As soon as we take medication, the body begins to absorb it, and the concentration of the drug in the blood stream increases quickly. The body also begins a slower process of eliminating the drug from our body. Therefore, the concentration of the medicine in the blood is constantly changing; first it goes up quickly and then decreases slowly.
For a person to benefit from a medication, the concentration must be above the Mini- mum Effective Concentration (MEC) (usually measured in milligrams (mg)); see Figure 1. However, a concentration above the Maximum Tolerance Concentration (MTC) (mg) is con- sidered harmful. For this reason it is important to maintain the amount of medicine between the MEC and the MTC.
Suppose that you are a consultant for a hospital and you help determine the drug dosage amount (mg) and frequency of administration (how often a patient should take a pill) in treatment plans. Doctors can prescribe pills that have the same amount of medicine in each of them.
Consider three different patients that the doctors have determined will take pain medica- tion after a surgery over the course of at maximum one week. Patient #1 will be prescribed oxycodone, Patient #2 will be prescribed ibuprofen, and Patient #3 will be prescribed a combination of oxycodone and ibuprofen. Determine an optimal treatment plan for each patient.
Figure 1: Pharmacokinetic parameters describing a typical time profile of drug concentration within the blood plasma after administration of medication. Cmax is the maximum drug concentra- tion; tmax is the time to Cmax; AUC is the area under the curve; MEC is the minimum effective concentration; and MTC is the maximum tolerated concentration. Figure source: The role of phar- macokinetics and pharmacodynamics in phosphodiesterase-5 inhibitor therapy by N. Mehrotra, M. Gupta, A. Kovar, and B. Meibohm, doi: 10.1038/sj.ijir.3901522.
