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Journal of Pharmaceutical and Biomedical Analysis 52 (2010) 484–492
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Journal of Pharmaceutical and Biomedical Analysis
journal homepage: www.elsevier.com/locate/jpba
Determination of ﬂow properties of pharmaceutical powders by
near infrared spectroscopy
Mafalda C. Sarraguc¸a a , Ana V. Cruz a , Sandra O. Soares a , Helena R. Amaral b ,
Paulo C. Costa b , João A. Lopes a,∗
a
b
REQUIMTE, Servic¸o de Química-Física, Faculdade de Farmácia, Universidade do Porto, R. Aníbal Cunha No. 164, 4099-030 Porto, Portugal
Servic¸o de Tecnologia Farmacêutica, Faculdade de Farmácia, Universidade do Porto, R. Aníbal Cunha No. 164, 4099-030 Porto, Portugal
a r t i c l e
i n f o
Article history:
Received 31 August 2009
Received in revised form 21 January 2010
Accepted 22 January 2010
Available online 1 February 2010
Keywords:
Near infrared spectroscopy
Pharmaceutical powders
Flow properties
Angle of repose
Aerated density
Tapped density
a b s t r a c t
The physical properties of pharmaceutical powders are of upmost importance in the pharmaceutical
industry. The knowledge of their ﬂow properties is of critical signiﬁcance in operations such as blending,
tablet compression, capsule ﬁlling, transportation, and in scale-up operations. Powders ﬂow properties
are measured using a number of parameters such as, angle of repose, compressibility index (Carr’s index)
and Hausner ratio. To estimate these properties, speciﬁc and expensive equipment with time-consuming
analysis is required. Near infrared spectroscopy is a fast and low-cost analytical technique thoroughly
used in the pharmaceutical industry in the quantiﬁcation and qualiﬁcation of products. To establish the
potential of this technique to determine the parameters associated with the ﬂow properties of pharmaceutical powders, blended powders based on paracetamol as the active pharmaceutical ingredient were
constructed in pilot scale. Spectra were recorded on a Fourier-transform near infrared spectrometer in
reﬂectance mode. The parameters studied were the angle of repose, aerated and tapped bulk density.
The correlation between the reference method values and the near infrared spectrum was performed by
partial least squares and optimized in terms of latent variables using cross-validation. The near infrared
based properties predictions were compared with the reference methods results. Prediction errors, which
varied between 2.35% for the angle of repose, 2.51% for the tapped density and 3.18% for the aerated density, show the potential of NIR spectroscopy in the determination of physical properties affecting the
ﬂowability of pharmaceutical powders.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
Pharmaceutical powders are described as heterogeneous systems with different physical and/or chemical compositions with
a range of particle sizes between a few micrometers to about a
millimeter. In a typical pharmaceutical industry, in average, more
than 80% of its production is based on powders in tablet form [1,2].
For those reasons, the knowledge and subsequent control of the
powders physical behavior is crucial in the development and processing of solid dosage forms. The powders ﬂow behavior is a key
factor in a series of unit processes such as blending, compression,
ﬁlling, transportation and in scale-up operations [1,3]. In tablets
compression and capsules ﬁlling, an optimal powder ﬂow must
be achieved in order to produce ﬁnal products with an acceptable
uniformity content, weight variation and physical consistence. In
the drug development stage, an accurate assessment of the ﬂow
∗ Corresponding author. Tel.: +351 222078994; fax: +351 222078961.
E-mail address: [email protected] (J.A. Lopes).
0731-7085/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.jpba.2010.01.038
properties is essential in order to identify the optimum formulation
[1,4–6].
To evaluate the powder ﬂow properties, parameters such as,
angle of repose, compressibility index or Carr’s index, and the
Hausner ratio, are generally employed. These methods are recommended by the pharmacopeia’s to evaluate powders ﬂowability,
they are easy to handle and their application is widely used in
industrial applications and in scale-up operations [3,4]. However,
they are indirect methods and its relation with the powders ﬂow
true behavior is not straightforward. Moreover, to have a complete
evaluation of the powders ﬂowability, various labor intensive and
time-consuming techniques must be used [7].
