following equation:
(1.22a)
Similarly, plasma and blood volume are related by
(1.22b)
1.2.4 Hepatic, Renal, and Biliary Clearances
The CL estimated from dose and AUC (Equation 1.10) is the overall clearance of the drug from blood, also called the total clearance. Several clearance pathways could contribute to the total clearance of a drug. Hepatic metabolism, renal, and biliary pathways are some of the clearance routes available for a xenobiotic. The most common route is hepatic metabolism. A drug may utilize one or more clearance pathways depending on its physicochemical properties. The total clearance of a drug is the sum of its hepatic (CLH ), renal (CLR ), and biliary (CLB ) clearances.
(1.23)
CLorgan is the clearance from an eliminating organ, Qorgan is the blood flow rate to that organ, CART and CVEN are the arterial and venous concentrations. (Qorgan × CART − Qorgan × CVEN ) is the rate of elimination from that organ.
1.2.4.1 Hepatic Clearance
The liver is the most important eliminating organ, where phase I and phase II metabolizing enzymes convert low molecular weight drugs into more hydrophilic compounds with greater molecular weight which can enter bile or undergo renal elimination. About 40 human CYP450 genes have been cloned and classified according to sequence homology. Of these, only 3 CYP450 families and <12 unique enzymes play a substantial role in the hepatic metabolism of drugs in humans. The rate of such an enzyme driven biotransformation reaction, v, depends on the free concentration of the drug, C, according to the Michaelis–Menten equation:
CLint is the intrinsic clearance of the drug, vmax is the maximum velocity of the reaction, and KM is the Michaelis–Menten constant (Figure 1.3). When the therapeutic concentration range is low relative to KM (true for many drugs), Equation 1.24 becomes:
Figure 1.3. Rate of an enzyme‐catalyzed reaction as a function of substrate concentration.
Equation 1.25 suggests that the rate of a metabolic reaction varies linearly with the drug concentration at concentrations not exceeding KM . CLint then equals the ratio of vmax to KM and is independent of the drug concentration. However, when drug concentrations are comparable with or exceeds KM, which can be the case at high drug doses, CLint is dependent on C (see Equation 1.24). The greater the drug concentration, the greater the extent of enzyme saturation and smaller the value of CLint . A maximal rate of metabolism vmax is reached at concentrations much higher relative to KM . Under these conditions, zero‐order kinetics is said to prevail, and a constant amount of drug is eliminated per unit time, independent of the amount of drug in the body. Well‐known examples of drugs exhibiting nonlinear clearance include phenytoin, ethanol, methyl salicylate, and theophylline (in some individuals). Apart from CLint, the hepatic clearance CLH is dependent on how fast the drug is delivered to the enzymes in the hepatocytes determined by the total blood flow rate to the liver, QLI . A basic tenet of pharmacokinetics is that only the fraction of drug that is not bound to blood, fub, is available for distribution into tissues and for clearance. The dependencies of CLH on CLint , QLI, and fub are encapsulated in the well‐stirred model, in which drug concentration in the liver is assumed to be uniform throughout the tissue. According to this model, the hepatic clearance from blood, CLH, is given by:
Equation 1.26 shows that when the product fup × CLint is high compared to QLI, then CLH is simply determined by the blood flow rate to the liver. The drug clearance is limited by the rate at which it is delivered to the drug metabolizing enzymes. On the other hand, when the product fup × CLint is low compared to QLI, then the hepatic clearance linearly varies with the product of fraction unbound in plasma and the intrinsic clearance.
The fraction of drug unbound in blood, fub is related to fup and R as follows:
(1.27)
1.2.4.2 Hepatic Extraction
The hepatic extraction ratio of a drug is obtained by taking QLI to the left‐hand side in Equation 1.26
For high CLint compounds, the displacement of the drug from plasma proteins is rapid and equilibrium cannot be established between concentrations of the bound and unbound drug in blood (Cb, Cu,b ) and in liver (Cu,liver ). This can be represented as:
For low CLint compounds, there is equilibrium between the bound drug and unbound drug in blood and liver and only the Cu,liver is available to the drug metabolizing enzymes. The equilibrium between the different drug concentrations is shown below:
