This research paper examines the use of terahertz time-domain spectroscopy (THz-TDS) to determine the optical properties of pharmaceutical tablets as functions of porosity and active pharmaceutical ingredient (API) mass fraction. Four training sets of tablets with varying porosity, height, and API content were studied. The study found linear correlations between terahertz effective refractive index and both porosity and API mass fraction for the first time using real pharmaceutical tablets. These correlations could be useful for basic research and quality inspection of tablets. Additionally, a novel "optical strain" parameter was proposed based on THz measurements that provides information on both conventional mechanical strain and changes in solid material fill fraction during tablet compression.

1. Research paper
Terahertz study on porosity and mass fraction of active pharmaceutical
ingredient of pharmaceutical tablets
Prince Bawuah a,⇑
, Nicholas Tan b
, Samuel Nana A. Tweneboah a
, Tuomas Ervasti c
, J. Axel Zeitler b
,
Jarkko Ketolainen c
, Kai-Erik Peiponen a
a
Institute of Photonics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
b
Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge CB2 3RA, United Kingdom
c
School of Pharmacy, Promis Centre, University of Eastern Finland, P.O. Box 1617, FI-70211 Kuopio, Finland
a r t i c l e i n f o
Article history:
Received 7 March 2016
Revised 4 May 2016
Accepted in revised form 7 June 2016
Available online 8 June 2016
Keywords:
Pharmaceutical tablet
Microcrystalline cellulose
Active pharmaceutical ingredient
Porosity
Terahertz
Effective refractive index
Effective absorption coefficient
Strain
a b s t r a c t
In this study, terahertz time-domain spectroscopic (THz-TDS) technique has been used to ascertain the
change in the optical properties, as a function of changing porosity and mass fraction of active pharma-
ceutical ingredient (API), of training sets of pharmaceutical tablets. Four training sets of pharmaceutical
tablets were compressed with microcrystalline cellulose (MCC) excipient and indomethacin API by
varying either the porosity, height, and API mass fraction or all three tablet parameters.
It was observed, as far as we know, for the first time, that the THz time-domain and frequency-domain
effective refractive index, as well as, the frequency-domain effective absorption coefficient both show
linear correlations with the porosity and API mass fraction for training sets of real pharmaceutical tablets.
We suggest that, the observed linear correlations can be useful in basic research and quality inspection of
pharmaceutical tablets.
Additionally, we propose a novel optical strain parameter, based on THz measurement, which yields
information on the conventional strain parameter of a tablet as well as on the change of fill fraction of
solid material during compression of porous pharmaceutical tablets.
We suggest that the THz measurement and proposed method of data analysis, in addition to providing
an efficient tool for basic research of porous media, can serve as one of the novel quality by design (QbD)
implementation techniques to predict critical quality attributes (CQA) such as porosity, API mass fraction
and strain of flat-faced pharmaceutical tablets before production.
Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction
Pharmaceutical solid dosage forms (tablets) are among the most
widely administered pharmaceutical products due to the ease of
large-scale production, stability and efficient means of drug intake
by patients. Even though much effort has been devoted to improv-
ing the efficacy and safety of pharmaceutical tablets, yet pharma-
cists are interested in search of fast and non-destructive methods
and techniques to optimize the quality and efficacy of all pharma-
ceutical tablets before reaching the end-users. To achieve this
demand, and bearing in mind the number of tablets produced
per hour in pharmaceutical industries, pharmacists have recently
resorted to the use of optical techniques [1–4]. This is due to the
fact that optical methods can meet the desired measuring speed,
for example in THz sensing [5]; that is, in principle, it is capable
of checking each tablet in the production line. As far as we know,
there is no in-process control for the detection of porosity during
tablet production, and off-line detection of porosity is typically
based on the use of commercial mercury porosimeters. Unfortu-
nately, commercial mercury porosimeters utilize destructive mea-
surement method. Hence, in the frame of process analytical
technology (PAT), there is a desire to have non-destructive
methods of measurement of porosity and also other important
properties of pharmaceutical tablets. For the purpose of visual
inspection of pharmaceutical tablets, several imaging techniques
have been employed, especially for the quality assessment of
imprint on tablet [6] and coating properties [7,8] of tablets.
Nonetheless, some of these optical techniques can be somewhat
destructive, especially due to the use of high power laser for tablet
inspection. For example, focusing of a laser beam over a pharma-
ceutical tablet can cause photo-bleaching, and therefore photo-
chemical changes of the tablet during optical inspection. The
quest to achieve both speed and non-destructive measurements
http://dx.doi.org/10.1016/j.ejpb.2016.06.007
0939-6411/Ó 2016 Elsevier B.V. All rights reserved.
⇑ Corresponding author.
E-mail address: prince.bawuah@uef.fi (P. Bawuah).
European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133
Contents lists available at ScienceDirect
European Journal of Pharmaceutics and Biopharmaceutics
journal homepage: www.elsevier.com/locate/ejpb

2. has recently triggered the use of THz-TDS technique for the assess-
ment of various properties of pharmaceutical tablets [9–11]. THz
radiation has relatively long wavelength and low energy (i.e. no
ionization of sample) that can interact with optical phonons in
their different crystal lattices [12,13]. This unique property of
THz radiation has been used for the identification of different poly-
morphs of some major pharmaceutical ingredients [14,15] based
on their intrinsic spectral fingerprints at THz frequencies. In a
recent review, THz-TDS has been used to study the crystallization
of amorphous drugs by monitoring the onset and strength of the
molecular mobility [16].
Porous media such as pharmaceutical tablets contain inclusions
(inhomogeneities) whose dimensions (ca. 1–100 lm) are relatively
small compared to the wavelength of a given THz wave (100–
3000 lm). The relatively small dimensions of these inclusions
compared to the THz wavelength result in no or low scattering of
the incident THz radiation. This condition has permitted the use
of effective medium theories such as Maxwell Garnett [17],
Bruggeman [18], Wiener bounds [19], and Hashin-Shtrikman
bounds [20] to predict the effective properties of bulk pharmaceu-
tical tablets including the intrinsic properties of the individual
inclusions in the tablet in the THz range of the electromagnetic
spectrum. The effective medium theories provide a link between
the microscopic and macroscopic properties of porous media.
A useful property, which forms the central objective of this
study is that, with THz-TDS, one can easily obtain the optical
constants such as refractive index and absorption coefficient of
pharmaceutical tablets via either the time-domain or frequency-
domain signal processing techniques. Usually, the extracted optical
constants are considered as effective properties due to the compo-
sition of a pharmaceutical tablet, i.e. excipient(s), API and air voids.
The knowledge of the optical constants can serve as the back-
bone for further extraction of other quality parameters such as
weight, height, porosity and the intrinsic properties of the various
inclusions of the tablet’s matrix using non-contact THz measure-
ment technique [18,21]. From these quality parameters, one could
further predict important tablet properties such as dissolution, fri-
ability, API mass fraction and tensile strength [22]. Due to the
inevitable dependence of the quality parameters of a given phar-
maceutical tablet on its optical constants, our previous work has
been devoted to finding the correlation between the effective
refractive index and parameters such as porosity and surface
roughness of training sets of pharmaceutical compacts composed
of MCC only [18]. However, a reliable generalization of our previ-
ous observations requires a more detailed assessment with real
pharmaceutical tablets. By real pharmaceutical tablet, we mean a
tablet that contains API in a solid matrix (excipient). This study
utilizes four different training sets of pharmaceutical tablets that
contain MCC (here we use different grades from that used in
[18]) as the excipient and indomethacin as an API. With these sets
of tablets, an important question arises whether a linear correla-
tion previously observed between the effective refractive index
and the porosity of tablets without API [18] is valid for tablets with
API. The answer is yes as will be shown in this article. Similarly, we
show, as far as we know, for the first time, a linear correlation
between the THz effective refractive index and the API mass frac-
tion of real pharmaceutical tablets instead of typical pellets used
in THz-TDS measurements. Furthermore, analysis was carried out
to quantify, compare and contrast the magnitude of change on
both the time-domain and frequency-domain refractive index by
varying either porosity only and API mass fraction only or both
parameters in the training sets of the pharmaceutical tablets. Lin-
ear correlation between tablet’s properties and optical constants,
such as effective refractive index and effective absorption coeffi-
cient, is demonstrated to hold also in the frequency-domain.
