### Accumulating doses

However if the second dose is given early enough so that not all of the first dose is eliminated then the drug will start to accumulate and we will get higher concentrations with the second and third dose. As an example we could consider a drug with a half-life of 6 hours. Giving a dose of 100 mg with an apparent volume of distribution of 25 liter the Cp0 = 4 mg/liter. (see Figure XIV-9)

After six hours the plasma concentration will fall to 2 mg/liter. If we give the same dose again the plasma concentration will increase by 4 mg/liter from 2 mg/liter to 6 mg/liter. Then after another half-life (6 hours) the plasma concentration will fall to 3 mg/liter. Again, another dose will increase the plasma concentration by 4 mg/liter to 7 mg/liter. After another half-life the plasma concentration will be 3.5 mg/liter. After repeated drug administration every six hours the plasma concentration will accumulate until it fluctuates between a maximum and minimum value of 8 mg/liter and 4 mg/liter. In this example the dose was given every drug elimination half-life of 6 hours.

Figure XIV-9, Plot of Cp Versus Time Showing Doses Every Six Hours

Using a JAVA aware browser you can create your own version of Figure XIV-9.

Plasma Concentration versus Time Plots

With each dose, drug accumulated until the amount of drug eliminated during each dosing interval was equal to the amount of the dose. In the first interval plasma concentrations fall from 4 to 2 mg/L. Continuing for a number of doses gives the following table.

 Start End Concentration lost during dosage interval 4 --> 2 mg/L 2 mg/L 6 --> 3 3 7 --> 3.5 3.5 7.5 --> 3.75 3.75 ... 8 --> 4 4 <- which is the same as the concentration increase caused by each dose

There is a limit to drug accumulation because as the plasma concentration increased the amount of drug eliminated during the dosing interval will also increase as the rate of elimination is equal to the amount of the drug in the body multiplied by the rate constant for a first order elimination. (Compare this with the case of a continuous infusion).

So far we can see that if we give repeated doses before the body can eliminate the previous doses then we will get accumulation of the drug. We have also seen that when we have first order elimination this accumulation will not proceed indefinitely but will level off.