Terahertz-Based Porosity Measurement of Pharmaceutical Tablets: a Tutorial
Porosity, one of the important quality attributes of pharmaceutical tablets, directly affects the mechanical properties, the mass transport and hence tablet disintegration, dissolution and ultimately the bioavailability of an orally administered drug. The ability to accurately and quickly monitor the porosity of tablets during manufacture or during the manufacturing process will enable a greater assurance of product quality. This tutorial systematically outlines the steps involved in the terahertz-based measurement method that can be used to quantify the porosity of a tablet within seconds in a non-destructive and non-invasive manner. The terahertz-based porosity measurement can be performed using one of the three main methods, which are (i) the zero-porosity approximation (ZPA); (ii) the traditional Bruggeman effective medium approximation (TB-EMA); and (iii) the anisotropic Bruggeman effective medium approximation (AB-EMA). By using a set of batches of flat-faced and biconvex tablets as a case study, the three main methods are compared and contrasted. Overall, frequency-domain signal processing coupled with the AB-EMA method was found to be most suitable approach in terms of accuracy and robustness when predicting the porosity of tablets over a range of complexities and geometries. This tutorial aims to concisely outline all the necessary steps, precautions and unique advantages associated with the terahertz-based porosity measurement method.
KeywordsTerahertz spectroscopy Pharmaceutical tablet Porosity Effective medium approximation Refractive index Optical path length
Terahertz technology has attracted considerable interest for a range of application scenarios. Among these applications are the detection of explosives [1, 2, 3] in the security sector and industrial implementations, for example, in automotive , paper  and pharmaceutical [6, 7] production lines. Building on the pharmaceutical sector, early terahertz-based spectroscopic studies were mainly focused on the study of crystal structure of drug molecules due to the ability of the terahertz radiation to probe intermolecular vibrations between hydrogen bonded molecules . As a result, exhaustive terahertz-based studies have been reported on crystalline material identification [9, 10, 11, 12, 13], drug polymorph and hydrate form identification [14, 15, 16, 17, 18, 19, 20], as well as the degree of crystallinity of drug substance [21, 22, 23, 24, 25].
By adopting the reflection configuration and exploiting the time-domain nature of modern terahertz instrumentation, several imaging-based studies (terahertz pulsed imaging, TPI) aimed at non-destructive inspection of tablets have seen considerable interest [7, 26, 27, 28, 29, 30, 31, 32]. The application of TPI for assessing coating uniformity of pharmaceutical tablets [7, 26, 27, 28] has been successfully demonstrated for both lab-based [26, 33] and production-scale in-line applications .
Besides the numerous terahertz imaging applications that are mostly operated in reflection mode, pharmaceutical applications based on the use of the THz-TDS in transmission configuration remained relatively unexploited until around a decade ago when Peiponen and his group showed the interplay between the porous matrix and the optical properties of tablets . The work demonstrated that there is a linear correlation between the bulk refractive index and the porosity of pharmaceutical tablets, which can be exploited through the so-called zero-porosity approximation (ZPA) as a method for measuring tablet porosity. In an attempt to accurately determine the optical properties of a tablet using THz-TDS, Parrot et al.  were among the first to adopt the concept of the effective medium approximation, i.e. the Maxwell-Garnett model, to calculate the optical coefficients of tablets. Just about the same time, Tuononen et al.  highlighted the interplay between the effective complex permittivity and the porosity of simple two-phase tablets using the concept of the Wiener bounds . The Wiener bounds give the extreme limits, i.e. upper and lower bounds/limits, of the effective permittivity of the tablets. The upper bound indicates an ideal parallel arrangement of the solid material and air voids with respect to direction of the THz electric field whereas the lower bound represents an ideal serial arrangement . These two studies triggered a number of completely new ways of assessing the quality of pharmaceutical tablet using THz-TDS.
