multivariate methods in tablet formulation by jon …

MULTIVARIATE METHODS

IN TABLET FORMULATION

by

JON GABRIELSSON

Akademisk avhandling Som med tillstånd av rektorsämbetet vid Umeå universitet för erhållande av Filosofie Doktorsexamen vid Teknisk–Naturvetenskapliga fakulteten, framlägges till offentlig granskning vid Kemiska institutionen, Umeå universitet, sal KB3B1, KBC, fredagen den 28 maj 2004, kl. 9.00. Fakultetsopponent: Dr. Marc Brown, Department of Pharmacy, King’s College, London, England.

COPYRIGHT © 2004 JON GABRIELSSON ISBN: 91-7305-653-7

PRINTED IN SWEDEN BY VMC–KBC UMEÅ UNIVERSITY, UMEÅ 2004

Title Multivariate Methods in Tablet Formulation Author Jon Gabrielsson, Department of Chemistry, Organic Chemistry, Research Group for Chemometrics, Umeå University, SE – 901 87, Umeå, Sweden. Abstract This thesis describes the application of multivariate methods in a novel approach to the formulation of tablets for direct compression. It begins with a brief historical review, followed by a basic introduction to key aspects of tablet formulation and multivariate data analysis. The bulk of the thesis is concerned with the novel approach, in which excipients were characterised in terms of multiple physical or (in most cases) spectral variables. By applying Principal Component Analysis (PCA) the descriptive variables are summarized into a few latent variables, usually termed scores or principal properties (PP’s). In this way the number of descriptive variables is dramatically reduced and the excipients are described by orthogonal continuous variables. This means that the PP’s can be used as ordinary variables in a statistical experimental design. The combination of latent variables and experimental design is termed multivariate design or experimental design in PP’s. Using multivariate design many excipients can be included in screening experiments with relatively few experiments.

The outcome of experiments designed to evaluate the effects of differences in excipient composition of formulations for direct compression is, of course, tablets with various properties. Once these properties, e.g. disintegration time and tensile strength, have been determined with standardised tests, quantitative relationships between descriptive variables and tablet properties can be established using Partial Least Squares Projections to Latent Structures (PLS) analysis. The obtained models can then be used for different purposes, depending on the objective of the research, such as evaluating the influence of the constituents of the formulation or optimisation of a certain tablet property.

Several examples of applications of the described methods are presented. Except in the first study, in which the feasibility of this approach was first tested, the disintegration time of the tablets has been studied more carefully than other responses. Additional experiments have been performed in order to obtain a specific disintegration time. Studies of mixtures of excipients with the same primary function have also been performed to obtain certain PP’s. Such mixture experiments also provide a straightforward approach to additional experiments where an interesting area of the PP space can be studied in more detail. The robustness of a formulation with respect to normal batch-to-batch variability has also been studied.

The presented approach to tablet formulation offers several interesting alternatives, for both planning and evaluating experiments. Keywords PCA, statistical experimental design, multivariate design, PLS, excipients, direct compression, tablet formulation, robustness testing.

ISBN: 91-7305-653-7

CCoonntteennttss 11.. LLiisstt ooff PPaappeerrss ____________________________________________________________________________________ 77 22.. LLiisstt ooff AAbbbbrreevviiaattiioonnss ________________________________________________________________________ 88 33.. IInnttrroodduuccttiioonn ______________________________________________________________________________________ 99

3.1. Tablet Formulation in a Historical Perspective ____________ 9 3.1.1. Tablet Formulation: Basic considerations ___________ 10

3.2. Tablet Formulation and Multivariate Methods ___________ 11 3.3. Scope of the Thesis ________________________________ 13

44.. MMuullttiivvaarriiaattee MMeetthhooddss ______________________________________________________________________ 1144 4.1. Principal Component Analysis________________________ 14

4.1.1. MSC and SNV ________________________________ 16 4.1.2. Missing Data _________________________________ 17

4.2. Multivariate Characterisation_________________________ 17 4.2.1. Physical Properties_____________________________ 18 4.2.2. FT-IR and NIR ________________________________ 20

4.3. Statistical Experimental Design _______________________ 21 4.3.1. Mixture Design________________________________ 23

4.4. Multivariate Design ________________________________ 24 4.5. PLS_____________________________________________ 26 4.6. Validity of Models _________________________________ 27

55.. MMuullttiivvaarriiaattee MMeetthhooddss AApppplliieedd ttoo TTaabblleett FFoorrmmuullaattiioonn ____________________ 2299 5.1. Screening Experiments______________________________ 29

5.1.1. Excipient Selection Based on Physical Properties_____ 31 5.1.2. Excipient Selection Based on Spectroscopic Properties 31

5.2. Model Interpretation________________________________ 33 5.3. Additional Experiments _____________________________ 35

5.3.1. Strategies for Excipient Selection _________________ 36 5.3.2. Evaluation of Results ___________________________ 38

5.4. Robustness Testing_________________________________ 40 66.. CCoonncclluuddiinngg RReemmaarrkkss ______________________________________________________________________ 4433 77.. FFuuttuurree PPrroossppeeccttss ______________________________________________________________________________ 4455 88.. RReeffeerreenncceess ______________________________________________________________________________________ 4477 99.. AAcckknnoowwlleeddggeemmeennttss ________________________________________________________________________ 5533

Multivariate Methods in Tablet Formulation

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This thesis is based on the papers listed below, which will be referred to in the text by the corresponding Roman numerals (I-V). I J. Gabrielsson, Å. Nyström, and T. Lundstedt, Multivariate

methods in developing an evolutionary strategy for tablet formulation, Drug Dev. Ind. Pharm., 26(3), 275-296, 2000

II J. Gabrielsson, N-O. Lindberg, M. Pålsson, F. Nicklasson, M. Sjöström, and T. Lundstedt, Multivariate Methods in the Development of a New Tablet Formulation, Drug Dev. Ind. Pharm., 29(10), 1053-1075, 2003

III J. Gabrielsson, N-O. Lindberg, M. Pålsson, F. Nicklasson, M. Sjöström, and T. Lundstedt, Multivariate Methods in the Development of a New Tablet Formulation; Optimization and Validation, Submitted Drug Dev. Ind. Pharm.

IV J. Gabrielsson, A-C. Pihl, N-O. Lindberg, M. Sjöström, and T.

Lundstedt, Multivariate Methods in the Development of a New Tablet Formulation: Excipient Mixtures and Principal Properties, Submitted Drug Dev. Ind. Pharm.

V J. Gabrielsson, A-C. Pihl, N-O. Lindberg, M. Sjöström, and T.

Lundstedt, Multivariate Design in Robustness Testing of a Tablet Formulation, Submitted Drug Dev. Ind. Pharm.

Reprinted with kind permission from Marcel Dekker, Inc.


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Abbreviation Meaning A Number of components in a PCA or PLS

model Ac Area of contact between tablet and die wall ANOVA Analysis of Variance API Active Pharmaceutical Ingredient DModX Distance to the Model in X FT-IR Fourier Transform-Infrared HPC Hydroxypropyl cellulose HPMC Hydroxypropyl methylcellulose,

Hypromellose MC Methyl cellulose MCC Microcrystalline cellulose MLR Multiple Linear Regression MgSt Magnesium Stearate MSC Multiplicative Scatter Correction NIR Near-Infrared O-PLS Orthogonal Partial Least Squares

Projections to Latent Structures OSC Orthogonal Signal Correction PCA Principal Component Analysis PLS Partial Least Squares Projections to Latent

Structures PP Principal Property, Score PRESS Prediction Error Sum of Squares R Force transmission ratio RMSEP Root Mean Squared Error of Prediction RSM Response Surface Methodology SIMCA Soft Independent Modelling of Class

Analogy SNV Standard Normal Variate Transformation SS Sum of Squares X Data matrix of descriptive variables Y Data matrix of one or several measured

responses


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This report, by its very length, defends itself against the risk of being read

Winston Churchill

33..11.. TTaabblleett FFoorrmmuullaattiioonn iinn aa HHiissttoorriiccaall PPeerrssppeeccttiivvee

RUGS ARE RARELY ADMINISTERED AS pure chemical substances. They are most frequently given as formulated

preparations or medicines, usually orally, the most popular dosage forms being tablets, capsules, suspensions, solutions and emulsions (1). Tablets account for more than 80% of all pharmaceutical dosage forms administered to people (2).

