7. Applications and Toxic Level

Using the generalized form of the sequence,

it is possible to solve questions such as the following.

Suppose the effective level for a particular drug in a particular patient is 500 mg, and dosages of 300 mg are given every 4 hours, with an initial dosage also of 300 mg. Given that the drug has a half-life of 4 hours, after which dosage will the drug first reach an effective amount in the patient's body?

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Suppose instead that the effective level for the same drug as in the question above in a particular patient is 900 mg. After which dosage will the drug first reach an effective amount in the patient's body?

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To visualize questions such as the one above, a simulator has been developed. You can click here to open the simulator in a new window, and here for the simulator help page. Experiment with the simulator to explore its capabilities.

On the simulator you may notice a red line labelled "toxic level", a green line labelled "effective level" and a dashed line labelled "steady state" . For now, ignore the steady state line—we will study it in the next section.

Using the simulator, set the toxic level to 100 mg, the half-life to 4 hours, pill size to 10 mg, to 3, and the number of pills to 5. After how many doses is this drug toxic?

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Finally, it is important to determine the level of a drug over a longer period of time. We do this by looking at steady states, and we will formalize the mathematics of steady states in the next section.