Near infrared spectroscopy (NIRS) is a fast non-destructive and
low-cost technique, vastly used in the pharmaceutical industry in
quality and process control [8–12]. NIR spectra carry signiﬁcant
information not only on the chemical composition but also on
the morphological structures of the sample due to light scattering
[13]. Applications such as, determination of water content, control of polymorphisms and optical isomers, identiﬁcation of raw
materials, homogeneity analysis, active principle and excipients
determination, are frequently used in the pharmaceutical industry
M.C. Sarraguc¸a et al. / Journal of Pharmaceutical and Biomedical Analysis 52 (2010) 484–492
[9,14]. However, the use of NIRS to determine physical parameters is still under exploration. Some work has been done in relating
the near infrared (NIR) spectrum with tablet hardness, drug stability, tablet coating and particle size of powders [15–18]. Otsuka
et al. [19] used NIRS to predict the angle of repose of granules
obtained after the granulation process using various amounts of
added water using principal component regression (PCR). In the
cited work, the authors discuss that the angle of repose is an index
to powder ﬂowability and that can be easily predicted by NIRS.
However, no extensive work has been done to explore the potential
of this spectroscopic technique to determine parameters associated
with the ﬂow properties of pharmaceutical powders in a systematic
approach.
In this work, the possibility to use NIRS to predict the ﬂow
properties of pharmaceutical powders, angle of repose and bulk
densities (aerated and tapped), during the scale-up operation was
assessed. For that purpose, blended powder samples based on
paracetamol as the active pharmaceutical ingredient (API), with
three excipients were constructed. NIR spectra were recorded on
Fourier-transform near infrared spectrometer in reﬂectance mode.
The tests to determine the angle of repose, and the bulk densities
were performed according to what is stipulated by the European
Pharmacopeia. The experimental results obtained were correlated
with the NIR spectrum by partial least squares (PLS) optimized in
terms of latent variables using cross-validation.
2. Theory
2.1. Flow properties of powders
The angle of repose can be deﬁned as the constant threedimensional angle measured relatively to the horizontal base,
assumed by a cone-like pile of material formed when the powder
is passed through a funnel-like container [20]. An angle of repose
lower then 40◦ , indicates good ﬂowability, conversely an angle of
repose superior to 40◦ is an indication of cohesiveness [21,22]. This
method is very simple but has some disadvantages. The powder
experiences segregation, consolidation or aeration, which inﬂuence
the cone formation [20]. The angle of repose is not considered for
many a good method to measure powder ﬂow, because is highly
dependent on experimental factors, since it is not an intrinsic property of the powder [4]. However, it is still considered useful since
it is a simple method that gives the powder tendency to ﬂow, and
has an associated general scale of ﬂowability consistence with the
classiﬁcation reported by Carr [22].
Another parameter used to evaluate the ﬂowability is the compressibility index (CI). This index measures the tendency of a
powder to consolidate, and is calculated according to Eq. (1)
[22,23]:
CI =
TD − AD
TD
(1)
In Eq. (1), TD and AD represent the tapped (or packed) and aerated bulk densities, respectively. The aerated bulk density is deﬁned
as the mass divided by the volume occupied by the powder when
the particles are not in direct contact with each other. However,
a more realistic deﬁnition can be given by the density measured
after the powder been aerated and left to settle gently. The tapped
bulk density is obtained after tapping the container enclosing the
aerated powder [21]. The compressibility index has an inverse relation with ﬂowability, i.e. the more compressible is the material the
less ﬂowable it will be [22]. A powder with a compressibility index
lower than 20% is considered to have a good ﬂowability [5]. The
Hausner ratio is deﬁned as the ratio between the tapped bulk density and the aerated bulk density. This ratio is a useful measure of
cohesion reﬂecting particle friction. With a Hausner ratio higher
485
than 1.4, the powder is considered a cohesive difﬁcult to ﬂuidize
powder. Ratios lower than 1.25 characterizes a free-ﬂowing powder [21]. Hereafter, the aerated bulk density and the tapped bulk
density will be designated by aerated and tapped density.
