nonlinear pharmacokinetic modelling approach

nonlinear pharmacokinetic modelling approach

1. Non-linear Pharmacokinetics:cause of non-linearity

2. Pharmacokinetics It is a science dealing with the biological fate of a drug and/or its metabolites in animal/human body with the help of mathematical modelling. It involves the kinetics of drug-ADME A bsorption D istribution M etabolism E xcretion

3. Linear Pharmacokinetics At therapeutic doses, the change in amount of drug in body or its plasma concentration due to ADME of the drug is PROPORTIONAL to its DOSE, whether administered as a single dose or as multiple doses. Rate processes follow First Order/ Linear Kinetics. Pharmacokinetic parameters (k a , k, t 1/2 , Cl, etc) remain unaffected by Dose. Pharmacokinetics is DOSE INDEPENDENT.

4. Non linear pharmacokinetics The rate process of a drug’s ADME are dependent upon carrier or enzymes that are

5. In such cases, an essentially first-order kinetics transform into a mixture of first-order and zero-order rate processes and the pharmacokinetic parameters change with the size of the administered dose. The pharmacokinetics of such drugs are said to be dose-dependent. Drug concentrations in the blood can increase rapidly once an elimination process is saturated . Nonlinear pharmacokinetics

6. CHARACTERISTICS…. Nonlinear elimination. Elimination half-life increases with an increase in dose due to enzyme saturation. Elimination half-life decreases with an increase in dose due to enzyme induction. Bioavailability is not directly related to AUC. Coadministration of drugs can induce competitive inhibition. Change in metabolite concentration with dose.

7. Linear V/S Nonlinear Pharmacokinetics

8. CAUSES OF NONLINEARITY Drug Metabolism Drug Distribution Drug Absorption Drug Excretion

9. F, Ka, Cmax AUC Drug absorption

10. Drug absorption

11. Drug Distribution Saturation of binding sites on plasma proteins e.g. phenylbutazone and naproxen. Saturation of tissue binding sites e.g. thiopental and fentanyl. Vd Vd In both cases, the free plasma drug concentration increases

12. Drug Distribution

13. Drug Metabolism

14. Drug Metabolism CAUSE EXAMPLES Cl h ( Hepatic Clearance ) Saturable metabolism Phenytoin, salicyclic acid, theophylline, valproic acid   Enzyme inhibition Metronidazole Enzyme induction Carbamazepine Decreased hepatic blood flow Propranolol, verapamil Hepatotoxicity Acetaminophen

15. Drug Excretion CAUSE EXAMPLES Cl r (Renal Clearance) Active secreation (saturable) Penicillin G Active reabsorption(saturable) Ascorbic acid Change in urine pH Salicyclic acid Saturable plasma protein binding Disopyramide Nephrotoxicity Aminoglycosides Increase in urine flow Theophylline

16. Drug Excretion

17. RECOGNITION OF NON LINEARITY Normalisation with respect to Initial Drug Concentration Linear pharmacokinetics Non linear pharmacokinetics

18. Plot of Area under Curve V/S Drug Dose RECOGNITION OF NON LINEARITY

19. When concentration that results from the dose is not proportional to that dose and/or the rate of elimination of the drug is not proportional to the concentration, the drug is said to exhibit non-linear kinetics RECOGNITION OF NON LINEARITY

20. The MRT v/s dose graph shows a dose dependent trend (either increasing or decreasing). This suggests non linearity. RECOGNITION OF NON LINEARITY Linear Pharmacokinetics Nonlinear Pharmacokinetics

21. Plasma Protein & Tissue Binding As A Function of Dose RECOGNITION OF NON LINEARITY Linear Binding Mixed order Non linear binding(decreasing with increasing dose)

22. If the magnitude of some or all of the parameters change with dose (and especially there are dose related trends) then non-linear pharmacokinetic are highly probable RECOGNITION OF NON LINEARITY

23. Effect of nonlinearity on AUC Introduction of nonlinear pharmacokinetics Linear vs nonlinear pharmacokinetics Causes of nonlinearity Tests for determining nonlinearity Michaelis-menten equation Determination of Km & Vm

24. LINEAR vs NONLINEAR PHARMACOKINETICS LINEAR NONLINEAR

25. CAUSES OF NONLINEARITY Saturable Absorption Saturable Distribution Saturable Metabolism Saturable Excretion Solubility Issues Mixed-order Kinetics