Pharmaceutical formulation is the process by which active ingredients of drugs are converted into preparations which are safe, effective and convenient to use (3). Back in the days when all drugs were of natural origin, pharmaceutical technology was concerned mainly with extracting and compounding natural products to provide the dispensed medicine. Most efforts were spent on the former while the latter process was considered more of an art than a proper subject for scientific study. The skill of the pharmacist was mainly devoted to producing something of presentable appearance from the somewhat complex recipes or prescriptions provided by the clinicians. Over time a group of standard recipes, published in national pharmacopoeias or similar reference books were developed, representing the first serious attempts at formulation.

With increasing demands and consequent large-scale manufacture, accompanied by needs for batch-wise uniformity, stability and quality control, a more careful study of the original recipes commenced to remove the more obvious technical defects. With the emergence of other sources of drugs, i.e. organic synthesis and biochemical fermentation

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processes, the efforts of the pharmacists were increasingly directed towards the final product, i.e. the formulation.

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ABLET FORMULATIONS TYPICALLY CONSIST OF an active pharmaceutical ingredient (API) together with nonactive

ingredients, or “excipients”, such as fillers or diluents, binders or adhesives, disintegrants, lubricants and glidants, colours, flavours and sweeteners (4). It might also be necessary to add miscellaneous components such as buffers, depending on the application.

Common goals in pharmaceutical development and research work are to develop formulations of required stability, with specific release profiles and to ensure that operating conditions are robust during production.

Materials with, for instance, variations in particle size distribution and moisture content are continuously being developed by manufacturers of excipients (5). Usually the excipients are classified according to some primary function they perform in the tablet. Many excipients will also have a secondary function, desirable or not. This may complicate both the choice of suitable excipients for a study, and evaluation of the results of such studies. These potential problems will be further discussed in section 5.1.

Fillers are normally thought of as inert ingredients. Nevertheless, the level of filler can affect the properties of a tablet. A filler is an inexpensive material added to appropriate levels to bring a formulation to a desired concentration in a convenient form, depending on the amount of API and excipients with other functions. Lactose is the most commonly used filler. Starch and microcrystalline cellulose (MCC) are also commonly used fillers in tablet formulation.

Several other kinds of excipients are often added, notably the following. Binders are present in tablet formulations in order to hold the particles together, thus giving the tablet enough strength to allow normal processing and packaging. The purpose of a disintegrant is to break up the tablet after administration, and thereby facilitate the drug to dissolve at the required time. The function of lubricants is primarily to reduce friction

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during compression and ejection of tablets. Glidants are added to powder mixtures to improve flow characteristics. Colours are generally present for one or more of the following reasons; to enable otherwise similar-looking products to be distinguished, to prevent mix-ups during manufacture and/or to enhance the aesthetic and thus market potential of the product. Sweeteners may be added to improve the taste and flavour, especially of chewable tablets.

Tablets are prepared by compressing either powders or granules. Granules are prepared by granulation, often wet granulation: a process in which powder particles are made to adhere to form larger agglomerates (6). The tablets manufactured in the work underlying this thesis were all made by direct compression of powders. There are several advantages of using direct compression, without preceding granulation, e.g. there are fewer processing steps and fewer potential stability problems for API’s that are sensitive to heat and moisture (2). However, there are also some disadvantages, e.g. segregation can occur if the API and excipients differ in particle size, and poorly flowing drugs and excipients are generally unsuitable for direct compression.

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HE APPLICATION OF CHEMOMETRIC METHODS in pharmaceutical research and development has increased over the years (7, 8).

Many published works include the use of statistical experimental design, especially designs that deal with optimisation, where much effort is spent on obtaining detailed knowledge about the investigated domain. Fewer studies have exploited multivariate data analysis techniques, such as PCA and PLS, but use of these methods is also increasing, as illustrated by the following examples.

Patel and Podczeck studied the effects of the type and source of MCC on capsule filling (9). In their investigation PCA was used to characterise eight MCC samples described by eight variables related to powder and particle properties. The latent variables were used to analyse the complex relationship between the powder properties of the MCC products and capsule filling performance.

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In the thesis by Westerhuis a multivariate approach was applied for selecting model drugs for the multivariate calibration of a tablet manufacturing process involving wet granulation (10). From a PCA model for 19 model drugs described by data on seven properties taken from the literature, eight model drugs were selected. Because of the diversity of the drugs, the design levels of the process variables of the granulation process also had to be varied.

Ahrabi et al. developed a tablet formulation, based on pectin, for colon delivery (11). A D-optimal design with constraints was implemented and the results were evaluated with PCA and PLS. Formulations for both granulation and direct compression were evaluated regarding specific release requirements and the mechanical strength of the tablets.

In a study by Gustafsson et al. samples of hydroxypropyl methylcellulose (HPMC) with different types of substitution, i.e. different contents of hydroxypropyl and methoxy groups, were characterized with NIR and FT-IR (12). Both particle properties and tablet properties were measured and quantitative relationships were established with PLS. The different properties were generally well predicted for a set of test samples.

Other attempts to incorporate multivariate models in tablet formulation, which are inevitably computer-based because of the complexity of the calculations, have included the use of non-linear processing, e.g. neural networks (NN), thus introducing “artificial intelligence” into the formulation process. The general idea is to use these systems to “learn” from experiments, and thus eventually evolve into expert systems mimicking the knowledge of experienced formulators. Software based on these methods has been developed, to aid less experienced formulators, which will give answers of the type “If this input, then this output”. One of the problems with these methods is that, depending on the method used, it is not always easy to understand the relationship between the factors and the responses. For more information on NN and expert systems various textbooks and articles are available (13-17).

Given the wide range of products and processes involved in pharmaceutical research and development, there is certainly no shortage of possible areas of application. However, with few exceptions, chemometric tools are applied in certain steps rather than throughout the


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entire formulation process, from preformulation to multivariate process control, at least in the works that have been published to date.

With the growing number of excipients there is a need for a general strategy for evaluating excipients in tablet formulation. No studies in which several excipients have been subjected to systematic multivariate analysis appear to have been reported.

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HE GOAL OF THIS THESIS IS to present a rational strategy for applying chemometric methods to tablet formulation. Topics

covered include the multivariate characterisation of the excipients, in terms of both physical and spectral properties, together with Principal Component Analysis (PCA), statistical experimental design in principal properties (PP’s) and Partial Least Squares Projections to Latent Structures (PLS) analysis.

Several reviews and textbooks have been written describing the many excipients with various functions that are available on the market (18, 2). Researchers have written articles and even based entire theses on one or a few of the excipients that were included in the studies underlying this thesis, but are only briefly mentioned in the text (19-26). To put this work into context, it is a general study that tries to cover the huge field of tablet formulation for direct compression. Attempts to replace years of extensive research with a model based on around thirty experiments, however carefully planned, would be belittling to pharmaceutical science and doomed to fail miserably. Instead, a different perspective and an alternative approach to planning and conducting tablet formulation are presented. The development of new materials, which is still a slow process, could possibly benefit from this approach (5). The strategy presented here is unique in the sense that the methods involved do not seem to have been applied to tablet formulation before.

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44.. MMuullttiivvaarriiaattee MMeetthhooddss

To err is human, but to really foul things up requires a computer.

Paul Ehrlich

44..11.. PPrriinncciippaall CCoommppoonneenntt AAnnaallyyssiiss

DATA TABLE X, THAT IS AN N x K DATA MATRIX, consists of N rows and K columns. The samples or objects in the rows are

described by measured or calculated variables given in the columns. In a graphical illustration of a data matrix the objects are a swarm of N points in a coordinate system of K variables.