2.2. Experimental design
All developed models were calibrated and tested using different
data sets. To construct the calibration and test sets an experimental
D-optimal design [24] was developed and applied. The concentrations of each component present in the samples were varied in the
experimental design in order to maximize the information in the
selected set of experimental runs with respect to a stated model
(e.g., a regression model). For a speciﬁc regression model in which
Y is a (N × 1) vector containing the N experimental runs of observed
responses, X is a (N × p) matrix, with p being the number of terms
of the model, the D-optimal design maximizes the determinant of
the Xt X matrix, which is an overall measure of the information in
X. Geometrically, this corresponds to maximizing the volume of X
in a p-dimensional space. In the case of a formulation, this design
provides different physical properties to each sample, generating
an ensemble of values that gives the necessary characteristics to
the model.
2.3. Multivariate modeling
To assess the consistency between the calibration and test spectra, a principal component analysis (PCA) was used. This method
reduces the data information originating new variables (principal
components) that are linear combinations of the original variables
[25]. The principal components are estimated to have maximum
variance amongst all linear combinations. The usefulness of this
method resides on the fact that multivariate data can be well
described in a more workable set of variables that contain almost
all the information, or variability of the original data.
The multivariate technique used to relate the experimental
values of the parameters, angle of repose, aerated and tapped densities, obtained with the reference methods with the NIR spectra was
partial least squares (PLS) with leave-one-out cross-validation [25].
This technique is commonly used in chemometrics analysis and is
applied with the objective to establish a model for the analysis of
unknown samples to determine physical or chemical properties
[26,27]. To assess the PLS model accuracy (bias), the root mean
square error of cross-validation (RMSECV) estimated according to
Eq. (2) was used:
RMSECV =
t
ˆ C ) × (YC − Y
ˆ C)
(YC − Y
NC
(2)
ˆ C and YC are the PLS cross-validation estimate and
In Eq. (2), Y
the measured reference value for the ith sample, respectively. NC
is the number of calibration samples. The model robustness was
evaluated in terms of the root mean square error of prediction
(RMSEP):
RMSEP =
t
ˆ P ) × (YP − Y
ˆ P)
(YP − Y
NP
(3)
ˆ P is the PLS prediction value of sample i, and YP is the
In Eq. (3), Y
reference value for the same sample, NP is the number of prediction
samples. Model performance was assessed using the range error
ratio (RER). This ratio is calculated by dividing the amplitude each
parameter range by the RMSECV value. With a RER > 10 the model
can be considered good for quality control purposes.
In a univariate analytical technique, uncertainty is assessed by
the standard deviation of replicates. In multivariate techniques
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such as NIRS, the estimation of the model uncertainty is not
straightforward. To overcome this difﬁculty, a statistical technique
called bootstrapping can be used. This method generates an ensemble of samples by sampling with replacement from an original data
set [28]. This technique is used to generate a large number of new
data sets, each one with the same size of the original data set. These
data sets yield an ensemble of estimations that can be used to obtain
statistical parameters such as the standard deviation [29].
Figures of merit, such as limit of detection (LOD), sensitivity (SEN) and selectivity (SEL) were calculated for each modeled
parameter using the net analyte signal (NAS) theory. Using NAS
theory, the ﬁgures of merit of a multivariate method can be easily determined as in univariate methods [30]. Further details on
the calculation of ﬁgures of merit based on the NAS theory can be
found elsewhere [31].
All calculations were carried out using Matlab version 6.5 release
13 (MathWorks, Natick, MA).
3. Experimental
Fig. 1. Apparent volume from the 26 calibration samples in function of the number
of taps.
