concentration =
= ((amount of drug) / (volume of distribution))
(concentration of drug in the body at time T) =
= ((concentration of drug in the body at time 0) * (EXP(-kT)))
The time it takes the concentration in the compartment to reach half of the initial concentration (T(half) or half-life) is independent of concentration and can be shown to be (derived from the above equations):
T(half) = 0.693 / (elimination rate constant)
Calculation of Half-Life
For a series of plasma levels (P1, P2, P3,..., Pn) at times (t1, t2, t3..., tn), the plot of LN(P1), LN(P2), LN(P3)....vs t1, t2, t3, .... is linear, with LN(plasma level) on y-axis and time on x-axis.
LN(concentration at time t) =
= ((-1) * (elimination rate constant) * (t)) + LN(concentration at time 0)
Thus:
slope of line for plot = elimination rate constant =
= SLOPE (LN(P1):LN(Pn), t1:tn)
intercept of line for plot = LN(concentration at time 0) =
= INTERCEPT (LN(P1):LN(Pn), t1:tn)
half-life =
= LN(2) / (SLOPE (LN(P1):LN(Pn), t1:tn))