In the realms of QbD [23], porosity is considered as one of the
CQA due to its direct effect on the dissolution rate and friability
of a pharmaceutical tablet. Hence, several studies have been con-
ducted to characterize pharmaceutical compacts using different
methods, e.g. depolarization metrics of laser light scattering [24].
Due to the observed linear correlation between effective refractive
index, porosity and API mass fraction of the training tablet sets, the
present study introduces and demonstrates a three-dimensional
(3D) plane concept that can serve as a visual aid to understand
how the three parameters namely effective refractive index,
porosity and API mass fraction depend on each other. Finally, the
findings of this study can serve as a process analytical technology
(PAT) tool to predict CQA such as porosity and API mass fraction
during the design of experiment (DoE), which is an important
element in QbD in the development of new product or the
optimization of existing ones.
2. Theory
In the context of a porous pharmaceutical tablet the refractive
index of the tablet is termed ‘‘effective” due to the various compo-
sitions of the pharmaceutical tablet such as air, excipients and API.
If H and Dt are the height and the measured THz pulse time
delay of the tablets respectively, the effective refractive index neff
can be obtained from the expression of optical path length as
follows,
ðneff ðfÞ À 1ÞH ¼ cDt; ð1Þ
where c is the speed of light in vacuum, f is the porosity of the tablet
and the assumption made is that, the effective refractive index has
the same value all over the tablet. The reference in the measure-
ment is typically air or nitrogen gas, and the refractive index of
the reference is assumed to be equal to one.
A linear relationship was observed between neff and a discrete
set of porosity values for pharmaceutical compacts containing
MCC only in our previous study as follows [18]:
neff ðfÞ ¼ nð0Þ þ ð1 À nð0ÞÞf; ð2Þ
where n(0) is a fitting parameter, namely the zero porosity estimate
of refractive index of MCC. The numerical value of n(0) is applicable
for data analysis by Eq. (2) at least inside the porosity range of mea-
surements where the linear relationship is valid. The present study
aims at ascertaining the effect of the combination of both porosity
and API mass fraction (x) on the effective refractive index of training
sets of real pharmaceutical tablets. These sets consisted of MCC
with refractive index of nMCC and API (indomethacin) with refrac-
tive index as nAPI. In order to graphically illustrate the linear depen-
dency of the effective refractive index on both the porosity and API
mass fraction, we imagine a triangle of vertices P1 (1,0,1), P2 (0,0,
nMCC), P3 (0,1,nAPI) drawn in the Cartesian coordinate system (f,x,
neff) (see Fig. 1). The chosen vertices of the triangle correspond to
reality since one would expect to have the effective refractive index
to be equal to that of air if the porosity of a tablet is 100% as
depicted by point P1. Point 2, P2, physically means that, at zero
porosity and zero API mass fraction, the effective refractive index
of the tablet is equal to the refractive index of MCC, nMCC, since
the composition of the tablet tends to be MCC only. Finally, P3
depicts a tablet made of API only since the API mass fraction is
100 wt% without any air voids (refractive index of API is nAPI). In
the simulation of Fig. 1, we have assumed that nMCC > nAPI. Natu-
rally, cases with greater refractive index of API than those of excip-
ient are possible. From the vertices of the triangle in Fig. 1, and by
utilizing the principles of analytic geometry [25], we derived the
equation of a plane as
P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133 123

3. neff ðf; xÞ ¼ nMCC À ðnMCC À 1Þf À ðnMCC À nAPIÞx; ð3Þ
where f and x are independent variables (the mass fraction of the
MCC is given by 1 À x). The validity of Eq. (3) will be shown for
the case of the four training tablet sets in this study. In reality,
the combination of values of f and x is restricted between (0,0) 6
(f,x) 6 (1,1), which is a rectangular unit area in the (f,x) - plane.
Obviously, Eq. (3) describes, instead of the full space of an infinite
tilted plane, a triangle, which is a ‘‘sub-space” of the infinite plane.
Practically speaking, the values of f, x and neff of real pharmaceutical
tablets usually occupy a relatively small local area in the graphical
description of the plane defined by Eq. (3). In order to test the
validity of Eq. (3), this study presents experimental data of real
pharmaceutical tablets with varying porosity and API mass fraction.
We show that all the obtained refractive index data will follow the
law of Eq. (3), and hence lie on the plane illustrated in Fig. 1.
Furthermore, a comparative analysis on the magnitude of the
changes in the neff due to changing only the porosity and only
the API mass fraction was conducted. From Eq. (3), one can write
the change of the effective refractive due to changing only the
porosity, Dneff (f), as
Dneff ðfÞ ¼ ÀðnMCC À 1ÞDf; ð4Þ
whereas in the case of the change of API mass fraction only, Dneff
(x), is given by
Dneff ðxÞ ¼ ÀðnMCC À nAPIÞDx; ð5Þ
where Df and Dx are the change in porosity and API mass fraction,
respectively.
Mechanical properties of pharmaceutical tablets have much
importance. Herein, we present theory for a novel concept that is
closely related to the true strain of pharmaceutical tablets in the
realms of THz time-delay measurement techniques. This approach
can serve as a novel technique for the inspection of the mechanical
properties of pharmaceutical tablets. The true ‘‘mechanical” strain
(emech) of a medium is defined by the integral
emech ¼
Z H
H0
dH
H
¼ ln
H
H0
; ð6Þ
where H0 is the initial height of the medium and H is the reduced
height after compression of the medium. In a similar analogy, we
can define an ‘‘optical” strain (eopt) using the concept of optical path
length of the porous tablet, namely
eopt ¼
Z neff H
neff;0H0
dðneff HÞ
neff H
¼ ln
neff H
neff;0H0
¼ ln
neff
neff;0
þ ln
H
H0
¼ ln
neff
neff;0
þ emech; ð7Þ
where neff,0 is the effective refractive index of a tablet with initial
height H0 and the property of logarithm, ln(AB) = lnA + lnB, was
used.
