Pharmaceutics II – Stability

1. Chemical Stability of Pharmaceuticals, Kenneth A Connors, Gordon L Amidon, Lloyd Kennon, John Wiley and Sons, 1979. Chemical Kinetics – The Study of Reaction Rates in Solution, Kenneth A Connors, VCH Publishers, Inc., 1990 STABILITY- Vital component of all product development. All about shelf-life • ensures efficacy • - physical eg. release characteristics • - chemical eg. potency • ensures safety • - physical eg. tablet weight / dose-dumping • - chemical eg. degradants • determines storage periods/conditions for formulations Pharmaceutics II – Stability

2. Pharmaceutics II - Stability TWO AREAS1 PHYSICAL stability Appearance All formulation types Disintegration Solid DFs Dissolution Solid DFs Hardness Solid DFs Fryability Solid DFs Caking Semi-Solid DFs Cracking Semi-Solid DFs Redispersion Semi-Solid DFs Clarity Liquids + Injectables Particulate Matter Liquids + Injectables Sterility Liquids + Injectables

3. Pharmaceutics II - Stability 2 CHEMICAL stability Degradation of API’s All Formulation Types Formation of related substances All Formulation Types Possibly toxic

4. Pharmaceutics II - Stability REGISTRATION AUTHORITIES – MCC of SA • Important part of the product registration dossier • Require real-time data for all components of Stability Program for determination of shelf-life. • Example of Stability Program – following slide • Storage conditions - 4°C Depends on Zone - 25°C/60% RH See ICH guidance - 30°C/65% RH (temperate) - 40°C/75% RH (tropical) - 60°C (accelerated)

5. Pharmaceutics II - Stability • Stability conducted in final packaging. • Any changes in formulation/packaging – re-do stability. • Place sufficient packs of product in storage under each condition. • Conditions maintained by Controlled Environment Incubators.

6. Pharmaceutics II - Stability HO General Sample Plan of a Stability Study for Tablets • 25°C/60% RH as above 30°C/65% RH (temperate) as above 40°C/75% RH (tropical) as above 4°C and 60°C (accelerated) abridged

7. Pharmaceutics II - Stability HO Useful Guidelines for Stability Testing • MCC of SA - www.mccza.com (documents) • ICH - International Conference on Harmonisation www.ich.org • FDA - www.fda.gov

8. Pharmaceutics II - Stability What is Shelf-Life • Time taken for any measured parameter to change more than the stated limits allowed Shelf-life for chemical stability: is generally determined by • Time taken for the API to reduce from 100% to 90%. • Time taken to attain unacceptable levels of toxic degradation products • Usually refers to API but can refer to other ingredients. • May need to tighten limits for API’s with lower tolerance limits (eg. Critical doses, esp. toxic deg. prod.).

9. Pharmaceutics II - Stability BASIC CONSIDERATIONS • Stability test results are unique for a specific formulation. 2. Any formulation change may change API stability e.g. mixing processes, compression etc. 3. Must re-assess stability, perhaps with an abridged stability plan. 4. Temperature changes during manufacture/storage can affect stability – v. imp. 5. Changes may occur during transportation e.g. reach high temperatures in trucks, rail wagon. This must be taken into account for shelf-life and storage conditions. 6. Changes in pH can significantly affect stability. Eg. if no buffers are used.

10. Pharmaceutics II - Stability Main Factors • We will consider in detail the two main factors which affect chemical stability: • TEMPERATURE - pertinent to all formulations but particularly for solutions. • pH – pertinent to liquid aqueous formulations

11. Pharmaceutics II - Stability REACTION KINETICS Order of Reaction • Order of Reaction is determined by the molecularity of the reaction. • The O-of-R is the sum of the exponents of the reacting species in the rate equation. • Eg for D + W → P Rate = –d[D] = k2 [D]1 [W]1 dt O-of-R = 1+1=2 (2nd Order) k2 = 2nd order rate constant • Determines the equations which best describe the reaction vs. time profile. • Determines the equations to use for calculation and prediction of stability parameters.

12. Pharmaceutics II - Stability 3 Useful O-of-Rs • Zero Order - independent of concentration • First Order -dependent on 1 reacting species. • Second Order - dependent on 2 reacting species. In pharmaceutics, degradation reactions generally involve two or more reacting species – first or second order. Units of Rate Constants • Second Order - [conc.]-1time-1 • First Order - time-1 • Zero Order - [conc.]time-1

13. Pharmaceutics II - Stability • It is generally assumed that only the concentration of the drug declines with time and that one or more other reacting species such as water or hydrogen ions remains essentially unchanged during the reaction so: • First Order - simplifies to Pseudo Zero Order • Second Order - simplifies to Pseudo First Order

14. Pharmaceutics II - Stability HO Important Kinetic Parameters • t90 - time taken to decline from 100 to 90% i.e. shelf-life • k - degradation rate constant • t½ - half-life ?

