Pharmaceutical dissolution models 2023.pptx

Model dependent description of dissolution process in pharmaceuticals

1. A.I.S.S.M.S COLLEGE OF PHARMACY, PUNE 01 DISSOLUTION MODELS M. PHARM (SEMESTER I) AISSMS College of Pharmacy, Kennedy Road, Pune - 411001 1

2. CONTENTS : INTRODUCTION PURPOSE OF DISSOLUTION USE OF MODELS IN METHOD DEVELOPMENT TYPES OF MODELS REFERENCES 2

3. INTRODUCTION The quantitative analysis of the values obtained in dissolution/release tests is easier when mathematical formulas that express the dissolution results as a function of some of the dosage forms characteristics are used . In some cases, these mathematical models are derived from the theoretical analysis of process . In most of the cases the theoretical concept does not exist and some empirical equations have proved to be more appropriate . Appropriate mathematical equations can be used to quantify The pharmacokinetic transport steps . 3

4. DEFINITION DISSOLUTION : It is a process in which solid substances solubilizes in a given solvent i.e . mass transfer from solid surface to the liquid phase.   RATE OF DISSOLUTION : It is the amount of drug substance that goes in solution per unit time under standardized conditions of liquid/ solid interface, temperature and solvent composition. 4

5. OBJECTIVE OF DISSOLUTION MODELS Designing of new drug delivery system based upon the general release expression. Prediction of the drug release rate and drug diffusion behaviour through polymers, thus avoid excessive experiment. Physical mechanism of drug transport is determined by comparing the release data with mathematical models . Prediction of the effect of design parameters viz. shape, size and composition on the overall drug release rate. Accurately prediction of drug release profile and improve overall therapeutic efficacy and safety of these drug. 5

6. USE OF DISSOLUTION MODELS Selection of dissolution medium Determination of appropriate dissolution apparatus Dosage form characteristics Determine key operation parameters utility during both the design stage of a pharmaceutical formulation  experimental verification of a release mechanism 6

7. DRUG RELEASE Drug release is the process in which drug comes out of its dosage form and gets converted into a suitable product form which undergoes ADME , becoming available for showing Pharmacological activity . Drug release  occurs because of: diffusion, degradation, swelling, and affinity-based mechanisms . In vitro dissolution studies/drug release are important for the development of new drug . Several theories or models are used to describe the drug release profile from the Pharmaceutical dosage form. 7

8. Assumptions for deriving Mathematical Model During the release of drug, pseudo-steady state is maintained ie The initial drug concentration in the system is much higher than the solubility of the drug . Pseudo steady state is a condition where the concentration of dissolved drug at the surface of a drug delivery system remains relatively constant over time, even though the drug is continuously being released At all times the release media is under perfect sink condition. Drug particles are smaller in diameter than the average distance of diffusion. The value of diffusion coefficients is constant. Between the drug and matrix, no interactions are occurred. 8

9. Fundamentals of kinetics of drug release Noyes-Whitney Rule The fundamental principle for evaluation of the kinetics of drug release was offered by Noyes and Whitney in 1897 dM / dt = KS (Cs - Ct ) where M, is the mass transferred with respect to time, t, by dissolution from the solid particle of instantaneous surface, S, under the effect of the prevailing concentration driving force (Cs - Ct ), where Ct is the concentration at time t and Cs is the equilibrium solubility of the solute at the experimental temperature. The rate of dissolution dM / dt is the amount dissolved per unit area per unit time and for most solids can be expressed in units of g cm-2 s-1. 9

10. When Ct is less than 15% of the saturated solubility Cs, Ct has a negligible influence on the dissolution rate of the solid. Under such circumstances, the dissolution of the solid is said to be occurring under sink conditions. In general, the surface area, S is not constant except when the quantity of material present exceeds the saturation solubility, or initially, when only small quantities of drug have dissolved. 10

11. Nernst and Brunner Film Theory Brunner and Nernst used Fick’s law of diffusion to establish a relationship between the constant in the equation and the diffusion coefficient of the solute, K = DS/ hγ where D is the diffusion coefficient, S is the area of dissolving surface or area of the diffusion layer, γ is the solution volume and h is the diffusion layer thickness. In formulating their theories, Nernst and Brunner assumed that the process at the surface proceeds much faster than the transport process and that a linear concentration gradient is confined to the layer of solution adhering to solid surface 11