It is obvious from the definition given in Eq. (7) that it is possi-
ble to separate mechanical strain and the contribution due to the
refractive index of the medium. Eq. (7) holds, generally, for any
optical technique in the absence of light scattering. However, in a
case similar to this study, where the time-delay (calculated based
on the time-of-flight difference between reference THz pulse and
sample THz pulse) is known, a practical definition of the optical
strain based on the utilization of the optical path length defined
by Eq. (1) should be derived. Hence, we redefine the optical strain
in terms of THz pulse delay measurement (eTHz) as follows:
eTHz ¼
Z ðneff À1ÞH
ðneff;0À1ÞH0
dððneff À 1ÞHÞ
ðneff À 1ÞH
¼ ln
ðneff À 1ÞH
ðneff;0 À 1ÞH0
¼ ln
neff À 1
neff;0 À 1
þ ln
H
H0
¼ ln
neff À 1
neff;0 À 1
þ emech: ð8Þ
Now, the logarithm given in the second equality in Eq. (8)
can be expressed in terms of the THz pulse time delay data
(see Eq. (1)), namely
eTHz ¼ ln
Dt
Dt0
¼ ln
neff À 1
neff;0 À 1
þ emech: ð9Þ
Next we utilize the linear relation between the effective
refractive index and porosity given in Eq. (2) and substitute this
expression of neff (f) into Eq. (9). Hence, after some algebra we
get an expression
eTHz ¼ ln
Dt
Dt0
¼ ln
1 À f
1 À f0
þ emech: ð10Þ
This is rather interesting expression because the first logarithm
in Eq. (10) is obtained by time delay measurement of a pulse of
electromagnetic radiation only, whereas the two expressions on
the right hand-side of the second equality in Eq. (10) describe
purely material and mechanical properties of the tablet. Note that
1 À f0 and 1 À f are the fill fractions of the solid medium of the
tablet before and after compression, and the change of the porosity
of the tablet is equal to Df = f0 À f. Evidently the optical strain is a
more general concept than the pure mechanical strain because, in
addition to containing information on the conventional true strain,
it also gives information on the relative change of the fill fraction of
the solid medium (ratio of fill fractions) due to compression and
hence reduction in the tablet height. This logarithmic ratio of fill
fraction can serve as a new useful quality parameter of pharmaceu-
tical tablets.
3. Materials and methods
3.1. Materials
Four sets of flat-faced pharmaceutical tablets with 13 mm
diameter were compacted from microcrystalline cellulose, MCC
(Avicell PH101, FMC BioPolymer, Philadelphia, USA) as the excipi-
ent with indomethacin (Hangzhou Dayangchem Co. Ltd, Hangzhou,
China) as the active pharmaceutical ingredient (API). These sam-
ples were used as received. The MCC grade, Avicell PH101, has a
nominal particle size of 50 lm and a true density of 1.56 g cmÀ3
whereas the indomethacin (mostly used as a painkiller), in its
Fig. 1. A simulated plane showing the relationship between the effective refractive
index, porosity and API mass fraction of pharmaceutical tablets. The points P1, P2
and P3 used in the derivation of Eq. (2) are shown as nair, nMCC, and nAPI respectively.
The black portions (marks) in the plane show the occupied locations of the training
sets of pharmaceutical tablets used in the study.
124 P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133

4. crystalline gamma polymorph has a true density of 1.37 g cmÀ3
.
The choice of MCC, apart from being a conventional pharmaceuti-
cal excipient, is based on the fact that MCC is a good disintegrant, a
filler and can be directly compacted at low pressure [26]. Due
to these merits, MCC has been an interesting object of study
using THz measurement techniques [27]. On the other hand,
molecular understanding of compressibility and resulting porosity
of c-polymorph of indomethacin have been studied in [28].
3.2. Tablet compaction
All the sets were compacted with a compaction simulator
(PuuMan Ltd, Kuopio, Finland) and the detailed tableting process
has been described previously in [29]. With a compaction simula-
tor, pharmacists have the possibility to adjust and control the
values of the compaction parameters such as porosity and height
of the tablet during the compression processing. Other advantages
of the compaction simulator include the following: the ability to
choose different compression cycles of lower and upper punches
and adjust the magnitude of the compression force. The porosity
and height properties of the tablets were changed by changing
the total mass of the MCC and indomethacin powders (see Tables
1 and 2) used during compaction.
In sets 1 and 2, the porosity and height were varied respectively,
but the API mass fraction in both sets was kept constant at ca.
10 wt%. Set 3 composed of tablets with varying API mass fraction
but constant porosity. In set 4, all the parameters (i.e. porosity,
height and API mass fraction) were varied. Both sets 1 and 3 tablets
had nominally constant value of height of $3 mm whereas for the
sets 2 and 3, the porosity was kept at a nominally constant value of
ca. 36%.
3.3. Tablet porosity
The density of each pharmaceutical tablet was calculated from
their dimensions (i.e. height and diameter) and weight. The dimen-
sions of the tablets were measured a day after compaction to avoid
measurement errors due to possible mechanical relaxation of the
tablets. The tablet dimensions were measured with a micrometer
(Digitrix, NSK, Japan) whereas an analytical balance (Mettler
Toledo AG245, Schwerzenbach, Switzerland) was used for the
weight measurement. The true densities of MCC (1.5573 g cmÀ3
)
and indomethacin (1.3701 g cmÀ3
), given by the manufacturers,
were used in the calculation of the porosities of the tablets.
It is worth noting that, for a given sample number (Table 1), five
pharmaceutical tablets were compressed. Hence, we present the
measured average values of the varying parameters for all tablets
in each set (Table 1). The total number of pharmaceutical tablets
used for the THz measurements was 110 tablets.
For each tablet sets, errors in the calculations made for
the nominal porosities are as follows: diameter ± 0.008 mm,
height ± 0.005 mm (standard deviation of the sample mean),
weight ± 0.01 mg (readability of the scale) and porosity ± 0.2%
(calculated using the error propagation law).
3.4. THz time-domain measurements
The terahertz pulse time delay of these sets was measured using
a THz-TDS with setup similar to that described previously [30,31].
The simplest case is when the effective refractive index is retrieved
from the THz pulse time delay that is calculated from the measured
time difference between the sample and reference pulses
(see Eq. (1)).
3.5. Frequency-domain analysis of time-domain THz measurement
data
Apart from the straightforward time-domain measurement
described above, we have also estimated the frequency-
dependent optical constants of the training sets of pharmaceutical
tablets. Accurate extraction of the frequency dependent optical
constants such as the effective refractive index and the effective
absorption coefficient in THz transmission measurement is based
on the measurement of the electric field amplitude of both the
sample and the reference signal in time-domain. These acquired
time-domain waveforms are converted to the frequency domain
via fast Fourier transform (FFT) before further processing. Normal-
izing the sample spectrum by the reference spectrum yields the
complex-valued transmission function from which both the fre-
quency dependent effective refractive index, neff, and the effective
absorption coefficient, aeff, are extracted. Readers interested in the
description of the data analysis, parameter retrieval processes and
the working principles of the THz-TDS are referred to [32–35].
In a similar manner as described in the time-domain analysis
below, the change of both the frequency-dependent effective
absorption coefficient and effective refractive index as a result of
changing porosity and API mass fraction is discussed in the next
section. Finally, we have investigated the correlation between the
change in the effective absorption coefficients at a given frequency
and the change in both porosity and API mass fraction of the train-
ing sets of pharmaceutical tablets.
4. Results and discussions
4.1. THz time-domain analysis
The measured pulse delay was used to estimate the effective
refractive index for the various sets of tablets using Eq. (1). This
straightforward refractive index extraction technique, as discussed
previously, is relatively fast and, in principle, capable of meeting
the measurement speed needed for an inline tablet inspection.
The measurement error of the effective refractive index is ca.
±0.002 [29]. The effective refractive index, under this contest, is
considered to be given at a virtual frequency since the THz pulses,
from which the refractive indices were extracted, are composed of
a broad band of THz frequencies.
The values recorded for both the Dt and neff for the different
sets, and even for tablets within the same set (see Table 5) varied,
as expected, due to the different compaction parameters used
Table 1
Data of tablet set 1. The mean values of the diameter d, height H, weight W, density q,
and porosity f. The API mass fraction and height are kept at a constant value of 10 wt%
and 3 mm, respectively.