3.1. Samples preparation
Paracetamol, a powder with poor ﬂowability and compactibility, was the base of the pharmaceutical formulation used in this
work. For that reason, the excipients added to a paracetamol formulation must improve the tablet processability and bioavailability
[2]. Microcrystalline cellulose is the excipient with higher concentration, acting as ﬁller, while talc and magnesium stearate are both
lubricants. To construct a model with robustness and generalization
ability necessary for quantitative applications, the samples must be
manufactured considering a wide composition variation. To comply
with the latter requirements, each component concentration in the
sample was varied according to an experimental D-optimal design
[24]. The calibration and test sets were constructed with independent but similar experimental designs. The experimental design
used to generate the calibration set was a 4 factor design (number
of components present in the samples) with 23 design runs and 3
central point replicates. The test set was build using the same strategy but the components concentration range was narrower than for
the calibration samples. Fourteen design runs without replicates
or central points were generated. Table 1 summarizes the mass
fraction interval for each component in each set of samples. Samples were prepared by mixing the individual powders, previously
weighed (110 g per sample), in a shaker mixer (Turbula WAB T2F,
Switzerland). An overall of 40 samples, 26 for calibration and 14 for
testing, consisting on blended powders of paracetamol (API) with
three excipients, microcrystalline cellulose, talc, and magnesium
stearate were prepared.
3.2. Flow properties determination
The angle of repose was determined in a powder ﬂow tester
(GTB, Erweka, Germany). The apparatus can determine the ﬂow
time and angle of repose by draining the sample through a funnel
Table 1
Calibration and test samples mass fraction range (% w/w).
Components
Calibration
Test
Minimum
Maximum
Minimum
Maximum
Paracetamol
Microcrystalline cellulose
Talc
Magnesium stearate
58.0
0.00
0.00
0.00
92.0
37.0
10.0
1.00
64.0
4.00
1.00
0.50
90.0
30.0
4.00
1.00
Number of samples
26
14
located at a predeﬁned height above a circular plate, thus forming a gravimetric cone. The angle of the powder cone is measured
optically by a laser. The funnel used can have different diameter apertures. For this work, three diameters were tested: 10 mm,
15 mm and 25 mm. Each sample was measured in triplicate with
the three apertures and at the end the average value was taken.
Some samples show a very cohesive behavior with arduousness to
ﬂow through the funnel. With the exception of one sample from
the calibration set, only the large aperture funnel samples showed
free ﬂow behavior. Free ﬂow designates the behavior of the powders when no external help (e.g., by shaking the funnel) is need to
the powder ﬂow in the funnel. Consequently, only the values for
the 25 mm diameter funnel were considered for the PLS analysis
since in this way no external factors are inﬂuencing the model.
A tap density tester (Electrolab ETD-1020, India) was used to
determine the tapped density. For each sample, the test tube was
ﬁlled with the powder and the initial volume (V0 ) was measured.
This volume was then used to calculate the aerated density. Afterwards, volume measurements were made following 10, 500, and
1250 taps. The latter has been described as the number of taps sufﬁcient to achieve maximum compaction equilibrium [5]. As can be
seen in Fig. 1, for all samples the volume tends to stabilize when
reaching 1250 taps. For that reason, volume measured after 1250
taps was used to determine the tapped density. Each sample was
measured in triplicate, and the average value was taken. The range,
mean and mean relative standard deviation (RSD) for the reference
values are gathered in Table 2.
3.3. Near infrared spectra acquisition
Near infrared spectra were recorded on a Fourier-transform
NIRS analyser (Antaris I, ThermoNicolet, Madison, WI) equipped
with a reﬂectance ﬁber optical probe (SabIR, ThermoNicolet) and
an indium–gallium–arsenide (InGaAs) detector. The equipment
was controlled via the Result software package (ThermoNicolet
Industrial Solutions, Madison, WI) which enables the automated
acquisition of the NIR spectra. The spectrum for each sample was
recorded with a 2 cm−1 resolution with an average of 64 scans
over a wavenumber range between 4250 cm−1 and 10,000 cm−1 .
The measurements were performed in diffuse reﬂectance mode,
using the ﬁber optical probe. Before each sample measurement, a
background spectrum was taken inserting the probe into the ﬁber
optical holder containing the internal reﬂectance reference (Spec-
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487
Table 2
Calibration and test samples reference values range, mean and mean relative standard deviation (RSD).
Properties
Calibration
Test
Range
Mean
RSD (mean) (%)
Range
Mean
RSD (mean) (%)
Angle of repose (◦ )
Aerated density (g ml−1 )
Tapped density (g ml−1 )
45.50–38.03
0.86–0.62
0.99–0.77
42.32
0.75
0.87
1.82
1.69
0.81
44.87–39.43
0.82–0.71
0.94–0.83
42.24
0.76
0.89
1.42
1.59
0.57
tralon). The powders were measured by directly inserting the probe
into the samples. Three measurements were made for each sample.
