Application of Nonlinear Fitting and Selection of the Most Fitted Equation by AIC in Stability Test of Pharmaceutical Ingredients

ABSTRACT

We proposed a method for objectively selecting the most fitted rate equation among candidate rate equations based on chemical kinetics by both nonlinear regression analysis and Akaike's information criterion (AIC), to express the decrease of pharmaceutical ingredient as an appropriate equation. Pseudo-zero, first, and second-order rate equations were prepared as candidates beforehand, and AIC was introduced for selecting the most fitted rate equation among the candidates. We compared the proposed method to the Weibull method that expressed any decrease patterns as a single equation.

We quantified the contents of thiamine nitrate (VB1) and taurine after storage for one, three, and six months under 40°C–75% relative humidity by high-pressure liquid chromatography. Decrease patterns of each sample were most fitted to one of the candidate rate equations, that is, pseudo-zero, first, and second-order rate equations, respectively, and the degree of fit in the most fitted equation was superior to that of the Weibull method, except for the pseudo-first-order rate equation.

Moreover, we confirmed that the proposed method was considerably precise for estimating the stability of pharmaceuticals by comparing estimated residual rates and confidence intervals to experimental data.     

Statistical Optimization of a Controlled Release Formulation Obtained by a Double Compression Process: Application of an Hadamard Matrix and a Factorial Design

A formulation containing an antiinflammatory agent (diclofenac sodium), two inert matrices (ethylcellulose and polyvinyl chloride) and two lubricants (magnesium stearate and talc) was optimized by a double compression process

In a first stage, preliminary trials were performed in order to study the effect of lubricants added before and after precompression

An Hadamard matrix H(8) was applied to estimate the main effects of four parameters: applied force at the upper punch (UPF) during precompression, particle size range after grinding, UPF during the final compression and concentration of ethylcellulose added before the final compression

Following the Hadamard matrix, a factorial design 2² was built. The complete linear models were fitted by regression for each response reflecting the compression behaviour and dissolution kinetics

In an optimal point, the validation was carried out with the area under the dissolution curve, being the major response to be optimized

The dissolution curves were well fitted by the Weibull distribution     

Comparison of In VitroRelease Rates of Multisource Sustained-Release Papaverine Hydrochloride Products

The extent of differences in the In vitro release rate among 24 lots of 150 mg sustained-release papaverine hydrochloride products from six manufacturers was investigated.

The rotating bottle method for timed-release capsules, official in N.F. XIV, was used. Quantitation of papaverine hydrochloride in solution was done using ultra-violet spectrophotometry at two wavelengths to assure that there was no interference from other components of the formulation.

While in vitro dissolution data by itself cannot predict in vivo performance, variations from one manufacturer to another and also for the same manufacturer were observed. These included variations in the amount released both in the first hour and also in the total amount released.

Of the six products tested, Pavabid and Cerespan demonstrated the most consistent release patterns with slightly better consistency observed for the former. Observed differences may or may not be of clinical significance.     

Mathematical Simulation of Controlled Drug Release from Cylindrical Matrix Devices

The general mathematical model for controlled drug release from the cylindrical matrix device was developed. The system under consideration is composed of an active agent which is dissolved homogeneously in a cylindrical porous matrix device. The method of lines was employed to solve the partial differential equation in the present study.

The effects of hydrodynamic diffusion layer, the rate of spontaneous decay reaction in the device, the height to radius ratio of the device and the porosity distribution in the device on the rate of drug release were investigated by solving the two dimensional diffusion equation under non-steady state conditions.

The results indicated that the release rate may be significantly underevaluated if the data obtained in the in vitro studies under a poor mixing condition are analyzed mistakenly on the assumption of well mixing condition.

The findings in the present analysis are of practical significance to the design and development of matrix-diffusion type controlled release drug products.     

