DIffusion, Dissolution and Pharmacokinetic Parameters.pptx

Diffusion, Dissolution and Pharmacokinetic Parameters, Modern Pharmaceutics

1. Modern Pharmaceutics Dr. Kailas Mali Professor in Pharmaceutics, Adarsh College of Pharmacy, Vita Study of Consolidation Parameters

2. Diffusion parameters Dissolution parameters Pharmacokinetic parameters Heckel plots , Similarity factors – f2 and f1, Higuchi and peppas plot, Concept and significance of Linearity, Standard deviation , chi square test, student T-test , ANOVA test. Contents

3. Diffusion of drug from dosage form Diffusion Parameters Diffusion It is a process of the mass transfer of the individual molecule of a substance brought about by random molecular motion associated with a driving force like concentration gradient (higher to lower concentration). Free diffusion of the substance through liquids, solids and the membranes are of special interest in designing of a dosage form. Studying diffusional parameters will help us to understand permeation and distribution of drug molecules in living systems.

4. Drug release form reservoir and matrix. Diffusion Parameters Applications of Diffusion The release of drugs from dosage forms is diffusion controlled (SR and CR Products). Molecular weight of polymers can be estimated form diffusion process. Absorption of drugs from various routes can be understood and predicted form the principles of diffusion. The diffusion of drugs into to tissues and their excretion through kidneys can be anticipated through diffusion studies. Principles of diffusion can be used as in vitro models for drug protein binding studies.

5. The change in mass transfer also occurs simultaneously with respect to distance. Fick’s first law states that the flux (the rate of mass transfer across a unit surface area of barrier) is directly proportional to the concentration gradient. Where, dC is change in concentration of material, g/cm 3 ; D is diffusion coefficient of a penetrant, cm 2 /sec; dx is change in distance, cm. D is affected by the concentration, temperature, pressure, solvent property and chemical nature of diffusant Diffusion Parameters Fick’s First Law In diffusion, molecules get transported from one compartment to another over a period of time- ie , rate of mass transfer ( dm / dt ). This is expressed as flux. Flux (J) is eual to the rate of mass transfer across a unit surface area of a barrier. Where, dM is change in the mass of material, g S is barrier surface area, cm 2 dt is change in time, sec.

6. If diffusion is the rate determining step, then we can use Ficks first law of diffusion to describe the overall process Diffusion Parameters The negative sign in the right side term in equation signifies a decrease in the concentration. But flux is always a positive quantity, because it increases continuously during process. The dx is perpendicular to the surface of the barrier. Combining above two equations: Equation represents the rate of mass transfer as per Ficks first law.

7. Later on, Nernst and Burner showed that k is a composite constant being proportional to the diffusion coefficient, D and the surface area of the dissolving body, A. Thus the modified equation is called as the Nernst and Burner equation: Where, h is the thickness of the boundary layer, A is the surface area of dissolving solid, Kw/o is the partition coefficient of drug and V is the volume of the dissolution medium. Diffusion Parameters Diffusion limited model or Film theory The first dissolution experiment were conducted by the Noyes and Whitney and found that the dissolution rate (dc/ dt ), is a linear function of the difference between the bulk concentration at time t and the saturation solubility: Where, k is the dissolution rate constant.

8. Plot of concentration versus distance from solid surface Diffusion Parameters Variables in Diffusion Process Surface area (A) : Surface area per gram of a solid drug can be changed by altering particle size. Diffusion layer thickness (h) : In vitro it is determined by the agitation in the bulk solution. In vivo no control over this parameter. Thickness of stagnant layer can be reduced when drug dissolves in reactive medium. Weakly basic drug in an acidic medium dissolves at faster rate than neutral medium because of reduction in thickness of stagnant layer.

9. Partition coefficient (Kw/o) : High water to oil partition increases drug dissolution. Concentration in bulk solution ( Cb ) : In vivo Cb is low due to sink conditions which increases rate of dissolution. In vitro addition of solvents and increase in volume of dissolution medium increases the rate of dissolution. Diffusion Parameters Variables in Diffusion Process Diffusion coefficient (D) : It depend on the size of molecule and the viscosity of the medium. Increasing the viscosity of medium will decrease the diffusion coefficient and thus dissolution rate. Drug solubility (Cs) : It is another determinant of dissolution rate. As Cs increases dissolution rate also increases.