3.4. Data processing
The spectral data was pre-processed to remove interferences
such as, base line drifts, light scattering effects and other instrumental variations [32]. A number of pre-processing methods were
tested, namely, Savitzky–Golay ﬁlter with different ﬁlter widths,
derivatives, standard normal variate (SNV) and multiplicative scatter correction (MSC).
4. Results and discussion
A graphic representation of the parameters used as ﬂowability
indicators maybe proven useful to best understand the ﬂow behavior of the samples. In Fig. 2, compressibility index, angle of repose,
and Hausner ratio are plotted for the calibration (white circles) and
test samples (black circles). In the upper part of the ﬁgure are positioned the samples with poor ﬂowability (e.g., samples 13, 15 of
the calibration set) while in the left down corner the samples with
high ﬂowability are situated (e.g., samples 6, 7, 25 of the calibration set). Analyzing the distribution of the samples according to
the classiﬁcation establish by these parameters it can be concluded
that the calibration samples have a large range and distinct ﬂow
behavior. Moreover, the ﬂow behavior of the test samples span the
same space has the calibration samples, a necessary condition for
a robust PLS model.
The samples used in this work had some moisture, for that
reason the spectral areas related with the water bands (7140–
6170 cm−1 and 5280–5000 cm−1 ) were removed prior to analysis
since no relevant information could be retrieved from those areas.
Fig. 2. Compressibility index, angle of repose and Hausner ratio for the 26 calibration () and the 14 test (䊉) samples.
Fig. 3 shows the standard normal variate (SNV) pre-processed NIR
spectra of the calibration and test samples. Despite the spectra of
the two sets of samples appear to be similar a further analysis
based on PCA was performed to ensure that the calibration samples cover the space spanned by the test samples, otherwise the
calibration could not be used to predict the test samples due to possible model generalization problems. A PCA model was therefore
developed on the calibration samples. The pre-processing technique applied in the PCA was SNV and mean-centering (MNCN).
The test samples were then subjected to the same pre-processing
Fig. 3. NIR spectra pre-processed with SNV of calibration (a) and test (b) samples.
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4.1. Calibration
Fig. 4. PCA score plot for the calibration () and test samples (䊉). The PCA model
captured 97.3% of the total variance in the ﬁrst three components.
and projected onto this model. The corresponding scores were plotted in Fig. 4. The capture variance was of 97.3% in total with 85.4%
captured in the ﬁrst component and 7.7% and 4.1% of variance captured in the second and third component, respectively. Analyzing
the PCA score plot it can be seen that the samples spectra span the
same area in the score plot conﬁrming the consistency between
the calibration and the test samples spectra. Moreover, the calibration samples encompass the space spanned by the test samples as
required.
The NIR spectra from the 26 calibration samples were correlated with the angle of repose, aerated density, and tapped density
values. The best pre-processing method, for each model, was chosen based on the lowest RMSECV achieved. For the angle of repose,
the pre-processing method applied was Savitzky–Golay ﬁlter (15
points width), second derivative followed by SNV and MNCN.
Savitzky–Golay ﬁlter (15 points width), ﬁrst derivative with MNCN
were the pre-processing methods optimized for aerated and tapped
density. The calibration results are shown in Table 3. The number
of latent variables was equally chosen based on the lowest RMSECV
value. In Fig. 5, the dependence of the RMSECV value on the number of latent variables is shown for the three-modeled parameters.
For the angle of repose, the minimum RMSECV value is very well
deﬁned. The RMSECV proﬁles for the densities are less deﬁned, but
a minimum is obtained when 5 latent variables are considered.
Therefore, 3 latent variables were used to model the angle of repose
and 5 to model the densities.
To be able to compare the cross-validation errors for the three
parameters the relative error (RMSECV divided by the average
parameter value) was calculated. The tapped density has the lowest error with 2.4% followed by the angle of repose with an error of
2.8%. The aerated density has the highest error with a value of 3.6%.