An Assessment of a Logarithmic Nonisothermal Storage Test

The expected biases in kinetic parameter estimates from a logarithmic nonisothermal storage test have been determined by simulation. The magnitude of the biases depends on heating rate, activation energy (E), and rate constant (k₀). Typical errors are -10 to -15% in k₀ and +0.5 to +1.0kcal per mole in E. An iterative linear solution is proposed to eliminate these errors.

A nonisothermal storage test enables the activation energy and frequency factor of a reaction to be obtained from a single experiment. Several methods have been described which differ in their time-temperature relationships or in the numerical methods used for parameter estimation^1-0. Within the pharmaceutical area the first of these methods was devised by Rogers (1963)¹.

In the Rogers' method the temperature is programmed so that the reciprocal of the absolute temperature varies logarithmically with time:

Substituting this into the Arrhenius and first-order equations and integrating yields:

Rogers has suggested that the last term on the right hand side becomes negligible as the temperature increases (i.e. k greatly exceeds k₀) so a plot of log[In(C₀/C)] versus log(1+t) will be linear provided initial data are omitted. Hence E and k₀ can be evaluated.

The method has been assessed experimentally by Cole & Leadbeater (1966)' who suggested that it yields accurate and reliable results. However an examination of their aqueous kinetic results indicates that parameter estimates may be biased; therefore the method has been re-assessed. This has been done using synthetic data so eliminating random variation which may obscure biases in individual experimental tests. Thus expected or long term average biases have been estimated.     

FORMATION OF FILTER CAKES WITH PARTICLE PENETRATION AT THE FILTER SEPTUM

The mass of solid particles entering the formation is an important factor in industrial cake filtration operations. Predictions of the concentration at the filter septum require the ability to predict the mass transport of solid particles under variety of conditions.

This study analyzes cake formation, including particle penetration at the filter septum. In addition to the total instantaneous mass balance equation, mass balance equations for captured and suspended particles and the fluid phase are averaged along the cake thickness taking into account conditions at the surface and the septum. Capture mechanisms, such as surface straining, and internal cake erosion and particle capture are included in the analysis.

The results are ordinary differential equations in terms of thickness, concentration of suspended particles in the filtrate, average particle concentration, average porosity, and such operational parameters, as slurry concentration, injection rate, and volumetric solid fraction.

To test tbe validity of the analysis presented here, the numerical results are compared to results for a simplified case. The conclusions from the sensitivity analysis conducted in this study agree with earlier conclusions. Results show that the concentration of suspended particles in the filtrate increases rapidly and then decreases gradually until it reaches zero after 13 hours. This yields that after 13 hours we have a clear filtrate.     

The use of optimazation techniques in pharmaceutical development

The lecture uses selected examples to illustrate the use of mathematical methods to optimize drug dosage forms:

Elucidation of compatibility between active ingredient and excipients required in the preformulation phase by factorial design.

Calculation of maximum allowable mean of particle sizes for active ingredient and the sum of auxiliary materials to achieve a sufficient content uniformity by applying the Stange-Pool equation.

Application of surface response research for identification of the working point in an “innocuous area of landscape” for scaling ups, handing over to production, of trouble shooting by using central composite desing and in the case of multiple constraints doing computerized grid search.

Only mentioned and not described in detail will be the methods for pharmacokinetical optimization, necessary for the development of modified release formulations.

Of course not for every development it is mandatory to use surface response research to get the necessary quality. But it is worthwile to apply refgularly factorial design for compatibility studies to calculate the necessary particle sizes and to compare in vivo results with dissolution rate data.     

Stability Indicating Hplc Method for Ribavirin and its Pharmaceutical Dosage Forms

The present work describes a specific, stability indicating HPLC method for determination of Ribavirin (1) and its pharmaceutical dosage forms.

Ribavirin was chromatographed on a microbondapak C18 column utilizing a simple mixture of 0.01M dibasic potassium phosphate and methanol (95: 5). The detection was done at 207 nm.

The available literature was scanned to locate the various methods(2,3) available along with the one reported in USP XXII.

