Noncompartment Model - Pharmacokinetics

1. Grcp CVS Noncompartment Model - Pharmacokinetics Dr C. V. S. Subrahmanyam Principal Gokaraju Rangaraju College of Pharmacy Hyderabad

2. Grcp CVS Noncompartment Model - Pharmacokinetics Objectives of this session The participant shall be able to: • Explain the concepts of noncompartment • model • Explain the differences between • compartment and noncompartment models • Describe different pharmacokinetic • parameters in noncompartment model

3. Grcp CVS Noncompartment Model - Pharmacokinetics Noncompartmen model pharmacokinetics is a new approach devised to study the time course of drug in the body based on the statistical moment theory Model independent method Overcomes some of the drawbacks associated with classical compartment modeling Peak plasma drug concentration, Cmax Time of peak concentration, tmax Area under the curve, AUC

4. Grcp CVS Noncompartment Model - Pharmacokinetics Cmax Graphic method Equation: Cmaxis a function of several factors F KaD Cmax=(e-k10tmax – e-katmax) V1(ka – k10)

5. Grcp CVS Noncompartment Model - Pharmacokinetics Cmax First point Cmax It raises a question about the measurement of true Cmax, because of insufficient early sampling times It requires a carefully chosen pilot study Early time points between 3 to 15 minutes Followed by additional sample collection (two to five) in the first hour

6. Noncompartment Model - Pharmacokinetics Grcp CVS tmax Graphic method Eq: tmax is a function of several factors 2.303 log (ka /k10) tmax = (ka – k10)

7. Grcp CVS AUC Area of one trapezoid = (1/2)(Cn-1 + Cn)(tn – tn-1) Area under the curve, AUC = (areas of the trapezoids)

8. Noncompartment Model - Pharmacokinetics Grcp CVS AUC

9. Grcp CVS Noncompartment Model – AUC Ct* [AUC]0 = [AUC]0t + Z Where Ct* = last measurable Ct, g/ml Z = termination elimination rate constant, h-1 Elimination rate constant is calculated separately

10. Grcp CVS Noncompartment Model - Pharmacokinetics Applications Useful for estimating certain pharmacokinetic parameters without specifically referring to any models Estimating PK parameters Clearance Bioavailability Apparent volume of distribution Fraction of dose of drug absorbed Mean absorption time Mean resident time, Average plasma steady state conc. of drug or its metabolite

11. Grcp CVS Noncompartment Model - Pharmacokinetics Advantages Derivation of PK parameters is easy, because of simple algebraic equations Mathematical treatment remains same, for drug or metabolite, provided elimination follows first order kinetics Drug disposition kinetics need not be described in detail

12. Grcp CVS Noncompartment Model - Pharmacokinetics Disadvantages a) Information regarding plasma drug concentration-time profile is expressed as an average b) Generally not useful for describing the time course of drug in the blood c) It is applicable only for linear pharmacokinetics

13. Grcp CVS Noncompartment and Compartment models – Comparison

14. Grcp CVS Noncompartment and Compartment models – Comparison

15. Grcp CVS Noncompartment Model – Statistical Moment Theory Approach is based on the statistical moment theory Categorisation of moments Zero Moment Zero moment of a drug concentration in plasma versus time curve is referred to as the total area under concentration from zero to infinity, or simply AUC [AUC]0 = C dt

16. Grcp CVS Noncompartment Model – Statistical Moment Theory Area of trapezoid = (1/2)(Cn-1 + Cn)(tn – tn-1) Area under the curve, AUC = (areas of the trapezoids) Ct* [AUC]0 = [AUC]0t + Z Where Ct* = last measurable Ct, g/ml Z = termination elimination rate constant, h-1 Elimination rate constant is calculated separately

17. Grcp CVS Noncompartment Model – Statistical Moment Theory Applications Used for calculating bioavailability and drug clearance First Moment First moment of a plasma drug concentration - time profile is referred to as mean residence time (MRT) [AUMC]0  t x C. dt MRT = = [AUC]0  C.dt

18. Grcp CVS Noncompartment Model – Statistical Moment Theory Area of one trapezoid Area under the curve, AUC t*Ct*C* [AUC]0 = [AUC]0t + + ZZ2 Where Ct* = last measurable Ct, g/ml Z = termination elimination rate constant, h-1 Elimination rate constant is calculated separately

19. Grcp CVS Noncompartment Models – Analysis I.v. bolus injection – Calculation of AUC and AUMC

20. Grcp CVS Noncompartment Models – Analysis I.v. bolus injection - AUC

21. Grcp CVS Noncompartment Models – Analysis I.v. bolus injection - AUMC

22. Grcp CVS Noncompartment Models – Analysis Oral product - Calculation of AUC and AUMC

23. Grcp CVS Noncompartment Models – PK Parameters Oral product - AUC

24. Grcp CVS Noncompartment Models – PK Parameters Oral product - AUMC

25. Grcp CVS Noncompartment Model – Statistical Moment Theory Second Moment Second moment is referred to as variance of the mean residence time (VRT) of the drug in the body t2.C dt (1–MRT)2 C dt VRT = = C dt AUC Higher moments are prone to unacceptable level of errors

