Multiple Dosing and Drug Accumulation

When prescribing a medication, practitioners must tell the patient to take repetitive doses of the drug in order to maintain the drug’s effects over days.

Lets say that after you take an initial dose C₀, you give a second dose before the first dose has completely disappeared. Clearly then the second peak (from the graph on handout p. 6—concentration of drug in plasma vs. time) will be higher than the first dose. This is called drug accumulation.

We must first define another parameter; dosing interval (t_d) is the time in between doses. Since the peak drug concentration in the plasma rises further and further above C₀ with each administration, the drug accumulates due to the repetitive dosing. However, the peak concentration eventually reaches a maximal value that does not increase with further administration of the drug. This is called the plateau or maintenance state of the drug.

This happens because of first order kinetics, as the drug begins to accumulate the higher it gets the faster the decay. You finally reach a place where the amount of drug eliminated in one dosing interval just equals the dose.

*** ALWAYS ASKED ON EXAM ***

Definition of Maintenance State: the dose administered equals the amount eliminated in time t_d (one dosing interval).

(handout p. 8) Once we’re in the maintenance state, we can take a portion of the curve between C_max and C_min, and this is a piece of the drug disappearance curve. Thus, the equation is:

C(t) = C_max e ^-ktd

The amount eliminated in time t_d is the difference between C_max and C_min in the maintenance state:

C_max – C_min = C_max (1 – e^-ktd)

***IMPORTANT: Know this equation!!! (Maintenance State Equation)***

Dose = C_max (1 – e^-ktd); where k = 0.69

t_½

The maintenance state equation shows the relationship among 4 parametes: (1) the dose C₀, (2) the maximum accumulation C_max, (3) the half-life t_½, (4) the dosing interval t_d. If any three of these are known, the fourth can be found.

Special Case

When t_d is chosen to be equal to t_½, a simple relation results… in this case the maintenance state equation becomes:

Dose = ½ C_max or C_max = 2x Dose

This result can be reasoned out: if t_d = t_½, then after the interval t_d, C has fallen from C_max to ½ C_max. The dose must make up for this loss, so Dose = ½ C_max.

Category: Pharmacology Notes