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study of consolidation parameters in pharmacy

This document discusses various parameters studied in the consolidation of pharmaceutical formulations, including diffusion, dissolution, pharmacokinetic parameters, and similarity factors. It provides details on Higuchi's equation for diffusion parameters and the Hixson-Crowell cube root law. For dissolution parameters, the effects of agitation, pH, surface tension, viscosity, additives, medium volume and temperature are examined. Pharmacokinetic parameters like peak plasma concentration, time to peak concentration, and area under the curve are also summarized.

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Study of consolidation parameters
• Content Diffusion parameters Dissolution parameters Pharmacokinetic parameters Heckel plot Similarity factors f1 and f2
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.
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 a) Effect of agitation b) Effect of dissolution fluid c) Influence of pH of dissolution fluid d) Effect of surface tension of the dissolution medium
e) Effect of viscosity of the dissolution medium f)Effect of the presence of unreactive and reactive additives in the dissolution medium. g)Volume of dissolution medium and sink conditions h) Deaeration of the dissolution medium i) Effect of temperature of the dissolution medium
Effect ofagitation • The relationship between the intensity of agitation and the rate of dissolution varies considerably according to the type of agitation used, degree of laminar and turbulent floe in the system, the shape and design of the stirrer and the physicochemical properties of the solid.
• Dissolution test using high speed agitation may lack discriminative value and can yield misleading results. • Accordingly, the compendial methods in general, are conducted under relatively low agitation. • For the basket method, 100 rpm usually is utilized, while for the paddle procedure, a 50 – 75 rpm is recommended. • In case of the non official continuous flow, column type methods, a flow rate of 10 – 100 Ml/ min commonly is employed.
Effect of dissolution fluid • Selection of proper medium for dissolution testing depends largely on the physicochemical properties of the drug. • In the early 1960s, when dissolution was still in its infancy, great effort was spent on emulatingthe in vivo conditions in the gastrointestinal tract, especially pH, surface tension, viscosity and sink conditions.
Influence of pH of dissolution fluid • In 1949, a committee assigned by the American drug and pharmaceutical manufacturers associations recommended the use of distilled water as the test medium for the distengration test. • It was observed that in many instances water and dilute acid gave closely comparable results. • USP XV included 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). • The medium again was changed to water in the USP XVIII.
• Changes in pH exert the greatest effect in terms of drug solubility. • For weak acids, the dissolution rate increases with increasing pH, whereas, for weak bases, the dissolution rate increases with decreasing ph. • [ average pH of stomach in men is 1.9 and 2.5 in women]. • Therefore for acetylsalicylic acid (pKa=3.5) tablets and capsules, the dissolution rate would be expected to increase if the pH of the dissolution medium was higher than 3.
• For tablets containing active ingredients, whose solubilities are independent of pH, the dissolution rate does not vary significantly with changes in pH of the dissolution medium unless they contain certain excipients that are influenced by pH. • For example, Tablets that are formulated with carbon dioxide producing compounds, such as sodium bicarbonate, magnesium carbonate or calcium carbonate, tend to have slightly faster dissolution rate in acid medium than in water because rapid disintegration increases the effective surface area.
Effect of surface tension of the dissolution medium • According to the diffusion film theory, dissolution of the drug is governed by the interplay between two processes, the release of the drug from the solid surface and its transfer throughout the bulk of the dissolution medium. • If the drug is hydrophobic the dissolution rate is influenced primarily by the release processes, whereas, for hydrophilic drugs the transfer process is more likely to be the rate limiting step.
• 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 reducing the interfacial tension and micelle formation. • Addition of surfactant below the Critical micelle concentration (CMC) can increase significantly the dissolution rate because of better penetration of the solvent into the tablet resulting in greater avaibility if drug surface.
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. • The stokes-einstein equation expresses the diffusion coefficient as a function of viscosity, as can be seen from the following treatment. 𝐷 = µ𝑘𝑇 • µ = mobility (velocity at a force of one dyne) • k = boltzmann constant (1.38× 10− 16
Effect of thepresence of unreactiveand 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.
Volume of dissolution medium and sink conditions • The proper volume of the dissolution medium depends mainly on the solubilty 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. • In order to maintain 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.
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. • Another serious effect is the tendency of the dissolved air to be released from the medium in the form of tiny air bubbles that circulate at random and invariably affect the of the hydrodynamic flow pattern generated by the stirring mechanism.
• The gathering of air bubbles on the solid surface could also lead to a reduction in the specific gravity to the point where the tablet, or its disintegrating powder bed, float to the top of he basket in the liquid medium with a minimum chance of being wetted efficiently.
Effect of temperature ofthe 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.
