consoliation

consoliation,diffusion parameter,dissolution parameters,pharmacokinetic parameters,similarity factors f1 and f2,heckel plots,higuchi model,korsmeyer-peppas model,chi-square test,student’s t-test,anova

1. STUDY OF CONSOLIDATION PARAMETERS By P . viji M.Pharm I Year (pharmaceutics)

2. CONSOLIDATION An increase in the mechanical strength of the material resulting from particle or particle interaction. ( Increasing in mechanical strength of the mass)

3. CONSOLIDATION PROCESS Cold welding: when the surfaces of two particles approach each other closely enough, their free surface energies results in strong attractive force, a process known as cold welding . Fusion bonding : Multiple point contacts of the particle upon application of load produces heat which causes fusion / melting. Upon removal of load it gets solidified and increase the mechanical strength of mass.

4. CONSOLIDATION MECHANISMS Mechanical theory : As the particles undergo deformation, the particle boundaries that the edges of the particle intermesh, forming a mechanical bond. Intermolecular forces theory : Under pressure the molecules at the point of true contact between new, clean surface of the granules are close enough so that van der Waals forces interact to consolidate the particle.

5. Liquid-surface film theory: Thin liquid films form which bond the particles together at the particle surface. The energy of compression produces melting of solution at the particle interface followed by subsequent solidification or crystallization thus resulting in the formation of bonded surfaces

6. FACTORS AFFECTING CONSOLIDATION: The chemical nature of the material The extent of the available surface The presence of surface contaminants The inter surface distance

7. DIFFUSION PARAMETERS

8. DIFFUSION PARAMETERS This is given by Higuchi. 𝑄 = 𝐾√𝑻 Where Q is the amount of drug released in time‘t ’ per unit area, K is higuchi constant T is time in hr . Plot : The data obtained is to be plotted as cumulative percentage drug release versus Square root of time. Application : modified release pharmaceutical dosage forms, transdermal systems and matrix tablets with water soluble drugs.

9. DISSOLUTION PARAMETERS

10. DISSOLUTION PARAMETERS Dissolution is a process in which a solid substance solubilizes in a given solvent i.e. mass transfer from the solid surface to the liquid phase . Dissolution parameters: Effect of agitation Effect of dissolution fluid Influence of pH of dissolution fluid

11. Effect of viscosity of the dissolution medium Effect of the presence of unreactive and reactive additives in the dissolution medium . Volume of dissolution medium and sink conditions Deaeration of the dissolution medium Effect of temperature of the dissolution medium

12. EFFECT OF AGITATION The relationship between the intensity of agitation and the rate of dissolution varies considerably according to the type of agitation used, the shape and design of the stirrer and the physicochemical properties of the solid . For the basket method, 100 rpm usually is utilized, while for the paddle procedure, a 50 – 75 rpm is recommended.

13. EFFECT OF DISSOLUTION FLUID Selection of proper medium for dissolution testing depends largely on the physicochemical properties of the drug .

14. INFLUENCE OF PH OF DISSOLUTION FLUID simulated gastric fluid as the test medium for tablets containing ingredients which reacted more readily in acid solution than in water (e.g., calcium carbonate ).

15. EFFECT OF VISCOSITY OF THE DISSOLUTION MEDIUM If the interaction at the interfaces, occurs much faster than the rate of transport, such as in the case of diffusion controlled dissolution processes, it would be expected that the dissolution rate decreases with an increase in viscosity. The rate of dissolution of zinc in HCl solution containing sucrose was inversely proportional to the viscosity of solution.

16. EFFECT OF THE PRESENCE OF UNREACTIVE AND REACTIVE ADDITIVES IN THE DISSOLUTION MEDIUM. When neutral ionic compounds, such as sodium chloride and sodium sulfate, or non ionic organic compounds, such as dextrose, were added to the dissolution medium,the dissolution of benzoic acid was dependent linearly upon its solubility in the particular solvent . When certain buffers or bases were added to the aqueous solvent , an increase in the dissolution rate was observed.