12. 1 . Diffusion model 2. Zero order kinetic model 3. First order kinetic model 4. Higuchi model 5. Korsemeyer-peppas model(the power law) 6. Hixson – crowell model 7. Weibull model 8. Baker –Lonsdale model 9. Hopfenberg model 10. Gompertz model 11. Sequential layer model DIFFERENT DISSOLUTION MODELS 12

13. Diffusion Model The transfer of solute molecule is possible by either simple molecular permeation or by movement through pore and channels . Diffusion is related with the moving of solute molecule. In our body diffusion of drug molecule is well explained by Fick’s law of diffusion. Fick’s first law of diffusion: The law is related with the diffusive flux to concentration under assumption of steady state. It postulates that the flux goes from region of higher concentration to region of lower concentration , which is proportional to the concentration gradient. In one dimension, the law is J= D(dc/ dx ) 13

14. Zero Order Kinetic Model Zero order describes the system where the release rate of drug is independent of its concentration. The equation is C= Co- Ko t Where, C = Amount of drug release or dissolved (assuming that release occur rapidly after the drug dissolved.) Co = Initial amount of drug in solution (it is usually zero) Ko = Zero order rate constant t = time For study of release kinetics, the graph plotted between cumulative amount of drug released verses time. 14

15. Applications Several types of modified release Pharmaceutical dosage form as in the case of some transdermal system as well as matrix tablet with low soluble drugs in coated forms, osmotic system, etc. Such models are important in certain classes of medicines intended, example for antibiotic delivery, heart and blood pressure maintenance, pain control and antidepressant . Slow first order Apparent zero order 15

16. First Order Kinetic Model This model is used to describe the absorption and elimination of some drugs . The drug release which follows the first order kinetic can be expressed by the equation….. Log C= Log Co-Kt/2.303 Where, Co=Initial concentration of drug K= First order constant t=time The data obtained are plotted as log cumulative percentage drug remaining verses time, which yield a straight line with slope=K/2.303. 16

17. APPLICATION This relationship can be used to describe the drug dissolved in Pharmaceutical dosage forms like those contained water soluble drugs in porous material. 17

18. Higuchi Model HIGUCHI in1961-1963  developed several theoretical models to study the release of water soluble and low soluble drugs incorporated in semi-solid and/or solid matrixes. Mathematical expressions were obtained for drug particles dispersed in a uniform matrix behaving as the diffusion media. Higuchi published the probably most famous and most often used mathematical equation to describe drug release from matrix system . This model is often applicable to the different geometrics and porous system. 18

19. The extended model is based on the following hypothesis such as- Initial concentration of drug in the matrix is much higher than the drug solubility. Diffusion of drug occurs only in one dimension (edge effect negligible). Drug particles much smaller than system thickness. Swelling of matrix and dissolution is negligible. Drug diffusivity is constant. In the release environment perfect sink conditions are maintained. 19

20. The basic equation of Higuchi model is….. C= [D (2qt-Cs) Cst ] 1/2 Where, C =total amount of drug release per unit area of the matrix[mg/cm 2 ] D =diffusion coefficient for the drug in the matrix[cm 2 /hr] qt =total amount of drug in a unit volume of matrix [mg/cm 3 ] Cs =dimensional solubility of drug in the polymer matrix[mg/cm 3 ] T =time[hr] Data obtained were plotted as cumulative percentage of drug release verses square root of time. 20

21. APPLICATION By using this model dissolution of drug from several modified release dosage forms like some transdermal system and matrix tablet with water soluble drugs are studied . The first example of a mathematical model aimed to describe drug release from a matrix system was proposed by Huguchi in 1961 (31). Initially conceived for planar systems, it was then extended to different geometrics and porous systems ( 21

22. Korsemeyer-Peppas Model (The Power law) Korsemeyer et al (1983) derived a simple relationship which describes the release of drug from a polymeric system. To illustrate the mechanism of drug release, first 60% of drug release data was fitted in Korsemeyer-Peppas model. Ct/C∞= kt n Where, Ct/C∞=fraction of drug release at time t. k=rate constant n=release exponent 22