In cases where a number of objects are described by many variables the variables tend to be correlated to some extent. This is especially true for spectral variables, where a high absorbance at one wavelength is usually accompanied by similar absorbance values at neighbouring wavelengths. PCA uses this correlation to describe the variation in the data with a minimum number of orthogonal components. Numerous descriptions of PCA can be found in the literature (27-29). PCA can be mathematically expressed as follows:

EptEPTXA

aaa +′⋅=+′⋅= ∑

=1

PCA corresponds to the least squares fitting of a straight line

(A=1) or an A-dimensional hyper plane to the data in the K-dimensional variable space. Objects are projected onto a subspace of lower dimension and receive new identities, t-values, often referred to as principal properties (PP’s) or scores. The variation of the objects is summarized in

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the T (N x A) matrix, which includes a score vector ta for each component.

Score values from two principal components, e.g. t1 and t2, together span a mathematical plane, often referred to as a score plot. Objects are projected onto the plane to form a two-dimensional model of the data. One could say the t1/t2 score plot constitutes a window through which data can be viewed. This facilitates the detection of groupings, trends and outliers (deviating objects) in data sets.

How the original variables influence the principal component is summarized in the P (K x A) matrix. The loading vector pa describes how the variables contribute to the score vector and explains the observed trends and groupings in the scores.

The difference between the original coordinates and the projections are termed residuals. The residual matrix E contains the part of the data matrix that is not explained by the model. Deviating objects in the data can cause problems. The process of detecting and diagnosing outliers is important both when fitting and interpreting the model. An outlier may be an object that does not fit very well into the model, i.e. one for which the distance to the model in X (DModX) is too large to be accepted. Examining the residuals of that particular object will reveal the cause of the deviation. An outlier may, alternatively, be an object that lies far away from other objects in the score plot. Since PCA is a least squares technique such an outlier may cause one of the principal components to run through it or very close to it, resulting in a skewed model. Such outliers should be removed upon identification.

PCA models can be calculated using the Nonlinear Iterative Partial Least Squares (NIPALS) algorithm, invented by Fisher and MacKensie (30) and later modified by Wold (31). The first component explains as much as possible of the variance, the second component is orthogonal to the first and explains as much as possible of the residual variance, and so on.

The diversity of PCA applications makes it a very powerful tool in many situations. PCA can be used as a means to discover trends, groupings and outliers in many types of data, to classify objects, as well as to reduce the number of dimensions and descriptive variables. The features of the PCA model of most interest in any particular study will depend on the systems being investigated and the purposes of the study.


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ULTIPLICATIVE SCATTER CORRECTION (MSC) was first presented by Geladi et al. as a method for linearization and

scatter correction of NIR (32). It is assumed that the factors affecting physical light scattering of a particular wavelength differ from the chemical factors affecting light absorption. Hence, a corrected spectrum should include only chemical information. In order to normalise the scatter level an “ideal” sample, often the average of the data set, is used to correct data for each of the samples. The following equations are used for the calculations:

exbax iii ++=

iiicorrMSCi baxx /)(, −=−

The sample spectrum xi is regressed onto the average x in order

to calculate the additive offset term ai and the multiplicative constant bi. MSC should be used carefully, as all of the samples influence the

correction terms, so a deviating sample could have adverse effects on the corrections.

Barnes et al. presented Standard Normal Variate Transformation (SNV) as a method for removing unwanted variation from NIR spectra (33). In contrast to MSC, the correction is performed on an individual sample basis, thus eliminating the possible negative effects of a deviating sample. Variations in variable spectral path length, e.g. from differences in packing density, and non-specific scatter of radiation at the surface of particles can be removed using SNV.

The following equation is used for calculations:

1)(

/)(2

, −∑ −

−=− nxx

xxx iicorrSNVi

Here the term xi is an individual absorbance value of a spectrum

with i sample points and x is the spectrum mean.

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One of the drawbacks of using SNV, as well as MSC, is that potentially interesting information regarding the particle size is lost.

In cases where a response matrix Y exists there are other methods for removing noise from spectra. The concept of Orthogonal Signal Correction (OSC), a method for removing information in spectra that is not related to the response prior to investigation, was introduced by Wold et al. (34). Orthogonal-PLS (O-PLS), first presented by Trygg and Wold and further developed by Trygg, removes unwanted systematic variation in X in much the same way as OSC, but without pre-processing the data (35, 36). Both methods offer the possibility to analyse the removed variation.

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ISSING DATA CAN GENERALLY BE HANDLED by NIPALS. As a rule of thumb, to use this approach there should be five times

as many observations in any row or column as the number of dimensions (A) being calculated. The missing values should also be randomly distributed. Nelson et al. and Walczak et al. have published articles on alternative approaches for handling missing data (37-39).

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ULTIVARIATE CHARACTERISATION is the basis for multivariate design and as such is very important. Descriptive variables

that are used to characterise the excipients (for example) may be either physical properties or other variables, see sections 4.2.1 and 4.2.2.

Usually a homogenous group of constituents are put in the same group and characterised by the same variables, as in Paper I, where the class of excipients commonly used as lubricants are described using literature data on relevant physical properties. By applying PCA to the descriptive data the important information is extracted in a few principal components (PC’s). The PC’s are often referred to as latent variables or the principal properties (PP’s) of the data set. Each excipient is assigned a score value in each PC. Thus, the excipients are compared and related to

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on a continuous scale of PP’s, which are assumed to reflect real differences in excipient properties and greater distances between excipients along the PC’s reflect greater differences in behaviour.

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NUMBER OF PHYSICAL PROPERTIES of the excipients influence the properties of the tablet, e.g. particle size and bulk volume

(4). The tensile strength of tablets made from HPMC of different particle sizes, methoxy/hydroxypropoxy substitution ratios, molecular sizes and moisture contents was studied by Malamataris and Karidas (40). They found, amongst other things, that changes in tensile strength were linked

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Figure 1. A p[1]/p[2] loading plot from the PCA model for lubricants. The lubricants were characterised in terms of six variables; density (d), melting point (M.P.), molecular weight (M.W.), refraction index (R.I.), ejection force (Fe) and force transmission ratio (R).

to particle size. Gustafsson et al. studied particle properties and compaction behaviour of HPMC with different degrees of substitution (12). Differences in tensile strength were found between samples of

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different substitution ratios. The degree of substitution was found to affect the mechanical as well as the particle properties of the investigated powders.

In multivariate characterisation of excipients, the use of physical properties has advantages as well as disadvantages. The models can be readily interpreted, i.e. the loadings are meaningful and the variables responsible for the spread in objects can be identified and analysed. Determining physical properties of excipients demands a systematic approach and may consume substantial resources.

In Paper I excipients commonly used as lubricants were described using literature data for relevant physical properties, see Figure 1. A region of interest in the score plot of the lubricants was observed, see Figure 2, and the superiority of the lubricants in this region was experimentally verified.

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Figure 2. With the information from the loadings in Figure 1 an expected area of interest can be identified in the t[1]/t[2] scores plot. The upper right quadrant contains many stearates, including MgSt, which is the most commonly used lubricant.

There are large amounts of documentation regarding excipients (18). However, not all properties have been determined for all excipients


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and not all tests have been standardized (41). This makes the development of comprehensive models difficult, if not impossible, but an alternative is to construct smaller, local models, for instance of all available HPMC batches.

44..22..22.. FFTT--IIRR aanndd NNIIRR

RGANIC MOLECULES, CONTAINING MAINLY C-H, O-H, N-H, C=C and C=O bonds, absorb light in the Infrared (IR) region

(42). The absorbed radiation is converted into energy of molecular rotation and vibration. The energy is quantized and a molecular spectrum of both rotations and vibrations consists of characteristic vibrational-rotational bands. It is unlikely that any two compounds, except enantiomers, will give identical IR spectra.

In Fourier Transform IR (FT-IR) no monochromator is used and the entire range of radiation is passed through the sample simultaneously. This saves time and allows for the average of several scans to be combined in order to average out artefacts. FT-IR gives information regarding functional groups of the characterised excipients. It should provide information about both the type of functional groups present and their relative abundance.

The Near Infrared (NIR) spectrum consists of overtones and combination bands that are attributed mainly to the hydrogen vibrations of the functional groups. NIR spectroscopy probes the sample to a certain depth, providing vast amounts of spectral information about the sample.