Around the mid 2010s, Bawuah et al.  successfully demonstrated that THz-TDS in conjunction with the Bruggeman effective medium approximation can be used to non-destructively and non-invasively measure the porosity of pharmaceutical tablets. In that preliminary study, the authors adopted the Bruggeman model due to its validity for tablets with a wide range of porosity. Despite its basic assumption that the inclusions are of spherical shape, the Bruggeman model could be used to accurately measure the porosity of flat-faced compacts containing only microcrystalline cellulose (MCC) and air . Following the success of this study, follow-up studies were conducted using tablets with a range of degree of complexity in terms of their formulations (tablets composed of more than one excipients and an active pharmaceutical ingredient, API)  and shapes [42, 43]. Based on the fast, non-invasive and non-destructive nature of the terahertz porosity measurement approach, the authors proposed possible at-line and in-line applications during tablet manufacturing. Compared with conventional but destructive porosity measurement methods like mercury porosimetry, the terahertz method has the additional merit of being able to probe isolated pores in the core of the matrix. Such pores are quite challenging to detect by conventional porosimetry methods that typically rely on accessing the pores from the outside of the porous medium for the measurement.
In subsequent studies, Markl el al.  showed that the assumption of the spherical inclusion in the Bruggeman effective medium approximation (from now onwards known as the traditional Bruggeman effective medium approximation, TB-EMA) can limit the accurate prediction of the effective refractive index when tablets containing API and those composed of a highly porous excipient, such as functionalised calcium carbonate, are tested. This led to the adoption of the anisotropic Bruggeman effective medium approximation (AB-EMA), which takes into consideration the presence of non-spherical inclusions within a tablet. The ability to predict the pore shape based on the AB-EMA model led to a stream of follow-up studies that sought to critically analyse the pore structure of pharmaceutical tablets using THz-TDS [39, 44, 45, 46]. A detailed description of pore structure analyses of tablets will be reported in a future tutorial paper.
Finally, we want to highlight that the insights on tablets using THz-TDS outlined above are fundamentally based on two unique properties of the terahertz radiation: (1) the relatively long wavelength of terahertz radiation in comparison to the typical particle sizes of materials that are used to make tablets results in low scattering losses, and (2) the ability of the terahertz radiation to permeate a wide range of polymers and ceramic materials that commonly serve as excipients in pharmaceutical tablets.
The current tutorial seeks to systematically take the reader through the steps required for the THz-TDS approach to non-invasively measure the total porosity of pharmaceutical tablets. Several batches of flat-faced and biconvex ibuprofen-based tablets are used to illustrate the concepts in a case study. By using tablets with different geometries the various approaches involved in the terahertz porosity method are compared and contrasted. The reasons for when and how to adopt a specific approach are outlined based on material properties, the complexity of the tablet formulations and the geometry of the tablets in concern.
Finally, we want to emphasise that the use of the terahertz porosity method on any batches of tablets compressed from a given formulation will ideally require an initial set of flat-faced tablets of the same formulation that are compressed at different porosity levels. Our recommendation is to have at least five porosity levels that cover the entire range of expected porosity values. The use of flat-faced tablets, aside from being simple and easy to compact, will ensure accurate material parameter estimation of the intrinsic refractive index of the solid matrix.
2 Terahertz Time-Domain Spectroscopy
A typical terahertz time-domain spectrometer has four major components: a femtosecond pulsed NIR laser, the terahertz emitter (photoconductive antenna), a delay mechanism between a pump and probe beam and a time-gated detector. Sub-picosecond coherent pulses of broadband terahertz radiation are generated based on the principle of photoexcitation . The photoconductive antenna (PCA) is basically made of a fast optically activated switch that is embedded in an antenna structure (e.g. DC biased semi-insulating GaAs substrate). The emitted coherent terahertz pulse is guided via an assembly of off-axis parabolic or ellipsoid mirrors and focused on the sample after which the transmitted waveform is detected either by a similar PCA detector  or by an electro-optic (EO) sampling technique [48, 49]. With THz-TDS the electric field, which encompasses both the amplitude and phase of the radiation, is measured and hence gives direct access to the complex refractive index of materials. The ability to directly access the complex refractive index makes THz-TDS advantageous compared with other far-infrared spectroscopic techniques like conventional Fourier-transform spectroscopy.
