In pharmacokinetics, the elimination rate of a drug following a capacity-limited model is primarily controlled by two parameters: Vmax and KM. These parameters are crucial in how the drug behaves inside the body after administration.

Following the administration of a single intravenous (IV) bolus injection, we can determine the concentration of the drug in the plasma at any given time. This calculation is achieved using a specific equation that integrates the values of Vmax and KM.

We can also calculate the total amount of drug present in the body post-injection. This calculation utilizes D0, which represents the initial drug amount in the body at time zero (t = 0).

One of the critical aspects of drug administration is understanding how long it takes for the drug dose to decline to a certain amount within the body. For instance, consider a drug administered as a single 400-mg dose with a KM value of 38 mg/L. If the Vmax varies from 200 to 100 mg/h, it will take around 2.46 hours for the drug concentration to decline to 20 mg at a Vmax of 200 mg/h. In contrast, at a Vmax of 100 mg/h, it would take approximately 4.93 hours — almost twice as long — to reach the same concentration.

Interestingly, an inverse relationship exists between the time the dose takes to decline and the Vmax. For example, when Vmax is held constant at 200 mg/h, the time required for the drug to decline to 20 mg is 2.46 hours when KM is 38 mg/L. However, if KM is increased to 76 mg/L, this time increases to 3.03 hours, indicating that an increase in KM will subsequently increase the time taken for the drug to be eliminated from the body.

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