The RSD’s for the three parameters are in the interval between 1
and 2%, which indicate models with good reproducibility. The RER
value for the densities is close to 10 indicating good models for
quality control purposes. A RER value of 6.3 for the angle of repose
is the consequence of the not so good experimental results, being
the experimental RSD for this parameter the highest with a value
of 1.82% (Table 2).
Table 3
Calibration results for the NIR based prediction of the three ﬂow properties analysed.
Properties
Angle of repose
Aerated density
Tapped density
a
b
c
Pre-processing
b
SG , SNV and MNCN
SGc and MNCN
SGc and MNCN
Latent variables
RMSECVa
Relative error (%)
2
RCV
RSD (mean) (%)
RER
3
5
5
1.18
0.03
0.02
2.79
3.60
2.39
0.67
0.84
0.88
0.94
1.75
1.24
6.32
8.68
10.61
Angle of repose units are (◦ ), aerated and tapped density units are g ml−1 .
Savitzky–Golay ﬁlter with a 15 points ﬁlter and a second-order polynomial ﬁt and second derivative.
Savitzky–Golay ﬁlter with a 15 points ﬁlter and a second-order polynomial ﬁt and ﬁrst derivative.
Fig. 5. RMSECV as function of the number of latent variables for the PLS models predictivity (left) angle of repose, (right) ()—aerated density and ()—tapped density.
M.C. Sarraguc¸a et al. / Journal of Pharmaceutical and Biomedical Analysis 52 (2010) 484–492
489
Fig. 6. PLS loadings for the three parameters under study: (a) ﬁrst loading for the angle of repose model, (b) third loading for the angle of repose model, (c) ﬁrst loading for
the aerated density model, (d) fourth loading for the aerated density model, (e) ﬁrst loading for the tapped density model, and (f) fourth loading for the tapped density model.
The lower relative error and higher determination coefﬁcient for
the tapped density compared with the other two parameters are
due to lower interference of experimental factors in the determination of these parameters. The angle of repose and aerated density
determinations are more subject to errors due to manual control of
the powder samples during measurement. This fact can be conﬁrmed by the experimental RSD value (Table 2) for the aerated
density, lower when compared with the values for the other two
parameters.
For a more fundamental explanation on how the three parameters affect the NIR spectra, the PLS models loading were analysed.
This discussion is based on the loadings that correspond to the components for which a substantial decrease on the error was observed.
In this paper, strategies like orthogonal-PLS (o-PLS) were not used,
therefore the information orthogonal to the parameter being modeled is sometimes not totally discarded by the method. Therefore,
it is possible that some components appear, although not contributing for a substantial decrease of error. This can be seen in
the cross-validation proﬁle (Fig. 5). In Fig. 6, it is shown the ﬁrst
and third loading for the angle of repose, and the ﬁrst and fourth
for the densities. The ﬁst loading of each model corresponds to an
average pre-processed spectrum and can be use for comparison.
The other loading represents the spectral features that were more
important in the PLS model construction. For the densities, the
fourth (and not the ﬁfth) model component was chosen because
the cross-validation error decrease is not very signiﬁcative (Fig. 5).
Analyzing the third loading for the angle of repose model, it can be
clearly seen that the peak around 7000 cm−1 is very important for
the model. This peak is caused by the presence of talc (see Fig. 7),
a lubricant excipient. The angle of repose can be seen as a ﬂuidity indicator which gives a qualitative assessment of the internal
cohesive and frictional effects of a powder, which is related with
the quantity of lubricant present in the mixture. In the forth loading for both densities models, the peak correspondent to talc is not
considered, but the peaks around 9000 cm−1 and 6000 cm−1 appear
as important spectral features to the models. These peaks can be
related with the paracetamol component (see Fig. 7). The densities
are a measure of the powder compressibility and this parameter
is closely related with particle size. The particle size distributions
of the samples and pure components were determined (results not
shown). The particle size distribution showed that paracetamol is
the component with the largest particle size. As consequence it is
the most important parameter associated to the densities determination. In a previous work by Blanco and Peguero [33] it was proved
that the NIRS can be used to determine the particle size distribution. In consequence, the relation between the particle size and the
ﬂowability parameters under study was explicitly incorporated in
the models because the information regarding the particle size is
already included in the NIR spectra.