15. Pharmaceutics II - Stability HO HYDROLYSIS in Solution • Consider a drug molecule - [D] reacting with - [W] i.e. hydrolysis • collision then rearrangement to products if there is sufficient energy. • [D] + [W] → [P] eg. Ester hydrolyses to Acid and Alcohol • RATE of reaction –d[D] is: dt • Rate is proportional to the number of collisions, so • Rate is proportional to the concentration of reacting species.

16. Pharmaceutics II - Stability HO • As the reaction proceeds [D] and [W] change so • Rate or –d[D]α [D][W] - [ ] of two species - Second Order dt • Rate or –d[D] = k2 [D][W] k2 = 2nd order rate constant dt

17. Pharmaceutics II - Stability HO • If D is in solution and W is in great excess • e.g. 0.1M of D in water where [W] » 55.5M • then [D] to [W] ratio is very high (1:555) so • any change in [W] due to reaction with D will be minute so [W] can be assumed to be constant and the rate of reaction will not be affected by a changing [W]. • Therefore: • Rate or -d[D] = k1 [D] - [ ] of one species - Pseudo First-Order dt • where k1 = k2[W] as [W] is constant • k1 = pseudo first-order rate constant

18. Pharmaceutics II - Stability HO • If [D] in solution also remains constant (such as in a suspension) then: • Rate = k0 - [ ] of no species Pseudo Zero-Order • k0 = pseudo zero-order rate constant • Where k0 = k1[D] = k2[D][W] Units of Rate Constants • Second Order - [conc.]-1time-1 • First Order - time-1 • Zero Order - [conc.]time-1

19. Pharmaceutics II - Stability HO ACID CATALYSED HYDROLYSIS / DEGRADATION in Solution [D] + [H+] → [P] Second Order • In BUFFERED solution where [H+] remains constant the rate of reaction is not affected by a changing [H+]. • Rate = k1 [D] - [ ] of one species - Pseudo First-Order • where k1 = k2[H+] • k1 = pseudo first-order rate constant • H+ can be substituted by OH- for alkali degradation. • E.g. Aspirin - + H2O C6H4(OH)COOH + CH3COOH

20. Pharmaceutics II - Stability HO • FIRST ORDER CALCULATIONS • A typical First-Order reaction can be written as: • D → P • Therefore the Rate Equation can be written as: • -d[D] = k1 [D] Since k1 [D] = k2 [D] [W] • dt • Integrating the rate equation yields an equation which describes the [D] vs time profile in terms of [D] and t:

21. Pharmaceutics II - Stability HO [D]t i.e. d[D] = - k1dt [D]t at t0 = [D]0 [D]0 • i.e. [D]t = [D]0 e-k t • or ln [D]t = ln [D]0 – k1 t • or Log [D]t = Log[D]0 – k1t 2.303 • Note: ln x = 2.303 Log x • Ln 10 = 2.303, Log 10 = 1

22. Pharmaceutics II - Stability HO First-order reaction of a solution [D]0 [D] Time Overall conc. of drug at t=0 All in solution, none in suspension Rate = d[D] = -k1[D] Actual rate of reaction dt changes with time

23. Pharmaceutics II - Stability HO First-order reaction of a solution Linear as Ln[D] vs time Ln [D]90 Ln [D]50 Time Ln[D]t = Ln[D]0 – k1t y = c - mx Slope = -k1 (units = time-1) t90 t50

24. Pharmaceutics II - Stability HO • Half-Life - t½, t50 • t½ is the time it takes for [D]0 to reduce to [D]0/2 • i.e. 50% of the initial concentration. • t½ can be calculated by substituting into the equation: • [D]t = [D]0 x e –k1t • [D0 x 0.5]= [D]0 x e –k1t ½ • Ln 0.5 = - k1 t½ Ln [D0 x 0.5] = Ln [D]0 – k1t½e.g If D0 = 1 then -0.693 0 • t½ = 0.693(-) k1 (-)

25. Pharmaceutics II - Stability HO • Shelf-Life – t90 • t90 is the time it takes for [D]0 to reduce to [D]0 x 0.9 • i.e. 90% of the initial concentration • or 10% degradation • t90 can be calculated by substituting into the equation: • [D]t = [D]0 x e –k1t • [D0 x 0.9]= [D]0 x e –k1t 0.9 • Ln 0.9 = - k1 t0.9Ln [D0 x 0.9] = Ln [D]0 – k1t0.9 e.g If D0 = 1 then -0.105 0 • t0.9 = 0.105 k1

