Color Atlas of Pharmacology (Part 5): Pharmacokinetics

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Color Atlas of Pharmacology (Part 5): Pharmacokinetics

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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...

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  1. 44 Pharmacokinetics Drug Concentration in the Body (t1/2) and the apparent volume of distri- as a Function of Time. First-Order bution Vapp (p. 28) by the equation: (Exponential) Rate Processes Vapp t1/2 = In 2 x –––– Cltot Processes such as drug absorption and elimination display exponential charac- The smaller the volume of distribu- teristics. As regards the former, this fol- tion or the larger the total clearance, the lows from the simple fact that the shorter is the half-life. amount of drug being moved per unit of In the case of drugs renally elimi- time depends on the concentration dif- nated in unchanged form, the half-life of ference (gradient) between two body elimination can be calculated from the compartments (Fick’s Law). In drug ab- cumulative excretion in urine; the final sorption from the alimentary tract, the total amount eliminated corresponds to intestinal contents and blood would the amount absorbed. represent the compartments containing Hepatic elimination obeys expo- an initially high and low concentration, nential kinetics because metabolizing respectively. In drug elimination via the enzymes operate in the quasilinear re- kidney, excretion often depends on glo- gion of their concentration-activity merular filtration, i.e., the filtered curve; hence the amount of drug me- amount of drug present in primary tabolized per unit of time diminishes urine. As the blood concentration falls, with decreasing blood concentration. the amount of drug filtered per unit of The best-known exception to expo- time diminishes. The resulting expo- nential kinetics is the elimination of al- nential decline is illustrated in (A). The cohol (ethanol), which obeys a linear exponential time course implies con- time course (zero-order kinetics), at stancy of the interval during which the least at blood concentrations > 0.02 %. It concentration decreases by one-half. does so because the rate-limiting en- This interval represents the half-life zyme, alcohol dehydrogenase, achieves (t1/2) and is related to the elimination half-saturation at very low substrate rate constant k by the equation t1/2 = ln concentrations, i.e., at about 80 mg/L 2/k. The two parameters, together with (0.008 %). Thus, reaction velocity reach- the initial concentration co, describe a es a plateau at blood ethanol concentra- first-order (exponential) rate process. tions of about 0.02 %, and the amount of The constancy of the process per- drug eliminated per unit of time re- mits calculation of the plasma volume mains constant at concentrations above that would be cleared of drug, if the re- this level. maining drug were not to assume a ho- mogeneous distribution in the total vol- ume (a condition not met in reality). This notional plasma volume freed of drug per unit of time is termed the clearance. Depending on whether plas- ma concentration falls as a result of uri- nary 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 un- changed 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 L llmann, Color Atlas of Pharmacology ' 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
  2. Pharmacokinetics 45 Concentration (c) of drug in plasma [amount/vol] Co Plasma half life t 1 ct = co · e-kt 2 1 c t 1 = — co ct: Drug concentration at time t 2 2 ln 2 co: Initial drug concentration after t 1 = —– administration of drug dose 2 k e: Base of natural logarithm k: Elimination constant Unit of time Time (t) Notional plasma volume per unit of time freed of drug = clearance [vol/t] Amount excreted per unit of time [amount/t] Total amount of drug (Amount administered) = Dose excreted Time A. Exponential elimination of drug Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
  3. 46 Pharmacokinetics Time Course of Drug Concentration in man function (k1 and k2 represent the Plasma rate constants for absorption and elimi- nation, respectively). A. Drugs are taken up into and eliminat- B. The velocity of absorption de- ed from the body by various routes. The pends on the route of administration. body thus represents an open system The more rapid the administration, the wherein the actual drug concentration shorter will be the time (tmax) required reflects the interplay of intake (inges- to reach the peak plasma level (cmax), tion) and egress (elimination). When an the higher will be the cmax, and the earli- orally administered drug is absorbed er the plasma level will begin to fall from the stomach and intestine, speed again. of uptake