PharmSim

Formulas for multiple vascular bolus administration

In multiple vascular bolus administration, the plasma concentration of a drug at a certain moment in time depends on:

• the administered dose

• the volume of distribution

• the clearance

• the dosing interval

The dose and the volume of distribution together determine the initial plasma concentration. After t=0, the plasma concentration decreases with a power of e, which depends on the elimination rate constant k, calculated by deviding the clearance by the volume of distribution. For each dose administered before the point of time that is considered, this process should be evaluated. The formulas, the plasma concentration (Cp) at a certain time is given by:

where and

The drug action over time depends on the plasma concentration, and, in addition on the maximal effect of the drug (Emax), which is 100% in this applet, and the EC50. If the plasma concentration equals the EC50, the drug action should be 50% by definition. Furthermore, when the plasma concentration is approaches 0, the action should also approach zero, and when the plasma concentration equals a number of times the EC50, the action equals 1. In a formula, this looks as follows:

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