26. Pharmaceutics II - Stability • APPLICATION • Acetyl Salicylic Acid (Aspirin, ASA) has a pH of maximum stability of 2.5. • At this pH and at 25ºC the Pseudo First Order rate constant is 5x10-7s-1 • Question: What is the t½ and t90 (shelf-life) of ASA? • Answer: t½ = 0.693 = 1.39 x 106 sec or 16 days 5 x 10-7 • t90 =0.105 = 2.1 x 105 sec or 2 days 5 x 10-7

27. Pharmaceutics II - Stability HO • ZERO-ORDER CALCULATIONS • The rate expression for zero-order reactions is: • -d[D] = k0 Note – no term for concentration on rhs dt rate is independent of conc.   since k0 = k1 [D] = k2 [D] [W] • Integration of this equation yields: [D]t • i.e. d[D] = - k0dt [D]t at t0 = [D]0 [D]0 • i.e. [D]t = [D]0 – k0 t • Zero-Order Reaction – [D] vs t is Linear

28. Pharmaceutics II - Stability HO Zero-order reaction (suspension) Linear as [D] vs time [D]0 [D]0 = [D] at t = 100% [D]90 [D]90 = 90% of [D]0 [D]50 = 50% of [D]0 [D]50 Time [D]t = [D0] – k0t y = c - mx Slope = k0 (units = conc.time-1) t90 t50

29. Pharmaceutics II - Stability HO • Half-life [D0] x 0.5 = [D0] – k0 t½ • t½ = 0.5 [D0] Zero order k0 • Shelf-life [D0] x 0.9 = [D]0 – k0 t90 • [D]0 – [D0] x 0.9 = k0 t90 • t90 = 0.1 [D0] Zero order k0

30. Pharmaceutics II - Stability HO HYDROLYSIS/ACID Degradation in Suspension • If [D] in solution also remains constant then: • Rate = k0 - [ ] of no species Pseudo Zero-Order • where k0 = k2[D][H+] • k0 = pseudo zero-order rate constant

31. Pharmaceutics II - Stability HO • APPLICATION • Ampicillin: pH of maximum stability is 5.8 Rate constant at pH 5.8 is 2 x 10-7s-1 at 35ºC (order?) Drug solubility is 1.1g/100mL Formulated as 125mg/5mL = 2.5g/100mL • Question 1: What is the shelf-life of a product formulated as a solution at this pH? • Question 2: If this is made as a suspension what is the shelf-life

32. Pharmaceutics II - Stability HO Zero-order reaction of a suspension [D]0 [D]90 [D] [D]sol t90 t90Time Soln. Susp. Overall conc. of drug at t=0 Majority of drug in suspension. Solution is saturated with a conc. of [D]sol Degradation occurs at a constant rate of d[D]sol = -k1[D] = -k0 while drug remains in dt suspension i.e. [D] in solution remains constant. d[D] = -k1[D] [D] changes when [D] < [D]sol dt Suspension Solution

33. Pharmaceutics II - Stability • Solution: If formulated as a solution e.g. with solubilisers or co-solvents to enhance solubility then: • Assume a first-order reaction as all drug is in solution. • Therefore t90 = 0.105 = 0.105 = 5.3 x 105s. k1 2 x 10-7s-1 = 6.1 days at 35ºC

34. Pharmaceutics II - Stability • Suspension: If formulated as a suspension the majority of API is undissolved and in equilibrium with a saturated solution (the formulation vehicle). • k1 = 2 x 10-7 s-1 However, assume a zero-order reaction. • By definition k0 = k1 [D] Therefore k1 = 2 x 10-7 s-1 x 1.1 g/100mL k0 = 2.2 x 10-7 g/100mL. s-1 • Since t90 = 0.1 [D] Zero order k0 • t90 = 0.1 x 2.5g/100mL 2.2 x 10-7 g/100mL.s-1 • t90 = 1.136 x 106 s = 13 days

35. Pharmaceutics II - Stability • Significant increase in stability when formulated as a suspension. • Most paediatric ampicillin products are formulated as dry granules for reconstitution at the time of dispensing and have a shelf-life thereafter of 14 days.

36. Pharmaceutics II - Stability EFFECT OF TEMPERATURE • Have looked at the rate equations pertaining to the degradation of an API. • Represents degradation reactions occurring under specific conditions e.g. at a specific temperature or pH. • k values are specific for a specific set of conditions. • What influences k? • NB - Temperature and pH • To explain the effect of temperature on reaction rates and the associated rate constants we have to look at activation energy theory.