A comparative study was made of the proposed method and USP method and the advantages over the USP method have been discussed.

The low value of Relative standard deviation and recovery of the drug in the range of 99.1% to 101.5% indicates a good precision and non-interference of the method.     

Research Papers: Preparation of Indobufen Pellets by Using Centrifugal Rotary Fluidized Bed Equipment Without Starting Seeds

ABSTRACT

Pellets containing Indobufen as model drug were prepared by using the centrifugal-rotary fluidized bed equipment without employing non-pareil seeds.

The influence of different amounts of spheronization enhancer (microcrystalline cellulose) and of different fillers (lactose, mannitol, calcium carbonate) on both processing and physical properties of the pellets were evaluated.

The preparation reproducibility was also investigated. The use of 30% w/w of microcrystalline cellulose was essential to produce a good quality pellets; the incorporation of filler decreased the qualitative characteristics of the pellets.

The water feeding rate proved to be an important parameter for the pellet growth.

Therefore, the results showed that this technology based on the rotary fluidized bed is a promising and alternative method in producing pellets.     

In Vitro and in vivo Availability of Spironolactone from Various Oral Preparations

The dissolution rates in vitro and the bioavailability in humans were determined for 6 preparations containing 25 mg spironolactone and 5 preparations containing 100 mg spironolactone. Linear relationships were obtained by pairwise correlation of in vitro parameters with in vivo parameters. The following parameters were used.

In vitro parameters of dissolution:

1. The area under the dissolution-time-curve up to 1 h

2. The fraction of active ingredient dissolved within 20 min.

3. The slope of the dissolution-time-curve at 50 % dissolution

4. The dissolution rate constant

5. The time up to 50 % dissolution of the substance

6. The maximum slope of the dissolution-time-curve

In vivo parameters of bioavailability:

1. The time of maximum plasmaconcentration

2. The area under the plasmaconcentration-time-curve up to 1 h and 2 h after application

3. The quantities of active ingredient excreted in the urine up to 2 h after application

The highest correlation coefficient was found between the areas beneath the dissolution-time-curve and the plasmaconcentration-time-curve up to 1 h each.

No significant correlations were found between the within 1 h dissolved substance and maximum plasma-concentration, the area under the plasmaconcentration-time-curve up to 4 h and 24 h and quantities of active ingredient excreted in the urine up to 4 h after application.     

Optimal Lane Depths for Single and Multiple Products in Block Stacking Storage Systems

Block Stacking is one of the most common storage methods for warehousing large quantities of palletized or boxed products, when high space utilization is the main concern. Efficient algorithms are currently only available to compute the optimal lane depth for a single product, assuming that all lanes have equal depth.

In most warehouses, the lane depth on each side of a single aisle is kept constant for layout arid material flow purposes. A layout procedure for selecting lane depths out of a limited number of allowable depths and for determining the number of lanes and aisles for each depth for the case of multiple products is developed. If the warehouse is perfectly balanced, then this procedure minimizes the required warehouse area.

One component of the layout procedure is an algorithm to compute the optimal number of lanes and the optimal lane depths for a single product, when the lanes are allowed to have a limited number of different depths.

The quality of this and other heuristics for the single product case is evaluated by comparing them to the optimal single product algorithm which allows an unlimited number of lane depths. It is shown that the optimal lane depths follow a triangular pattern     

Carboxymethylstarches in Wet Granulation

Commercialized carboxymethystarches (CMS) are both carboxyme-thylated and cross linked potato starch.

The influence of carboxymethylation and cross linkage on the disintegrating properties of starch are studied.

Tablets are made with acetaminophen as drug, Emcompress as diluant, Magnesium stearat as lubricant, and potato starch or its derivatives as disintegrants.

Tablets are prepared by direct compression or by wet granulation with the disintegrant intervening only in internal phasis.

Five disintegrants were studied, with two different concentrations:

native potato starch

potato starch simply cross linked

potato starch simply carboxymethylated

two potato starches both cross linked and carboxymethylated at two different degrees

Compressibility of powders blending and grain for compression are discussed.

