Clearance

Clearance (CL) is the most important pharmacokinetic parameter because it determines the steady-state concentration for a given dosage rate. When a drug is given at a continuous IV infusion rate equal to k₀, the steady-state concentration (C_ss) is determined by the quotient of k₀ and CL (C_ss = k₀/CL). If the drug is administered as individual doses (D) at a given dosage interval (), the average steady-state concentration (C_ss) over the dosage interval is given by the equation⁴

where F is the fraction of dose absorbed into the systemic vascular system. The average steady-state concentration over the dosage interval is the steady-state concentration that would have occurred had the same dose been given as a continuous IV infusion (e.g., 300 mg every 6 hours would produce an average C_ssequivalent to the actual C_ss produced by a continuous infusion administered at a rate of 50 mg/h).

Physiologically, clearance is determined by (a) blood flow (Q) to the organ that metabolizes (liver) or eliminates (kidney) the drug and (b) the efficiency of the organ in extracting the drug from the bloodstream.⁵ Efficiency is measured using an extraction ratio (E), calculated by subtracting the concentration in the blood leaving the extracting organ (C_out) from the concentration in the blood entering the organ (C_in) and then dividing the result by C_in:

Clearance for that organ is calculated by taking the product of Q and E (CL = QE). For example, if liver blood flow equals 1.5 L/min, and the drug's extraction ratio is 0.33, hepatic clearance equals 0.5 L/min. Total clearance is computed by summing all the individual organ clearance values. Clearance changes occur in patients when the blood flow to extracting organs changes or when the extraction ratio changes. Vasodilators such as hydralazine and nifedipine increase liver blood flow, whereas congestive heart failure (CHF) and hypotension can decrease hepatic blood flow. Extraction ratios can increase when enzyme inducers increase the amount of drug-metabolizing enzyme. Extraction ratios may decrease if enzyme inhibitors inhibit drug-metabolizing enzymes or necrosis causes loss of parenchyma.

Intrinsic Clearance

The extraction ratio also can be thought of in terms of the unbound fraction of drug in the blood (f_b), the intrinsic ability of the extracting organ to clear unbound drug from the blood (CL_int), and blood flow to the organ (Q):^6,7

By substituting this equation for E, the clearance equation becomes

Clearance changes will occur when blood flow to the clearing organ changes (in conditions where blood flow is reduced, e.g., shock and CHF, or where blood flow is increased, e.g., administration of medications, such as vasodilators, and resolution of shock or CHF), binding in the blood changes (e.g., if the concentration of binding proteins is low or highly protein-bound drugs are displaced), or intrinsic clearance of unbound drug changes (e.g., when metabolizing enzymes are induced or inhibited by other drug therapy or functional organ tissue is destroyed by disease processes).

If CL_int is large (enzymes have a high capacity to metabolize the drug), the product of f_b and CL_int is much larger than Q. When f_b(CL_int) is much greater than Q, the sum of Q and f_b(CL_int) in the denominator of the clearance equation almost equals f_b(CL_int):

Substituting this expression in the denominator of the clearance equation and canceling common terms leads to the following expression for drugs with a large CL_int: CL  Q. In this case, clearance of the drug is equal to blood flow to the organ; such drugs are called high-clearance drugs and have large extraction ratios.Propranolol, verapamil, morphine, and lidocaine are examples of high-clearance drugs. High-clearance drugs such as these typically exhibit high first-pass effects when administered orally.

If CL_int is small (enzymes have a limited capacity to metabolize the drug), Q is much larger than the product off_b and CL_int. When Q is much greater than f_b(CL_int), the sum of Q and f_b(CL_int) in the denominator of the clearance equation becomes almost equal to Q: Q  Q + f_b(CL_int). Substituting this expression in the denominator of the clearance equation and canceling common terms leads to the following expression for drugs with a small CL_int: CL  f_b(CL_int). In this case, clearance of the drug is equal to the product of the fraction unbound in the blood and the intrinsic ability of the organ to clear unbound drug from the blood; such drugs are known as low-clearance drugs and have small extraction ratios. Warfarin, theophylline, diazepam, and phenobarbital are examples of low-clearance drugs.

