U

Slow conversion in liver to hydrophilic metabolite

Slow conversion in liver to hydrophilic metabolite

Renal excretion of metabolite

Lipophilic drug

Rapid and complete conversion in liver to hydrophilic metabolite

Renal excretion of metabolite

A. Elimination of hydrophilic and hydrophobic drugs

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 glo-merular filtration, i.e., 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 (t1/2) and is related to the elimination rate constant k by the equation t1/2 = 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 biotrans-formed 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 equation:

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 with decreasing blood concentration.

The best-known exception to exponential kinetics is the elimination of alcohol (ethanol), which obeys a linear time course (zero-order kinetics), at least at blood concentrations > 0.02 %. It does so because the rate-limiting enzyme, alcohol dehydrogenase, achieves half-saturation at very low substrate concentrations, i.e., at about 80 mg/L (0.008 %). Thus, reaction velocity reaches a plateau at blood ethanol concentrations of about 0.02 %, and the amount of drug eliminated per unit of time remains constant at concentrations above this level.

Concentration (c) of drug in plasma [amount/vol] Co

Concentration (c) of drug in plasma [amount/vol] Co

Time Course Adverse Effects

Time

A. Exponential elimination of drug

Time

A. Exponential elimination of drug

Time Course of Drug Concentration in Plasma

A. Drugs are taken up into and eliminated from the body by various routes. The body thus represents an open system wherein the actual drug concentration reflects the interplay of intake (ingestion) and egress (elimination). When an orally administered drug is absorbed from the stomach and intestine, speed of uptake depends on many factors, including the speed of drug dissolution (in the case of solid dosage forms) and of gastrointestinal transit; the membrane penetrability of the drug; its concentration gradient across the mucosa-blood barrier; and mucosal blood flow. Absorption from the intestine causes the drug concentration in blood to increase. Transport in blood conveys the drug to different organs (distribution), into which it is taken up to a degree compatible with its chemical properties and rate of blood flow through the organ. For instance, well-perfused organs such as the brain receive a greater proportion than do less well-perfused ones. Uptake into tissue causes the blood concentration to fall. Absorption from the gut diminishes as the mucosa-blood gradient decreases. Plasma concentration reaches a peak when the drug amount leaving the blood per unit of time equals that being absorbed.

Drug entry into hepatic and renal tissue constitutes movement into the organs of elimination. The characteristic phasic time course of drug concentration in plasma represents the sum of the constituent processes of absorption, distribution, and elimination, which overlap in time. When distribution takes place significantly faster than elimination, there is an initial rapid and then a greatly retarded fall in the plasma level, the former being designated the a-phase (distribution phase), the latter the p-phase (elimination phase). When the drug is distributed faster than it is absorbed, the time course of the plasma level can be described in mathematically simplified form by the Bate-Lullmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.

man function (k1 and k2 represent the rate constants for absorption and elimination, respectively).

B. The velocity of absorption depends on the route of administration. The more rapid the administration, the shorter will be the time (tmax) required to reach the peak plasma level (cmax), the higher will be the cmax, and the earlier the plasma level will begin to fall again.

The area under the plasma level time curve (AUC) is independent of the route of administration, provided the doses and bioavailability are the same (Dost's law of corresponding areas). The AUC can thus be used to determine the bio-availability F of a drug. The ratio of AUC values determined after oral or intravenous administration of a given dose of a particular drug corresponds to the proportion of drug entering the systemic circulation after oral administration. The determination of plasma levels affords a comparison of different proprietary preparations containing the same drug in the same dosage. Identical plasma level time-curves of different manufacturers' products with reference to a standard preparation indicate bio-equivalence of the preparation under investigation with the standard.

Time (t)

A. Time course of drug concentration

A. Time course of drug concentration

B. Mode of application and time course of drug concentration

Time Course of Drug Plasma Levels During Repeated Dosing (A)

When a drug is administered at regular intervals over a prolonged period, the rise and fall of drug concentration in blood will be determined by the relationship between the half-life of elimination and the time interval between doses. If the drug amount administered in each dose has been eliminated before the next dose is applied, repeated intake at constant intervals will result in similar plasma levels. If intake occurs before the preceding dose has been eliminated completely, the next dose will add on to the residual amount still present in the body, i.e., the drug accumulates. The shorter the dosing interval relative to the elimination half-life, the larger will be the residual amount of drug to which the next dose is added and the more extensively will the drug accumulate in the body. However, at a given dosing frequency, the drug does not accumulate infinitely and a steady state (Css) or accumulation equilibrium is eventually reached. This is so because the activity of elimination processes is concentration-dependent. The higher the drug concentration rises, the greater is the amount eliminated per unit of time. After several doses, the concentration will have climbed to a level at which the amounts eliminated and taken in per unit of time become equal, i.e., a steady state is reached. Within this concentration range, the plasma level will continue to rise (peak) and fall (trough) as dosing is continued at a regular interval. The height of the steady state (Css) depends upon the amount (D) administered per dosing interval (t) and the clearance (Cltot):

The speed at which the steady state is reached corresponds to the speed of elimination of the drug. The time needed to reach 90% of the concentration plateau is about 3 times the ti/2 of elimination.

Time Course of Drug Plasma Levels During Irregular Intake (B)

In practice, it proves difficult to achieve a plasma level that undulates evenly around the desired effective concentration. For instance, if two successive doses are omitted, the plasma level will drop below the therapeutic range and a longer period will be required to regain the desired plasma level. In everyday life, patients will be apt to neglect drug intake at the scheduled time. Patient compliance means strict adherence to the prescribed regimen. Apart from poor compliance, the same problem may occur when the total daily dose is divided into three individual doses (tid) and the first dose is taken at breakfast, the second at lunch, and the third at supper. Under this condition, the nocturnal dosing interval will be twice the diurnal one. Consequently, plasma levels during the early morning hours may have fallen far below the desired or, possibly, urgently needed range.

A Dosing interval
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