Nonlinear Pharmacokinetics

1. Quantitative Pharmacokinetics Nonlinear Pharmacokinetics Dr. Chalet Tan

2. Learning Objectives • profiles of nonlinear kinetics • sources and effects of dose dependency on ADME • Michaelis-Menten equation and parameters (Vmax, Km) for capacity-limited metabolism

3. Case Study An epileptic patient who has not responded to phenytoin after 2 weeks on 300 mg/day is observed to have a plasma concentration of 4 mg/ml. Twenty days after the daily dose is subsequently increased to 500 mg/day, the patient develops severe toxicities. The plasma concentrations of phenotoin is now 36 mg/L.

4. Review of Linear Pharmacokinetics • ADME all obeyfirst-order kinetics • Pharmacokinetic parameters, e.g. elimination half-life (t1/2), the elimination rate constant (k), the apparent volume of distribution (V) and the clearance (CL) remain constant. • Plasma drug concentration at a given time and AUC are directly proportional to the dose. • Concentrations of drug in plasma and tissues are below protein binding saturation , i.e. fu and fuTremain constant.

5. 100 mM 10 mM 100 mg 1 mM 10 mg 1 mg 1 h Review of Linear Pharmacokinetics i.v. bolus i.v. bolus Log C normalized by dose Log C 1 mg 1 h time time • Drug plasma concentrations are proportional to the dose. • Drug plasma concentration-time profiles are superimposable when normalized to the dose.

6. 0.1 mM 25 mg 5 mg 1 mg Review of Linear Pharmacokinetics p. o. p. o. Log C Log C 2.5 mM normalized by dose 0.5 mM 0.1 mM 1 mg tmax tmax time time • Drug plasma concentrations are proportional to the dose. • tmax remains unchanged. • Drug plasma concentration-time profiles are superimposable when normalized to the dose.

7. Review of Linear Pharmacokinetics Cp or AUC VD or CL or t1/2 Dose Dose

8. 800 mM 8 mM 20 mM 2 mM 1 mM 1 mM 1 h Nonlinear Pharmacokinetics i.v. bolus i.v. bolus 100 mg normalized by dose Log C Log C 10 mg 100 mg 1 mg 1 mg 10 mg 1 h time time • Drug plasma concentrations are not proportional to the dose. • Drug plasma concentration-time profiles are not superimposable when normalized to the dose.

9. p. o. Log C 1 mM 0.5 mM 1 mg 0.1 mM 10 mg 100 mg time Nonlinear Pharmacokinetics p. o. 10 mM 5 mM Log C normalized by dose 1 mM 100 mg 10 mg 1 mg time • Drug plasma concentrations are not proportional to the dose. • tmax may or may not change. • Drug plasma concentrations are not superimposable when normalized to the dose.

10. Nonlinear Pharmacokinetics F, V, CL or t1/2 Cp or AUC linear linear Dose Dose

11. Common Sources for Nonlinear Pharmacokinetics

12. Linear vs. Nonlinear Pharmacokinetics Nonlinear Linear (dose-dependent) (dose-independent) • at least one of the ADME processes is saturable. • ≥1 PK parameters are dose-dependent. • AUC is disproportional to the dose. • Concentration vs. time profile is not superimposable for different doses. • ADME all obey first-order kinetics. • PK parameters (CL, V, F, Ka, and t1/2) are constant. • AUC is directly proportional to the dose. • Concentration vs. time profile is superimposable for all doses.

13. Most Common Sources for Nonlinear Pharmacokinetics • Capacity-limited oral absorption (F) • Capacity-limited metabolism (CLH ) • Saturable protein binding (CLH, CLR, V) • Capacity-limited excretion(CLR )

14. Capacity-Limited Oral Absorption (F) • limited dissolution/solubility as the oral dose increases • saturabletransport across the intestinal mucosa as the oral dose increases • saturable first-pass metabolism in the intestinal epithelium (gut wall) and/or liver as the oral dose increases

15. e. g. normalized to the dose • limited dissolution/solubility in the GI tract • - Griseofulvin is poorly water-soluble (10 mg/L). • - Less proportion of the drug is being dissolved and absorbed with the higher dose. • Fdecreases as the dose increases. • tmax remains the same.

16. e. g. 375 mg 750 mg 1500 mg 3000 mg • Saturable transport across the intestinal epithelium • - Amoxicillin is actively transported by peptide transporter in the small intestine. • - The active transport becomes saturated as the dose increases. • Fdecreases as the dose increases. • tmax remains the same.

17. e. g. • Saturable first-pass metabolism • - Nicardipine is metabolized by CYP3A4 in the intestinal epithelium and hepatocytes. • - First-pass metabolism is saturated as the dose increases. • Fincreases as the dose increases.

18. e. g. • Saturable first-pass metabolism

19. Saturable Drug-Plasma Protein binding (CL,V) • Drug-plasma protein binding is saturable The saturation drug concentrations for binding with plasma albumin and a1-acid glycoprotein are ~ 600mM and 15mM, respectively. • May increase CLH and/or CLR • May increase V • May be difficult to identify due to effect on both V and CL

20. 2 g/day • saturable plasma protein binding • - AUC and Cp of trandolaprilat do not increase proportionally with D; Cp does not accumulate with multiple doses. • As the dose increases, binding to ACE (angiotensin-converting enzyme) in plasma is saturated. • Trandolaprilat is elminated by glomerular filtration • CLR= fu GFR • As fu increases with higher Cp, CLRincreases.

