Clearance and Maintenance Dose
Clearance can be thought of as the intrinsic ability of the body or its organs of elimination (usually the kidneys and the liver) to remove drug from the blood or plasma. Clearance is expressed as a volume per unit of time. It is important to emphasise that clearance is not an indicator of how much drug is being removed; it only represents the theoretical volume of blood or plasma which is completely cleared of drug in a given period. The amount of drug removed depends on the plasma concentration of drug and the clearance.
As steady state, the rate of drug administration (RA) and the rate of drug elimination (RE) must be equal, so that, RA = RE. Because RA can be described as (S)(F)(Dose/τ), and the RE equals to (Cl)(Css ave), we get the formula for Cl as Cl = (S)(F)(Dose/τ)/(Css ave) [Equation 1].
If an estimate for clearance is obtained from the literature, the clearance formula of [Equation 1] can be rearranged and used to calculate the rate of administration or maintenance dose that will produce a desired average plasma concentration of (Css ave) at steady state: Maintenance Dose = (Cl)(Css ave)(τ)/[(S)(F)] [Equation 2].
Attention must be paid that the units of all factors in these formulas must be consistent.
Factors Affecting Clearance
Body Surface Area/Weight
Most literature values for clearance are expressed as volume/kg/time or as volume/70 kg/time. There is some evidence, however, that drug clearance is best adjusted on the basis of BSA rather than weight. BSA can be calculated using BSA in m2 = (Patient’s Weight in kg/70 kg)0.7(1.73 m2) [Equation 3] or it can be obtained from various charts and nomograms. The value of a patient’s weight divided by 70 taken to the 0.7 power is an attempt to scale or size a patient as a fraction of the average 1.73 m2 or 70-kg individual. Weight divided by 70 taken to the 0.7 power has no units and should be thought of as the fraction of the average-size person.
As an example, a 7-kg patient has a weight ratio relative to 70 kg of 0.1 and, therefore, may be thought of as having a size and thus a metabolic and renal capacity that is one-tenth of the average 70-kg person (7 kg/70 kg = 0.1). If the same weight individual was compared to the 70-kg standard using weight to the 0.7 power, the ratio becomes 0.2 or 20%, (7 kg/70 kg)0.7 = 0.2. Therefore in these two examples, the difference between 0.1 and 0.2 is large. However, when patients do not differ significantly from 70 kg, the difference between using weight versus weight to the power 0.7 (BSA) becomes less significant.
The underlying assumption in using weight or surface area to adjust clearance is that the patient’s liver and kidney size (and hopefully function) vary in proportion to these physical measurements (weight or BSA). However, this may not always be the case; therefore, clearance values derived from the patient population having a similar age and size should be used whenever possible. When a patient’s size is substantially greater or less than the standard 70 kg, or 1.73 m2, a careful assessment should be made to determine if the patient’s body stature is normal, obese, or emaciated. In obese and emaciated patients, neither weight nor surface area is likely to be helpful in predicting clearance, since the patient’s body size will not reflect the size or function of the liver and kidney.
Plasma Protein Binding
For highly protein-bound drugs, diminished plasma protein binding is associated with a decrease in reported steady-state plasma drug concentrations (total of unbound plus free drug) for any given dose that is administered. According to Equation 1, a decrease in the denominator, (Css ave), increases the calculated clearance. This actually would be misleading, however, to assume that because the calculated clearance is increased, the amount eliminated of drug per unit of time has increased. Equation 1 assumes that when (Css ave) changes, the free drug concentration, which is available for metabolism and renal elimination, changes proportionately. In actuality the free or unbound fraction of drug in the plasma generally increases with diminished plasma protein binding. As a result, the amount of free drug eliminated per unit of time remains unchanged. This should be apparent if one considers that at steady state, the amount of drug administered per unit of time (RA) must equal the amount eliminated per unit of time (RE). If RA has not changed, RE must remain the same.
In summary, when the same daily dose of a drug is given in the presence of diminished protein binding, an amount equal to that dose will be eliminated from the body each day at steady state despite a diminished steady-state plasma concentration (Css ave) and an increase in the calculated clearance (Cl). This lower plasma concentration (C bound + C free) is associated with a decreased C bound, no change in C free, and as a result there is an increase in the fraction of unbound drug (fu). Therefore, the pharmacologic effect achieved will be similar to that produced by the higher serum concentration observed, under normal protein binding conditions. This example re-emphasizes the principle that clearance alone is not a good indicator of the amount of drug eliminated per unit of time (RE).
The direct proportionality between calculated clearance and fraction unbound (fu) does not apply to drugs that are so efficiently metabolised or excreted that some (perhaps all) of the drug bound to plasma protein is removed as it passes through the elimination organ. In this situation the plasma protein acts as a “transport system” for the drug, carrying it to the eliminating organs, and clearance becomes dependent on the blood or plasma flow to the eliminating organ. To determine whether the clearance for a drug with significant plasma binding will be influenced primarily by blood flow or plasma protein binding, its extraction ratio is estimated and compared to its (fu) value.
The extraction ratio is the fraction of the drug presented to the eliminating organ that is cleared after a single pass through that organ. It can be estimated by dividing the blood or plasma clearance of a drug by the blood or plasma flow to the eliminating organ. If the extraction ratio exceeds the (fu), then the plasma proteins are acting as a transport system and clearance will not change in proportion to (fu). If, however, the extraction ratio is less than (fu), clearance is likely to increase by the same proportion that (fu) changes. This approach does not take into account other factors that may affect clearance such as red blood cell binding, elimination from red blood cells, or changes in metabolic function.
Renal and Hepatic Function
Drugs can be eliminated or cleared as unchanged drug through the kidney and by metabolism in liver. These two routes of clearance are assumed to be independent of one another and additive. A decrease in the function of an organ of elimination is most significant when that organ serves as the primary route of drug elimination. However, as the major elimination pathway becomes increasingly compromised, the “minor” pathway becomes more significant because it assumes a greater proportion of the total clearance. For example, a drug that is usually 67% eliminated by the renal route and 33% by the metabolic route will be 100% metabolised in the event of complete renal failure; the total clearance, however, will only be one-third of the normal value.
Cardiac output also affects drug metabolism. Hepatic or metabolic clearances for some drugs can be decreased by 25% to 50% in patients with CHD. For example, the metabolic clearances of theophylline and digoxin are reduced by approximately one-half in patients with CHD. Since the metabolic clearance for both of these drugs is much lower than the hepatic blood or plasma flow (low extraction ratio), it would not have been predicted that their clearances would have been influenced by cardiac output. The decreased cardiac output and resultant hepatic congestion must, in some way, decrease the intrinsic metabolic capacity of the liver.