NIR has found widespread use in pharmaceutical applications as a method for characterizing raw materials, pharmaceutical intermediates and finished dosage forms (43-45). O’Neil et al. measured the median particle size of drugs and excipients using NIR reflectance and MLR (46). In another work by O’Neil et al. the cumulative particle size distribution of MCC was measured using NIR reflectance (47). A study by Gustafsson et al. shows that both NIR and FT-IR spectra contain information regarding particle properties, and that the spectra contain information that can be linked directly to tablet properties (12). This suggests that spectroscopic characterisation of excipients is a relevant and reasonable alternative to using physical properties.

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Hence, PP’s calculated from both FT-IR and NIR spectra should reflect properties of the excipients that are related to the way the particles bind together (e.g. friability, crushing strength and disintegration time) and how they flow (e.g. Hausner ratio and weight variations). This is all relevant information for a formulator that provides indications of important factors to consider when choosing excipients for an experimental design.

The main advantages of spectroscopic characterisation of excipients are that it can be performed quickly and it does not consume large amounts of resources. The major drawback is that the loadings from a model of spectroscopic data are less informative and more difficult to interpret than loadings of a similar model of physical characteristics.

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XPERIMENTS ARE CARRIED OUT TO TEST a proposed theory, or to gain knowledge about a studied system. For either objective it

is essential to plan the experiments in such a way that statistically sound conclusions can be drawn and as much information as possible can be gained from the experiments. Statistical experimental design has been applied in diverse fields of science (48-50).

The objective of experimental design is to plan and conduct experiments so that the experimental domain is systematically investigated with as few experiments as possible. The independent variables or factors are experimental variables that can be changed independently of each other. The factor settings define the experimental domain, i.e. the area to be investigated. The response variables, the dependent variables, are measured results of the performed experiments.

The factors can be either quantitative or qualitative. A quantitative variable is a continuous variable that can take any number between predefined levels in the design. A factor that may only be varied at distinct levels such as present/not present, on/off or excipient A, B or C is termed a qualitative factor.

The experimental variables, Xk, are given maximum and minimum values based on pre-existing knowledge. In a full factorial experimental design all k factors are changed simultaneously. Not only does this cover

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the entire area of interest with as few experiments as possible, it also makes it possible to examine interaction effects. All combinations of the extreme values of the k factors are included as experiments. The geometrical representation of the experimental design is a square in the case of two factors and with three factors it is a cube, four factors make up a hypercube, and so on. If k variables are investigated at two levels the number of experiments in the full factorial design is given by the expression 2k.

The number of experiments in an experimental design grows rapidly with an increasing number of variables. As a rule of thumb only about k number of factors are found to be significant in a screening. Hence, when dealing with many variables, k>5, a full factorial design is not a realistic option for the purpose of screening. It is more appropriate then to use fractional factorial, Plackett-Burman or D-Optimal designs (51, 52). A fractional factorial design, which uses a fraction of the full factorial design, will give the maximum amount of variation possible with fewer experimental runs. A 2k-1 experimental design is a half fraction and a 2k-2 experimental design is one of four quarter fractions, and so on, of the 2k full factorial design. The drawback of fractional factorial designs is that information is lost due to interaction effects being confounded with other interactions effects and/or main effects, the amount lost depending on the number of factors and experiments. However, confounded interaction effects can be resolved by performing additional experiments.

A centre point, the middle value for each variable interval, should also be included to detect curvature in the experimental region. It is recommended that the centre point be repeated three times for statistical validation, e.g. for estimation of confidence intervals.

The experiments should be performed in random order to eliminate the influence of systematic errors.

Data obtained from experimental designs are usually evaluated with MLR or PLS. The calculated model is only valid in the experimental domain.

Several text books and articles regarding theoretical aspects of experimental design have been written (51, 53-57).


23

44..33..11.. MMiixxttuurree DDeessiiggnn

IXTURE DESIGNS ARE COMMON IN TABLET FORMULATION because of the nature of formulations (58-63). In a mixture

design the sum of all components add up to 100%, i.e. ∑Xk = 1. Hence, mixture factors are expressed as the fraction of the total amount they account for, and their experimental ranges lie between 0 and 1. This constraint means that the factors cannot be changed totally independently of one another. The geometrical representation of the design also differs from an ordinary factorial design. A mixture design with two factors can be represented by a line, a design with three factors by a triangle and in the case of four factors by a tetrahedron, see Figure 3.

Excipient A

Excipient B Excipient C

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Figure 3. Two examples of mixture designs for three-component excipient mixtures. The design to the left supports a linear model and the design to the right supports a quadratic model. The filled circles represent mandatory experiments and the open circles represent optional experiments.

A mixture factor may be a formulation factor or a filler factor. Only one mixture factor can be defined as filler. Formulation factors are the usual mixture factors used in formulations and they have specifically defined experimental ranges. A filler is a mixture component, usually of little interest, which comprises a large percentage of the mixture and is added at the end of a formulation to bring the total amount of the mixture to the desired level. The presence of the designated filler allows the mixture factors to be changed independently of each other, with the reservation that the varying amounts of filler might influence the

M


24

properties of the mixture. This makes it easier to evaluate the mixture design.

Eriksson et al. have published a comprehensive article on the topic of mixture designs (64).

44..44.. MMuullttiivvaarriiaattee DDeessiiggnn

S STRAIGHTFORWARD AS MULTIVARIATE DESIGN is in theory, as difficult can it be in practice. The first articles that reported

applications of multivariate design and multivariate data analysis were published by Carlson et al. in 1985 and 1987 (65, 66). The first publication addressed the difficulties of selecting test solvents for studies of new organic synthetic methods and different strategies for selection were discussed. In the latter publication a multivariate design was applied to the PP’s of substituents, amines and solvents in order to select test systems for the Willgerodt-Kindler reaction. The results were analysed using PLS and optimum conditions of new untested systems were predicted.

In 1986 Wold et al. presented the concept of multivariate design (67) as a means for obtaining diversity in the selection of peptides for a QSAR study or constituents for an organic synthesis. Several examples are presented, e.g. the articles by Carlson et al. from 1985 and 1987.

The combination of the two methods described in sections 4.2 and 4.3 forms the basis for multivariate design, often referred to as design in PP’s. The first step is multivariate characterisation of the materials, see section 4.1. As illustrated in Figure 4 the statistical experimental design is applied using PP’s obtained from the multivariate characterisation instead of ordinary factors. The latent variables are continuous variables and can be handled as ordinary design factors. Not having to use qualitative variables is a major advantage for many reasons, both when generating and evaluating the experimental design. Far more excipients can be evaluated in a limited number of experiments, while ensuring that the

A


25

Figure 4. The principles of multivariate design illustrated by excipient selection for a tablet formulation. The settings of the fractional factorial design correspond to a quadrant in the respective coordinate systems of the excipients.

most diverse set of excipients are included in the design. Also, novel excipients can be assessed using, for instance, the SIMCA classification method (68).


26

44..55.. PPLLSS

ARTIAL LEAST SQUARES PROJECTIONS to Latent Structures (PLS) is essentially a regression extension of PCA. The objective is to

find the latent structure in the X matrix, the descriptive variables, and the Y matrix, the response variables, and to maximise the covariance between the two matrices.

For each component a weight vector, w, containing the contributions from the descriptive variables to the explanation of Y, in that particular component is calculated. The corresponding weight matrix for Y is termed C. The P loading matrix is calculated in order to describe X in the usual way.

The following equations describe X and Y.

EPTX +′⋅=

FCTY +′⋅=

The PLS regression coefficients, B, can be calculated from the

following equation.

CWPWB ′⋅⋅′= −1)(

Thus an estimation of Y, here termed Ypred, can be obtained.

XBCWPXWYpred =′′= −1)(

For further information, several articles and text books are

available (69-73).

P


27

44..66.. VVaalliiddiittyy ooff MMooddeellss

HE VALIDITY OF A MODEL can be assessed in a number of ways. Two common parameters that are used to describe the quality

of a model are goodness of fit, R2Y, and goodness of prediction, Q2. These parameters are calculated using the following equations.

