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nonlinear pharmacokinetic modelling approach
nonlinear pharmacokinetic modelling approach
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nonlinear pharmacokinetic modelling approach
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- 2. Pharmacokinetics It is ascience 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 Absorption Distribution Metabolism Excretion
- 3. Linear Pharmacokinetics At therapeuticdoses, 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 (ka, k, t1/2, 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 Enzyme or carrier Substrate specific Definite capacities Susceptible to saturation
- 5. In suchcases, 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…. 1. Nonlinear elimination. 2.Elimination half-life increases with an increase in dose due to enzyme saturation. 3. Elimination half-life decreases with an increase in dose due to enzyme induction. 4. Bioavailability is not directly related to AUC. 5. Coadministration of drugs can induce competitive inhibition. 6. Change in metabolite concentration with dose.
- 7. Linear V/S Nonlinear Pharmacokinetics Linear (Dose-independent) AllADME processes obey first-order kinetics. PK parameters (Cl, Vd, F, Ka, and t1/2) are constant. AUC is directly proportional to the dose. Concentration vs. time profile (corrected w.r.t. dose) is superimposable for all doses. Nonlinear (Dose-dependent) At least one of the ADME processes is saturable. PK parameters are dose- dependent. AUC is disproportional to the dose. Concentration vs. time profile is not superimposable for different doses.
- 8. CAUSES OF NONLINEARITY Drug Metabolism Drug Distribution DrugAbsorption Drug Excretion
- 9. When presystemic gutwall or hepatic metabolism attains saturation e.g. propranolol, hydralazine and verapamil. When absorption is solubility or dissolution rate-limited. e.g. griseofulvin When absorption involves carrier- mediated transport systems . e.g. absorption of riboflavin, ascorbic acid, cyanocobalamin, etc F, Ka, Cma x AUC Drug absorption
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- 11. Drug Distribution • Saturationof 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
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- 14. Drug Metabolism CAUSE EXAMPLESClh (Hepatic Clearance) Saturable metabolism Phenytoin, salicyclic acid, theophylline, valproic acid Enzyme inhibition Metronidazole Enzyme induction Carbamazepine Decreased hepatic blood flow Propranolol, verapamil
- 15. Drug Excretion CAUSE EXAMPLESClr (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
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- 17. RECOGNITION OF NON LINEARITY Normalisationwith respect to Initial Drug Concentration 0 20 40 60 80 100 120 0 20 40 60 80 100 120 140 Series1 Series3 Series5 Series7 Time (h) C/C0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 140 Series1 Series3 Series5 Series7 Time (h) C/C0 500mg 100m g 325m g 250m g Linear pharmacokinetics Non linear pharmacokinetics
- 18. Plot of Areaunder Curve V/S Drug Dose RECOGNITION OF NON LINEARITY
- 19. When concentration thatresults 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/sdose graph shows a dose dependent trend (either increasing or decreasing). This suggests non linearity. RECOGNITION OF NON LINEARITY 0 100 200 300 0.54 0.56 0.58 0.60 0.62 0.64 Dose (mg) MRT (h) 50 100 150 200 250 300 0.5 0.52 0.54 0.56 0.58 0.6 Dose (mg) MRT (h) 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 magnitudeof 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 nonlinearityon AUC Introduction of nonlinear pharmacokinetics Linear vs nonlinear pharmacokinetics Causes of nonlinearity Tests for determining nonlinearity Michaelis-menten equation Determination of Km & Vm
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- 26. VARIOUS PLOTS INNON LINEAR KINETICS
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- 29. SATURABLE DRUG ABSORPTION SourcesCause 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, Chlorothiazid e, Danazol When absorption involves carrier- mediated transport systems Saturation of the transport system at higher doses F, Ka, Cmax & AUC↓ Riboflavin, Ascorbic acid, Cyanocobala min 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.
- 30. 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 tmax remains same
- 31. 2. DRUG DISTRIBUTION •e.g. Phenylbutazone, Naproxen, Phenytoin, Warfarin A. Saturation of binding sites on plasma proteins • e.g. Thiopental, Fentanyl, Imipramine B. Saturation of tissue binding sites Free plasma drug conc. V d V d
- 32. 3. DRUG METABOLISM CAUSEEXAMPLES AFFECTED PARAMETERS A. Saturable metabolism Phenytoin, Salicylic acid, Theophylline, Valproic acid CLH (hepatic Clearance) CSS (steady state conc.) B. Enzyme inhibition Metronidazole CLH CSS C. Enzyme induction Carbamazepine CLH CSS D. Decreased hepatic blood Propranolol, Verapamil CLH 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.
- 33. 4. DRUG EXCRETION a.Active tubular secretion e.g. Penicillin G b. Active tubular reabsorption e.g. water soluble Vitamins and Glucose 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.
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- 38. One compartment openmodel-intra venous bolus injection-drug elimination by saturated kinetics
- 39. Determination of Kmand V
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- 47. Relationship between the areaunder the curve and the administered dose when drug follows nonlinear kinetics
- 48. DOSE CALC. WITHNONLINEARITY 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.
- 49. Conclusion Nonlinear pharmacokineticsis 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 Vmax values for a drug that follows the MichaelisMenten kinetics, such as graphical methods, empirical methods.