Beta (β) rate constant

The first-order rate constant for the exponential elimination of a two-compartment drug from the plasma. It can be found from the slope of the elimination portion of a two-compartment curve (i.e. the straight handle of the hockey stick on a hockey stick curve), which may be facilitated by extrapolating the straight handle of a hockey-stick curve back to the Y-axis, or from the half-life of elimination for a two-compartment drug (from 0.693/half-life). The example  shows how to obtain the value of β from the slope of elimination data plotted on a logarithmic Y-axis.

Plotting plasma concentrations of a two-compartment drug following IV bolus administration yields a “hockey stick plot” when a logarithmic concentration axis is used. Calculating the slope of the handle of the hockey stick, corresponding to the terminal elimination phase after distribution is complete, yields a value for the first-order elimination rate constant, beta. The elimination half life in this example would be ln2/0.0116, or 60 minutes. Note that data are plotted on a natural logarithm axis. If instead a base 10 logarithmic axis was used, the rate constant would be equal to the slope multiplied by -2.303. This process for obtaining a first order rate constant from a semi-logarithmic plot may also be used with one-compartment data.

β is a proportionality constant (similar to kel and α) with units of “per time” and indicates the proportion of remaining drug that will be eliminated in unit time (or, similarly, the proportion of the total apparent volume in which the drug is distributed that will be cleared of drug in unit time) if the current rate of elimination is maintained.

While both β and kel are concerned with elimination of drug from the central compartment, β is typically smaller (i.e. yields a longer half life) than an equivalent kel value, because β, but not kel, is impacted by the slow redistribution of drug from the tissues back into the plasma. With a one-compartment drug, redistribution back into the plasma is very rapid and so the elimination from the plasma is able to work as fast as it wants to, without any brake being put on the process due to slow redistribution from the tissues. It is this slow redistribution that also causes a lag leading to the increased tissue:plasma drug concentration ratio observed during the terminal elimination phase, and the value for a drug’s non-compartmental apparent volume of distribution (AVD area) being larger than  that for its steady-state apparent volume of distribution (AVD SS).

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An ABC of PK/PD Copyright © 2023 by Dr. Andrew Holt is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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