuming the drug is not very, very highly plasma protein bound. Clearance of a drug can be affected by plasma protein binding, in general it is only the unbound drug that is subject to hepatic clearance. Similarly renal clearance is reduced for compounds with high plasma protein binding

t_1/2=ln(2)Vd/Cl

As the plot below shows acids (red) usually have a relatively low volume of distribution, in contrast bases (blue) tend to have a larger volume of distribution than neutral (green) molecules for a given LogP, Vd tends to increase with LogP for both bases and neutral compounds.

However attempts to increase Vd by increasing LogP may not always increase half-life since this may serve to also increase metabolic clearance. Most CYP450 enzymes tend to favour lipophilic substrates. In the case of Metoprolol replacing the potentially metabolically labile methyl by cyclopropylmethyl (Betaolol) serves improve Vd and Cl resulting in a 4.7-fold increase in half-life.

Renal clearance tends to be favoured for small polar molecules, so increasing LogP may reduce renal clearance and thus increase half-life.

Worth reading

Volume of Distribution in Drug Design DOI
Strategy for Extending Half-life in Drug Design and Its Significance DOI

Last Updated 26 April 2018