Introduction Biopharmaceutics history 2

DRUG ELIMINATION, CLEARANCE, METHABOLISM
DRUG ELIMINATION 149-150 1
DRUG ELIMINATION
Drugs are removed from the body by various elimination processes. Drug elimination refers to the irreversible removal of drug from the body by all routes of elimination. The declining plasma drug concentration observed after systemic drug absorption shows that the drug is being eliminated from the body but does not necessarily differentiate between distribution and elimination, and does not indicate which elimination processes are involved.
Drug elimination is usually divided into two major components: excretion and biotransformation. Drug excretion is the removal of the intact drug. Nonvolatile and polar drugs are excreted mainly by renal excretion, a process in which the drug passes through the kidney to the bladder and ultimately into the urine. Other pathways for drug excretion may include the excretion of drug into bile, sweat, saliva, milk (via lactation), or other body fluids. Volatile drugs, such as gaseous anesthetics, alcohol, or drugs with high volatility, are excreted via the lungs into expired air. Biotransformation or drug metabolism is the process by which the drug is chemically converted in the body to a metabolite. Biotransformation is usually an enzymatic process. A few drugs may also be changed chemically1 by a nonenzymatic process (eg, ester hydrolysis). The enzymes involved in the biotransformation of drugs are located mainly in the liver (see Chapter 12). Other tissues such as kidney, lung, small intestine, and skin also contain biotransformation enzymes. Drug elimination in the body involves many complex rate processes. Although organ systems have specific functions, the tissues within the organs are not structurally homogeneous, and elimination processes may vary in each organ. In Chapter 4, drug elimination was modeled by an overall first-order elimination rate process. In this chapter, drug elimination is described in terms of clearance from a hypothetical well-stirred compartment containing uniform drug distribution. The term clearance describes the process of drug elimination from the body or from a single organ without identifying the individual processes involved. Clearance may be defined as the volume of fluid removed of the drug from the body per unit of time. The units for clearance are sometimes in milliliters per minute (mL/min) but most often reported in liters per hour (L/h). The volume concept is simple and convenient, because all drugs are dissolved and distributed in the fluids of the body.
Clearance is even more important clinically than a half-life for several reasons. First and foremost, clearance directly relates to the systemic exposure of a drug (eg, AUCinf), making it the most useful PK parameter clinically as it will be used to calculate doses to administer in order to reach a therapeutic goal in terms of exposure. While the terminal halflife gives information only on the terminal phase of drug disposition, clearance takes into account all processes of drug elimination regardless of their mechanism. When the PK behavior of the drug follows linear PK, clearance is a constant, whereas the rate of drug elimination is not. For example, firstorder elimination processes consider that a certain portion or fraction (percent) of the distribution volume is cleared of drug over a given time period. This basic concept (see also Chapter 3) will be elaborated along with a review of the anatomy and physiology of the kidney.
As will be seen later on in this chapter and in the noncompartmental analysis chapter (Chapter 25), the clearance of a drug (Cl) is directly related to the dose administered and to the overall systemic exposure achieved with that dose as per the equation
Cl = DOSE/AUC0-inf.
The overall systemic exposure (AUC0-inf) of a drug resulting from an administered dose correlates with its efficacy and toxicity. The drug clearance (Cl) is therefore the most important PK parameter to know in a given patient. If the therapeutic goal in terms of AUC0-inf is known for a drug, then the dose to administer to this patient is completely dictated by the clearance value (Cl). Hence, after IV administration DOSE = Cl × AUC0-inf or more generally
DOSE = Cl/F × AUC0-inf (7.2)
in which Cl/F can be called the “apparent clearance” when the absolute bioavailability (F) is unknown or simply not specified or assumed.