∑ −−∑−=

−= 2

22

)()(

1YRmeanobs

calcobs

Y

resY

YYYY

SSSSSS

∑ −∑ −

−=−

= 2

22

)(

)(1Q

meanobs

predobs

Y

Y

YY

YY

SSPRESSSS

In R2Y the total sum of squares, SSY, is compared to the residual

sum of squares, SSres, to give the fraction of the variance that is explained by the model. In order to determine the fraction of the variance that can be predicted by the model the prediction error sum of squares (PRESS) is calculated. These parameters, R2X and Q2, can also be determined for PCA models in the same way.

Models such as PCA and PLS will describe a decreasing part of the variance in subsequent components. R2 and Q2 values are also used in order to decide the number of components in the model, i.e. the rank of the model. The size of the eigenvalues is also commonly used to decide the number of components in PCA.

The validation tests can be divided into two categories: internal and external. An internal test uses objects that are part of the fitted model, which is not the case in external validation. A representative set of test samples cannot always be acquired, due for instance to limitations in the resources for experiments.

Cross validation is by far the most commonly applied method for internal validation (74). The objects in the model are divided into a number of groups that are kept out of the calculations once. A model is calculated for the remaining objects and a partial PRESS is determined for the set of objects that is kept out. The partial PRESS values are summed to form PRESS.

T


28

The most stringent validity test is the use of an external test set. For the objects of the test set the measured response is compared to the predictions made by the model. This gives an indication of the real predictive abilities of the model. Rather than using the average of the absolute values of the prediction errors the Root Mean Squared Error of Prediction (RMSEP) is often used. Since the prediction errors are squared, deviating values have a great impact on the estimate. RMSEP is calculated with the following equation.

N

PRESS settest=RMSEP


29

55.. MMuullttiivvaarriiaattee MMeetthhooddss AApppplliieedd ttoo TTaabblleett

FFoorrmmuullaattiioonn

If we knew what we were doing, it wouldn't be called research, would it?

Albert Einstein

55..11.. SSccrreeeenniinngg EExxppeerriimmeennttss

HE OBJECTIVE OF A SCREENING STUDY is to gain knowledge about parameters that influence the measured results. If the

studied systems are excipients the interest lies in gathering information relating excipient properties to responses that are relevant to tablet formulation.

The traditional approaches to experimental design are difficult to implement when choosing factors to use in a screening study investigating more excipients than can possibly be managed in a mixture design. One alternative is to use physical properties as factors, e.g. viscosity or some measure of particle size, for each class of excipients. One of the problems associated with such an approach was briefly touched upon in section 4.2.1, namely missing data due to the fact that the same physical properties are rarely determined for a large number of diverse excipients. Only a limited number of descriptive variables can be used for each excipient class for a manageable number of experiments. Orthogonal factors can also be difficult to acquire, e.g. it would be difficult to find an excipient with both a large mean particle diameter (a high setting in an imaginary design) and high density (also a high setting in such a design). These factors, together with factors for e.g. loss on drying and particle shape can clearly make the task of finding excipients representing extreme settings difficult or impossible. Use of a D-Optimal selection

T


30

from a candidate set described in a few variables could be a feasible option. This alternative has not been investigated by the author or reported in the literature.

Another alternative is to use qualitative variables. The drawback of this approach is that only a few excipients, i.e. levels in the design, can be included before the number of experiments becomes unfeasibly high.

Using PP’s and multivariate design instead of qualitative factors is a viable alternative if many excipients are to be included in a screening study. In many cases, of course, the resulting model will be less detailed compared to a model derived from a set of experiments where physical properties of one or a few excipients are studied. Nevertheless, it should at least give a good indication of areas in the multivariate domain that should be further explored, which may be sufficient in some cases.

The work reported in Paper I was planned and carried out at Pharmacia & Upjohn, Uppsala, Sweden. When starting the investigation, personnel at three different Pharmacia & Upjohn sites were asked what excipients were used in formulation work. It transpired that the different sites routinely used different excipients. As pointed out by Peck et al., the number of commonly used excipients is probably quite low and the excipients concerned have been evaluated repeatedly in the literature (4). As is often the case, people tend to stick with what they know. The screening included 53 lubricants, 21 binders and 19 disintegrants.

Lubricants were not part of the screening study described in Paper II, although the formulation contains a lubricant, but fillers and an API were added to the investigation. Rather than just including excipients that were commonly used at the site, one of the three mentioned above, a great number of excipients were considered for the formulation in the screening part of the investigation. In the second screening study six batches of API, 68 batches of binders, 28 batches of fillers and 27 batches of disintegrants were included. Some excipients are reported in the literature to have dual functions, e.g. they have been used as both binders and disintegrants. Rather than trying to decide the primary function of the excipients they were included in more than one model, which meant that approximately 100 excipient samples were characterised.


31

55..11..11.. EExxcciippiieenntt SSeelleeccttiioonn BBaasseedd oonn PPhhyyssiiccaall PPrrooppeerrttiieess

HYSICAL PROPERTIES WERE USED IN THE multivariate characterisation of the lubricants reported in Paper I. The data

were gathered from an article by Strickland et al. (75). Consistent measurements for the force transmission ratio (R) and ejection force (Fe) for 63 from a list of 74 lubricants were available. Additional information on four physical and chemical variables was gathered from text books and chemical catalogues (76-81, 18). Nine of the lubricants had to be excluded because of missing data for these four variables. Eventually, 53 lubricants were kept in the investigation, and six variables were included, although a large proportion (52%) of data points was missing for one of them (R.I.). For the lubricants two components explained 87% of the variance in X. The second component had an eigenvalue of less than 2, but was kept because it contributed as much as 20% to the explained variance.

In the work leading to the screening study described in Paper II large amounts of data were collected for the excipients. There was an average of 41% missing data points for the variables for which there were enough values to be considered for use in the characterisation. By that time the spectroscopic characterisation, which had previously worked well, had already been performed. Therefore, due to problems with scaling it was decided not to use physical properties as part of the basis for the multivariate characterisation in the study.

55..11..22.. EExxcciippiieenntt SSeelleeccttiioonn BBaasseedd oonn SSppeeccttrroossccooppiicc PPrrooppeerrttiieess

BTAINING PHYSICAL AND CHEMICAL DATA for the binders and disintegrants evaluated in Paper I proved difficult. Instead, the

excipients were characterised with an FT-IR instrument that was available on site at the Pharmacia & Upjohn facility in Uppsala. The spectra were pre-treated with MSC due to baseline fluctuations. The numbers of components in the PCA of the binders and disintegrants, three and two, respectively, were based on the eigenvalue criteria. The spread of the excipients was generally good, which allowed selections to be made without much compromise.

P

O


32

The spectroscopic characterisation in Paper II has the added strength of NIR. Separate pre-treatments of the NIR and FT-IR spectra with SNV were performed. The excipients were divided into classes prior to the pre-treatment, but this is an unnecessary precaution since SNV is a separate transformation of the spectra. Pre-treatment with MSC was also tested, but SNV was found to decrease the spread of the replicates in both

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Figure 5. Binders in Paper II characterised by spectroscopic data. The binders are divided into two groups in the t[1]/t[2] score plot: cellulose-based binders to the left and other binders to the right. Selections within the groupings are, in agreement with e.g. cluster-based design, as well spread as possible.

NIR and FT-IR. The investigation of pre-treatment methods was not comprehensive. As suggested by the eigenvalue criteria, three PP’s were used for each of the excipient classes of binders, fillers and disintegrants. The spread of the objects was again generally good, but a few compromises had to be made, as briefly discussed in Paper II, in the selections of the excipients for the screening design. The first PP of the binders separates the objects into two groups, see Figure 5. A selection in


33

subsets was made, one subset containing cellulose-based binders and the other binders of other types.

In none of the investigations were attempts made to interpret the loadings.