The calibration results showed that good models can be estimated for the determination of the three parameters using NIRS.
However, some considerations have to be made on the dependence
of the three parameters regarding factors such as moisture and temperature and experimental errors. As mentioned before, the manual
control of the powder ﬂow during the angle of repose and aerated
density measurements makes them more subjected to experimental errors, which is reﬂected by the experimental RSD. Temperature
and moisture will affect in a very signiﬁcant manner the powder particles ﬂowability, and consequently the three parameters
under study. Studies were performed in which was showed that
ﬂowability of powders ﬁrst decreases with moisture content. This
effect is due to the increase in powder aggregation due to liquid
bridges formed between particles. Above a critical water content
the ﬂowability increases, however this critical point is dependent
on the powder. An increase in the temperature may lead to a drying process and result on the opposite effect [4,34]. These factors
were not controlled during the experiments which lead to some
experimental errors that are reﬂected into the PLS models.
4.2. Testing
To test the calibration models robustness, 14 samples were
constructed. The samples spectra were projected onto each PLS
model and the prediction values were compared with the refer-
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Fig. 7. NIR spectra from the pure components present in the powder samples.
Table 4
Test results for the NIR based prediction of the three ﬂow properties analysed.
Properties
RMSEPa
Relative error (%)
2
Rtest
RSD (mean) (%)
LODa
SEN (dimensionless)
SEL (mean) (dimensionless)
Angle of repose
Aerated density
Tapped density
1.00
0.02
0.02
2.35
3.18
2.51
0.68
0.71
0.93
0.98
1.64
1.13
3.00
0.06
0.06
5.23
0.04
0.05
0.19
0.13
0.15
a
Angle of repose units are (◦ ), aerated and tapped density units are g ml−1 .
ence methods results. The predictions were assessed by calculation
the RMSEP. The mean RSD, determination coefﬁcient, and ﬁgures
of merit were also determined for each model.
The prediction results are expressed in Table 4 and the predicted
versus reference values are depicted in Figs. 8–10, for the angle of
repose, aerated density and tapped density, respectively.
The angle of repose and the tapped density have a relative error
very close, around 2.5%, although the determination coefﬁcient of
the density is considerably better, 0.93 compared with 0.68 for the
angle of repose. Comparable with the calibration results the aerated density has the worst result with a relative error of 3.18%.
The RSD is lower for the angle of repose (0.98%) followed by the
tapped density (1.13%) and by the aerated density (1.64%). These
results conﬁrm what was said for the calibration models. The aerated density is more affected by external variables such as operator
control, because is the less precise (higher relative error) and less
exact (higher RSD). The LOD value is for the angle of repose, the
highest of the three parameters, since it is directly related with the
Fig. 8. Angle of repose NIR based predictions versus reference method values for the
calibration samples () and test samples (䊉).
Fig. 9. Aerated density NIR based predictions versus reference method values for
the calibration samples () and test samples (䊉).
M.C. Sarraguc¸a et al. / Journal of Pharmaceutical and Biomedical Analysis 52 (2010) 484–492
491
will possibly be reﬂected in an enhancement of the near infraredbased prediction results.
Acknowledgements
The authors acknowledge the ﬁnancial support given by the
Reitoria da Universidade do Porto and Caixa Geral de Depósitos
(Project IRIC IPG2007-131).
Mafalda Cruz Sarraguc¸a acknowledges the ﬁnancial support
from the Fundac¸ão para a Ciência e Tecnologia (FCT), Portugal (Ph.D.
grant, ref: SFRH/BD/32614/2006).
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Fig. 10. Tapped density NIR based predictions versus reference method values for
the calibration samples () and test samples (䊉).
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compared between the angle of repose and the densities, since the
value for this parameter is affected by the spectral pre-processing
technique used. The sensitivity value for the both densities is similar. The angle of repose has a selectivity value slightly higher than
the other parameters. The same problems in terms of environmental conditions that were referred in the calibration section can
also be applied in this section. However, relative prediction errors
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5. Conclusions
The potential of near infrared spectroscopy to determined
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