17. VOLUME OF DISSOLUTION MEDIUM AND SINK CONDITIONS The proper volume of the dissolution medium depends mainly on the solubility of the drug in the selected fluid . If the drug is poorly soluble in water, a relatively large amount of fluid should be used if complete dissolution is to be expected .

18. DEAERATION OF THE DISSOLUTION MEDIUM Presence of dissolved air or other gases in the dissolution medium may influence the dissolution rate of certain formulations and lead to variable and unreliable results . Example, the dissolved air in distilled water could significantly lower its pH and consequently affect the dissolution rate of drugs that are sensitive to pH changes, e.g., weak acids .

19. EFFECT OF TEMPERATURE OF THE DISSOLUTION MEDIUM Drug solubility is temperature dependent, therefore careful temperature control during the dissolution process is extremely important . Generally a temperature of 37°±0.5 is maintained during dissolution determination of oral dosage forms and suppositories . For topical preparations as low as 30° and 25°have been used.

20. PHARMACOKINETIC PARAMETERS

21. PHARMACOKINETIC PARAMETERS Pharmacokinetics is defined as the kinetics of drug absorption, distribution, metabolism, and excretion and their relationship with pharmacologic, therapeutic or toxicologic response in mans and animals.

22. PLASMA DRUG CONCENTRATION-TIME PROFILE

23. Three important pharmacokinetic parameters : Peak plasma concentration ( Cmax ) Time of peak concentration ( tmax ) Area under the curve (AUC)

24. PEAK PLASMA CONCENTRATION ( Cmax ) The point of maximum concentration of a drug in plasma is called as peak and the concentration of drug at peak is known as peak plasma concentration . It is also called as peak height concentration and maximum drug concentration . Cmax is expressed in mcg/ml.

25. TIME OF PEAK CONCENTRATION ( tmax ) The time for drug to reach peak concentration in plasma ( after extravascular administration) is called the time of peak concentration . It is expressed in hours .

26. AREA UNDER THE CURVE ( AUC) It represents the total integrated area under the plasma level-time profile and expresses the total amount of drug that comes into the systemic circulation after its administration . AUC is expressed in mcg/ml X HRS . It is important for the dugs that are administered repetitively for the treatment of chronic conditions like asthma or epilepsy.

27. SIMILARITY FACTORS f1 AND f2

28. SIMILARITY FACTORS f1 AND f2 DIFFERENCE FACTOR ( f1) The difference factor (f1) as defined by FDA calculates the % difference between 2 curves at each time point and is a measurement of the relative error between 2 curves . where , n = number of time points Rt = % dissolved at time t of reference product ( prechange ) Tt = % dissolved at time t of test product (post change)

29. SIMILARITY FACTOR (F2) The similarity factor (f2) as defined is a measurement of the similarity in the percentage (%) dissolution between the two curves

30. LIMITS FOR SIMILARITY AND DIFFERENCE FACTORS Inference Dissolutions profile are similar Similarity or equivalence of two profiles ≥50 ≤15 100 Difference factor Similarity factor

31. Data structure and steps to follow : This model-independent method is most suitable for the dissolution profile comparison when three to four or more dissolution time points are available . Determine the dissolution profile of two products (12 units each) of the test (post-change) and reference (pre-change) products.

32. Some recommendations: The dissolution measurements of the test and reference batches should be made under exactly the same conditions . The dissolution time points for both the profiles should be the same (e.g. 15, 30, 45, 60 minutes ).

33. Advantages They are easy to compute. They provide a single number to describe the comparison of dissolution profile data . Disadvantages The basis of the criteria for deciding the difference or similarity between dissolution profile is unclear.

34. HECKEL PLOTS

35. HECKEL EQUATION The heckel analysis is a most popular method of deforming reduction under compression pressure . Powder packing with increasing compression load is normally attributed to particles rearrangement , elastic & plastic deformation & particle fragmentation.