55..22.. MMooddeell IInntteerrpprreettaattiioonn

HEN ASSESSING THE SUITABILITY of a lubricant Fe and R are important properties. Fe should be low, since low Fe values

are indicative of weak friction between the tablet and the die wall. The R value is an indirect measure of the friction. The forces exerted on lower and upper punches are compared and a high ratio indicates low friction. More recently Fe divided by the area of contact between the tablet and the die wall (Ac), i.e. Fe/Ac, was shown to give a better estimate of friction at the die wall (82). The R value is not straightforward to use in practice as it requires constant tablet dimensions and constant compression loads (82). Hence, these two measures of lubricating ability are negatively correlated, as shown in Figure 1. A good lubricant can thus be expected to be located in the first quadrant of the t[1]/t[2] score plot in Figure 2. This was verified experimentally, as shown in Paper I, with a highly significant model for the analogue of Fe; the standard deviation of the compression pressure (pressure STD). However, the results also showed that the first PP was most important, and that excipients from the fourth quadrant could be used as lubricants if necessary.

The models based on spectroscopic data do not offer the same interpretability. The score plots show how the excipients are related to each other in terms of light absorbance at certain wavelengths. The loadings contain information about these wavelengths and, hence, about the bonds and functional groups that are components of the excipients. The division of the binders along the first PC into two groups, one consisting of cellulose-based excipients and the other containing mainly alginic acid or alginate, is mainly due to C-H and O-H bond stretching. The excipients consisting of alginic acid or alginate display more O-H bond stretching and less C-H bond stretching compared to cellulose-based types of excipients.

W


34

The regression model of the investigated response gives information about which of the PP’s are significant and how they affect the response, see Figure 6. In cases where many factors are significant the model offers more than one alternative for achieving the specified aim.

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Figure 6. Schematic diagram of model interpretation with the aim of maximising the disintegration time. The regression coefficients are used to identify regions in the score plots that should contain excipients with suitable properties.

The model that was presented in Paper I was also significant for tensile strength, friability and disintegration time. In the study the aim was to develop a formulation which would yield tablets with high tensile strength and low friability, as well as a short disintegration time. Tensile strength and friability are almost inevitably negatively correlated to each other as a tablet of high tensile strength is not likely to wear easily. The disintegration time is also often correlated to tensile strength, since hard tablets usually have a long disintegration time. Many significant factors in


35

the model allowed alternative strategies for the selection of excipients in order to obtain tablets with suitable properties.

Models for a number of responses were presented in Paper II. General conclusions were drawn regarding the values excipients should have in certain PP’s to increase or decrease the response in question. The fact that tablets from a number of formulations never disintegrated within the time allowed for the test was very unfortunate. Had these experiments been included, i.e. had their actual disintegration times been measured (even though they would have been very far from the objective of the formulation), it is possible that the model would have been different and led to other conclusions and decisions.

The aim of the study described in Paper III was to develop a formulation with a certain disintegration time. Both filler and binder had a significant effect on the disintegration time and the strategy for additional experiments was based on the choice of these two types of excipient. The model indicated that the buffer had a significant influence, as well as the API.

The models calculated for the mixture experiments described in Paper IV can be interpreted by looking at the regression coefficients or, preferably, by creating a contour plot of the investigated area of the score plots. A point in this area of the contour plot corresponds roughly to a mixture of a certain composition.

55..33.. AAddddiittiioonnaall EExxppeerriimmeennttss

S STATED IN PREVIOUS SECTIONS, multivariate methods can be used in a number of ways and it sometimes seems that only

imagination sets limits on what can be accomplished. Using these techniques it is possible to plan, conduct and evaluate experiments in a structured manner. However, no matter how well-planned a screening study may be, it might still be necessary to venture outside the experimental domain.

In the following sections strategies for selecting and evaluating additional experiments are discussed.

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36

55..33..11.. SSttrraatteeggiieess ffoorr EExxcciippiieenntt SSeelleeccttiioonn

PICTURE SAYS MORE THAN A THOUSAND WORDS. The phrase is well known and while many consider it somewhat

exaggerated, most will agree that there is some truth in it. One way of seeking a suitable formulation, based on the experiments described in Paper I for instance, would be to scrutinise the table of responses. However, although there were only four responses and a limited number of experiments in this case, the task would still not be trivial. Another approach is to calculate a PCA model of the responses and create a picture of the matrix of response data. By projecting a set of desired properties onto this model, a picture with the stipulated demands in the form of an object can be generated and studied. Analogues, if they exist, or formulations with acceptable properties can thus be identified.

Yet another alternative is to use the model calculated from the experiments. Solving the problem addressed in Paper I was quite simple, and could be done by simply looking at the coefficient plots. When the objective is to optimise one or a few responses (e.g. to maximise tensile strength or minimise pressure STD, disintegration time or friability), the coefficients essentially contain enough information to identify good formulations and experimental settings. Even in this case, however, application of the Optimizer, which uses a Nelder-Mead simplex method (83), in Modde 5.0, offered a novel compromise solution that had not been considered until then.

Since the desired tablet properties were different for the study described in Paper II, the objective of the optimisation part of the study (Paper III) was also quite different. For a number of reasons the Optimizer was employed as a means to find a starting point for further investigations. Finding a target time is more difficult than minimising the disintegration time. The direction given by the regression coefficients rarely gives an answer straight away. Instead, a number of more or less desirable alternatives for achieving the goal are possible. Applying a technique such as the Optimizer helps in such situations. Even if there is no convergence, at least a number of alternatives are presented for further evaluation, both in terms of desirability (which can be elaborated before additional actions are taken), and experimental performance (which can be tested in practice).

A


37

The model used for predicting the disintegration time, and ultimately the composition of the formulation, presented in Paper III indicated that there were significant influences from the buffer and the API. These constituents were not varied in the additional experiments, for two distinct reasons. A suitable buffer was identified and there was no desire to test further alternatives. There is no way to manipulate the PP’s of the API and instead the task is simply to identify a suitable batch.

The additional experiments in Paper III were chosen in a very optimistic fashion. Three fillers and five binders were evaluated with a 25-2 fractional factorial design and eleven experiments. The ratio between binder and filler and the amount of disintegrant was also varied in the design.

In Paper IV mixtures of excipients were investigated. The basic idea was to use mixtures of an appropriate set of excipients in order to obtain formulations that would give the desired disintegration time. Thus, mixtures with PP’s that would cover an area of the PP space that might be of interest, based on the predictions made in Paper III, were created. In the first study reported in Paper IV it was decided to vary both the binder and filler. A D-Optimal design was generated from a candidate set containing all binder and filler mixtures given in PP’s. The design contained many experiments with pure excipients, since such experiments span the largest possible experimental domain. The inclusion of many experiments with pure excipients also makes it possible to evaluate the designs as ordinary mixture experiments, should this be necessary. In the second study only binder mixtures were studied and the strategy for the selection of experiments was also quite different. Two factorial designs, with one common centre point, were generated within the mixture domain spanned by the three excipients and the mixtures were characterised post selection. Only one pure excipient was included: the rest of the experiments consisted of binary or ternary mixtures. The idea behind that experiment was to use it to compare a similar experiment in the screening design in order to obtain estimates of the influence of flavours and other additives.


38

55..33..22.. EEvvaalluuaattiioonn ooff RReessuullttss

INCE NONE OF US WERE, AND MOST WOULD still claim not to be, experienced formulators the SIMCA classification approach

described in Paper I was applied mainly to verify that the results were acceptable to those experienced in this field. Being very pleased with the results of the optimisation experiments, no effort was made to check the RMSEP. It was enough that the formulations met the demands of many experienced formulators. In Table 1, values for RMSEP and corresponding percentages of the investigated intervals are given. The results are generally comparable to those in Paper III. At first glance the predictions for disintegration time might seem much better for this study. However, since the objective was to minimise this response, both the predictions and the results are numerically quite small, which naturally decreases the prediction errors. Nevertheless, the results are reasonable for practical use.

Table 1. Validation data for the model in Paper I.