10. To study the dissolution from a planar system having a homogenous matrix , the relation obtained is: Where, Q is the amount of drug released in time t per unit area, C is the drug initial concentration, Cs is the drug solubility in matrix media and D is the diffusivity of the drug molecules in the matrix substance. Higuchi Equation Higuchi developed theoretical models to study the release of water soluble and low soluble drugs incorporated in semi-solid and/or solid matrix . Cumulative % drug release vs. square root of time. Drug release through diffusion mechanism ( Fickian diffusion mechanism) Mathematical expressions were obtained for drug particles dispersed in a uniform matrix behaving as the diffusion media.

11. For the case in which the drug is dissolved from a saturated solution (where Co is the solution concentration) dispersed in a porous matrix. Where, Q is the amount of drug released in time t by surface unity , ε is the matrix porosity, C is the solution concentration dispersed in a porous matrix and D the diffusion constant of the drug molecules in that liquid. Higuchi Equation Planar or spherical systems having a granular (heterogeneous) matrix, where the drug concentration in the matrix is lower than its solubility and the release occurs through pores in the matrix obtained relation is: Where, Q is the amount of DR in time t by surface unity, C is the initial concentration of the drug, ε is the matrix porosity , τ is the tortuosity factor of the capillary system, C S is the drug solubility in the matrix /excipient media and D the diffusion constant of the drug molecules in that liquid .

12. Higuchi Plot Higuchi Equation According to simplified Higuchi model equation is as follows: Where, K H is the Higuchi dissolution constant. Higuchi describes drug release as diffusion process based in the Fick’s law, square root time dependent. This relation can be used to describe the drug dissolution from several types of modified release pharmaceutical systems.

13. Effect of agitation Effect of dissolution fluid Influence of pH of dissolution fluid Effect of surface tension of the dissolution medium 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 temp on the dissolution medium Dissolution Parameters Dissolution is the process in which a solid substance solubilizes in a given solvent. Mass transfer from the solid surface to the liquid phase.

14. Dissolution tests using high-speed agitation may lack discriminative value and can yield misleading results. The lowest value (25 rpm) is characteristic for suspensions. In compendial methods agitation speed is relatively low. For the basket method 100rpm and for paddle 50-75 rpm. Dissolution Parameters Effect of agitation The relationship between the intensity of agitation and the rate of dissolution differs considerably according to the type of agitation used, degree of laminar and turbulent flow in the system, the shape and design of the stirrer, and the physicochemical properties of the solid. Speed of agitation generates a flow that continuously changes the liquid/solid interface between solvent and drug. To sustain a reproducible laminar flow, which is essential for gaining reliable results, agitation should be maintained at a relatively low rate.

15. Dissolution fluid with example Dissolution Parameters Effect of Dissolution Fluid The selection of a proper medium for dissolution testing depends largely on the physicochemical properties of the drug. The media typically used in dissolution studies include acidic solutions, buffers, surfactants, and surfactants with acid or buffers. Surface active agents are used in dissolution test methods to improve the solubility or wettability of a drug . Dissolution Fluid Example Water Ampicillin Capsule Buffers Azithromycin Capsule Simulated gastric fluid Piroxicam Capsule HCl solution Cimetidine tablet

16. For tablets containing active ingredients, whose solubility is independent of pH, the dissolution rate does not vary considerably with changes in pH of the dissolution medium unless they contain certain excipients that are influenced by pH . Sodium bicarbonate, magnesium carbonate, calcium carbonate promotes disintegration of tablet in acidic medium by producing gas. Dissolution Parameters Influence of pH of dissolution fluid Variations in pH exert the greatest effect in terms of drug solubility. For weak acids, the rate of dissolution increases with increasing pH, whereas, for weak bases, the rate of dissolution increases with decreasing pH. pH of stomach is ~2. Acetylsalicylic acid pKa is 3.5.