2.1 Measurements and Data Acquisition Routines
In this tutorial, the transmitted terahertz pulse through a pharmaceutical tablet was detected using a Terapulse 4000 (TeraView Ltd., Cambridge, UK) with generation and detection routines similar to that described previously [22, 23]. It is worth mentioning that, with the Terapulse 4000, the emitted terahertz beam is not tightly focused on the sample. The THz beam therefore does not rapidly diverge at the vicinity of the focal plane and can be assumed to be a propagating plane wave. In other words, the Rayleigh range of the focused beam is significantly long compared with samples’ thicknesses. This should ensure a near constant beam geometry through the tablets and hence accuracy of the measured optical constants. On the contrary, a tightly focused beam will rapidly diverge (short Rayleigh range compared with the sample thickness) and the plane wave assumption will add significant errors to the extracted optical constants. The effect of beam focusing, Gouy phase shift and sample thickness on the extracted optical constants, has been reported [50, 51] and is discussed in Section 6.
Due to the significant absorption of the terahertz radiation by water vapour , the sample compartment of the THz-TDS was continuously purged with nitrogen gas throughout the measuring process. The Terapulse 4000 comes with two waveform scanning methods: the slow, but high-resolution, scanning method (HiResScannerSeries) and the fast scan with low resolution (SpectralSeries). For example, with the slow scan option, it takes about a minute to acquire and average 20 time-domain waveforms whereas for the fast scan method, it takes just about a second to acquire similar waveform averages. In this tutorial, the fast scan option was used due to our current target of developing an in-line/at-line terahertz porosity method for pharmaceutical tablets. As a typical routine, a reference measurement, i.e. conducting the measurement with an empty (nitrogen gas) compartment, was acquired before each sample measurement. Figure 1 illustrates the measurement principle of measuring the time delay between a reference pulse (time of flight given as tr) and sample pulse (time of flight given as ts).
3 Data Processing and Analysis
The time- and frequency-domain data processing routines are typically performed for comparison purposes and also based on the terahertz absorption behaviour of the concerned material. For example, the frequency-domain approach is the best option when dealing with materials that exhibit distinct absorption features within the frequency range of 0.1–3.0 THz as it allows for the selection of the effective refractive index values at a portion of the spectra with little or no additional dispersion effects. However, the extraction of the frequency-domain effective refractive index demands extra mathematical steps such as the use of the fast Fourier transform, phase extraction and correction, the Beer Lamberts law and the Fresnel coefficients. On the other hand, the time-domain method is a straightforward approach to quickly calculate the effective refractive index based on the optical path length difference between the measured reference and sample signals. It is worth mentioning that the time-domain method is limited in terms of yielding an accurate prediction of the effective refractive index in cases where the terahertz pulse suffers significant broadening as a result of dispersion or absorption.
3.1 Time-Domain Signal Processing
As already mentioned, the time-domain (TD) method is a fast and a straightforward way of measuring the effective refractive index of a tablet from the terahertz pulse delay without the need of expertise in signal processing. The pulse delay is calculated from the measured time-of-flight (TOF) difference between the sample (ts) and reference (tr) pulses (see Fig. 1a).
