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**Equation 5.5.1 Clearance as the Ratio of Rate of Excretion to Cp**

For this particular example where elimination = excretion and kel = ke we can derive another equation for clearance which may useful.

Since

**Equation 5.5.2 Rate of Excretion**

**Equation 5.5.3 Clearance calculated from kel and V**

As we have defined the term here CL is the total body clearance. We have assumed that the drug is cleared totally by excretion in urine. Below we will see that the total body clearance can be divided into clearance due to renal excretion and that due to other processes such as metabolism.

Clearance is a useful term when talking of drug elimination since it can be related to the efficiency of the organs of elimination and blood flow to the organ of elimination. It is useful in investigating mechanisms of elimination and renal or hepatic function in cases of reduced clearance of test substances. The units of clearance, volume/time (e.g. ml/min) may be easier to visualize, compared with elimination rate constant (units 1/time, e.g. 1/hr) although half-life (in units of time) is probably even easier. Some people view clearance as a primary pharmacokinetic parameter along with the apparent volume of distribution although both these parameters can be related to more fundamental terms.

**Figure 5.5.1 Drug clearance via the Kidney**

As an example if the kidney removes all of the drug presented by blood flow then the renal clearance will be equal to renal blood flow, Q_{renal} (= Q_{kidney}). In later chapters we will look at some of these more fundamental terms.

When a drug is eliminated by more than one pathway total body clearance, CL, can be separated into various clearance terms describing these pathways. Thus, total body clearance might be split into clearance due to renal excretion, CL_{R} and clearance due to another pathway such as metabolism, CL_{M}.

**Equation 5.5.4 Renal Clearance from ke and V**

This is a mathematical representation of CL_{R}. Later, in Chapter 16, we will see that renal clearance is functionally dependent on processes such as glomerular filtration rate, renal secretion and reabsorption.

and

**Equation 5.5.5 Metabolic or Hepatic Clearance from km and V**

Again this is a mathematical representation of CL_{M}. Later, in Chapter 17, we will see that liver or hepatic clearance is functionally dependent on factors such as liver blood flow, fraction of unbound drug and intrinsic liver metabolism.

Note

**Equation 5.5.6 Total Body Clearance from kel and V**

**Equation 5.5.7 Renal Clearance**

Integrating both sides gives

**Equation 5.5.8 Renal Clearance Integrated Equation**

Rearranging gives

**Equation 5.5.9 Renal Clearance calculated from U ^{∞} and AUC**

Hepatic or metabolic clearance can be derived in a similar fashion.

**Equation 5.5.10 Hepatic Clearance calculated from Mu ^{∞} and AUC**

Since the total amount eliminated is the IV dose (the total amount absorbed) total body clearance can also be calculated from the AUC.

**Equation 5.5.11 Total body clearance Calculated from Dose and AUC**

Unlike Equations 5.5.4, 5 and 6 which use model derived parameter values. Equations 5.5.9, 10 and 11 use the model independent parameters AUC and Dose, U^{∞} or Mu^{∞}.

- Clearance has been discussed on the PharmPK listserv.

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