As mentioned previously, the concentration of unbound drug in the blood is probably more important pharmacologically than the total (bound plus unbound) concentration. The unbound drug in the blood is in equilibrium with the unbound drug in the tissues and reflects the concentration of drug at its site of action. Therefore, the pharmacologic effect of a drug is thought to be a function of the concentration of unbound drug in the blood. The unbound steady-state concentration (C_ss,u) can be calculated by multiplying C_ss and f_b: C_ss,u= C_ss f_b. The effect that changes in Q, f_b, and CL_int have on C_ss,u and therefore on the pharmacologic response of a drug depends on whether a high- or low-clearance drug is involved. Because CL = Q for high-clearance drugs, a change in f_b or CL_int does not change CL or C_ss(C_ss = k₀/CL). However, a change in unbound drug fraction does alter C_ss,u(C_ss,u = f_bC_ss), thereby affecting the pharmacologic response. Plasma protein-binding displacement drug interactions can be very important clinically, but they are also dangerous because the changes in C_ss,u are not reflected in changes in C_ss for high-clearance drugs. Because laboratories usually measure only total concentrations (concentrations of unbound drug are difficult to determine), the interaction is hard to detect. If CL_int changes for high-clearance drugs, CL, C_ss, C_ss,u, and pharmacologic response do not change. Changes in Q cause a change in CL; changes in C_ss, C_ss,u, and drug response are indirectly proportional to changes in CL.

For low-clearance drugs, total clearance is determined by unbound drug fraction and intrinsic clearance: CL =f_b(CL_int). A change in Q does not change CL, C_ss, C_ss,u, or pharmacologic response. However, a change in f_b or CL_int does alter CL and C_ss (C_ss = k₀/CL). Changes in CL_int will cause a proportional change in CL.

Changes in C_ss, C_ss,u, and drug response are indirectly proportional to changes in CL. Altering f_b for low-clearance drugs produces interesting results. A change in f_b alters CL and C_ss (C_ss = k₀/CL). Because CL andC_ss change in opposite directions with changes in f_b, C_ss,_u (C_ss,u = f_bC_ss) and pharmacologic response do not change with alterations in the fraction of unbound drug in the blood. For example, a low-clearance drug is administered to a patient until steady-state is achieved:

Suppose that another drug is administered to the patient that displaces the first drug from plasma-protein-binding sites and doubles f_b (f_b now equals 2f_b). CL doubles because of the protein-binding displacement [2CL = 2f_b(CL_int)], and C_ss decreases by one-half because of the change in clearance [½(C_ss) = k₀/(2Cl)]. C_ss,udoes not change because even though f_b is doubled, C_ss decreased by one-half (C_ss,u= f_bC_ss). The potential for error in this situation is that clinicians may increase the dose of a low-clearance drug after a protein-binding displacement interaction because C_ss decreased. Because C_ss,u and the pharmacologic effect do not change, the dose should remain unaltered. Plasma protein binding decreases occur commonly in patients taking phenytoin. Low albumin concentrations (as in trauma or pregnant patients), high concentrations of endogenous plasma protein-binding displacers (as with high concentrations of bilirubin), or plasma protein-binding drug interactions (as with concomitant therapy with valproic acid) can result in subtherapeutic total phenytoin concentrations. Despite this fact, unbound phenytoin concentrations usually are within the therapeutic range, and often the patient is responding appropriately to treatment. Thus, in these situations, unbound rather than total phenytoin serum concentrations should be monitored and used to guide future therapeutic decisions.

Clearances for Different Routes of Elimination and Metabolic Pathways

Clearances for individual organs can be computed if the excretion the organ produces can be obtained. For example, renal clearance can be calculated if urine is collected during a pharmacokinetic experiment. The patient empties his or her bladder immediately before the dose is given. Subsequent urine production is collected until the last serum concentration (C_last) is obtained. Renal clearance (CL_R) is computed by dividing the amount of drug excreted in the urine by AUC_0–t,last. Biliary and other clearance values are computed in a similar fashion.

Clearances also can be calculated for each metabolite that is formed from the parent drug. This computation is particularly useful in drug-interaction studies to determine which metabolic pathway is stimulated or inhibited. In the following metabolic scheme, the parent drug (D) is metabolized into two different metabolites (M₁, M₂) that subsequently are eliminated by the kidney (M_1R, M_2R):

To compute the formation clearance of M₁ and M₂ (CL_FM1, CL_FM2), urine would be collected for five or more half-lives after a single dose or during a dosage interval at steady state. The amount of metabolite eliminated in the urine is then determined. The fraction of the dose (in moles, because the molecular weights of the parent drug and metabolites are not equal) eliminated by each metabolic pathway (f_M1 = M_1R/D and f_M2 =M_2R/D) can then be computed. Formation clearance for each pathway can be calculated using the following equations: CL_FM1 = f_M1CL_M and CL_FM2 = f_M2CL_M, where CL_M is the metabolic clearance for the parent drug