3.2 Frequency-Domain Signal Processing
The FD analysis, despite being relatively cumbersome compared with the TD method, has an added merit of revealing specific phonon vibrations (spectral features) of crystalline constituents of tablets. Due to the crystalline nature of most active pharmaceutical ingredients (APIs), THz-TDS has been used for the identification of specific drugs in pharmaceutical tablets [58, 59]. The presence of the spectral features can cause significant dispersion or variations in the effective refractive at the respective resonant frequencies. Dispersion will cause each wavelength component of the terahertz pulse to travel at a different group velocity and in turn broadens the transmitted terahertz pulse. A broadened pulse, as already mentioned, will limit the use of the TD method to accurately measure the effective refractive index and hence the terahertz porosity of the tablets. In such cases the application of the FD method becomes very useful since it allows for the selection of the effective refractive index at a spectral region where no significant dispersion effect is observed. By measuring the effective refractive index over the same frequency range for all tablets within a given batch, accuracy and consistency are assured in the extracted tablets porosity.
Finally, potential scattering from individual particles, granules or clusters within the powder matrix will further affect the choice of the most suitable frequency (range) for subsequent porosity analysis. For example, in this work the particle size distribution for the powders used range from a few tens of micrometres to a few hundreds of micrometres in diameter: for example the dominant material has an average particle size in the range of about 160–340 μm. Hence, significant scattering is expected at frequencies above 0.9 THz, which can be clearly seen in the refractive index spectra presented in Fig. 3. Nevertheless, the relatively narrow frequency range due to scattering and absorption should not limit the applicability of the method since the refractive index can be selected at any frequency(ies) based on the above selection criteria.
4 Tablet Compaction
Material composition of the formulation used in the direct compaction of all the batches of tablets used as a case study in this tutorial
Microcrystalline cellulose, Avicel PH-102
Lactose anhydrous, Supertab21AN
After the blending, five batches of both the flat-faced and biconvex tablets with different porosities and thicknesses, within the respective range of 6–25% and 3.7–5.5 mm, were directly compressed using a compaction simulator (HB50, Huxley Bertram Engineering Ltd., UK). For a given batch, 15 tablets were compacted with each tablet stored in a labelled and sealed plastic bag. By using the compaction simulator, we were able to mimic the manufacturing characteristics of tablets produced in a typical industrial setting at full production scale and speed. In this study, the production-scale tablet press, Fette 2090 compression profile, with a compression speed of 60 rpm, i.e. ≈ 0.35 s to compress and eject a tablet, was used for compacting all the batches. The targeted porosity for each batch was achieved by keeping the weight of all tablets at about 400 mg and adjusting their thickness.
5 Porosity Measurement
Porosity, a potential critical quality attribute (CQA) of tablets, is one of the most important contributors to tablet disintegration and dissolution characteristics . Porosity governs the mass transport processes and mechanical changes in tablets during disintegration and hence directly affects the dissolution time of tablets. Since porosity is a volumetric property, the use of the THz-TDS method, which is conducted in the transmission configuration, has been demonstrated to accurately measure porosity of homogenous tablets compared to conventional methods like mercury porosimetry . This is due to the fact that the terahertz method is able to probe both connected and isolated pores whereas conventional methods like mercury porosimetry only capture connected pores. Adding to the above merits, THz-TDS is a reliable method for measuring the bulk properties of tablets compared with other spectroscopic counterparts, e.g. Raman and near infrared (NIR) spectrometers, that typically probe only surface properties that do not necessarily represent the bulk tablet property. Finally, we want to reiterate that the terahertz method is robust, non-destructive, contactless and sufficiently fast (within a second) to meet the speed requirements for both at-line and in-line applications.
This tutorial explains the chronological steps involved in the use of the THz-TDS method for the accurate measurement of tablet porosity. We shall commence by discussing the steps involved in measuring a tablet porosity from its weight and dimensions, which is dubbed as its nominal porosity, and proceed with how the nominal porosity in conjunction with the measured effective refractive index is used for the extraction of the terahertz porosity based on the Bruggeman EMA. It should be made clear at this point that the use of the terahertz porosity method will always demand the preparation and measurement of a materials characterisation set composed of tablets that were compacted over a range of porosities. Results obtained from this set will then be used as a yardstick for tracking the porosity of all batches compressed with the same formulation.