26. Grcp CVS Noncompartment Models – PK Parameters Mean Residence Time – Half Life Mean residence time (MRT) defined as the average amount of time spent by the drug in the body before being eliminated AUMC  t x C. dt MRT = = AUC  C.dt MRT represents the time for 63.2% of drug eliminated when given i.v. bolus injection It is analogous to plasma elimination half life, t1/2, i.e., 50% elimination

27. Grcp CVS Noncompartment Models – PK Parameters Mean Residence Time – Half Life Like half life, MRT is a function of both distribution and elimination 1 MRT = k10 0.693 Plasma elimination half life, t1/2 = k10 Plasma elimination half life, t1/2 = 0.693MRT In two compartment model, concept of MRT would be still useful, because of non compartment model

28. Grcp CVS Noncompartment Models – PK Parameters Mean Residence Time – Half Life MRTiv is used for comparison. For eg: following constant rate of infusion T MRTiv = MRTinst - 2 Where T = duration of infusion, h

29. Grcp CVS Noncompartment Models – PK Parameters Apparent Volume of Distribution at Steady State Apparent volume of distribution (V1ss)is independent of drug elimination AUMC V1ss = doseiv (AUC)2 This equation is applicable to i.v. bolus administration It solely reflects the anatomic space occupied by the drug and the relative degree of drug binding in blood and extravascular space

30. Grcp CVS Noncompartment Models – PK Parameters Apparent Volume of Distribution at Steady State If drug is given by short term constant rate i.v. infusion Infused dose (AUMC) V1ss = (AUC)2 Infused dose x  V1ss = 2(AUC) Since infused dose is equal to R0 R0 x  (AUMC) R0 2 V1ss = = 2(AUC)2 2(AUC)

31. Grcp CVS Noncompartment Models – PK Parameters Drug Clearance (Cl) Clearance is defined as the ratio of the dose after a single i.v. injection to the total area under the drug concentration – time curve After a single i.v. bolus injection Doseiv Cl = AUC Since infused dose is equal to R0 R0 Cl = C1ss

32. Grcp CVS Noncompartment Models – PK Parameters Mean Absorption Time (MAT) - Drug Absorption MAT is defined as the differences in mean residence time (MRT) after different modes of administration MAT = MRTni – MRTiv MRTni = mean residence time of drug by non- instantaneous route, h MRTiv = mean residence time of drug by i.v. bolus injection, h Same equation is used for i.m. injection Absorption follows first order kinetics

33. Grcp CVS Noncompartment Models – PK Parameters Mean Absorption Time (MAT) 1 MAT = ka 0.693 Absorption half life, t1/2 = ka Absorption half life, t1/2 = 0.693MAT When absorption follows zero order T MAT = 2 T = time over which absorption takes place, h

34. Grcp CVS Noncompartment Models – PK Parameters MAT - Applications Used for the comparison of dosage forms Eg: comparison of furosemide dosage forms

35. Grcp CVS Noncompartment Models – PK Parameters

36. Grcp CVS Noncompartment Models – PK Parameters Steady State Plasma Drug Concentration The C1ss is a function of the effective rate of dosing and total body clearance of the drug in a patient In continuous infusion Ro C1ss = Cl In multiple dosage regimen AUCss Cavss =  When absorption follows zero order

37. Grcp CVS Noncompartment Models – PK Parameters Steady State Plasma Drug Concentration Average plasma drug concentration at steady state, Cavss F x dosing rate Cavss= Cl If a drug is given in a dose of 400 mg every 8 hours, dosing rate is 400/8, i.e., 50 mg/hour

38. Grcp CVS Noncompartment Models – PK Parameters Predicting the Time to Steady State Time required for the drug to reach steady state, i.e., 99%, takes 6.65 half lives. • In extravascular route (or prolonged release drug products), the time required to attain ss takes longer than predicted by biological half life • In multicompartment disposition, time required to attain to ss is shorter than that predicted by terminal half life

39. Grcp CVS Noncompartment Models – PK Parameters Predicting the Time to Steady State In noncompartment models, when the drug is administered repetitive dosing, fss AUC0’ fss= AUC AUC = area under the curve in single dose Bioavailability Bioavailability refers to the fractional dose of a dosage form reaches systemic circulation For i.v. bolus injection, bioavailability is referred as unity (=1)

40. Grcp CVS Noncompartment Models – PK Parameters Bioavailability Bioavailability (F) of a dosage form AUCoralDiv Absolute bioavailability, F = AUCivDoral Equation assumes equal clearances in oral and i.v. doses Relative bioavailability, Fr, may be expressed by comparing the zero moments of a product with a standard product

41. Grcp CVS Noncompartment Models – PK Parameters Fraction of Drug Metabolised, fm Fraction of a drug metabolized, fm, is equal to ratio of zero moments of the metabolite, administered the drug to the metabolite directly AUCx1 Fraction metabolized, fm= AUC1 AUCx1 = AUC of metabolite, when drug is administered by i.v. bolus injection, zero to infinity time, g.h/ml AUC1 = AUC of metabolite, when metabolite is administered by i.v. bolus injection,

42. Grcp CVS Noncompartment Models – PK Parameters Fraction of Drug Metabolised, fm Metabolite is administered in equimolar i.v. dose

43. Grcp CVS Thank you

44. Grcp CVS Thank you