Nuclear Medicine: Using Integration to Determine the Drug-Time Relationship in a Patient

A drug is excreted in a patient’s urine. The urine is monitored continuously using a catheter. A patient is administered 10 mg of drug at time t = 0 which is excreted at a RATE of -3t1/2 mg/h .

  1. What is the general equation for the amount of drug in the patient at time t > 0?
  2. When will the patient be drug free?

Solution:

  1. The solution involves solving a simple differential equation through integration.

    Therefore the amount of drug in the patient at time t>0 is

  2. The patient will be drug free when A=0

    The patient will be drug free in 2.9 hours.

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Written by Louise Routledge, September 1, 1998