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24. A modified form of this equation was developed to adjust the lag time (l) in the beginning of release of drug from the Pharmaceutical dosage form. C(t-1)/C∞= a(t-l) n Where there is possibility of a burst effect, b this equation becomes…… Ct/C∞= at n +b In the absence of lag time or burst effect l and b values would be zero and only at n is used . To find out the mechanism of drug release, first 60% drug release data were fitted in KorsmeyerñPeppas model 24

25. There are several simultaneous processes considered in this model: Diffusion of water into the tablet. Swelling of tablet as water enters. Formation of gel. Diffusion of drug and filler out of the tablet. Dissolution of the polymer matrix. 25

26. In this model, the value of n characterizes the release mechanism of drug as described. For the case of cylindrical tablets, 0.45 ≤ n corresponds to a Fickian diffusion mechanism, 0.45 < n < 0.89 to non- Fickian transport, n = 0.89 to Case II ( relaxational ) transport, and n > 0.89 to super case II transport. 26

27. 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 27

28. Fickian diffusional release occurs by the usual molecular diffusion of the drug due to a chemical potential gradient. Super Case-II release is  the drug transport mechanism associated with stresses and state transition in hydrophilic glassy polymers which swell in water or biological fluids . 28

29. Following assumptions were made in this model……. The generic equation is applicable to small values of t or short terms and the portion of release curve, where Ct/C∞ < 0.6 should only be used to determine the exponent n. ‘n’ value is used to characterize different release for cylindrical shaped matrices Drug release is in a one dimensional way. The ratio of system length to thickness should be at least. Plot made by log cumulative percentage drug release verses log time. Application This model describe the drug release from several modified release dosage forms. 29

30. Hixson and Crowell Model Hixson and Crowell in 1931  recognised that the particle regular area is proportional to the cubic root of its volume, derived an equation Drug powder that having uniformed size particles , Hixson and Crowell derived the equation which expresses rate of dissolution based on cube root of weight of particles and the radius of particle is not assumed to be constant. The equation is Co 1/3 -Ct 1/3 = K HC t Where, Ct=amount of drug released in time t. Co=initial amount of drug in the tablet. K HC =rate constant for Hixson-Crowell equation. 30

31. When this model is used, it is considered the release rate is limited by the drug particles dissolution rate and not by the diffusion that might occur through the polymeric matrix. This model is used to describe the release profile keeping in mind the surface of the drug particles diminishes during the dissolution. Plot made in between cube root of drug percentage remaining in matrix verses time. Applications This expression is applied to Pharmaceutical dosage form such as tablet ; where the dissolution occurs in planes which is parallel to drug surface if dimensions of the tablet diminish proportionality, in such a manner that the initial geometry form keep constant all the time. 31

32. Weibull Model This model has been described for different dissolution processes as the equation….. C= Co [1 – exp-(t-T) b ]/ a Where, C= amount of dissolved drug as a function of time t. Co= total amount of drug being released. T= lag time measured as a result of dissolution process parameters. a= scale parameter that describe the time dependence. b= shape of dissolution curve progression. Applications It is more useful for comparing release profiles of matrix type drug release. 32

33. Because this is an empiric model, not deducted from any kinetic fundament, it presents some deficiencies and has been the subject of some criticism (P edersen and Myrick, 1978; Christensen et al., 1980 , such as: There is not any single parameter related with the intrinsic dissolution rate of the drug. It is of limited use for establishing in vivo/in vitro correlations. 33

34. Baker-Lonsdale Model This model was modified form of Higuchi model, developed by Baker and Lonsdale (1974). It described the drug release from spherical matrix . According to the equation….. f1= 3/2[1-(1-Ct/C∞) 2/3 ] Ct/C∞= kt Where, Ct= drug release amount at time’t ’. C∞= amount of drug release at an infinite time. K= release constant, which corresponds to the graph when plotted as,[d(Ct/C∞]/ dt with respect to root of time inverse. 34

35. Applications This model used to linearization of release data from several formulations of microcapsules or microspheres . 35

36. Hopfenberg Model This model was made to correlate the release of drug from eroding surface of polymers so, surface area remains constant during the degrade process. The cumulative fraction of released drug at time ‘t’ was described as Ct/C∞= 1-[1-Kot/CL a] n Where, Ko =zero order rate constant, describing polymer degradation (surface erosion process.) CL=initial drug loading through the system. a=system half thickness (that is radius for a sphere or cylinder.) n=exponent that varies with geometry, n=1, 2, 3 for slab (flat, cylindrical and spherical geometry, respectively.) 36