17. The addition of surfactant below the CMC can increase significantly the dissolution rate because of better penetration of the solvent into the tablet resulting in greater availability of the drug surface. Dissolution data for benzocaine in different concentrations of polysorbate 80. Dissolution Parameters Effect of surface tension of the dissolution fluid Surface tension shows a significant effect on the dissolution rate of drugs and their release rate from solid dosage forms. Surfactants and wetting agents lower the contact angle and, consequently, improve penetration by the dissolution medium. The incorporation of surface-active agents in the dissolution medium is expected to enhance the dissolution rate of a poorly soluble drug in solid dosage forms by decreasing the interfacial tension and micelle formation.

18. Relationship of viscosity to dissolution rate of benzoic acid in aqueous methylcellulose solutions at 25 °. Dissolution Parameters Effect of viscosity of the dissolution fluid In case of diffusion-controlled dissolution processes, it would be expected that the dissolution rate decreases with an increase in viscosity. In the case of interfacial-controlled dissolution processes , however, viscosity should have little effect. The Stokes-Einstein equation describes diffusion coefficient, D, as a function of viscosity, D=µ kT Where, µ is the mobility (velocity at a force of one dyne); k is the Boltzmann constant.

19. Volume of dissolution medium and sink condition The suitable 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 reasonably large amount of fluid should be used. To minimize the effect of the concentration gradient and maintain sink conditions, the concentration of the drug should not exceed 10 – 15% of its maximum solubility in the dissolution medium selected . Volume generally 500ml , 900 ml and 1000ml used. Dissolution Parameters 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 nonionic organic compounds such as Dextrose were added to the dissolution medium the benzoic acid solubility was directly dependent on its solubility in a particular solvent. When certain buffers or bases were added to the aqueous solvent, an increase in the dissolution rate was observed .

20. This inhibits wetting and lowers the dissolution rate. Some drug products are known to be tremendously sensitive to dissolved gas, the presence of air bubbles should be expected to increase the measurement uncertainty in dissolution testing. In USP Apparatus 2, released air bubbles deposit on the paddle shaft, the release of air bubbles alters the hydrodynamics of the system by changing the fluid flow characteristics in the dissolution vessel. Dissolution Parameters Deaeration of the dissolution medium The presence of dissolved air or other gases in the dissolution medium may impact the dissolution rate of certain formulations and lead to variable and unreliable results. Soluble air in distilled water can significantly lower its pH and as a result, affect the rate of dissolution of pH-sensitive drugs. Another severe effect is the tendency of the dissolved air to be released from the medium in form of a tiny air bubble. These bubbles collect at the surface of the dosage form thereby acting as a hydrophobic barrier between solvent and solid surface .

21. For a dissolved molecule, the diffusion coefficient, D, depends on the temperature T, according to the Stokes equation: Where k is the Boltzmann constant and 6π ηr is the Stokes force for a spherical molecule (η is the viscosity in cgs or poise units , and r is the radius of the molecule). Dissolution Parameters Effect of temperature of the dissolution medium Because drug solubility is temperature-dependent, careful temperature control during the dissolution process is very important and should be maintained within 0.5°. Generally, a temperature of 37°C is always maintained during dissolution determinations . The effect of temperature variations of the dissolution medium depends mainly on the temperature / solubility curves of the drug and excipients in the formulation.

22. Release profile by diminishing surface of the drug particles during the dissolution. It gives Erosion release mechanism. Applies to pharmaceutical dosage forms such as tablets, where the dissolution occurs in planes that are parallel to the drug surface if the tablet dimensions diminish proportionally in such a manner that the initial geometrical form keeps constant all the time. Hixson and Crowells Cube Root Law Particle regular area is proportional to the cubic root of its volume and equation is express as follows: Where, W is the initial amount of drug in the pharmaceutical dosage form . W t is the amount of drug remaining as a solid state at time t . K S is the constant incorporation the surface volume relation . Cube root of drug % remaining in matrix vs. time Drug release is limited by the dissolution rate of the particles, and not by diffusion through the polymer matrix .