Sample number d (mm) H (mm) W (mg) q (g cmÀ3
) f (%) x (wt%)
1 13.123 3.031 342.49 1.54 46 10
2 13.113 3.033 356.90 1.54 43 10
3 13.120 3.018 370.92 1.54 41 10
4 13.106 3.013 385.17 1.54 38 10
5 13.110 3.007 400.10 1.54 36 10
Table 2
Data of tablet set 2. The mean values of the diameter d, height H, weight W, density q,
and porosity f. The API mass fraction and porosity are kept at a constant value of
10 wt% and 36% respectively.
Sample number d (mm) H (mm) W (mg) q (g cmÀ3
) f (%) x (wt%)
1 13.097 2.742 361.47 1.539 36 10
2 13.078 3.333 438.73 1.539 36 10
3 13.066 3.626 476.45 1.539 36 10
4 13.062 3.927 514.70 1.539 36 10
P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133 125

5. during the tableting process. Comparatively, these new sets seem
to have higher values of neff than the sets of our previous studies
[18]. This observed difference in magnitude of the effective refrac-
tive indices is most probably due to the use of different MCC grades
and the presence of the API in these new sets 1–4.
In order to investigate the effect of porosity and API mass
fraction on the effective refractive index, we have utilized Eqs.
(4) and (5). In these equations one has to know the zero-porosity
refractive indices of MCC and API. These are obtained by an extrap-
olation process similar to that suggested in [21]. In Fig. 2, set 3
tablet samples with varying API mass fraction were utilized. By
extrapolating the API mass fraction within the range of 0–100 wt
%, the refractive indices of MCC only and that of API only at 36%
porosity were obtained (see Fig. 2(a)). The obtained refractive
index values at 36% in addition to the choice of an anchor point
namely (n = 1 at f = 100%) were used in the linear extrapolation
(Fig. 2(b)) to determine the estimates of the zero-porosity refrac-
tive index of both MCC and API, i.e. nMCC = 1.85, nAPI = 1.61. These
‘‘intrinsic” refractive index values were used only for an illustrative
purpose (Fig. 1) and also for theoretical estimation of effective
refractive index change of a tablet that is due to porosity or API
mass fraction change only, as will be demonstrated below.
An experimental clue of how the effective refractive index
varies as a function of both the porosity and the API mass fraction
given by Eq. (3) has been illustrated (Fig. 3). In Fig. 3, we have plot-
ted data points of all the tablets used under each sample number
(see Tables 1–5) for sets 1–4 samples without taking their average.
The linear relation observed between neff and f, for example, of sets
1 and 4 further proves the validity of Eq. (3). Apart from proving
the validity of Eq. (3), we show for the first time that, even for
three-phase (i.e. air-MCC-API) pharmaceutical tablets, a linear rela-
tion still exists between the effective refractive index and the
porosity range we are dealing with.
It is interesting to get theoretical but quantitative estimates for
the effective refractive index change regarding the change of
porosity only and API mass fraction only. By substituting the value
of 0.1 for the change in the porosity (i.e. set 1) and 0.15 as the
change in the API mass fraction (i.e. set 3) into Eqs. (4) and (5)
respectively, we obtained 0.085 as the recorded change in the
effective refractive index due to the change in porosity only and
0.036 as the recorded change due to changing only the API mass
fraction. This shows that changing the porosity induces higher
change in the effective refractive index than changing the API mass
fraction. A close manifestation of this observation is shown in the
experimental data of sets 1 and 3 (Fig. 3(a) and (c)). Thus, a com-
parison made between Df (i.e. 10%) and Dx (i.e. 15%) of sets 1
and 3 to their respective experimental change in the effective
refractive index (i.e. Dneff (f) = 0.083, Dneff (x) = 0.022) has further
strengthened the validity of the calculated change of the effective
refractive index value obtained from Eqs. (4) and (5) above.
Furthermore, by bearing in mind the narrow change in the API
mass fraction in set 4, and considering Figs. 3(a) and 3(d), we infer
that doubling Df approximately doubles Dn.
Moreover, the change in the effective refractive index values of
set 2 samples (Fig. 3(b)) shows that varying only the height of a
tablet, as expected, has no significant effect on the neff (therefore
in the latter part of this study we do not present data for the set
2 anymore). By this observation, it is valid to attribute the change
observed in the effective refractive index of the set 4 (i.e. where all
the parameters are being varied) to only two varying parameters,
namely porosity and API mass fraction. Hence in the discussion
below we present data for sets 1, 3 and 4 only. But before that
we briefly deal with the concept of the height of pharmaceutical
tablets.
Building on the issue concerning the variations in the height of
pharmaceutical tablets, we next briefly demonstrate the use of THz
time-delay measurement for checking the presence of an unac-
ceptable height variation of tablets, which can inform pharmacists
the possible mechanical relaxation of pharmaceutical tablets after
compaction. The presence of possible height change due to
mechanical relaxation of pharmaceutical tablets can alter the
porosity of such tablets. Hence, this study seeks to ascertain and
to demonstrate how the porosity variations of tablets can be mon-
itored in cases where the height of the pharmaceutical tablets falls
within the optimum/acceptable range. By this demonstration, we
have assumed that the set 2 (see Table 2) presents tablets with a
Fig. 2. An illustration of the use of the linear extrapolation technique in the estimation of the zero-porosity refractive indices of MCC, nMCC (0%) and API, nAPI (0%). Set 3
samples with varying API mass fraction were used for the analysis. (a) Illustrates a linear extrapolation of the effective refractive index in terms of the API mass fraction
whereas (b) shows similar extrapolation in terms of the porosity.
126 P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133

6. targeted constant porosity and API mass fraction but with thick-
nesses that are subject to abnormal change. Since the effective
refractive index of the tablets is a constant in such a case, the time
delay of the THz depends on the height of the tablet. This is evident
from Eq. (1) because Eq. (1) presents a straight line as a function of
H. It is evident from Eq. (1) that at H = 0, Dt = 0, hence the line goes
via the origin (Fig. 4). The slope of the line provides information on
the effective refractive index (set 2 in this case) for the given poros-
ity. Using the data of set 2 samples (Fig. 4), we got an estimate for
the effective refractive index of neff = 1.536 from the slope of the
fitted line. This value matches quite well with the effective refrac-
tive index of set 2 samples (Table 5). Thus, by keeping both the f
and x constant and varying only the height, we can get information
about the effective refractive index of the tablet. This is interesting
since pharmacists may set an optimal height for a batch of tablets
and hence we can use this idea to get any variation of THz pulse
delay which is due to variation of f of such batch of tablets or vice
versa. To buttress this argument, we utilize the data of tablet set 1
Fig. 3. Comparison of the effect of porosity and API mass fraction on the effective refractive index for (a) set 1, (b) set 2, (c) set 3 and (d) set 4. Dneff, Df, Dx and DH give the
differences between maximum and minimum values for the change in the effective refractive index, porosity, API mass fraction and height respectively. The values of the
slope, s, for sets 1 and 4 are given.
Table 3
Data of tablet set 3. The mean values of the diameter d, height H, weight W, density q,
porosity f, and API mass fraction x. The porosity and height are kept at a constant
value of 36% and 3 mm, respectively.