Responses RMSEP % of interval

Disintegration time (s) 275 6.1

Tensile strength (Nm-2) 312712 14.1

Friability (%) 0.38 13.8

Pressure STD 0.55 17.4

The results presented in Paper III were encouraging in that a

formulation with a disintegration time close to the target time was obtained. However, it was discouraging that once again some tablets did not disintegrate within the time allowed for the test. This should not have come as a surprise, however, as excipients that were part of non-disintegrating formulations in the screening study were once again included in amounts that were too high. The results of the optimisation study also served as a test set in the validation of the screening model. The calculated RMSEP value is acceptable. However, the two formulations that never disintegrated within the time allowed for the test did not contribute to this value.

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39

Both of the mixture studies described in Paper IV either contain or encompass formulations of the desired disintegration time. The experiments lacked a disintegrant, but contained flavours as well as other additives that were not part of the screening experiments. Using the screening model for predictions of such experiments does not necessarily aid in determining the predictive ability. If the agreement between observed and predicted values is good this could also be interpreted as a sign that the formulation is not sensitive to these changes, or that the additives somehow cancel out each other. Should the agreement be poor this is also indicative of a system that responds to these additions. Furthermore, since a diverse set of excipients are included, they likely respond differently to these additives. In either case, comparing observed disintegration times to those predicted by the screening model is bound to be misleading. Instead of, or rather in the absence of, other viable alternatives, separate local models were calculated for the mixture experiments. The predictive ability of the model for the first part of the study was found to be quite good, comparable with that of other published models.

PP’s were used in these local models, both because they gave better condition values for the designs and because the original predictions were made in PP’s. Also, a ternary mixture can be described with just two factors without leaving anything out. The problem with lack of fit in the study of both binders and fillers is indicative of nonlinearities within the investigated domain.

Studying contour plots from the mixture models can be compared to examining the score plots through a magnifying glass. This is an excellent way of assessing the alternatives that are available for the formulation in question. In the case of the first mixture study, which included formulations with acceptable disintegration times, the composition could be changed if necessary, while still maintaining the disintegration time. In the second study different options for achieving the stipulated disintegration time were revealed.


40

55..44.. RRoobbuussttnneessss TTeessttiinngg

N ROBUSTNESS TESTING THE OBJECTIVE is to explore the sensitivity of the investigated system towards changes in critical

factors (57). Excipients are usually produced by a batch process, raising the possibility of batch-to-batch variation (41). The possibility that excipients or API’s from different batches that are all within the specification limits might not have identical properties is illustrated in Figure 7. Hence, in tablet formulation such critical factors may be the variability of the excipients or API’s that are part of the formulation.

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Figure 7. A t[1]/t[2] score plot of API batches that were characterised in the course of the project. The batches from the two suppliers, S1 and S2, have the same chemical specification but differ in particle size distribution, which is evident in the first PC. Batches marked with an X before the numbers were not included in published studies.

Suitable designs for robustness testing are fractional factorial designs of resolution III and Plackett and Burman (P-B) designs (57). The analysis of the results in robustness testing is much the same as for other designed experiments, attention being focused on an acceptable limit of

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variation, model parameters such as R2 and Q2 and the ANOVA results (57).

The presented approach is well suited for robustness testing and the application is straightforward. The spectroscopic characterisation makes it possible to detect artefacts that are not part of the product description or variation that is within the specification, but still has a significant impact on the outcome of the process. When selecting excipients for the robustness experiments described in Paper V the objective was to obtain as diverse a set of ingredients as possible. Separate models for each of the constituents of the formulation were made, and with few exceptions the most diverse batches were chosen.

In robustness testing the model is interpreted as being either significant or not significant: the latter usually being the desired outcome. Should a significant model be obtained the size of the fluctuations in the response should be evaluated to see whether they are large enough to warrant further investigation. The constituent causing the observed systematic variation should also be identified. In the robustness tests here, one of the constituents in particular appeared to affect the tensile strength.

No attempt at interpreting the separate models of the different excipients and API for information they may contain on the robustness of the studied system was made. Knowledge about the effects of factors such as differences in particle size distribution and shape could likely be gained from the spectra of such models.

Depending on the outcome of the robustness tests, the calculated models can also serve as the starting point for the quality control of excipients and API.


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43

66.. CCoonncclluuddiinngg RReemmaarrkkss

I may not have gone where I intended to go, but I think I have ended up where I intended to be.

Douglas Adams

N PRODUCT DEVELOPMENT, WHERE PRODUCTION parameters must be considered as well as scientific and technical issues, the best

laid plans and intentions can often go astray. A project has its own life and, at times it seems, a will of its own. Conditions and objectives almost inevitably change during the course of a project, and projects where every source of error was thought of prior to commencing the investigation are few and far between.

With the benefit of hindsight, the knowledge gained over the years seems trivial, concerning things that could (and should) have been realised in advance. However, I believe I have at least learned from my mistakes and gained enough experience to be able to give a worthwhile opinion on how to perform experiments with PP’s in general, and the application of PP’s to tablet formulation in particular. This is the fruit of not just a number of successful experiments, but also quite a few disappointments.

When using PP’s in screening experiments the objective is to obtain an overview of a diverse set of excipients with few factors and a limited number of experiments. In these studies, including such an important factor as the amount of the respective excipients at this early stage in the investigation proved to be a poor idea, for a number of reasons. Excipients are complex entities and the relationships between their amounts in the formulation and tablet properties are rarely linear, at least not over large intervals. The behaviour of an excipient might be highly dependent on the amount of it included in a tablet. In a small amount an excipient might act as a disintegrant and swell upon contact with water, thus disintegrating the tablet. In contrast, if present in large amounts it is possible that the same excipient will act as a binder and keep the particles together.

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To obtain a general screening model it is appropriate to set a fixed amount for each of the investigated excipient types, e.g. binders, fillers and disintegrants. If it is necessary to investigate amounts of excipients at such an early stage of the investigation, use of a blocked design is one alternative. The separate blocks of each of the levels can then be evaluated separately if necessary. Should a poor model be obtained for the complete design, block(s) of interesting level(s), i.e. the design(s) that yield(s) tablets with properties similar to those targeted, can be focused on. This approach places more demands on resources, but it should yield compensatory benefits.

This kind of model can also be continuously updated with new experiments. When additional experiments are performed (for an optimisation study for instance) and the amounts are varied, at least one or two experiments should be performed according to the basic design, regardless of the excipients used. If the same excipients are used, additional information about normal variation will be obtained and if additional excipients are tested entirely new entries to the model will be acquired.

The finding that the disintegrant did not have a significant effect on disintegration time in these studies (other than indirectly for the models presented in Paper I) suggests that excipients with this function should be investigated separately. Present in a limited amount the effect of the disintegrant is difficult to elucidate when other excipients are present in large and varying amounts.

I think it has been proven that the approach to tablet formulation presented in this thesis offers several interesting alternatives, for both planning and evaluating experiments.


45

77.. FFuuttuurree PPrroossppeeccttss

Science is a wonderful thing if one does not have to earn one's living at it.

Albert Einstein

LOGICAL NEXT STEP IS TO START all over again. This idea is not as drastic as it might sound. The PP’s should be thoroughly

analysed and possibly recalculated. A recommendation would be to base the PP’s on spectroscopic methods that are robust and user-friendly. It would be advantageous if PP’s could be based on spectroscopic data with guidance from measured properties. This would eliminate the need for MSC or SNV as pre-treatment procedures and enable the use of methods such as OSC or O-PLS. Judging by the literature it should be possible to extract at least the PP’s that are concerned with particle data. The problem with lack of data relating to physical properties could possibly be reduced by predicting PP’s for excipients for which no measurements on the studied variables are available.

With a characterisation based on both physical and spectroscopic properties of the excipients new PP’s could possibly be calculated, depending on the application and prior knowledge. In this way new and expensive measurements would not be needed for a rapid assessment of a novel excipient.

Such an approach would provide an alternative to expert systems that are being developed. Being somewhat more complex, this procedure based on PP’s will not yield simple answers, but on the other hand the approach is more flexible and offers better interpretability.

Alternative approaches for testing the influence of the amounts of excipients on tablet properties could also be further explored. Use of a small factorial design in amounts around every formulation in a set of planned experiments is one option. The number of formulations would be considerably increased, but the detailed knowledge about the studied system that could be gained might make it worthwhile. Another

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alternative is to use screening to exclude all but a few excipients and test them at several levels in an RSM design.

