Pharmacokinetics (t1/2) and the apparent volume of distribution Vapp (p. 28) by the equation: Vapp t1/2 = In 2 x –––– Cltot The smaller the volume of distribution or the larger the total clearance, the shorter is the half-life. In the case of drugs renally eliminated in unchanged form, the half-life of elimination can be calculated from the cumulative excretion in urine; the final total amount eliminated corresponds to the amount absorbed. Hepatic elimination obeys exponential kinetics because metabolizing enzymes operate in the quasilinear region of their concentration-activity curve; hence the amount of drug metabolized per unit of time diminishes. | 44 Pharmacokinetics Drug Concentration in the Body as a Function of Time. First-Order Exponential Rate Processes Processes such as drug absorption and elimination display exponential characteristics. As regards the former this follows from the simple fact that the amount of drug being moved per unit of time depends on the concentration difference gradient between two body compartments Fick s Law . In drug absorption from the alimentary tract the intestinal contents and blood would represent the compartments containing an initially high and low concentration respectively. In drug elimination via the kidney excretion often depends on glomerular filtration . the filtered amount of drug present in primary urine. As the blood concentration falls the amount of drug filtered per unit of time diminishes. The resulting exponential decline is illustrated in A . The exponential time course implies constancy of the interval during which the concentration decreases by one-half. This interval represents the half-life ti 2 and is related to the elimination rate constant k by the equation ti 2 ln 2 k. The two parameters together with the initial concentration co describe a first-order exponential rate process. The constancy of the process permits calculation of the plasma volume that would be cleared of drug if the remaining drug were not to assume a homogeneous distribution in the total volume a condition not met in reality . This notional plasma volume freed of drug per unit of time is termed the clearance. Depending on whether plasma concentration falls as a result of urinary excretion or metabolic alteration clearance is considered to be renal or hepatic. Renal and hepatic clearances add up to total clearance Cltot in the case of drugs that are eliminated unchanged via the kidney and biotransformed in the liver. Cltot represents the sum of all processes contributing to elimination it is related to the half-life t1 2 and the apparent volume of distribution Vapp p. 28 by the