5.1 Nominal Porosity
The measured averaged parameters of the five batches of flat-faced tablets. Each batch composed of 15 tablets. The tablet density, ρtablet, was calculated from the weight and dimensions using Eq. 5. The measured true density was, ρtrue = 1.439 g cm−3, and the nominal porosity was estimated using Eq. 7
393.3 ± 3
7.57 ± 0.45
401.2 ± 3
11.52 ± 0.63
393.6 ± 2
17.51 ± 0.47
395.3 ± 4
21.02 ± 0.79
402.6 ± 3
23.48 ± 0.63
The measured averaged parameters of the five batches of biconvex tablets. Each batch contained 15 tablets. From Eq. 6 the tablets’ volume was calculated with the parameters h = 1.01 mm and L = H − 2h. The tablet density, ρtablet, was then determined from the weight and volume using Eq. 5. With the measured true density, ρtrue = 1.439 g cm−3, the nominal porosity was estimated using Eq. 7
396.5 ± 3
7.22 ± 0.21
397.2 ± 2
11.83 ± 0.22
396.9 ± 2
15.85 ± 0.33
396.7 ± 2
20.20 ± 0.48
409.0 ± 3
22.41 ± 0.57
5.2 Terahertz Porosity Measurement
Three approaches based on refractive index-porosity relationships have mostly been exploited for the extraction of the porosity of tablets from terahertz measurements. For all the approaches, a pharmaceutical tablet is assumed to be a two-phase effective medium that composes of air and a solid medium. In the simplest case the solid medium could be a particular compound for tablets made of one powder only or, more commonly, it would constitute a mixture of different solid compounds of excipient(s) and API(s) for typical commercial tablets.
A typical limitation of the TB-EMA approach arises when the actual shape of the inclusions significantly deviates from a sphere. This phenomenon leads to the introduction of a symmetric error, which is observed when the extracted terahertz porosity is plotted against the nominal porosity.
The AB-EMA allows the calculation and use of the g factor and therefore corrects the existing symmetric error (a major limitation of the TB-EMA), which enhances the accuracy of the measured terahertz porosity. Moreover, the knowledge of the g factor permits the prediction of the pore shape, which is an added merit of the AB-EMA compared with both the ZPA and TB-EMA methods.
6 Case Study and Discussions
This tutorial has utilised prepared batches of flat-faced and biconvex tablets as a case study to systematically demonstrate the application of the terahertz porosity measurement technique.
6.1 Terahertz Effective Refractive Index by TD and FD Methods
Comparing and contrasting the performance of the TD and the FD signal processing techniques for the accurate measurement of the effective refractive index of a tablet
Involves straightforward signal processing technique and does not demand expertise in data processing.
Prone to errors due to dispersion and absorption that cause broadening of the terahertz pulse.
Insensitive to errors due to dispersion and hence applicable for samples with profound absorption peak(s) in the terahertz region.
Involves technical signal processing and data analyses method that requires expertise.
6.2 Terahertz Porosity Measurement
Comparing the performance of the three terahertz porosity measurement methods for both the flat-faced and biconvex tablets (Fig. 6)
From the above observation, the choice of a particular method depends on the type of materials and their relative composition as well as the geometry of the tablet. By bearing in mind the close performance of the three methods in case of the flat-faced tablets, one can conveniently adopt any of the three methods without worrying so much about errors in the extracted parameters. From a research point of view, flat-faced tablets are more convenient to study due to the ability to precisely measure their dimensions (thickness and diameter) and the nominal porosity that serve as the basic input parameters in the terahertz porosity method. Additionally, it is quite intuitive to assume that flat-faced compression tooling will naturally allow for a more even distribution of pressure across the surface of the tablet during compaction; hence, the anisotropic phenomena that can take place during compaction of tablets may be less pronounced since the pores are more likely to assume spherical shape.
