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Concept of nonlinear pharmacokinetic
This document discusses linear and non-linear pharmacokinetics. Linear pharmacokinetics follows first-order kinetics where the rate of change in drug concentration depends only on the current concentration. In non-linear pharmacokinetics, the rate depends on carrier enzymes that can become saturated at high drug concentrations, causing the kinetics to follow mixed or zero-order processes and parameters to change with dose. Non-linearity can be caused by saturation of absorption, distribution, metabolism or excretion processes. The Michaelis-Menten equation describes non-linear kinetics and parameters. Km and Vmax can be estimated from plasma concentration data using Lineweaver-Burk, Eadie-Hofstee or Han
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Concept of nonlinear pharmacokinetic
- 1. CONCEPT OF NON-LINEAR PHARMACOKINETICS BY:Kavita Bahmani Assistant Professor Department of Pharmaceutical Sciences GJUS&T, Hisar, Haryana, India
- 2. CONTENTS Introduction Comparison b/w linear& non-linear pharmacokinetic Tests for detection of nonlinearity in pharmacokinetics Causes of nonlinearity Michaelis – Menten equation Estimation of Km and Vmax Estimation of Km and Vmax from steady-state concentration
- 3. Linear Pharmacokinetics,the characteristic of drugs that indicates the instantaneous rate of change in drug concentration depends only on the current concentration. The half-life will remain constant, irrespective of how high the concentration At therapeutic doses, the change in the amount of drug in the body or the change in its plasma concentration due to absorption, distribution, binding, metabolism or excretion, is proportional to its dose, whether administered as a single dose or as multiple doses. In such situation the rate processes are said to follw first order or linear kinetics and all semilog plots of C v/s T for different doses when collected for dose administered, are superimposable. This is called principle of superposition LINEAR PHARMACOKINETICS
- 4. IMPORTANT PHARMACOKINETIC FACTORS Fractionof drug absorbed/unabsorbed Ka: absorption rate constant KE: Elimination rate constant Vd: volume of distribution CLR: Renal clearance CLH: Hepatic clearance These describes the time course of a drug in the body remain unaffected by the dose i.e. Pharmacokinetics is dose-dependent
- 5. NONLINEAR PHARMACOKINETICS The rateprocess of drug’s ADME are depend upon carrier or enzymes that are substrate specific, have definite capacities and are susceptible to saturation at a high drug concentration. In such cases, an essentially first-order kinetics transform into a mixture of first-order and zero-order rate processes and the pharmacokinetic parameters are changed with the size of the administered dose. Pharmacokinetics of suchdrugsare said to be dose- dependent.Terms synonymous with itare mixed- order, nonlinear and capacity-limited kinetics.
- 6. TESTS FOR DETECTIONOF NONLINEARITY IN PHARMACOKINETICS 1. Determination of steady state plasma concentration at different doses. * If the steady state conc. are directly proportional to the dose, then linearity in the kinetics exists. Such proportionality is not observable when there is nonlinearity 2. Determination of some important pharmacokinetic parameters such as fraction bioavailability, elimination half life or total systemic clearance at different doses of drug. Any change in these parameters is indicative to non-linearity which are usually constant is indicative of nonlinearity.
- 7. CAUSES OF NONLINEARITY Causes of non linearity Drug Absorption Distribution Metabolism Excretion
- 8. When absorption is Solubility/ dissolution of drug is rate-limited; When absorption is Carrier - mediated transport system Pre systemic gut wall / hepatic metabolism attains saturation Griseofulvin - at high concentration in intestine Ascorbic acid - saturation of transport system Propranolol, Hydrazine and verapamil Parameters affected will be F, Ka, Cmax and AUC. DRUG ABSORPTION
- 9. Saturation of bindingsites on plasma proteins Saturation of tissues binding sites Phenybutazone & naproxen Thiopental & fentanyl In both cases, the free plasma conc. Increases but Vd increases only in the former case whereas it decrease in the later. DRUG DISTRIBUTION Saturation of binding sites on plasma proteins Saturation of tissues binding sites
- 10. Capacity - limitedmetabolism - enzyme &/ cofactor saturation; Phenytoin; Enzyme induction - decrease in plasma concentration; Phenytoin, alcohol, theophylline etc. carbamazepine Saturation of enzymes results in decreased hepatic clearance and therefore increased steady state concentration. DRUG METABOLISM
- 11. Active tubular secretionActive tubular reabsorption Penicillin G. Water soluble vitamins & Glucose. Others sources are renal excretion, changes in urine pH, nephrotoxicity and saturation of binding sites DRUG EXCRETION There are 2 process in renal excretion of a drug that are saturable.
- 12. MICHAELIS MENTEN EQUATION •Best suitable for the capacity limited or saturable processes E + D ED E + M • Enzymes usually react with the substrate to form enzyme substrate complexes; then the product is formed. • The enzyme can go back to react with another substrate to form another molecule of the product.