Sample number d (mm) H (mm) W (mg) q (g cmÀ3
) f (%) x (wt%)
1 13.104 3.034 410.55 1.557 36 0.00
2 13.079 3.023 403.13 1.550 36 3.75
3 13.103 3.025 403.04 1.543 36 7.50
4 13.100 3.001 401.90 1.541 36 8.75
5 13.097 3.016 401.15 1.539 36 10.00
6 13.099 3.036 400.56 1.536 36 11.25
7 13.096 3.034 399.82 1.534 36 12.50
8 13.110 3.039 400.20 1.529 36 15.00
Table 4
Data of tablet set 4. The values of the diameter d, height H, weight W, density q,
porosity f, and API mass fraction x.
Sample number d (mm) H (mm) W (mg) q (g cmÀ3
) f (%) x (wt%)
1 13.081 2.738 405.86 1.54 28 9.0
2 13.090 2.960 405.44 1.54 34 9.5
3 13.093 3.279 405.92 1.54 40 10.0
4 13.083 3.654 403.45 1.54 47 10.5
5 13.081 3.947 403.56 1.54 50 11.0
Table 5
The calculated pulse delay (Dt) and the effective refractive index (neff) of the four sets
of pharmaceutical tablets. The absolute measurement error of effective refractive
index is ca. ±0.002 and the porosity ca. ±0.5% [29].
Sample
number
Set 1 Set 2 Set 3 Set 4
Dt
(ps)
neff Dt
(ps)
neff Dt
(ps)
neff Dt
(ps)
neff
1 4.551 1.444 4.850 1.529 5.589 1.543 5.535 1.602
2 4.780 1.464 5.948 1.533 5.497 1.537 5.480 1.551
3 4.959 1.484 6.491 1.536 5.442 1.527 5.470 1.498
4 5.160 1.506 7.023 1.535 5.437 1.529 5.404 1.441
5 5.345 1.527 5.437 1.526 5.372 1.405
6 5.426 1.524
7 5.415 1.522
8 5.372 1.521
P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133 127

7. and simulate by setting for a tablet, an optimal height of 3 mm,
porosity of 0.36 and API mass fraction of 10 wt%, respectively.
We then compared the optical path length of tablets with the
optimal optical path length cDt (Fig. 4).
To throw more light on how the change of porosity affects the
effective refractive index, a linear correlation, with an average
slope, s, of 0.0089, was observed between the change in the
effective refractive index and the change in porosity for both sets
1 and 4 samples (see Fig. 5). It is clearly seen that even at narrow
intervals of porosity change, the linear relationship between poros-
ity and effective refractive index still seems to be valid. This obser-
vation is true for flat-faced tablets as well as tablets containing
either fixed or varying amount of API (Fig. 5).
Furthermore, a linear correlation was observed between the neff
and the x (Fig. 6). This observation further proves, at least, a local
validity of Eq. (3) in the Cartesian 3D system.
Although this linear observation between neff and f (see Fig. 3
(a) and (d)) is quite promising, it was demonstrated in the present
study to be applicable to flat-faced tablets. Since most pharmaceu-
tical tablets have curved surfaces, there is a need for further inves-
tigations on curved surface samples containing API using a concept
similar to the training sets 1–4 of this study. This requires more
theoretical and experimental investigations and will be the moti-
vation for our future studies.
Finally, the black portions (marks) on the tilted plane (Fig. 1)
give a visual demonstration of the correlation between the effec-
tive refractive index, porosity and API mass fraction of the four
training sets of pharmaceutical tablets. Also for a given range of
porosity and API mass fraction for pharmaceutical tablets and
using Fig. 1, one can envisage a rectangle on the f, x plane that
can be projected on the 3D plane to predict the range of the effec-
tive refractive index as well. This concept of 3D plane could also
serve as a quick visual quality inspection aid to monitor the history
of the properties of batches of pharmaceutical tablets produced
over time.
4.2. THz frequency-domain analysis
Building on the frequency domain analysis, we have retrieved
both the frequency dependent effective absorption coefficient (aeff)
and the effective refractive index, of sets 1–4 samples and have
compared the magnitude of variation of these optical constants
due to the change in the porosity and API mass fraction. The ampli-
tude data utilized for the data analysis were obtained by scanning
both the sample and reference THz electric field through proper
adjustment of the delay line during the measurement. Fast Fourier
transform (FFT) technique was employed to convert the time-
domain amplitude signal into frequency-domain. From the
complex-valued frequency dependent transmittance coefficient,
it is possible to extract information on effective refractive index
and effective absorption coefficient of the pharmaceutical tablet.
Although the scanning of the THz pulse to detect the amplitude
is time-consuming compared to the time-domain analysis dis-
cussed above, modern advancement in detector technology has
made it possible to measure high-quality terahertz spectra in less
than 20 ms [5].
Similar analysis performed as in the case of the neff (Fig. 3),
reveals from Fig. 7 that the increment in both the porosity and
API mass fraction causes a decrease in the frequency dependent
effective absorption coefficient of sets 1, 3 and 4 (see Fig. 7(a), (c)
and (e)) samples. As an example, we plotted the magnitude of
the change in the effective absorption coefficient (Daeff) at 0.8
THz of sets 1 and 3 due to changing porosity only (Fig. 7(a)), and
API mass fraction only (Fig. 7(c)). Based on the calculated values
of Daeff (Fig. 7(a), (c) and (e)), it is obvious that the combined effect
of both porosity and API mass fraction on the change in the effec-
tive absorption coefficient can be relatively strong especially at
higher frequencies but we will take a closer look at this property
a bit later.
For the change in frequency-dependent effective refractive
index (Dneff), which is due to the change of porosity and API mass
fraction of sets 1, 3 and 4 (Fig. 7(b), (d) and (f)), the observations
made are akin to that of neff (Fig. 3). Even the recorded Dneff values
at 0.8 THz closely match with their counterparts in Fig. 3. Obvi-
ously the effective refractive index curves (Fig. 7) show a
plateau-like behavior at 0–1.5 THz, which suggests no or low dis-
persion of the THz wave. Dispersion, when present, plays an
important role regarding the THz pulse position since it broadens
and thus, causes re-shaping of the THz pulse. Relatively strong dis-
persion is accompanied with relatively high absorption [36]. In
such a case, detecting a THz transmission signal from 3 mm thick
sample is usually problematic.
Next we pay attention to the spectral interpretation of the
absorption data. It is interesting to observe from the absorption
coefficient curves (Fig. 7) the absence of the spectral fingerprints
Fig. 4. Variation of cDt as a function of H for set 2 tablets. The solid line (calibration
line with slope s) has been fitted to four data points, and the fifth point in origin
comes from the theory. The dashed horizontal and vertical lines indicate the
optimal tablet height and THz time delay. The value of 3 mm is used as an optimal
tablet height. Points (b)–(d) present data for the tablet set 1 which deviate from the
optimum operation point due to variation of porosity of the tablet. Point (a) is close
to the optimum point.
Fig. 5. An illustration of the correlation between the change in the refractive index
and the change in porosity for sets 1 and 4 samples.
128 P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133

8. of c-crystalline form of indomethacin despite its reported finger-
prints at 1.2, 1.5 and 2.0 THz [37,38] for powder substance. This
might be due to the possible phase change of the API from
crystalline to amorphous phase during the tablet compression
but more probable reason is the relatively low API mass fractions
of these training sets compared to the API mass fractions used in
[37,38]. Anyhow, it is obvious from Fig. 7(a), (c) and (e) that there
are actually three things that have an effect on the absolute mag-
nitude of the effective absorption coefficient, namely porosity
and API plus MCC mass fractions of a tablet. In the case of Fig. 7
(a) the API mass fraction is fixed but the porosity is a variable.