37. Assumption of this model is the rate limiting step of release of drug is the erosion of the matrix itself and that time dependent diffusional resistance internal or external to the eroding matrix do not influence it. Applications This model is used to identify the mechanisms of release from the optimized oily sphere using derived data from the composite profile, which displayed the site specific biphasic release kinetics . 37

38. Release Profiles Comparisons   Some methods to compare drug release profiles were recently proposed (CMC, 1995; Shah and Polli , 1996;  Ju and Liaw , 1997;  Polli et al., 1997;  Fassihi and Pillay , 1998. ) 38

39. Those methods were classified into several categories, such as: • Statistical methods ( Tsong and Hammerstrom , 1996) based in the analysis of variance or in  t -student tests ◦ Single time point dissolution ◦Multiple time point dissolution •Model-independent methods •Model-dependent methods , using some of the previously described models, or lesser used models such as the quadratic, logistic. 39

40. Model Dependence and Independence Some models result in comparison between two dissolution curve been represented by a single number. Whereas, most model dependent approaches result in each curve being represented as two or more emperical parameters . Using one way ANOVA we can compare the models and understand the difference between two models. 40

41. Model dependent methods Model dependent methods are based on different mathematical functions, which describe the dissolution profile. Once a suitable function has been selected, the dissolution profiles are evaluated depending on the derived model parameters 41

42. Model Mathematical Equation Release Mechanism Zero order C=C o - K o t Diffusion Mechanism First order logC = logCo- k t / 2.303 Fick’s first law, diffusion Mechanism Higuchi Model C=[D(2qt-Cs)Cs t ] 1/2 Diffusion medium based Mechanism in Fick’s first law Korsemeyer - Peppas Model Ct/C∞= K t n Semi empirical model, diffusion based mechanism Hixson–Crowell Model C o 1/3 -C t 1/3 = K HC t Erosion release mechanism Weibull Model C = C o [ 1 – exp[-(t-T) b ] a Empirical model ,life-time distribution function Baker–Lonsdale Model f1=3/2[1-(1-Ct/C∞) 2/3 ] C t /C ∞ = Kt Release of drug from spherical matrix Hopfenberg Model C t /C ∞ =1-[1-Ko t /C L a] n Erosion mechanism Gompertz Model C t = C max exp [- αe βlog t ] Dissolution model 42

43. 43 Model Independent Approach Using a Similarity Factor (17-19, 58) A simple model independent approach uses a difference factor (f1) and a similarity factor (f2) to compare dissolution profiles. The difference factor calculates the percent difference between the two curves at each time point and is a measurement of the relative error between the two curves. It is expressed as: f1 = {[ Σt =1 n ( Rt ñ Tt )]/[ Σt =1 n Rt ]} ◊ 100 where n is the number of time points, R is the dissolution value of the reference ( prechange ) batch at time t, and Tt is the dissolution value of the test ( postchange ) batch t at time t.

44. 44 The similarity factor is a logarithmic reciprocal square root transformation of the sum of squared error and is a measurement of the similarity in the percent dissolution between the two curves. This model independent method is most suitable for dissolution profile comparison when three to four or more dissolution time points are available

45. References Hina Kouser Shaikh , R. V. Kshirsagar , S. G. Patil , Mathematical models for drug release characterization: a review, World Journal of Pharmacy and Pharmaceutical Sciences, Volume 4, Issue 04, pg no-324-338. Ramteke K.H., Dighe P.A., Kharat A.R., Patil S.V., Mathematical Models of Drug Dissolution: A Review, Scholars Academic Journal of Pharmacy, 2014, pg no-388-396. Hussain Lokhandwala , Ashwini Deshpande and Shirish Deshpande, Kinetic modeling and dissolution profiles comparison: an overview, International Journal of Pharma and Bio Sciences, 2013 Jan; 4(1), pg no-728 – 737. R.W. Baker,  H.S.  Lonsdale Controlled release: mechanisms and rates A.C.  Taquary ,  R.E.  Lacey (Eds.), Controlled Release of Biologically Active Agents, Plenum Press, New York (1974), pp. 15-71 45

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