• The effect of temperature variations of the dissolution medium depends on the temperature/ solubility curves of the drug and the excipients in the formulation. • Carstetensen pointed out that for a diffusion coefficient D is dependent upon the temperature according to equation 𝐷 = 𝑈𝑘𝑇 • U = mobility ( defined as the velocity when exposed to a force of one dyne) • k = boltzmann constant • T = absolute temperature
Hixson-Crowells cube root law • Hixson and Crowell described this W0 1/ 3 − Wt 1 /3 = Kt Where W0 is the initial amount of drug Wt is the remaining amount of drug at time t . • Plot: Data is to be plotted as cube root of drug percentage remaining in matrix versus time. • Application: This expression applies to pharmaceutical dosage form 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.
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.
Plasma drugconcentration-time profile
• Three important pharmacokinetic parameters: 1. Peak plasma concentration (Cmax) 2. Time of peak concentration (tmax) 3. Area under the curve (AUC)
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.
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. • Onset time and onset of action is dependent upon tmax. • The parameter is of particular importance in assessing the efficacy of drugs used to treat acute conditions like pain and insomnia.
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.
Similarity factorsf1 and f2
 DIFFERENCE FACTOR (f1) & SIMILARITY FACTOR(f2)  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. × 100 where, n = number of time points Rt = % dissolved at time t of reference product (pre change) Tt = % dissolved at time t of test product (post change) 3 0 /7          n Rt  Tt R t 1 f =        t 1  n  t 1
 The similarity factor (f2) as defined by FDA is logarithmic reciprocal square root transformation of sum of squared error and is a measurement of the similarity in the percentage (%) dissolution between the two curves         100 f2 = 50 × log1 1 n wt(RtTt) 0.5   nr1 3 1 /7
• Limits for similarity and Difference factors Difference factor Similarity factor inference 0 10 0 Dissolutions profile are similar ≤1 5 ≥5 0 Similarity or equivalence of two profiles
• 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.
• Using the mean dissolution values from both curves at each time interval, calculate the difference factor (f1) and similarity factor (f2) using the above equations. • For curves to be considered similar, f1 values should be close to 0, and f2 values should be close to 100. Generally, f1 values up to 15 (0-15) and f2 values greater than 50 (50-100) ensure sameness or equivalence of the two curves and, thus, of the performance of the test (post-change) and reference (pre- change) products.
• In dissolution profile comparisons, especially to assure similarity in product performance, the regulatory interest is in knowing how similar the two curves are, and to have a measure which is more sensitive to large differences at any particular time point. For this reason, the f2 comparison has been the focus in agency guidance and used to make a decision.
• 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). • The reference batch used should be the most recently manufactured pre-change product.
• Only one measurement should be considered after 85% dissolution of both the products (when applicable). • Toallow use of mean data, the percent coefficient of variation (% CV) at the earlier time points (e.g. 15 minutes) should not be more than 20%, and at other time points should not be more than 10%. • The mean dissolution values for reference can be derived either from last pre-change batch or the last two or more consecutively manufactured pre-change batches.
• Applications • • This method is more appropriate when more than three or four dissolution time points are available. • • The f2 may become invariant with respect to the location change and the consequence of failure to take into account the shape of the curve and the unequal spacing between sampling time points lead to errors. • • Nevertheless, with a slight modification in the statistical analysis, similarity factor would definitely serves as an efficient tool for reliable comparison of dissolution profiles.
• • Nevertheless, with a slight modification in the statistical analysis, similarity factor would definitely serves as an efficient tool for reliable comparison of dissolution profiles.
• Advantages • 1. They are easy to compute. • 2. They provide a single number to describe the comparison of dissolution profile data. • Disadvantages • 1. The values of f1 and f2 are sensitive to the number of dissolution time points used. • 2. The basis of the criteria for deciding the difference or similarity between dissolution profile is unclear.
Heckel plot
• 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.
• It is analogous to first order reaction ,where the pores in the mass are the reactant , that is: Log 1/E= Ky . P + Kr • Where….. Ky =material dependent constant inversely proportional to its yield strength ‘s’ Kr=initial repacking stage hence E0
• 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.
• Heckel plot is density v/s applied pressure • Follows first order kinetics • As porosity increases compression force also increases • Thus the Heckel’s plot allows for the interpretation of the mechanism of bonding. • Materials that are comparatively soft & that readily undergo plastic deformation retain different degree of porosity , depending upon the initial packing in the die.
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).
Type-a plots exhibits higher slop (Ky) thentype-b. because type-a materials have lower yieldstress. Type-b plots exhibits lower slop because brittle, hard materials are more difficult to compress.
• References: • • Dissolution, bioavaibility and bioequivalence by Hamed M. Abdou. • • The theory and practice of industrial pharmacy by Lachmann Liberman. • • Biopharmaceutics and pharmacokinetics by D.M. Bhramankar and Sunil b. Jaiswal