Obviously, an increase in porosity decreases the frequency-
dependent effective absorption coefficient (Fig. 7(a)). In the case
of set 3 samples (Fig. 7(c)), the porosity is fixed to the nominal
value of 36%, but the API mass fraction and hence the mass fraction
of MCC are subject to vary. If we compare the curves of the absorp-
tion coefficients of sets 1 and 3 samples (Fig. 7(a) and (c)) with
almost the same thickness ca. 3 mm, it is obvious that the magni-
tude of the effective absorption coefficient, aeff, is a bit higher in set
3 samples (Fig. 7(c)) than in set 1 samples (Fig. 7(a)). It is quite
interesting that while the API mass fraction is increasing, the
absorption coefficient is decreasing (Fig. 7(c)). A common feature
for all absorption curves (Fig. 7(a), (c) and (e)) is that there is a
‘‘shoulder” toward the high frequencies. As it can be seen from
Fig. 7(c), the shoulder exists already for MCC only (0 wt% API), a
fact that was reported in a previous article [39]. The behavior of
the curves in Fig. 7(c) can be interpreted that the absorption coef-
ficient of MCC is higher than that of the API. In other words,
increasing the wt% of API (i.e. decreasing the wt% of MCC)
decreases the frequency-dependent absorption coefficient of the
pharmaceutical tablet for the case where porosity is constant. In
the case of set 4 samples (Fig. 7(e)), both porosity of tablet and
mass fraction of API and MCC are subject to change. Again, the pro-
nounced absorption role of MCC over API is here manifested
because the change of API wt% is at relatively narrow range of
9–11 wt% compared to the rather wide porosity range of 28–51%.
Anyhow, the observations made above suggest useful information
to pharmaceutical scientists, namely in order to detect a transmis-
sion signal for relatively high absorbing samples, it is possible to
try to find and work within ‘‘spectral window(s)” (e.g. the band
0.1–1.5 THz of this study) where absorption is relatively weak to
allow the transmission of a THz pulse through a relatively thick
pharmaceutical tablet. Generally, the tablet can actually have
strong THz fingerprints in the absorption spectrum, but the key
point is to work on the wings of spectral features where THz
absorption is low enough to allow transmission of the THz pulse.
In order to test the correlation between the effective absorption
coefficient and both the porosity and API mass fraction similar to
the data of Figs. 3 and 6, we took the values of the effective absorp-
tion coefficient of sets 1, 3 and 4 at the frequency of 0.8 THz. We
chose the effective absorption coefficient values at 0.8 THz because
at that frequency value, the recorded change in the frequency-
dependent refractive index values (see Fig. 7(b), (d) and (f)) is
almost the same as the effective refractive index change obtained
from the measured THz pulse delay of the tablet samples (Fig. 3).
A linear correlation was observed between the effective absorption
coefficient and the porosity for sets 1 and 4 samples (see Fig. 8
(a) and (b)). Similarly, there exists a linear correlation between
the effective absorption coefficient and the API mass fraction as
depicted by sets 3 and 4 samples (Fig. 8(c) and (d)). However, by
comparing the magnitude of the slopes, s, of the graphs related
to set 4 samples (Fig. 8(b) and (d)) to their respective counterparts
(Fig. 8(a) and (c)), it was observed that the set 4 samples (i.e. where
both porosity and API mass fraction vary) appear to have higher
slope than sets 1 and 3 (Fig. 8(a) and (c)) in terms of porosity
and API mass fraction respectively. This observation buttresses
our previous assertion that, changing both porosity and API mass
fraction of pharmaceutical tablets has a profound combined effect
on the effective absorption coefficient. In other words, the change
of both porosity and API mass fraction causes strong change in the
effective absorption coefficient than changing only one parameter.
This can be an asset when monitoring of minute change of porosity
and API mass fraction of a tablet. In addition, by comparing the
magnitude of the slopes of the effective absorption coefficient ver-
sus porosity (Fig. 8(a)) and API mass fraction (Fig. 8(c)) for sets 1
and 3 samples respectively, one can infer that the change of only
API mass fraction causes a bit higher change of the effective
absorption coefficient for these samples than changing only the
porosity.
Finally, we discuss the optical strain concept defined in the the-
ory section using experimental data obtained from the study. In
practice, it is quite challenging to simultaneously monitor both
the change of tablet thickness and THz time-delay. Herein, we
briefly deal with the concept of optical strain and compare it with
the conventional true strain using experimental data for simula-
tion purpose. We have used the data of tablet set 4 due to its com-
pression parameters which fit quite well for the purpose of the
simulation. However, for a rigorous measurement of the optical
and conventional strain one should have one single tablet that is
gradually compressed from the initial height to the final height,
and to monitor the changes. In such a case the weight of the tablet
is expected to be a constant. Set 4 samples consist of five different
Fig. 6. Linear correlation observed between the effective refractive index and the API mass fraction of (a) set 3 and (b) set 4 tablet samples.
P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133 129

9. pharmaceutical tablets with almost the same weight and hence,
the best choice for this simulation. We assume that tablet number
5 presents the initial state of the tablet, and this tablet is com-
pressed to the successive porosities (Table 4). Therefore, initial
height of 3.947 mm and initial effective refractive index of 1.405
that correspond to the sample number 5 in Table 4 were used
for the analysis. As it has been shown above, the small change of
API mass fraction has a negligible role on the effective refractive
index change. Instead the relatively big change of porosity is cru-
cial (see Table 4) for the change of the effective refractive index,
and also the strain (different models for porosity-dependent
Young’s modulus were considered in the frame of THz sensing in
[20,22]). Using the height and refractive index data for the tablet
set 4, we have calculated (simulating the compression of a single
tablet to different porosities) eTHz, emech and eopt using Eq. (10)
and Eq. (7) (see Fig. 9(a) and (b) respectively). For the sake of com-
parison, both the conventional true strain, emech, and the optical
strain, eopt, are plotted as a function of height reduction (Fig. 9
(b)). Obviously, both the conventional true strain and the optical
strain parameters have similar functional behavior (the strain is
considered as a positive number). It is therefore possible to
monitor conventional true strain using nondestructive THz time-
delay measurement technique by calibrating the data in Fig. 9.
In principle, the measured data of optical strain could serve as
an indirect method to nondestructively estimate the friability
and dissolution rate of pharmaceutical tablets. Furthermore, infor-
mation on fill fraction ratio of solid medium of the tablet can be
achieved.
Fig. 7. Analysis of the variations of the estimated frequency dependent effective absorption coefficient and effective refractive index of sets 1, 3 and 4 samples. (a) and (b)
Give the respective frequency-dependent absorption coefficient and the effective refractive index for set 1 samples, (c) and (d) show similar data of sets 3 samples whereas (e)
and (f) represent set 4 samples. Both Daeff and Dneff values shown were estimated at 0.8 THz as indicated by the arrows. Numerical values of Daeff and Dneff denote the
difference between maximum and minimum values of the effective absorption coefficient and the effective refractive index, respectively.
130 P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133

10. 5. Conclusions
This study has highlighted the effect of porosity and API mass
fraction on the effective refractive index and effective absorption
coefficient of pharmaceutical tablets using both time-domain and
frequency-domain analytical techniques of transmitted THz waves.
A THz-TD spectrometer in its transmission mode was used for the
measurement. In order to learn how the change in porosity and API
mass fraction affects the optical constants, four training sets (sets
1–4) of real pharmaceutical tablets composed of MCC and indo-
methacin with different compaction parameters were compacted.