23. Peak plasma concentration ( C max ) Time of peak concentration ( t max ) Area under the curve (AUC) 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.

24. Plasma concentration time profile indicating C max Pharmacokinetic Parameters Peak plasma concentration ( C max ) It is the maximum plasma drug concentration obtained after oral administration of drug. The point of maximum concentration of drug in plasma is known as the peak and the concentration of drug at peak is known as peak plasma concentration. Cmax is expressed in µg/ml or mg/L. It is related with intensity of action.

25. Plasma concentration time profile indicating t max Pharmacokinetic Parameters Time of Peak Concentration ( t max ) It is the time required to reach maximum drug concentration in plasma after extravascular drug administration. It is useful in estimating the rate of absorption. It is expressed in hours. Onset time and onset of action depends on time of peak concentration . Parameter is of particular importance in assessing the efficacy of drugs used to treat acute conditions like pain and insomnia.

26. Plasma concentration time profile indicating AUC Pharmacokinetic Parameters Area Under Curve (AUC) The area under the plasma drug concentration versus time curve. AUC is a measurement of the extent of drug bioavailability. The AUC reflects the total amount of active drug that reaches the systemic circulation. AUC is expressed in mcg*hour/ml . It is important for the drugs that are administered repetitively for the treatment of chronic conditions like asthma or epilepsy.

27. Disadvantages The values of f1 and f2 are sensitive to the number of dissolution time points used. If test and reference formulations are interchanged, f2 is unchanged but f1 is not, yet differences between the two mean profiles remain the same. The basis of the criteria for deciding the difference or similarity between dissolution profiles is unclear. Similarity Factor Model independent analysis (f1 & f2 Factor) Most popular methods recommended for use in a number of FDA guidance documents . Difference factor (f1) Similarity factor (f2) Advantages Easy to compute. Provide a single number to describe the comparison of dissolution profile data .

28. Similarity factor (f2) Logarithmic transformation of the sum-squared error of differences between the test and the reference products over all time points . Where, Rj is the percentage of dissolved product for a reference batch at time point t, Tj is the percentage of dissolved product for the test batch, N is the number of time points and wj is an optional weight factor, If each time point is weighted equally then it means wj =1. Similarity Factor Difference factor ( f1) The difference factor (f1) measures the percent error between two curves over all time points Where, Rj is the percentage of dissolved product for a reference batch at time point t, Tj is the percentage of dissolved product for the test batch, N is the number of time points.

29. Comparison Similarity Factor For rapid dissolving products, that may dissolve 85% in 15 minutes, comparison of dissolution profiles is not mandatory Difference factor Similarity factor It is proportional to the average difference between the two profiles It is inversely proportional to the average squared difference between the two profiles with emphasis on the larger difference among all the time points Measures the closeness between the two profiles Measures similarity F1 F2 Inference 100 Dissolution profiles are similar < 15 >50 Similarity or equivalence of two profiles

30. Applications New ANDA submission Filing variation to the original submission CBE filings Formula changes To waive the requirement of bioequivalence for smaller strengths of formulation Site transfer Scale up of the lots Regulatory submission Similarity Factor Data Structure and steps to follow This model independent method is most suitable for the dissolution profile comparisons when three to four or more dissolution time points are available. Determine the dissolution profile of two products (12 units each) of test (post-change) and reference (pre-change) products Using mean dissolution values from both curves at each time interval, calculate the difference factor and similarity factor. For curves to be considered similar, if f1 values close to 0 and f2 values close to 100.

31. This model is used to analyze the release of dosage forms when release mechanism is not well known or when more than one type of release phenomena could be involved. Korsmeyer – Peppas Plot It a simple, semiempirical model, relating exponentially the drug release to the elapsed time (t): According to this model, drug dissolution is function of the exponent of time, defined as ‘n’ in the formula. Where, n is indicative of drug release mechanism; t is time, k is rate constant; M / M  is fractional release of drug.

32. In non linear it is not possible to determine other variable value. In linear case if we have one variable value its possible to determine other variable value. Linearity Concept Linearity is a mathematical relationship between two variables quantities (they may be same unit), which are directly proportional to each other. Graphically it represents a straight line when plotted against each other.