The hardness, the tablet disintegration and the rate of drug dissolution are studied.

The results showed that the simply carboxymethylated starch has a totally different behaviour after direct compression or wet granulation. The poor results after wet granulation could be imputed to the bursting of starch granules during grain drying. Since it has lost its granular structure, the carboxymethylated starch will only allow a poor disintegration and a slow dissolution of the drug.

A very similar behaviour of native and simply cross linked starch: the results of which are bad for tablets either prepared by wet granulation or direct compression.

A very similar behaviour of the starches both carboxymethylated and cross linked, allowing a very good disponibility, either with tablets prepared by direct compression or wet granulation. These experiments prove :

the need for an sufficient cross linkage for CMS in a wet granulation process     

TRACER ANALYSIS OF FLUID CATALYST FLOW IN REFINERY CATALYTIC CRACKING UNITS

Tracer studies of fluid catalyst flow have been conducted in five different fluid catalytic cracking units containing from 200 to 1000 tons of circulating catalyst. A single pulse injection of about 2 pounds of catalyst labeled with Au198 or Sc46 can yield the following Information:

1. Catalyst circulation rate.

2. Mean catalyst residence time in specific parts of the circuit.

3. Catalyst Inventory in the corresponding vessels.

4. Catalyst residence time distribution in these vessels.

5. Total unit inventory by tracer dilution.

6. Attrition rate and average lifetime of the labeled catalyst.

Experimental methods and data analysis are described, and examples are given. The effects of residence time distribution on reaction kinetics are discussed.     

Disintegrants in Solid Dosage Forms

The dynamic approach to tablet disintegration, which is based on the measurement of the force that develops inside the compact upon water entrance, is basically taken up.

The combined measurements of force development and water uptake, simultaneously effected on the same compact, provide a novel parameter that is proposed to quantify and compare the efficiency of disintegrants.

The new parameter, which is based on the “force-equivalent” concept, expresses the capability of a disintegrant of transforming water uptaken into swelling (or disintegrating) force. A few examples, that illustrate the usefulness of this parameter for disintegrant characterization, are given.

In parallel to the quantification of swelling (or disintegrating) efficiency inside compacts, attention is also being paid to the characterization of swelling disintegrants as pure materials.

In particular the case of the so-called limited swelling materials, for which the quantification of intrinsic swelling (particle volume increase in swelling media) is critical, is considered.

The applicability of an instrumental method, which is based on the employment of a Coulter Counter, is discussed alternatively to microscopic methods.

Disintegrant characterization may also be considered in view of new possible exploitations of the swelling properties of polymers in controlling drug release.     

Methods for the Determination of the Carbon Dioxide Evolved from Effervescent Systems

Different methods for determining the carbon dioxide evolved from effervescent systems are described. In addition, a comparison between some of them is carried out when a stoechiometric mixture of L-tartaric acid and sodium bicarbonate reacts.

The methods compared are: gravimetric, volumetric and gasometric.

The gravimetric methods can be direct or indirect. The direct ones are based on taking in the carbon dioxide by a sorbent substance. The increase of weight after the absorption represents the CO₂ evolved. In the indirect gravimetric methods the amount of carbon dioxide is determined by substraction of the weight of the sample after and before the effervescent reaction.

The volumetric methods are based on an acid-base titration. In the method used, the carbon dioxide released reacts with barium hydroxide. The excess of barium hydroxide is titrated with oxalic acid. It is possible to calculate then the carbon dioxide produced in the reaction from the volume of oxalic acid used.

In the gasometric methods the volume of gas is directly determined by the displacement of a solution when the gas is released.

The gasometric method seems to be the most efficient among the studied ones.     

Polymorphic Transitions of Carbamazepine During Grinding and Compression

Carbamazepine is a potent anticonvulsivant, but, irregular plasma levels are noticed. The variability of therapeutic efficiency can be attributed to interindividual sensibility, chronobiologic effect, but also to rates of dissolution which can differ when polymorphs are induced by technologic operations.