depends on many factors, in- The area under the plasma level time cluding the speed of drug dissolution (in curve (AUC) is independent of the route the case of solid dosage forms) and of of administration, provided the doses gastrointestinal transit; the membrane and bioavailability are the same (Dost’s penetrability of the drug; its concentra- law of corresponding areas). The AUC tion gradient across the mucosa-blood can thus be used to determine the bio- barrier; and mucosal blood flow. Ab- availability F of a drug. The ratio of AUC sorption from the intestine causes the values determined after oral or intrave- drug concentration in blood to increase. nous administration of a given dose of a Transport in blood conveys the drug to particular drug corresponds to the pro- different organs (distribution), into portion of drug entering the systemic which it is taken up to a degree compat- circulation after oral administration. ible with its chemical properties and The determination of plasma levels af- rate of blood flow through the organ. fords a comparison of different proprie- For instance, well-perfused organs such tary preparations containing the same as the brain receive a greater proportion drug in the same dosage. Identical plas- than do less well-perfused ones. Uptake ma level time-curves of different into tissue causes the blood concentra- manufacturers’ products with reference tion to fall. Absorption from the gut di- to a standard preparation indicate bio- minishes as the mucosa-blood gradient equivalence of the preparation under decreases. Plasma concentration reach- investigation with the standard. es 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 characteris- tic phasic time course of drug concen- tration in plasma represents the sum of the constituent processes of absorp- tion, distribution, and elimination, which overlap in time. When distribu- tion takes place significantly faster than elimination, there is an initial rapid and then a greatly retarded fall in the plas- ma level, the former being designated the !-phase (distribution phase), the latter the "-phase (elimination phase). When the drug is distributed faster than it is absorbed, the time course of the plasma level can be described in mathe- matically simplified form by the Bate- Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
  4. Pharmacokinetics 47 Absorption Distribution Elimination Uptake from into body from body by stomach and tissues: biotransformation intestines !-phase (chemical alteration), into blood excretion via kidney: ß-phase Drug concentration in blood (c) Bateman-function Dose k1 c= x x (e-k1t-e-k2t) ˜ Vapp k2 - k1 Time (t) A. Time course of drug concentration Drug concentration in blood (c) Intravenous Intramuscular Subcutaneous Oral Time (t) B. Mode of application and time course of drug concentration Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
  5. 48 Pharmacokinetics Time Course of Drug Plasma Levels Time Course of Drug Plasma Levels During Repeated Dosing (A) During Irregular Intake (B) When a drug is administered at regular In practice, it proves difficult to achieve intervals over a prolonged period, the a plasma level that undulates evenly rise and fall of drug concentration in around the desired effective concentra- blood will be determined by the rela- tion. For instance, if two successive dos- tionship between the half-life of elimi- es are omitted, the plasma level will nation and the time interval between drop below the therapeutic range and a doses. If the drug amount administered longer period will be required to regain in each dose has been eliminated before the desired plasma level. In everyday the next dose is applied, repeated intake life, patients will be apt to neglect drug at constant intervals will result in simi- intake at the scheduled time. Patient lar plasma levels. If intake occurs before compliance means strict adherence to the preceding dose has been eliminated the prescribed regimen. Apart from completely, the next dose will add on to poor compliance, the same problem the residual amount still present in the may occur when the total daily dose is body, i.e., the drug accumulates. The divided into three individual doses (tid) shorter the dosing interval relative to and the first dose is taken at breakfast, the elimination half-life, the larger will the second at lunch, and the third at be the residual amount of drug to which supper. Under this condition, the noc- the next dose is added and the more ex- turnal dosing interval will be twice the tensively will the drug accumulate in diurnal one. Consequently, plasma lev- the body. However, at a given dosing els during the early morning hours may frequency, the drug does not accumu- have fallen far below the desired or, late infinitely