It was observed that both the time-domain and frequency-
domain effective refractive index and effective absorption coeffi-
cient have linear correlation with the porosity and API mass frac-
tion even for three-phase pharmaceutical tablets. Though both
porosity and API mass fraction have linear dependence on the opti-
cal constants, it was revealed that, in terms of the effective refrac-
tive index, porosity has dominant effect over the API mass fraction.
Fig. 8. The correlation between the effective absorption coefficient at 0.8 THz and both the porosity (f) and API mass fraction (x) for (a) set 1, (b) set 4, (c) set 3 and (d) set 4.
Fig. 9. (a) Optical strain calculated from measured THz pulse delay as a function of optical path length and (b) absolute value of conventional true strain and optical strain as a
function of change of the optical path length of set 4 tablets.
P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133 131

11. Thus, doubling the change in porosity almost doubled the change
in the effective refractive index. In terms of the effective absorption
coefficient, it was observed that the change in porosity and API
mass fraction has almost similar effect, with the change of API
mass fraction dominating a bit over the change in porosity. How-
ever, a relatively strong combined effect of the change of both
porosity and API mass fraction was observed on the change in
the absorption coefficient of pharmaceutical tablets.
We introduced and demonstrated a 3D plane concept that could
serve as a practical visual tool to monitor the production history of
batches of pharmaceutical tablets in the industrial setting. Addi-
tionally, this 3D plane concept that is based on THz measurement
of training sets of pharmaceutical tablets, in principle, can serve as
a tool for computer-aided design of tablet products, and also for
quality inspection of pharmaceutical tablets.
Furthermore, we have introduced and demonstrated the use of
a novel method that gives information on true strain and change of
fill fraction ratio of solid medium of pharmaceutical tablets by THz
pulse time delay measurement technique.
The promising outcome of this work could serve as a PAT tool
for the fast estimation and monitoring of the porosity and API mass
fraction of pharmaceutical tablets during and after production.
This is the first time we have worked on training samples that
contain API and we look further to the extraction of the weight,
density and height by THz measurement technique. The scope of
this current study is limited to only flat-faced tablets; however,
we envisage the effect of changing the porosity and API mass frac-
tion on the optical constants (that is absorption coefficient and
refractive index) for curved surface tablets as well. The final goal
is to provide both theory and experimental methods to manage
not only with curved tablets but also with pharmaceutical tablets
that strongly absorb THz radiation. In such a case, the reflected
THz signal detected from the tablet’s surface will be a plausible
option to be used for the detection of the properties of pharmaceu-
tical tablets.
References
[1] S. Virtanen, O. Antikainen, J. Yliruusi, Determination of the crushing strength of
intact tablets using Raman spectroscopy, Int. J. Pharm. 360 (2008) 40–46,
http://dx.doi.org/10.1016/j.ijpharm.2008.04.022.
[2] P. Narayan, B.C. Hancock, The relationship between the particle properties,
mechanical behavior, and surface roughness of some pharmaceutical excipient
compacts, Mater. Sci. Eng. A 355 (2003) 24–36, http://dx.doi.org/10.1016/
S0921-5093(03)00059-5.
[3] M. Juuti, B. van Veen, K.-E. Peiponen, J. Ketolainen, V. Kalima, R. Silvennoinen,
et al., Local and average gloss from flat-faced sodium chloride tablets, AAPS
Pharmscitech 7 (2006) E7, http://dx.doi.org/10.1208/pt070107.
[4] M. Juuti, H. Tuononen, T. Prykäri, V. Kontturi, M. Kuosmanen, E. Alarousu, et al.,
Optical and terahertz measurement techniques for flat-faced pharmaceutical
tablets: a case study of gloss, surface roughness and bulk properties of starch
acetate tablets, Meas. Sci. Technol. 20 (2009) 015301, http://dx.doi.org/
10.1088/0957-0233/20/1/015301.
[5] Y.C. Shen, Terahertz pulsed spectroscopy and imaging for pharmaceutical
applications: a review, Int. J. Pharm. 417 (2011) 48–60, http://dx.doi.org/
10.1016/j.ijpharm.2011.01.012.
[6] M. Mozˇina, D. Tomazˇevicˇ, F. Pernuš, B. Likar, Automated visual inspection of
imprint quality of pharmaceutical tablets, Mach. Vis. Appl. 24 (2013) 63–73,
http://dx.doi.org/10.1007/s00138-011-0366-4.
[7] J.A. Zeitler, Y. Shen, C. Baker, P.F. Taday, M. Pepper, T. Rades, Analysis of coating
structures and interfaces in solid oral dosage forms by three dimensional
terahertz pulsed imaging, J. Pharm. Sci. 96 (2007) 330–340, http://dx.doi.org/
10.1002/jps.20789.
[8] I.-S. Russe, D. Brock, K. Knop, P. Kleinebudde, J.A. Zeitler, Validation of terahertz
coating thickness measurements using X-ray microtomography, Mol. Pharm. 9
(2012) 3551–3559. http://www.ncbi.nlm.nih.gov/pubmed/23116336.
[9] M. Kawase, K. Yamamoto, K. Takagi, R. Yasuda, M. Ogawa, Y. Hatsuda, et al.,
Non-destructive evaluation method of pharmaceutical tablet by terahertz-
time-domain spectroscopy: application to sound-alike medicines, J. Infrared,
Millimeter, Terahertz Waves 34 (2013) 566–571, http://dx.doi.org/10.1007/
s10762-013-9994-2.
[10] P.F. Taday, I.V. Bradley, D.D. Arnone, M. Pepper, Using terahertz pulse
spectroscopy to study the crystalline structure of a drug: a case study of the
polymorphs of ranitidine hydrochloride, J. Pharm. Sci. 92 (2003) 831–838,
http://dx.doi.org/10.1002/jps.10358.
[11] R. Nishikiori, M. Yamaguchi, K. Takano, T. Enatsu, M. Tani, U.C. de Silva, et al.,
Application of partial least square on quantitative analysis of L-, D-, and DL-
tartaric acid by terahertz absorption spectra, Chem. Pharm. Bull. (Tokyo) 56
(2008) 305–307, http://dx.doi.org/10.1248/cpb.56.305.
[12] J.M. Chamberlain, Where optics meets electronics: recent progress in
decreasing the terahertz gap, Philos. Trans. A Math. Phys. Eng. Sci. 362
(2004) 199–213, http://dx.doi.org/10.1098/rsta.2003.1312 (discussion 212–3).
[13] J. Han, H. Xu, Z. Zhu, X. Yu, W. Li, Terahertz spectroscopy of naphthalene, a-
naphthol, b-naphthol, biphenyl and anthracene, Chem. Phys. Lett. 392 (2004)
348–351, http://dx.doi.org/10.1016/j.cplett.2004.05.094.
[14] N.Y. Tan, J.A. Zeitler, Probing phase transitions in simvastatin with terahertz
time-domain spectroscopy, Mol. Pharm. 12 (2015) 810–815, http://dx.doi.org/
10.1021/mp500649q.
[15] E.P.J. Parrott, B.M. Fischer, L.F. Gladden, J.A. Zeitler, P.U. Jepsen, Terahertz
spectroscopy of crystalline and non-crystalline solids, in: K.-E. Peiponen, J.A.
Zeitler, M. Kuwata-Gonokami (Eds.), Terahertz Spectroscopy and Imaging,
Springer, Berlin, 2013, pp. 191–227, http://dx.doi.org/10.1007/978-3-642-
29564-5.
[16] J. Sibik, J.A. Zeitler, Direct measurement of molecular mobility and
crystallisation of amorphous pharmaceuticals using terahertz spectroscopy,
Adv. Drug Deliv. Rev. (2016), http://dx.doi.org/10.1016/j.addr.2015.12.021.
