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Clearance

Clearance can be defined as the volume of plasma which is completely cleared of drug per unit time. The symbol is CL and the units are ml/min, L/hr, i.e. volume per time. One way of looking at Clearance is to consider the drug being eliminated from the body ONLY via the kidneys. [If we were to also assume that all of the drug that reaches the kidneys is removed from the plasma then we have a situation where the clearance of the drug is equal to the plasma flow rate to the kidneys. All of the plasma reaching the kidneys would be cleared of drug]. The amount cleared by the body per unit time is dU/dt, the rate of excretion (also the rate of elimination in this example). To calculate the volume which contains that amount of drug we can divide by Cp. That is the volume = amount/concentration.

Equation 12.10.1 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.

Equation 12.10.2 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) are probably even easier. Some people view clearance as a primary pharmacokinetic parameter along with the apparent volume of distribution.

Figure 12.10.1 Drug clearance via the Kidney

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).

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 12.10.3 Renal Clearance from ke and V

and

Equation 12.10.4 Metabolic or Hepatic Clearance from km and V

Note

Equation 12.10.5 Total Body Clearance from kel and V

Clearance can also be Calculated using AUC

Another more general method of calculating clearance can be derived from the basic definition, Equation 12.10.1. For renal clearance we can write:

Equation 12.10.6 Renal Clearance

Integrating both sides gives

Equation 12.10.7 Renal Clearance Integrated Equation

Rearranging gives

Equation 12.10.8 Renal Clearance calculated from U^∞ and AUC

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

Equation 12.10.9 Hepatic Clearance calculated from M^∞ and AUC

Since the total amount eliminated is the dose (or at least F • Dose) total body clearance can also be calculated from the AUC.

Equation 12.10.10 Total body clearance Calculated from Dose and AUC

Unlike Equations 12.10.3, 4 and 5 which use model derived parameter values. Equations 12.10.8, 9 and 10 use the model independent parameters AUC and Dose, U^∞ or M^∞.

Variable Renal Clearance

Equation 12.10.6 can be useful in determining if renal clearance is consistent throughout or between dosing intervals. Plotting ΔU/Δt versus Cp_midpoint for the collection interval, Δt, should provide a straight line if renal clearance is constant. Dividing ΔU/Δt by Cp_midpoint provides estimates of renal clearance for each collection period (Equation 12.10.1).

References

Clearance has been discussed on the PharmPK listserv.

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