# One Compartment IV Bolus

## Total Body Clearance, CL

Total body clearance or clearance is an important pharmacokinetic parameter that describes how quickly a drug is eliminated from the body. It is often defined as the volume of blood or plasma completely cleared of the drug per time. However, it may be easier to view it as the proportionality constant relating the rate of elimination and drug concentration. The rate of elimination of a drug can be described by Equation 4.8.1. Equation 4.8.1 Rate of Elimination versus Concentration

In Equation 4.8.1 the elimination rate, dX/dt, is related to the concentration of drug remaining. The proportionality constant for this relationship is Clearance. The symbol for clearance is CL and the units are volume per time such as ml/min, L/hr.

Equation 4.8.1 can be rearranged to solve for clearance. Equation 4.8.2 Clearance calculated from Rate and Concentration

Clearance can be calculated from this equation by measuring the amount of drug eliminated during some time interval and the drug concentration at the midpoint of this collection interval. The clearance of the endogenous material, creatinine, is measured by this method as described in Chapter 16 to provide a measure of renal function. The renal clearance of other compounds can be calculated in a similar fashion.

Clearance can also be calculated using the integral of Equation 4.8.2. Integrating dX/dt and Cp with respect to time give Dose and AUC, respectively. The total amount that can be eliminated is the total amount administered, that is, the dose. Thus clearance can be calculated from the dose and the calculated area under the concentration versus time curve, AUC. Equation 4.8.3 Clearance calculated from Dose and AUC

In the case of the one compartment model with an IV bolus dose the rate of elimination can be expressed as: thus a value for Total Body Clearance, CL, can be estimated from kel and V for the one compartment model. Equation 4.8.4 Clearance calculated from kel and V

The clearance of a drug can be used to understand the processes involved in drug elimination, distribution and metabolism. Relating clearance to a patient renal or hepatic function can be used in the determination of suitable drug dosage regimens.

Although clearance may be calculated using Equation 4.8.4 a more fundamental calculation may be the determination of kel and half-life from CL and V. AND Equation 4.8.5 kel and half-life as a function of V and CL Figure 4.8.1. Concentration versus time

Click on the figure to view the interactive graph

The interplay between V, CL and kel or t1/2 can be explored using the graph above or the diagram below. Notice, as V increases the amount of drug per volume of plasma, i.e. the concentration, decreases. Therefore for a given value of clearance the rate of elimination and the elimination rate constant decreases (with a corresponding increase in half-life). Figure 4.8.2 Clearance, V, kel and t1/2

Click on the figure to view the interactive graph

References