33. The closer r is to zero, the weaker the linear relationship. In positive correlation , the values of both variables tend to increase together. Negative correlation , the values of one variable tend to increase when the values of the other variable decrease. The values 1 and -1 both represent "perfect" correlations, positive and negative respectively. Two perfectly correlated variables change together at a fixed rate. They have a linear relationship; when plotted on a scatterplot, all data points can be connected with a straight line . Linearity Concept The strength and direction of the linear relationship between two variable quantities is termed as correlation coefficient (r) (-1 to 1). Coefficient of determination (r2) ranges form 0-1. It denotes linearity of line / two variables.

34. In this formula, σ is the standard deviation, x1 is the data point, µ is the mean, and N is the total number of data points . Standard Deviation A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Standard Deviation is a statistical term used to measure the amount of variability or dispersion around an average. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.

35. If there is a difference between the observed and the expected frequencies then the value of Chi square would be more than 0. The larger the Chi-square the greater the probability of a real divergence of experimentally observed from expected results. This statistical test follows a specific distribution known as chi square distribution. Chi square test A chi-square test is a statistical test used to compare observed results with expected results. The purpose of this test is to determine if a difference between observed data and expected data is due to chance, or if it is due to a relationship between the variables you are studying . Thus, Chi-square is a measure of actual divergence of the observed and expected frequencies. If there is no difference between expected and observed frequencies the value of Chi-square is 0.

36. Uses of Chi-Square Test Although test is conducted in terms of frequencies it can be best viewed conceptually as a test about proportions. Χ 2 test is used in testing hypothesis and is not useful for estimation. Chi-square test can be applied to complex contingency table with several classes. Chi-square test has a very useful property i.e., ‘the additive property’. If a number of sample studies are conducted in the same field, the results can be pooled together. This means that χ2 values can be added. Chi square test The applications of χ2 Testing the divergence of observed results from expected results when our expectations are based on the hypothesis of equal probability. Chi-square test when expectations are based on normal distribution. Chi-square test when our expectations are based on predetermined results. Correction for discontinuity or Yates’ correction in calculating χ 2 Chi-square test of independence in contingency tables .

37. t test depends on the properties of normal distribution curves. Student’s t test This is parametric test used to compare samples form two different batches. It is usually used with small (<30) samples that are normally distributed. Types of t tests Single sample t test: only one group tested against a hypothetical mean. Independent sample t test: Two groups, two means, no relation between groups. Example test drug with placebo. Paired t test: Samples of matched pairs of similar units or group of units tested twice. Example before and after treatment effect.

38. The analysis of variance involves determining if the observed values belong to the same population, regardless of the group, or whether the observations in at least one of these groups come from a different population . ANOVA The ANOVA is used to identify and measure sources of variation within a collection of observations , hence the name analysis of variance . Analysis of variance is a parametric statistical technique that has found extensive applications in scientific research, mainly because of its flexibility . This method may be employed to analyse both paired and independent data and also is used to simultaneously compare large number of variables. The one-way ANOVA is nothing more than an expansion of the t-test to more than two groups of sample.

39. Two way ANOVA It is used when the data are classified on the basis of two factors. It is statistical test used to determine the effect of two nominal predictor variables on a continuous outcome variable. It analyses the effect of the independent variables on the expected outcome along with their relationship to the outcome itself. Two-way design may have repeated measurements of each factor or may not have repeated values. ANOVA One way ANOVA T is the simplest type of ANOVA, in which only one source of variation, or factor, is investigated. It is an extension to three or more samples of the t test procedures for use with two independent samples. In another way t test for use with two independent samples is a special case of one way analysis of variance.

40. ANOVA Applications of ANOVA Similar to t test. More versatile than t-test. ANOVA is the synthesis of several ideas and 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. Pharmacokinetic and pharmacodynamic data can be evaluated.

41. Thank you Professor in Pharmaceutics, Adarsh College of Pharmacy, Vita, Sangli 415311 [email protected] [phone]