26. VARIOUS PLOTS IN NON LINEAR KINETICS

27. DETECTION OF NONLINEARITY

28. SATURABLE DRUG ABSORPTION Sources Cause of non linearity Affected parameters Examples When absorption is solubility or dissolution rate-limited Saturated solution formed at higher doses & rate of absorption attains constant value F, Ka, Cmax & AUC ↓ Griseofulvin, Chlorothiazide, Danazol When absorption involves carrier-mediated transport systems Saturation of the transport system at higher doses F, Ka, Cmax & AUC ↓ Riboflavin, Ascorbic acid, Cyanocobalamin When presystemic gut wall or hepatic metabolism attains saturation Saturation of presystemic metabolism of drugs at high doses F, Ka, Cmax & AUC ↑ Propranolol, Hydralazine and Verapamil Other causes of nonlinearity in drug absorption are changes in gastric emptying and GI blood flow and other physiologic factors .

29. DRUG ABSORPTION Drug Example : Griseofulvin : Limited solubility/ dissolution in G.I.T Poorly water soluble drug (10 mg/L) Less proportion of the drug is being dissolved and absorbed with the higher dose F decreases as the dose increases t max remains same

30. 2. DRUG DISTRIBUTION Free plasma drug conc. V d V d

31. 3. DRUG METABOLISM CAUSE EXAMPLES AFFECTED PARAMETERS A. Saturable metabolism Phenytoin, Salicylic acid, Theophylline, Valproic acid CL H (hepatic Clearance) C SS (steady state conc.) B. Enzyme inhibition Metronidazole CL H C SS C. Enzyme induction Carbamazepine C L H C SS D. Decreased hepatic blood flow Propranolol, Verapamil CL H E. Hepatotoxicity Acetaminophen CL H The nonlinear kinetics of most clinical importance is capacity-limited metabolism since small changes in dose administered can produce large variations in plasma concentration at steady-state.

32. 4. DRUG EXCRETION The two active processes in renal excretion of a drug that are saturable are – CL R CL R Other sources : Increase in urine flow, (e.g. Theophylline) changes in urine pH, (e.g. Salicylic acid) Nephrotoxicity, (e.g. Aminoglycosides) saturation of binding sites, (e.g. Disopyramide) Biliary secretion (e.g. Iodipamide)

33. Michaelis Menten equation

34. One compartment open model-intra venous bolus injection-drug elimination by saturated kinetics

35. Determination of Km and V

36. Direct plot method

37. Relationship between the area under the curve and the administered dose when drug follows nonlinear kinetics

38. DOSE CALC. WITH NONLINEARITY Phenytoin doses based on population characteristics may not achieve optimal serum concentrations due to pharmacokinetic variability and nonlinear kinetics. Therefore phenytoin levels are measured for most patients to ensure efficacy and safety. Patient outcomes (seizure frequency, side effects, etc.) should also be monitored. To adjust phenytoin doses based on serum concentrations, clinicians should use the simplest and most effective method. Several methods can estimate new doses or parameters with one steady-state concentration 1. The empiric dosing method: It is a common technique that uses typical parameters and can work with one or more concentrations. 2 . The GravesCloyd method: This uses one concentration and a power function, but it is complex. 3. The VozehSheiner (Orbit Graph) method : This method uses one concentration and a special graph with Bayesian concepts, but it is time consuming. To adjust phenytoin doses, sometimes phenytoin pharmacokinetic constants are computed for a patient using two or more steady-state concentrations from different doses. Two graphical methods can calculate Vmax and Km for phenytoin, but they are difficult and slow. These are 1. The Mullen method: This method uses the same graph as the VozehSheiner method, but finds the patient’s own MichaelisMenten parameters instead of Bayesian estimates.

39. Conclusion Nonlinear pharmacokinetics is a complex but important topic in pharmacology and pharmacokinetics, as it affects the relationship between the dose, concentration, and effect of many drugs. In this chapter, we have covered the following aspects of nonlinear pharmacokinetics: ● The general concepts and characteristics of nonlinear pharmacokinetics, such as the deviation from the first-order kinetics, the dose-dependent changes in pharmacokinetic parameters, and the increased variability and unpredictability of drug response. ● The factors that can cause nonlinearity in drug absorption, distribution, metabolism, or excretion, such as saturable enzyme kinetics, capacity-limited protein binding, autoinduction or inhibition of drug metabolism, and nonlinear absorption or elimination processes. ● The MichaelisMenten equation and its derivation from the enzyme kinetics theory, and the methods to determine the K m and V max values for a drug that follows the MichaelisMenten kinetics, such as graphical methods, empirical methods.