In medical treatment, drugs are often applied either continuously or in a series of small,...

In medical treatment, drugs are often applied either continuously or in a series of small, closely spaced doses. Assume that oral ingestion and absorption of a particular drug are rapid compared with the rate of utilization and elimination and that (after a single dose) the latter process occurs by a simple exponential decrease. We can represent this by a scheme (not a mechanism)

where [A] is the concentration of the drug at its site of introduction, [B] is the concentration of the drug in blood, and [C] represents the elimination of the drug. In this model, the delivery k1 of the drug is zero order kinetically, and the elimination k2 is first order.

a. Write the rate law, in terms of d[B]/dt that is appropriate to this model.

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b. Assuming that the first introduction of the drug occurs at time zero, draw a curve showing how [B] will change with time during continuous, prolonged administration of the drug. [If this is not intuitively obvious to you, proceed first to part (f).]

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c. After some time, the patient is cured, and the use of the drug is stopped. Add to your drawing a sketch of how [B] changes subsequently.

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d. From an experimental record or monitor of [B] vs. time, how would you determine k2?

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e. How would you determine k1

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f. Derive a mathematical expression for [B] as a function of time during drug administration starting with the rate law from part (a). (A simple variable substitution should convert it to a form that was treated explicitly in this chapter.) Demonstrate that the result is consistent with your rise curve.

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g. To what level does [B] rise after a long time of administration?