Testing different API’s for direct compression in a systematic manner would also be interesting. A characterisation of API’s, based on either physical or spectroscopic properties, would enable the selection of a diverse set for testing. Evaluating the API’s in a model formulation, as in the thesis by Westerhuis, would give information relating the properties of the API to tablet properties as well as responses that are relevant for direct compression, e.g. flow parameters and ejection force.

In order to determine possible interactions between the API and excipients the model formulation should be varied according to a design as well. If the API and formulation, i.e. one or more excipients, are included in statistically designed experiments the PP’s of the API and excipient can be related to a measured response in the usual way. Thus, knowledge about how the properties of the different API’s affect the tablet properties, as well the extent to which the different formulation systems vary with each of the API’s, could be gained.

By applying these ideas in future projects it will be possible to develop an evolutionary system for tablet formulation.


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88.. RReeffeerreenncceess 1. York, P., The design of dosage forms. In Pharmaceutics : the

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75. Strickland, W.A.; Higuchi, T. and Busse, L.W. The physics of tablet compression X - Mechanism of action and evaluation of tablet lubricants. J. Am. Pharm. Ass., Sci. Ed. 1960; 49 35-40.

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99.. AAcckknnoowwlleeddggeemmeennttss

My life has no purpose, no direction, no aim, no meaning, and yet I'm happy. I can't figure it out. What am I doing right?

Charles M. Schulz

Det är många som förtjänar ett omnämnande och det är min uppriktiga förhoppning att jag kommit ihåg er allihop. Nedanstående rader har jag, i stunder av klarsyn, knåpat ihop under de senaste veckorna. Så, ett stort tack till: Torbjörn Lundstedt, biträdande handledare och mentor, för hjälp med det mesta som har med kemometri att göra. Att det även är ett sant nöje att svinga en bägare med dig är ytterligare ett plus. Nils-Olof Lindberg, min industrihandledare, inte bara för att den här avhandlingen inte skulle finnas utan din insats, utan främst för ditt engagemang och entusiasm under alla projekt och ditt outtröttliga korrekturläsande och öga för detaljer, samt för trevliga kvällar i Helsingborg. Michael Sjöström, min handledare på universitetet, för att du alltid ställt upp när det behövts trots ett stundtals omöjligt schema. Organisk kemi, för att jag fått vara en del av avdelningen med allt vad det innebär. Avdelningen är en härlig mix av individer och intressen och var en stor anledning till att jag valde att börja doktorandutbildningen. Fast jag tycker koncentrationen av fiskefanatiker är underlig, för att inte säga kuslig. Ann-Helén, Carina och Bert, för hjälp med sånt som hör till vardagen på en avdelning.


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Nuvarande och tidigare doktorander i kemometrigruppen, och alla andra doktorander på avdelningen. De jag plågat mest om dagarna har nog varit Andreas ”Paltskallen” Larsson, som genom att alltid ha en, därtill ofta felaktig, åsikt om allt, ofta inbjudit till ”diskussioner”. Och Henrik Antti, som varit till stor hjälp med det kemometriska men även låtit mig greja med Corollan, vilket varit bra för självförtroendet… Birdie-gruppen, som Nils-Olof kallar er, Magnus, Gunilla, Fredrik, Anki, Mia och Kristina, för att jag fått delta i era projekt och framförallt för ert bidrag till mitt arbete. Andra som jobbar eller jobbat på Pharmacia&Upjohn, Pharmacia och Pfizer (det är samma företag) och har varit inblandade i projekt tillsammans med mig; Lennart Frigren, Åsa Waltermo, Roland Olsson, Gertrud Grudén, Lena Montell, Anette Schlüter och Bengt Bosson. SPOC, som förutom Torbjörn bestod av Åsa, Elisabeth, Jarle och Rolf, för ett trevligt år ute i ”verkligheten”, som även var inledningen till avhandlingen. John Blackwell, för en språkgranskning som, förutom att vara mycket snabb, förbättrade avhandlingen avsevärt. Bulls Press, Sverige, för att jag fick använda Ernie-stripen. Kjell, för hjälp med IR-instrumentet, både när det gått bra och framförallt när det strulat. Mina rumskompisar, en del surrigare än andra; Pelle-Per, Lissan och Mattias. Fram för allt ett stort tack till Pelle-Per för o värderlig hjälp med av handlingen samt mycket trevlig sam varo genom åren. David, för hjälp med datorer och för att jag fick tanka lite ljud från din hårddisk, det har om inte underlättat skrivandet så i alla fall gjort det mer uthärdligt. Alla olika konstellationer av innebandylaget Bunsen Burners (”när endast final är gott nog”) för intensiva bataljer, och för T-shirten.


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Tipparna, Per, Pära, Neas, Tomme och Henke, för ett visst mått av spänning varje lördag eftermiddag under säsongen. Och för lyckan att få uppleva 13 rätt, även om jag inte kommer att ge upp ”karriären”… Jocke, Lars, Niklas, Nicklas och Matte och alla som hör till, som genom åren sett till att fritiden varit synnerligen fri från kemi, annat än den som har med rusdrycker att göra, och full av diverse trevligheter. Hans A. Muth, för en speciell insats inom området design som gjort världen till en bättre och vackrare plats. Min släkt som till stora delar huserar i Jämtland, och bland annat befolkar orter med exotiska namn som Grytan och Tand, och som jag alltid har stort nöje av att träffa. Ullabritt, Östen och Sara, för att det alltid är kul att komma till Sundsvall och för att ni tog hand om de mina under ett par kritiska veckor. Mamma Ann-Britt, som inte tvingat mig att bli kemist men väl hjälpt mig på vägen, och Pappa Robert, för att du fått mig att tro att jag kan. Lisa och Anna, numera med anhang, för att jag trots att jag är ”mittenbarn” inte blivit så värst konstig. Kristina, för att du är den som får mig att må som bäst och för att allting har fungerat trots att jag inte varit så närvarande på sistone. Jakob och Matilda, för att jag alltid har ett leende på läpparna när jag går de sista stegen mot vårt hem.


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Här följer en kort populärvetenskaplig sammanfattning på svenska: Den här avhandlingen beskriver användningen av kemometriska

metoder, dvs försöksplanering och multivariat dataanalys, vid urvalet av tabletthjälpämnen för tablettformulering. Försöksplanering, där flera faktorer varieras på ett strukturerat sätt, används för att få ut så mycket information som möjligt från en serie experiment. Multivariat dataanalys, som gör det möjligt att utvärdera många variabler samtidigt, är en typ av matematiska modeller som används för att sammanfatta stora datamängder på ett överskådligt sätt.

Tabletthjälpämnen, som utgör allt förutom den aktiva substansen i en tablett, har karakteriserats med många fysikaliska eller (främst) spektrala variabler. Genom att använda multivariat dataanalys kan de variabler som beskriver ämnena summeras till ett fåtal nya variabler. På detta sätt kan antalet variabler minskas avsevärt och de nya variablerna kan användas som faktorer i försöksplanering, vilket gör att många tabletthjälpämnen kan studeras med relativt få försök. Försöken ska värdera effekterna av båda val av olika hjälpämnen och den kvantitativa sammansättningen av dem i tabletterna.

De olika tabletterna testas, t.ex. för att fastställa sönderfallstid och krosshållfasthet, så att kvantitativa samband mellan olika blandningar av tabletthjälpämnen och tablettegenskaper kan etableras. De beräknade modellerna kan sedan användas för olika ändamål, beroende på målet med studien, t ex göra en tablett så snabblöslig eller så hård som möjligt, eller att sönderfalla efter en viss tid.

Avhandlingen baseras på ett samarbete med Pharmacia AB, Consumer Healthcare, Helsingborg, Sverige, som i huvudsak utvecklar produkter för rökavvänjning. Sammanfattningsvis kan man säga att mycket möda kunde sparats om Dr. Pork’s rön beaktats på ett tidigt stadium.

multivariate methods in tablet formulation by jon …

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