36. It is analogous to first order reaction , Log 1/E= Ky . P + Kr Where Ky =material dependent constant inversely proportional to its yield strength ‘s’ Kr=initial repacking stage hence E0

37. The applied compressional force F & the movement of the punches during compression cycle & applied pressure P , porosity E . For a cylindrical tablets p=4F/л . D2 Where … D is the tablet diameter similarly E can be calculated by E=100 .(1-4w/ ρt .л.D2.H ) Where… w is the weight of the tableting mass , ρt is its true density , H is the thickness of the tablets.

38. HECKEL PLOTS Heckel plot is density v/s applied pressure Follows first order kinetics Materials that are comparatively soft & that readily undergo plastic deformation retain different degree of porosity , depending upon the initial packing in the die.

39. This in turn is influenced by the size distribution , shape etc of the original particles . Ex: sodium chloride (shown by type a in graph ) Harder material with higher yield pressure values usually undergo compression by fragmentation first , to provide a denser packing . Ex: Lactose, sucrose ( shown in type b in graph).

40. Type-a plots exhibits higher slop (Ky) then type-b. because type-a materials have lower yield stress . Type-b plots exhibits lower slop because brittle , hard materials are more difficult to compress.

41. APPLICATION OF HECKEL EQUATION The crushing strength of tablets can be correlated with the values of k of the Heckel plot . Larger k values usually indicate harder tablets . Such information can be used as a means of binder selection when designing tablet formulations . Heckel plots can be influenced by the overall time of compression, the degree of lubrication and even the size of the die, so that the effects of these variables are also important and should be taken into consideration

42. HIGUCHI MODEL

43. HIGUCHI MODEL The first example of a mathematical model aimed to describe drug release from a matrix system was proposed by Huguchi in 1961 . This model is based on the hypothesis that ( i ) drug diffusion takes place only in one dimension (ii ) drug particles are much smaller than system thickness (iii) drug diffusivity is constant (iv) perfect sink conditions are always attained in the release environment.

44. Accordingly , model expression is given by the equation : ft = Q = A √D(2C ñ Cs) Cs t where Q is the amount of drug released in time t per unit area A, C is the drug initial concentration, Cs is the drug solubility in the matrix media and D is the diffusivity of the drug molecules (diffusion coefficient) in the matrix substance.

45. In a general way it is possible to simplify the Higuchi model as (generally known as the simplified Higuchi model ): f t = Q = KH x t1/2 where , KH is the Higuchi dissolution constant. The data obtained were plotted as cumulative percentage drug release versus square root of time . Application: This relationship can be used to describe the drug dissolution from several types of modified release pharmaceutical dosage forms, as in the case of some transdermal systems and matrix tablets with water soluble drugs.

46. KORSMEYER-PEPPAS MODEL

47. KORSMEYER-PEPPAS MODEL Korsmeyer et al. (1983) derived a simple relationship which described drug release from a polymeric system equation . To find out the mechanism of drug release, first 60% drug release data were fitted in Korsmeyer- Peppas model

48. Mt / M∞ = Ktn where Mt / M∞ is a fraction of drug released at time t, k is the release rate constant and n is the release exponent . The n value is used to characterize different release for cylindrical shaped matrices.

49. To find out the exponent of n the portion of the release curve, where Mt / M∞ < 0.6 should only be used . To study the release kinetics, data obtained from in vitro drug release studies were plotted as log cumulative percentage drug release versus log time.

50. CHI-SQUARE TEST

51. CHI-SQUARE TEST Karl Pearson introduced a test to distinguish whether an observed set of frequencies differs from a specified frequency distribution The chi-square test uses frequency data to generate a statistic

52. Test for comparing variance Chi- Square Test as a Parametric Test

53. Chi- Square Test as a Non-Parametric Test Test of Goodness of Fit. Test of Independence.

54. 2. AS A TEST OF GOODNESS OF FIT It enables us to see how well does the assumed theoretical distribution(such as Binomial distribution, Poisson distribution or Normal distribution) fit to the observed data. When the calculated value of χ2 is less than the table value at certain level of significance, the fit is considered to be good one and if the calculated value is greater than the table value, the fit is not considered to be good.