21. Capacity-Limited Excretion (CLR) • Active secretion and active reabsorption are saturable processes. • Saturated tubular secretion decreases CLR Saturated tubular reabsorption increases CLR CLR = fu GFR + (CLsecretion – CLreabsoption)

22. e. g. When concentration is about lower than 7 mg/L, it could be linear. Since clearance is linear. But once it gets above 7, the clearance rises, which makes it non-linear. • capacity-limited renal excretion CLinulin = GFR p.o. 30-80 mg When Cp above 10 mg/L starts to saturate renal reabs of Vit C. i.v. 1.5-6 g • - Vitamin C is reabsorbed from urine by active transporter. • Tubular reabsorption becomes saturated as Cp increases, i.e. as Cp increases, CLreabsorption (= Ratereabsorption /Cp) decreases. • ClR (=fu GFR –CLreabsorption) approaches GFR (fu=1) as Cp increases.

23. Capacity-Limited Metabolism (CLH ,F) • Enzymatic reactions are saturable. • Saturated hepatic metabolism decreases CLH. • Saturated first-pass metabolism increases F.

24. e. g. • capacity-limited metabolism • - Phenytoin is eliminated by hepatic metabolism only. • - As the dosing rate increases, Cp increases disproportionally. • As the dosing rate increases, hepatic metabolism is saturated and CL decreases. • As the dosing rate increases, it takes longer time to reach steady state.

25. Michaelis-Menten Kinetics Applied to Metabolism n: rate of metabolism Vmax: maximum rate of metabolism Km : Michaelis constant, disassociation constant of ES [S]: drug concentration

26. Michaelis-Menten kinetics Rate of Metabolism is NOT ALWAYS proportional to drug concentrations n Zero order - When [S]= Km , n=1/2 nmax Km is the drug concentration at which half of the active sites on enzymes are occupied. Non linear - When [S]<<<Km , First order [S] Km - When [S] >>>Km ,

27. Rate of metabolic elimination = Michaelis-Menten Kinetics Applied to CLM Rate of elimination = CL x Cp

28. Michaelis-Menten Kinetics Applied to Metabolism n zero-order nmax When Cp<< Km , linear PK non-linear first-order [Drug] Km When Cp>> Km ,

29. Linear vs. Saturable Metabolism nonlinear linear Clearance is independent of Cp CL CL Cp Cp

30. Rate of metabolic elimination = Michaelis-Menten Kinetics Applied to Metabolism At the steady-state following multiple dosing ,

31. Linear vs. Saturable Metabolism linear nonlinear CSS CSS D/t D/t

32. Most Common Sources for Nonlinear Pharmacokinetics • Capacity-limited oral absorption (F) • Capacity-limited metabolism (CLH ) • Saturable protein binding (CLH, CLR, V) • Capacity-limited excretion(CLR ) 32

33. Case Study At a daily intake of 75 mg of ascorbic acid (vitamin C), the steady-state plasma concentration is 9 mg/L, whereas at a daily dose of 10,000 mg, the steady-state concentration is about 19 mg/L in a healthy volunteer. The renal clearance of ascorbic acid is less than 0.5 ml/min at the plasma concentration of 9 mg/ml, whereas the renal clearance is 21 ml/min at 19 mg/L. Vitamin is absorbed by passive facilitated diffusion in the small intestine, and undergoes tubular reabsorption in the kidney.

34. Maintenance Dose Selection for Phenytoin • Phenytoin is eliminated by hepatic metabolism(CYP2C9) only. • Variability in Vmax and Km values in patients causes a wide range in the effective doses needed to achieve therapeutic levels. therapeutic range= 10-20 mg/ml = 10-20 mg/L

35. Rate of metabolic elimination = Michaelis-Menten Kinetics Applied to Metabolism At the steady-state following multiple dosing ,

36. Slope = m = y2-y1 x2-x1 * y * * x * Slope = Vmax /F -b Css Css / Dose rate -Km How to Obtain Vmax/F and Km y= m x - b

37. The Direct Linear Plot Vmax/F dosing rate 2 dosing rate 1 Km -C2 -C1 Biochem J, 139:715-20 (1974)

38. Maintenance Dose Selection for Phenytoin A patient has been taking phenytoin (PHE) 150 mg b.i.d for 4 months. His plasma levels of PHE averaged 5 mg/L on this dose. Adjustment in dose to 250 mg b.i.d eventually led to a new plateau level of 20 mg/L. Assuming true steady state, strict patient compliance and that the measured plasma concentrations represent average levels over the dosing interval. a) use a graphical method to estimate the patient's operative Vmax/F and Km values; b) estimate a daily dose which should provide a steady-state plasma level of 12 mg/L.

39. Vmax/F dosing rate 2 dosing rate 1 Rate of metabolic elimination = Km -C2 -C1 Drug-Protein Binding Nonlinear Pharmacokinetics Clearance Concepts * * Slope=Vmax/F Css Css / Dose rate -Km