Concept of nonlinear pharmacokinetic

non linear pharmacokinetics

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 K m and V max Estimation of K m and V max 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 Fraction of drug absorbed/unabsorbed Ka: absorption rate constant K E : Elimination rate constant V d : volume of distribution CL R : Renal clearance CL H : 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 rate process 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 such drugs are said to be dose- dep e n d e n t . Te r m s s y non y m ous w ith it a r e m ix e d - orde r , nonlinear and capacity-limited kinetics.

6. Tests for detection of nonlinearity in pharmacokinetics 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 non linearity

8. Parameters affected will be F, Ka, Cmax and AUC. DRUG ABSORPTION

9. In both cases, the free plasma conc. Increases but Vd increases only in the former case whereas it decrease in the later. DRUG DISTRIBUTION

10. Saturation of enzymes results in decreased hepatic clearance and therefore increased steady state concentration. DRUG METABOLISM

11. 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 K M = C: under this situation , eq I reduces to 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 - = rate of decline of drug concentration with time = theoretical maximum rate of the process = Michaelis constant   There are 3 situations can be considered upon the values of Km and C ………  

14. PLOT OF MICHAELIS MENTON EQUAION

15. • 2. When Km ˃˃ C Then C approaches to zero, So Km+C = Km Equation 1 becomes 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 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 K m & V max 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 + ……………….( eqn 5 )  

17. On plotting semilog graph b/w C and t , we get curve with terminal linear portion having slop and on back extrapolation Y intercept becomes log . SO, equn for above line will be + ……………….( eqn 6)  

18. At low plasma conc. Equn 5 &6 are identical. Equating the both eqns and on simplification, we get: = log …………( 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 -Burke plot It the alternative approach for calculation of Vmax & Km Using reciprocal of equn 1, we get = ……….( 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 plot is not reliable as points are more clustered Other reliable plots are Hanes-Woolf Plot & Woolf- Augustinsson - Hofstee Plot

21. CALCULATION OF K m & V max 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 = C ss Cl T • 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 eq un . become as: From a plot of C ss v / s DR, a typical curve having a shape of hocky -stick will be obtained DR=   …………….. equn …1 …………………equn..2

22. Curve for drug with nonlinear kinetics obtained by plotting the steady state concentration V/S dosing rate

23. Graphical E stimation of K m & V max Lineweaver -Burke Plot Direct Linear Plot Graphical Method

24. ……………….. (3) # Lineweaver -Burk Plot On reciprocating of eq. (2) we get   On plotting 1/DR against 1/ Css , a straight line will be obtained slope Km/ Vmax & intercept 1/ Vmax

25. Lineweaver -Burk Plot for estimation of Km and Vmax at steady-state concentration of drug

26. Direct Linear Plot

27. DR DR/C ss # Graphical Method

28. For estimation of Km & Vmax rearranging eq. (2 ) In graph DR is plotted against DR/Css, a straight line is obtained with slope –K M & y - intercept Vmax . K M & Vmax can be estimated by simultaneous eq. as ……………….. ( 2 ) ……………….. ( 5 ) …………….…...( 4 ) DR=   We get DR = Vmax _ …………………….(3)   DR1=   DR2=  

29. • By substituting values of DR 1 , DR 2 , C ss1 & C ss2 we get value of K M & from K M we can found value of V max at steady-state concentration. From experimental observations, it shows that K M is much less variable than V max . ……………….. (7) On solving the equations, we get Km=   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