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**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 t

**Figure 4.8.2 Clearance, V, kel and t _{1/2}**

Click on the figure to view the interactive graph

- Clearance has been discussed on the PharmPK listserv.

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