55. 3.AS A TEST OF INDEPENDENCE χ2 test enables us to explain whether or not two attributes are associated. Testing independence determines whether two or more observations across two populations are dependent on each other (that is, whether one variable helps to estimate the other. If the calculated value is less than the table value at certain level of significance for a given degree of freedom, we conclude that null hypotheses stands which means that two attributes are independent or not associated. If calculated value is greater than the table value, we reject the null hypotheses.

56. Steps involved 1)Determine The Hypothesis: Ho : The two variables are independent Ha : The two variables are associated 2) Calculate Expected frequency

57. 3)

58. 4)determine degrees of freedom df = (R-1)(C-1) = (2-1)(3-1 ) = 2

59. 5)Compare computed test statistic against a tabled/critical value If calculated  2 is greater than  2 table value, reject Ho

60. Student’s t-test

61. Student’s t-test The test is used to compare samples from two different batches. It is usually used with small (<30) samples that are normally distributed.

62. There are two types of t-test: Matched pairs independent pairs

63. ANALYSIS OF VARIANCE (ANOVA)

64. ANALYSIS OF VARIANCE (ANOVA) The analysis of variance(ANOVA) is developed by R.A.Fisher in 1920 . The technique of variance analysis developed by fisher is very useful in such cases and with its help it is possible to study the significance of the difference of mean values of a large no.of samples at the same time.

65. CLASSIFICATION OF ANOVA The Analysis of variance is classified into two ways: One-way classification Two-way classification In a one-way classification we take into account the effect of only one variable . If there is a two way classification the effect of two variables can be studied.

66. One Way ANOVA Steps 1. State null & alternative hypothesis 2.State Alpha 3.Calculate degrees of Freedom 4.State decision rule 5. Calculate test statistic 6.Calculate F statistic

67. 1)Null hypothesis No significant difference in the means of 3 samples 2)State Alpha i.e 0.05 3)Calculate degrees of Freedom k-1 & n-k = 2 & 12 4)State decision rule Table value of F at 5% level of significance for d.f 2 & 12 is 3.88 The calculated value of F > 3.88 ,H0 will be rejected

68. 5) Calculate test statistic

69. Sum of squares between samples (SSC) Sum of squares between samples (SSC) = n1 ( M1 – Grand avg) 2 + n2 ( M2 – Grand avg) 2 + n3( M3 – Grand avg) 2 5 ( 10 - 10) 2 + 5 ( 8 - 10) 2 + 5 ( 12 - 10) 2 = 40

70. Sum of squares WITH IN samples

71. Calculation of ratio F

72. Two Way ANOVA Example we have test score of boys & girls in age group of 10 yr,11yr & 12 yr. If we want to study the effect of gender & age on score. Two independent factors- Gender, Age Dependent factor - Test score

73. Source of variance d.f Sum of squa r es Mean sum of squares F-Ratio Between sa m p l e s ( co lumns) d f 1 =C- 1 SSC=B-D MSC=SSC ̸ d f F=MSC ̸ MSE Between R e p li c ant s (rows) d f 2 =r-1 SSR=C-D MSR=SSR ̸ d f 2 Within sa m p l e s ( R e s i du a l) d f 3 =( c-1)(r-1) SSE=SST- ( SSC+SS R ) MSE=SSE ̸ d f 3 F=MSR ̸ MSE Total n-1 SST=A-D

74. APPLICATIONS OF ANOVA Similar to t-test More versatile than t-test ANOVA is the synthesis of several ideas & it is used for multiple purposes. The statistical Analysis depends on the design and discussion of ANOVA therefore includes common statistical designs used in pharmaceutical research

75. In the bioequivalence studies the similarities between the samples will be analyzed with ANOVA only. Pharmacokinetic data also will be evaluated using ANOVA. Pharmacodynamics (what drugs does to the body) data also will be analyzed with ANOVA only.