DRUG CLEARANCE 150-152 2

DRUG CLEARANCE
Drug clearance is a pharmacokinetic term for describing drug elimination from the body without identifying the mechanism of the process. Drug clearance (also called body clearance or total body clearance, and abbreviated as Cl or ClT) considers the entire body as a single drug-eliminating system from which many unidentified elimination processes may occur. Instead of describing the drug elimination rate in terms of amount of drug removed per unit of time (eg, mg/h), drug clearance is described in terms of volume of fluid removed from the drug per unit of time (eg, L/h). There are several definitions of clearance, which are similarly based on a volume removed from the drug per unit of time. The simplest concept of clearance regards the body as a space that contains a definite volume of apparent body fluid (apparent volume of distribution, V or VD) in which the drug is dissolved. Drug clearance is defined as the fixed volume of fluid (containing the drug) removed from the drug per unit of time. The units for clearance are volume/time (eg, mL/min, L/h). For example, if the Cl of penicillin is 15 mL/min in a patient and penicillin has a VD of 12 L, then from the clearance definition, 15 mL of the 12 L will be removed from the drug per minute.
Alternatively, Cl may be defined as the rate of drug elimination divided by the plasma drug concentration. This definition expresses drug elimination in terms of the volume of plasma eliminated of drug per unit time. This definition is a practical way to calculate clearance based on plasma drug concentration data.

where DE is the amount of drug eliminated and dDE/dt is the rate of elimination. Rearrangement of Equation 7.4 gives Equation 7.5.
Elimination rate = dDE = p dt C Cl (7.5)
The two definitions for clearance are similar because dividing the elimination rate by the Cp yields the volume of plasma cleared of drug per minute, as shown in Equation 7.4.
As discussed in previous chapters, a first-order elimination rate, dDE/dt, is equal to kDB or kCpVD. Based on Equation 7.3, substituting elimination rate for kCpVD,
= p D =pCl DkC VC kV (7.6)
Equation 7.6 shows that clearance is the product of a volume of distribution, VD, and a rate constant, k, both of which are constants when the PK is linear. As the plasma drug concentration decreases during elimination, the rate of drug elimination, dDE/dt, decreases accordingly, but clearance remains constant. Clearance is constant as long as the rate of drug elimination is a first-order process.
EXAMPLE »»»»»
Penicillin has a Cl of 15 mL/min. Calculate the elimination rate for penicillin when the plasma drug concentration, Cp, is 2 mg/mL.
Solution
Elimination rate = Cp × Cl (from Equation 7.5) dDE = 2 µg/mL ×15 mL/min = 30 µg/min
dt
Using the previous penicillin example, assume that the plasma penicillin concentration is 10 mg/mL.

From Equation 7.4, the rate of drug elimination is dDE =10 µg/mL ×15 mL/min =150 µg/min dt Thus, 150 mg/min of penicillin is eliminated from the body when the plasma penicillin concentratio n is 10 mg/mL. Clearance may be used to estimate the rate of drug elimination at any given concentration. Using the same example, if the elimination rate of penicillin was measured as 150 mg/min when the plasma penicillin concentration was 10 mg/mL, then the clearance of penicillin is calculated from Equation 7.4:µ= µ =150 g/min Cl 10 g/mL 15 mL/min

Just as the elimination rate constant (k or kel) represents the total sum of all of the different rate constants for drug elimination, including for example the renal (kR) and liver (kH) elimination rate constants, Cl is the total sum of all of the different clearance processes in the body that are occurring in parallel in terms of cardiac blood flow (therefore excepting lung clearance), including for example clearance through the kidney (renal clearance abbreviated as ClR), and through the liver (hepatic clearance abbreviated as ClH):