Several crystalline forms of Carbamazepine have been characterized. As for us, we have studied three crystalline modifications which can be found in commercialized galenic forms: the most usual beta form, the alpha form and the dihydrate.

The aim of this work was to investigate:

- the behaviour of these three crystalline forms during compression

- the possibility of crystalline structural changes under grinding and tabletting conditions. Indeed, polymorphous transformations may occur during technologic operations such as grinding or compression owing to the increase of internal energy.

Grinding was performed in a ball mill for 15 and 60 minutes. Compression was carried out using an instrumented single punch machine. The different parameters of compression, and hardness of resulting tablets were investigated.

X Ray diffraction and Differential scanning calorimetry were carried out on the different samples of ground powders and on carefully crushed samples of each batch of tablets.

The results point out at the best compressibility of dihydrate, and the most effective stability of the alpha form. However, the usual beta form remains stable in normal conditions of fabrication and storage.     

A Novel Method for Rapid Non Destructive Determination of O/W Creams Stability

A nonconventional method for evaluation of emulsion stability was developed. The method was found to be valid for viscous emulsions and results obtained are in good correlation to conventional methods compared.

The technique is based on electrical conductivity measurements during nondestructive short heating-cooling-heating cycles carried out on cosmetic viscous emulsions. Conductivity curves were obtained on a recorder, where the second heating cycles were lower and almost parallel to the first heating curves. The bigger the conductivity differences between the two heating curves, the lower is the emulsion stability.

A relative Stability Index Δ/h, indicating relative change in conductivity between two cycles was elaborated. This index was usefull in finding out

- optimal required HLB values for required emulsion

- optimal amount of oily phase

- emulsifier concentration.     

Controlled Release from Glycerol Palmito-Stearate Matrices Prepared by Dry-Heat Granulation and Compression at Elevated Temperature

Diprophylline release from glycerol palmito-stearate “precirol” matrices containing different direct compression (DC) excipients, with variable dissolving/disintegrating ability, is investigated. The matrices are formed by employing dry-heat granulation and compression at elevated temperature.

Greater drug release prolongation is achieved with the dissolving DC excipients than with the swelling ones. The release is described on the basis of two biexponential first order models and the Weibull function as well.

The effect of compression conditions (temperature and pressure) on the drug release is found to be related to the compaction behaviour of the DC excipients, i.e. plastic deformation or fragmentation.     

Effect of Eudragit Type Polymers on the Drug Release from Magnesium Oxide Granules Produced by Laboratory Fluidization

The differences in the bioavailability of different drug products are most frequently caused by differences in the dissolution rates of the active ingredient. In case of magnesium oxide the drug release can be directly determined by reaction kinetics method based on acid neutralization.

For a more precise study of the factors influencing the kinetical characteristics of the neutralization rates it is advisable to use homogeneous granule fractions. Before the granulation the substance was pretreated with silicone oil. The granulation of the obtained grains having hydrophobe surface was carried out in an AEROMATIC STREA-I type laboratory fluidization equipment with Eudragit polymer solved in isopropyl alcohol.

For determining the acid neutralization kinetics of the granules the “constant pH” method and the Rossett-Rice test were used.

As a result of the granulation the neutralization rate decreased. The granules can be considered as an Eudragit matrix which contains the pretreated magnesium oxide in embedded form. During the chemical reaction the resulted salt (magnesium chloride) leaves the surface of the unreacted magnesium oxide unless having a chemical reaction with the polymer. Meanwhile the residual matrix forms a mesh which increases the viscosity of the solution and the thickness of the diffusion layer. The dissolution rate decreases in both cases.

Under the same conditions the kinetic values of the neutralization change by several magnitudes depending on the utilized methods. In this way different systems of medicine, which alter their reaction capacity according to the expected physiological purposes, can be created.