and a steady state (Css) or possibly, urgently needed range. accumulation equilibrium is eventual- ly reached. This is so because the activ- ity of elimination processes is concen- tration-dependent. The higher the drug concentration rises, the greater is the amount eliminated per unit of time. Af- ter 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 concentra- tion range, the plasma level will contin- ue to rise (peak) and fall (trough) as dos- ing is continued at a regular interval. The height of the steady state (Css) de- pends upon the amount (D) adminis- tered per dosing interval (!) and the clearance (Cltot): D Css = ––––––––– (! · Cltot) The speed at which the steady state is reached corresponds to the speed of elimination of the drug. The time need- ed to reach 90 % of the concentration plateau is about 3 times the t1/2 of elimi- nation. Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
  6. Pharmacokinetics 49 Dosing interval Drug concentration Time Dosing interval Time Accumulation: Steady state: administered drug is drug intake equals not completely eliminated elimination during during interval dosing interval Drug concentration Time A. Time course of drug concentration in blood during regular intake Drug concentration Desired therapeutic level ? ? ? Time B. Time course of drug concentration with irregular intake Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
  7. 50 Pharmacokinetics Accumulation: Dose, Dose Interval, and optimal plasma level is attained only af- Plasma Level Fluctuation ter a long period. Here, increasing the initial doses (loading dose) will speed Successful drug therapy in many illness- up the attainment of equilibrium, which es is accomplished only if drug concen- is subsequently maintained with a low- tration is maintained at a steady high er dose (maintenance dose). level. This requirement necessitates regular drug intake and a dosage sched- Change in Elimination Characteristics ule that ensures that the plasma con- During Drug Therapy (B) centration neither falls below the thera- peutically effective range nor exceeds With any drug taken regularly and accu- the minimal toxic concentration. A con- mulating to the desired plasma level, it stant plasma level would, however, be is important to consider that conditions undesirable if it accelerated a loss of ef- for biotransformation and excretion do fectiveness (development of tolerance), not necessarily remain constant. Elimi- or if the drug were required to be nation may be hastened due to enzyme present at specified times only. induction (p. 32) or to a change in uri- A steady plasma level can be nary pH (p. 40). Consequently, the achieved by giving the drug in a con- steady-state plasma level declines to a stant intravenous infusion, the steady- new value corresponding to the new state plasma level being determined by rate of elimination. The drug effect may the infusion rate, dose D per unit of time diminish or disappear. Conversely, !, and the clearance, according to the when elimination is impaired (e.g., in equation: progressive renal insufficiency), the mean plasma level of renally eliminated D Css = ––––––––– drugs rises and may enter a toxic con- (! · Cltot) centration range. This procedure is routinely used in intensive care hospital settings, but is otherwise impracticable. With oral ad- ministration, dividing the total daily dose into several individual ones, e.g., four, three, or two, offers a practical compromise. When the daily dose is given in sev- eral divided doses, the mean plasma level shows little fluctuation. In prac- tice, it is found that a regimen of fre- quent regular drug ingestion is not well adhered to by patients. The degree of fluctuation in plasma level over a given dosing interval can be reduced by use of a dosage form permitting slow (sus- tained) release (p. 10). The time required to reach steady- state accumulation during multiple constant dosing depends on the rate of elimination. As a rule of thumb, a pla- teau is reached after approximately three elimination half-lives (t1/2). For slowly eliminated drugs, which tend to accumulate extensively (phen- procoumon, digitoxin, methadone), the Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
  8. Pharmacokinetics 51 Drug concentration in blood Desired plasma level 4 x daily 50 mg 2 x daily 100 mg 1 x daily 200 mg Single 50 mg 6 12 18 24 6 12 18 24 6 12 18 24 6 12 A. Accumulation: dose, dose interval, and fluctuation of plasma level Inhibition of elimination Drug concentration in blood Desired plasma level Acceleration of elimination 6 12 18 24 6 12 18 24 6 12 18 24 6 12 18 B. Changes in elimination kinetics in the course of drug therapy Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
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