37. Pharmaceutics II - Stability • Consider the reaction: • A + H+ → B • Rate of reaction is prop. to: • # of collisions between A and H+ • # of collisions with sufficient energy to favour the reaction. • Energy required within collisions before the reaction can proceed is determined by the ACTIVATION ENERGY of the reaction. • Reacting molecules must attain the energy of the TRANSITION STATE

38. Pharmaceutics II - Stability HO Transition State Theory M‡ ΔG1‡ Influences Rate ΔG1‡ ΔG-1‡ Reactants ΔG0 ΔG0 Influences Extent Products k (k+1 and k-1) A + B P K+1 k (k+1 and k-1) A + B M‡ P K-1

39. Pharmaceutics II - Stability • Points to note on Transition State and Activation Energy: • A ↔ B • 1 A must attain the activated state A++ in order to go to B • 2 B can go to A – reverse reaction BUT the activation energy required is greater than going from A to B i.e. the forward reaction is favoured • 3 As ΔG0 increases the reaction tends towards B. If the energy of B<<<A then the reaction approaches completion. i.e. the difference in energy between A and B determines the extent of reaction at the end point.

40. Pharmaceutics II - Stability • 4. The lower the activation energy the greater the number of collisions which will attain the activation complex energy level in a unit time interval. • 5. Therefore - the activation energy determines the rate of reaction at a particular temperature i.e. the stability of the API. • The SMALLER the activation energy • the FASTER the rate of reaction • 6. Overall - ↑ Temp → ↑ collisions → ↑ [A++] → ↑ Rate. ↓ Ea → ↑ [A++] → ↑ Rate

41. Pharmaceutics II - Stability • 7. The relationship between temperature, reaction rate and activation energy is described by the ARRHENIUS EQUATION • k = Ae-Ea/RT • Where k = reaction rate constant (any order). • A = constant • Ea = Activation energy of reaction (kcal/mol) • T = absolute temperature (K) • i.e. 273.16 °C + t °C at which the reaction is taking place. • R= Universal gas constant. • i.e. 1.987 cal/mol.degree • 8.314 x 107 erg/mol.degree Note units

42. Pharmaceutics II - Stability • This equation can be re-arranged into a log linear equation which are easy to use: • log K = log A - Ea Ea . 1 2.303 R T 2.303R T • y = c - mx where 1/T = x • This indicates that a plot of log k vs 1/T will be LINEAR with a slope of -Ea 2.303R • This is known as a Arrhenius Plot.

43. Pharmaceutics II - Stability HO °C °K 1/k 40 313 3.19 x 10-3 60 333 3.00 x 10-3 353 2.83 x 10-3 100 373 2.68 x 10-3 • Arrhenius Plot -1 -2 -3 Log k -4 -5 -6 k373 k353 k333 Slope = -Ea 2.303.R k313 1 2 3 4 5 6 1/T (°K) x 10-3

44. Pharmaceutics II - Stability • EXPERIMENTAL DETERMINATION OF Ea • Conduct stability studies at various temperatures to obtain a number of k’s e.g. using solutions if the k for a hydrolytic degradation is required etc. etc. • e.g. at 100°C → k100 (373°K) • 80°C → k80 (353°K) • 60°C → k60 (333°K) • 40°C → k40 (313°K) • Use elevated temperatures to speed up the reaction and reduce experimental time when reactions are slow, which is the case for most pharmaceuticals.

45. Pharmaceutics II - Stability • Determine k at various elevated temperatures [D] 313°K 333°K 353°K 373°K Time

46. Pharmaceutics II - Stability HO • Determine k at various elevated temperatures Ln[D] Or Log [D] (1/2.303) k313 k333 k353 k373 Time

47. Pharmaceutics II - Stability • Plot kTvs 1/T as per the arrhenius plot. • Determine slope of plot. • Determine Ea since Slope = Ea/R using Ln • = Ea/(R.2.303) using Log • Can use: linear paper – plot ln or log • Ln-linear paper – remember that ln= 2.303log.

48. Pharmaceutics II - Stability HO °C °K 1/k 40 313 3.19 x 10-3 60 333 3.00 x 10-3 353 2.83 x 10-3 100 373 2.68 x 10-3 • Arrhenius Plot -1 -2 -3 Log k -4 -5 -6 k373 k353 k333 Slope = -Ea 2.303.R k313 1 2 3 4 5 6 1/T (°K) x 10-3

49. Pharmaceutics II - Stability • From an Arrhenius Plot, the Activation Energy of a reaction can be calculated. • Once the Activation Energy is known, the reaction rate constant k can be calculated for any temperature. • t90 and t½ can then be calculated at any temperature. • Note: Activation Energy of a reaction is specific for a reaction conducted under specific conditions. • However, it does not change with temperature.

50. Pharmaceutics II - Stability • The Arrhenius Equation can be re-arranged into several useful forms: • log (k2) = - Ea ( 1 - 1 ) ( k1 ) 2.303 R ( T2 T1 ) log of the ratio of k2 / k1 • or log k2 = Ea (T2 – T1) k1 2.303 R.T2.T1 • Where k1 and k2 are the rate constants at temperature T1 and T2 in °K (°C+273).