- 13. • • • • 1) when KM=C: under this situation , eq I reduces to − 𝑑𝑐 𝑑𝑡 = 𝑉𝑚𝑎𝑥 2 … … . . 𝑒𝑞𝑛 2 The rate of process is equal to half of its maximum rate. This process is represented in the plot of dc/dt vs. C. shown in fig. 1 Where - 𝑑𝑐 𝑑𝑡 = rate of decline of drug concentration with time 𝑉𝑚𝑎𝑥 = theoretical maximum rate of the process 𝐾𝑚= Michaelis constant There are 3 situations can be considered upon the values of Km and C − 𝑑𝑐 𝑑𝑡 ≡ 𝑉𝑚𝑎𝑥 𝐶 𝐾𝑚+𝐶 ……… 𝑒𝑞𝑛 1
- 14. PLOT OF MICHAELISMENTON EQUAION
- 15. • 2. When Km˃˃ C Then C approaches to zero, So Km+C= Km Equation 1 becomes − 𝑑𝑐 𝑑𝑡 = 𝑉𝑚𝑎𝑥 𝐶 𝐾𝑚 … … . . 𝑒𝑞𝑛 3 This equn is identical to the first order elimination of drug where Vmax/Km=Ke. This means that the drug concentration in the body that results from usual dosage regimens of most drugs is well below the Km of the elimination process with certain exceptions such as phenytoin & alcohol 3. When Km ˂˂ C Then Km approaches to zero, So Km+C=C. Equn 1 becomes − 𝑑𝑐 𝑑𝑡 = 𝑉𝑚𝑎𝑥 … … . . 𝑒𝑞𝑛 4 The above equn describes a zero order process means the rate process occurs at a constant rate Vmax and is independent of drug concentration. e.g. metabolism of ethanol
- 16. ESTIMATION OF Km& Vmax Processes like metabolism, renal tubular secretion and biliary excretion can be easily defined by assumption of 1 compartment kinetics The values of Km & Vmax can be calculated from eqn 1 by plasma concentration data collected from i.v. bolus admn On integration of eqn 1 and then conversion to log form we get 𝑙𝑜𝑔 𝐶 = log 𝐶0 + (𝐶0−𝐶) 2.303 𝐾𝑚 − Vmax 2.303 𝐾𝑚 ……………….(eqn 5)
- 17. On plotting semiloggraph b/w C and t , we get curve with terminal linear portion having slop Vmax 2.303 𝐾𝑚 and on back extrapolation Y intercept becomes log 𝐶0 . SO, equn for above line will be 𝑙𝑜𝑔 𝐶 = log 𝐶0 + Vmax 2.303 𝐾𝑚 ……………….(eqn 6)
- 18. At lowplasma conc. Equn 5 &6 are identical. Equating the both eqns and on simplification, we get: (𝐶0−𝐶) 2.303 𝐾𝑚 = log 𝐶0 𝐶0 …………(equn 7) value of kmcan be obtained from above equn and Vmax can be computed by substituting the value of km in the slope value
- 19. DOUBLE RECIPROCAL PLOT/LINEWEAVER- BURKEPLOT It the alternative approach for calculation of Vmax & Km Using reciprocal of equn 1, we get 1 𝑑𝑐/𝑑𝑡 = 𝐾𝑚 𝑉𝑚𝑎𝑥 𝐶𝑚 + 1 𝑉𝑚𝑎𝑥 ……….(equn 8) Where, Cm= plasma conc at mid point of sampling In plot b/w 1/(dc/dt) V/S 1/Cm yields straight line with slope= Km/Vmax and y-intercept= 1/Vmax
- 20. Lineweaver-Burke plotis not reliable as points are more clustered Other reliable plots are Hanes-Woolf Plot & Woolf-Augustinsson-Hofstee Plot
- 21. CALCULATION OF Km&Vmax STEADY- STATE CONCENTRATION • If drug is administered for constant rate IV infusion/ in a multiple dosage regimen, the steady-state conc. is given in terms of dosing rate (DR): DR = CssClT • If the steady-state is reached, then the dosing rate = the rate of decline in plasma drug conc. & if the decline occurs due to a single capacity-limited process then above equn. become as: • From a plot of Css v/s DR, a typical curve having a shape of hocky-stick will be obtained DR= 𝑉𝑚𝑎𝑥 𝐶𝑠𝑠 𝐾𝑚 +𝐶𝑠𝑠 ……………..equn…1 …………………equn.. 2
- 22. Curve for drugwith nonlinear kinetics obtained by plotting the steady state concentration V/S dosing rate
- 23. 1.Lineweaver-Burke Plot 2.Direct LinearPlot 3.Graphical Method
- 24. ……………….. (3) # Lineweaver-Burk Plot Onreciprocating of eq. (2) we get 1 𝐷𝑅 = 𝐾𝑚 𝑉𝑚𝑎𝑥 𝐶𝑠𝑠 + 1 𝑉𝑚𝑎𝑥 On plotting 1/DR against 1/Css, a straight line will be obtained slope Km/Vmax & intercept 1/Vmax
- 25. Lineweaver-Burk Plot forestimation of Km and Vmax at steady-state concentration of drug
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- 28. For estimation ofKm & Vmax rearranging eq. (2) In graph DR is plotted against DR/Css, a straight line is obtained with slope – KM& y - intercept Vmax. • KM& Vmax can be estimated by simultaneous eq. as ……………….. (2) ……………….. (5) …………….…...(4) DR= 𝑉𝑚𝑎𝑥 𝐶𝑠𝑠 𝐾𝑚 +𝐶𝑠𝑠 We get DR= Vmax _ 𝐾𝑚 𝐷𝑅 𝐶𝑠𝑠 …………………….(3) DR1= 𝑉𝑚𝑎𝑥 𝐶𝑠𝑠1 𝐾𝑚 +𝐶𝑠𝑠1 DR2= 𝑉𝑚𝑎𝑥 𝐶𝑠𝑠2 𝐾𝑚 +𝐶𝑠𝑠2
- 29. • • By substitutingvalues of DR1, DR2, Css1& Css2we get value of KM& from KMwe can found value of Vmaxat steady-state concentration. • From experimental observations, it shows that KMis much less variable than Vmax. ……………….. (7) On solving the equations, we get Km= 𝐷𝑅2−𝐷𝑅1 𝐷𝑅1 𝐶𝑠𝑠1 − 𝐷𝑅2 𝐶𝑠𝑠2 if value of Km of any drug is known earlier, there is no need of calculation of 2 Css values , so single value of Css can be used to calculate Vmax