[17] E.P.J. Parrott, J.A. Zeitler, L.F. Gladden, Accurate determination of optical
coefficients from chemical samples using terahertz time-domain spectroscopy
and effective medium theory, Opt. Lett. 34 (2009) 3722–3724, http://dx.doi.
org/10.1364/OL.34.003722.
[18] P. Bawuah, A. Pierotic Mendia, P. Silfsten, P. Pääkkönen, T. Ervasti, J. Ketolainen,
et al., Detection of porosity of pharmaceutical compacts by terahertz radiation
transmission and light reflection measurement techniques, Int. J. Pharm. 465
(2014) 70–76, http://dx.doi.org/10.1016/j.ijpharm.2014.02.011.
[19] H. Tuononen, K. Fukunaga, M. Kuosmanen, J. Ketolainen, K.-E. Peiponen,
Wiener bounds for complex permittivity in terahertz spectroscopy: case study
of two-phase pharmaceutical tablets, Appl. Spectrosc. 64 (2010) 127–131.
http://www.ncbi.nlm.nih.gov/pubmed/20132608.
[20] P. Bawuah, K.-E. Peiponen, A terahertz time-domain study on the estimation of
opto-mechanical properties of pharmaceutical tablets using the Hashin-
Shtrikman bounds for refractive index: a case study of microcrystalline
cellulose and starch acetate compacts, Opt. Rev. 23 (2016) 502–509, http://dx.
doi.org/10.1007/s10043-016-0198-6.
[21] P. Bawuah, P. Silfsten, T. Ervasti, J. Ketolainen, J.A. Zeitler, K.-E. Peiponen, Non-
contact weight measurement of flat-faced pharmaceutical tablets using
terahertz transmission pulse delay measurements, Int. J. Pharm. 476 (2014)
16–22, http://dx.doi.org/10.1016/j.ijpharm.2014.09.027.
[22] K.-E. Peiponen, P. Bawuah, M. Chakraborty, M. Juuti, J.A. Zeitler, J. Ketolainen,
Estimation of Young’s modulus of pharmaceutical tablet obtained by terahertz
time-delay measurement, Int. J. Pharm. 489 (2015) 100–105, http://dx.doi.org/
10.1016/j.ijpharm.2015.04.068.
[23] L.X. Yu, Pharmaceutical quality by design: product and process development,
understanding, and control, Pharm. Res. 25 (2008) 781–791, http://dx.doi.org/
10.1007/s11095-007-9511-1.
[24] S. Savenkov, A. Priezzhev, Y. Oberemok, P. Silfsten, T. Ervasti, J. Ketolainen,
et al., Characterization of porous media by means of the depolarization
metrics, J. Quant. Spectrosc. Radiat. Transf. 113 (2012) 2503–2511, http://dx.
doi.org/10.1016/j.jqsrt.2012.05.009.
[25] R.A. Adams, Calculus: A Complete Course, third ed., Addison-Wesley, Don
Mills, Ont., 2003. http://books.google.com/books?id=5juibwAACAAJpgis=
1.
[26] S. Inghelbrecht, J.P. Remon, Roller compaction and tableting of
microcrystalline cellulose/drug mixtures, Int. J. Pharm. 161 (1998) 215–224,
http://dx.doi.org/10.1016/S0378-5173(97)00356-6.
[27] S. Yassin, D.J. Goodwin, A. Anderson, J. Sibik, D.I. Wilson, L.F. Gladden, et al.,
The disintegration process in microcrystalline cellulose based tablets, part 1:
influence of temperature, porosity and superdisintegrants, J. Pharm. Sci. 104
(2015) 3440–3450, http://dx.doi.org/10.1002/jps.24544.
[28] K.S. Khomane, P.K. More, G. Raghavendra, A.K. Bansal, Molecular
understanding of the compaction behavior of indomethacin polymorphs,
Mol. Pharm. 10 (2013) 631–639, http://dx.doi.org/10.1021/mp300390m.
[29] T. Ervasti, P. Silfsten, J. Ketolainen, K.-E. Peiponen, A study on the resolution of
a terahertz spectrometer for the assessment of the porosity of pharmaceutical
tablets, Appl. Spectrosc. 66 (2012) 319–323, http://dx.doi.org/10.1366/11-
06315.
[30] E.P.J. Parrott, J.A. Zeitler, T. Frišcˇic´, M. Pepper, W. Jones, G.M. Day, et al., Testing
the sensitivity of terahertz spectroscopy to changes in molecular and
supramolecular structure: a study of structurally similar cocrystals, Cryst.
Growth Des. 9 (2009) 1452–1460, http://dx.doi.org/10.1021/cg8008893.
[31] R. Li, J.A. Zeitler, D. Tomerini, E.P.J. Parrott, L.F. Gladden, G.M. Day, A study into
the effect of subtle structural details and disorder on the terahertz spectrum of
crystalline benzoic acid, Phys. Chem. Chem. Phys. 12 (2010) 5329, http://dx.
doi.org/10.1039/b926536h.
[32] T.D. Dorney, R.G. Baraniuk, D.M. Mittleman, Material parameter estimation
with terahertz time-domain spectroscopy, J. Opt. Soc. Am. A-Opt. Image Sci.
Vis. 18 (2001) 1562–1571, http://dx.doi.org/10.1364/JOSAA.18.001562.
[33] P.U. Jepsen, D.G. Cooke, M. Koch, Terahertz spectroscopy and imaging –
modern techniques and applications, Laser Photon. Rev. 5 (2011) 124–166,
http://dx.doi.org/10.1002/lpor.201000011.
132 P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133

12. [34] W. Withayachumnankul, M. Naftaly, Fundamentals of measurement in
terahertz time-domain spectroscopy, J. Infrared, Millimeter, Terahertz Waves
35 (2013) 610–637, http://dx.doi.org/10.1007/s10762-013-0042-z.
[35] M. Scheller, Data extraction from terahertz time domain spectroscopy
measurements, J. Infrared, Millimeter, Terahertz Waves 35 (2014) 638–648,
http://dx.doi.org/10.1007/s10762-014-0053-4.
[36] K.-E. Peiponen, E.M. Vartiainen, T. Asakura, Dispersion, Complex Analysis and
Optical Spectroscopy, Springer, Berlin, 1999, http://dx.doi.org/10.1007/
BFb0119581.
[37] C.J. Strachan, T. Rades, D.A. Newnham, K.C. Gordon, M. Pepper, P.F. Taday,
Using terahertz pulsed spectroscopy to study crystallinity of pharmaceutical
materials, Chem. Phys. Lett. 390 (2004) 20–24, http://dx.doi.org/10.1016/j.
cplett.2004.03.117.
[38] M. Otsuka, J.I. Nishizawa, N. Fukura, T. Sasaki, Characterization of poly-
amorphous indomethacin by terahertz spectroscopy, J. Infrared, Millimeter,
Terahertz Waves 33 (2012) 953–962, http://dx.doi.org/10.1007/s10762-012-
9910-1.
[39] P. Silfsten, V. Kontturi, T. Ervasti, J. Ketolainen, K.-E. Peiponen, Kramers-Kronig
analysis on the real refractive index of porous media in the terahertz spectral
range, Opt. Lett. 36 (2011) 778–780, http://dx.doi.org/10.1364/OL.36.000778.
P. Bawuah et al. / European Journal of Pharmaceutics and Biopharmaceutics 105 (2016) 122–133 133