Elimination rate constant:
k or kel where k = kR + kH + kother (7.7)
Clearance: Cl where Cl = ClR + ClH + Clother (7.8)
where
Renal clearance: ClR = kR × V (7.9)
Hepatic clearance: ClH = kH × V (7.10)
Total clearance: Cl = k × V = (kR + kH + kother) × V (7.11)
From Equation 7.11, for a one-compartment model (ie, where V = Vss and where k = lz), the total body clearance Cl of a drug is the product of two constants, lz and Vss, which reflect all the distribution and elimination processes of the drug in the body.
Distribution and elimination are affected by blood flow, which will be considered below (and in Chapter 11) using a physiologic model. For a multicompartment model (eg, where the total volume of distribution [Vss] includes a central volume of distribution [Vc], and one [Vp] or more peripheral volumes of distributions), the total body clearance of a drug will be the product of the elimination rate constant from the central compartment (k10) and Vc. The equations become:
Renal clearance: ClR = kR × VC (7.12)
Hepatic clearance: ClH = kH × VC (7.13)
Total clearance: Cl = k10 × VC = (kR + kH + kother) × VC (7.14)
Clearance values are often adjusted on a per-kilogram-of-actual-body-weight (ABW) or on a per-meter-square-of-surface-area basis, such as L/h per kilogram or per m2, or normalized for a “typical” adult of 72 kg or 1.72 m2. This approach is similar to the method for expressing V, because both pharmacokinetic parameters vary with body weight or body size. It has been found, however, that when expressing clearance between individuals of varying ABW, such as predicting Cl between children and adults, Cl varies best allometrically with ABW, meaning that Cl is best expressed with an allometric exponent (most often 0.75 is recommended) relating it to ABW as per the following expression (see also Chapter 25):
Cl (predicted in a patient) = Cl(population value for a 72-kg patient) × (ABW/72)0.75 (7.15)
EXAMPLE »»»»»
Determine the total body clearance for a drug in a 70-kg male patient. The drug follows the kinetics of a one-compartment model and has an elimination half-life of 3 hours with an apparent volume of distribution of 100 mL/kg.
Solution
First determine the elimination rate constant (k) and then substitute properly into Equation 7.11.

CLEARANCE MODELS

The calculation of clearance from a rate constant
(eg, k or k10) and a volume of distribution (eg, V or Vc)
assumes (sometimes incorrectly) a defined compart-mental model, whereas clearance estimated directly
from the plasma drug concentration-time curve using
noncompartmental PK approaches does not need one
to specify the number of compartments that would
describe the shape of the concentration-time curve.
Although clearance may be regarded as the product of
a rate constant k and a volume of distribution V,
Equation 7.11 is far more general because the reaction
order for the rate of drug elimination, dDE/dt, is not
specified, and the elimination rate may or may not
follow first-order kinetics. The various approaches for
estimating a drug clearance are described in Fig. 7-1
and will be explored one by one below:

Static volume and rst-order processes are assumed in simpler models. Here Cl = k10 x Vc.



FIGURE 7-1 General approaches to clearance. Volume and elimination rate constant not defined.

Physiologic/Organ Clearance
Clearance may be calculated for any organ involved in the irreversible removal of drug from the body. Many organs in the body have the capacity for drug elimination, including drug excretion and biotrans-formation. The kidneys and liver are the most com-mon organs involved in excretion and metabolism, respectively. Physiologic pharmacokinetic models are based on drug clearance through individual organs or tissue groups (Fig. 7-2).
For any organ, clearance may be defined as the fraction of blood volume containing drug that flows through the organ and is eliminated of drug per unit time. From this definition, clearance is the product of the blood flow (Q) to the organ and the extraction ratio (E). The E is the fraction of drug extracted by the organ as drug passes through.
Cl (organ) = Q (organ) × E (organ) (7.16)
If the drug concentration in the blood (Ca) entering the organ is greater than the drug concentration of blood (Cv) leaving the organ, then some of the drug has been extracted by the organ (Fig. 7-2). The E is Ca - Cv divided by the entering drug concentration (Ca), as shown in Equation 7.17.

E is a ratio with no units. The value of E may range from 0 (no drug removed by the organ) to 1 (100% of the drug is removed by the organ). An E of 0.25 indi-cates that 25% of the incoming drug concentration is removed by the organ as the drug passes through.
Substituting for E into Equation 7.16 yields

Equation 7.16 adapted for the liver as an organ yields the hepatic clearance (ClH)
ClH = QH × EH (7.19)
Therefore, if Cl = ClH + ClNH (where ClNH is the nonhepatic clearance), then Cl = (QH × EH) + ClNH (7.20)
For some drugs Cl ~ ClH, and so Cl ~ QH × EH.
The physiologic approach to organ clearance shows that the clearance from an organ depends on its blood flow rate and its ability at eliminating the drug, whereas the total clearance is that of a constant or static fraction of the volume in which the drug is distributed or is removed from the drug per unit of time. Organ clearance measurements using the physiologic approach require invasive techniques to obtain measurements of blood flow and extraction ratio. The physiologic approach has been used to describe hepatic clearance, which is discussed further under hepatic elimination (Chapter 12). More classical definitions of clearance have been applied to renal clearance because direct measurements of plasma drug concentration and urinary drug excretion may be obtained. Details will be presented in the