In contrast, for biconvex tablets, the situation can become more complicated due to possible uneven pressure distribution as well as the difficulty to precisely measure the compaction parameters during compaction. Furthermore, it is more difficult to ensure that the terahertz beam propagates exactly through the centre of the tablet during the transmission measurements as well as maintaining consistency to accurately measure the thickness of the tablets at exactly the same spot. These are additional challenges that need to be considered when dealing with biconvex tablets. Studies have shown that the presence of uneven pressure distribution during compaction yields biconvex tablets with high density distribution along the centre , which may partly explain the higher neff values obtained for the biconvex tablets compared with the flat-faced tablets (Fig. 5).
Differences observed in the refractive index values can also be attributed to thickness variations (≈ 1 mm) between the flat-faced and the biconvex tablets. The relatively thick biconvex tablets, during the transmission measurement, may cause a significant shift in the focal plane of the terahertz beam compared with its reference measurement. The shift in the focal plane of the transmitted terahertz beam means that the reference and sample signal will be detected at a different axial position with different Gouy phases at the detector level. The induced relatively larger Gouy phase shift for the biconvex tablets will introduce a significant uncertainty in the extracted refractive index [50, 51]. Nonetheless, by considering the relatively long Rayleigh range of the focused terahertz beam used in this study, a shift in the Gouy phase due to a thickness difference should have negligible effect on the extracted refractive index of the tablets. The estimated Rayleigh range at 1 THz of the beam with a waist radius of 1 mm is about 10.5 mm, which is greater than the maximum thickness of the analysed tablets, i.e. 5.53 mm.
Moreover, curvature and possible lensing effect of the biconvex tablets can cause further refraction of the THz beam and hence influence the level of uncertainty in the extracted refractive index.
An extensive study aimed to critically ascertain the effect of density distribution, Gouy phase shift, geometry and lensing effects of pharmaceutical tablets on the measured optical constants and hence the porosity using the proposed THz method is currently ongoing. We recently conducted experiments by mapping over biconvex tablets in transmission using a moving sample stage. The preliminary results (unpublished) have shown the possibility of resolving density differences/spatially dependent porosity values within the tablets using the terahertz method.
It is important to emphasise that the thickness and the nominal porosity measurements are absolutely critical for the accuracy of the terahertz porosity method. Thickness and nominal porosity serve as the basic inputs variables for all analyses involved in the terahertz porosity method. For example, an error introduced in the measured thickness and porosity will propagate, and significantly affect, the measured effective refractive index, the solid refractive index and hence the predicted terahertz porosity as well as the pore structure. It is therefore strongly recommended that care and consistency must be maintained especially during the thickness measurement as it affects every aspect involved in the data analysis process.
This tutorial has outlined the steps required in the use of THz-TDS to quickly and non-destructively measure the porosity of the pharmaceutical tablets. As a case study, two sets of tablets, i.e. flat-faced and biconvex tablets, were prepared and measured. Five batches of each set composed of 10% ibuprofen were compacted with varying porosity within the range of 7–23%. A comparison made from the use of the TD and FD signal processing techniques has clearly shown that the FD approach comes with additional merits that typically outperforms the TD approach. For example, the FD approach is insensitive to dispersion-based errors and allows consistency in the extraction of the effective refractive index for all the samples.
The results of a similar comparison of the three terahertz porosity measurement methods (ZPA, TB-EMA and AB-EMA) have resulted in the recommendation to use the AB-EMA method due to its ability to account for non-spherical inclusions and is therefore more robust for tablets of a wide range of size and geometry. The performance of the AB-EMA method was found to be independent of the pore shape, material, complexity and geometry of the tablets. The ZPA and the TB-EMA methods were found to be strongly influenced by the pore shape, formulation material, tablet complexity and geometry and hence should only be chosen and used in well-defined situations.
The authors would like to acknowledge funding from Innovate UK, project reference 104196. All raw data shown in this manuscript can be downloaded from https://doi.org/10.17863/CAM.47564
- 1.J. Beckmann, B. Marchetti, L.S. von Chrzanowski, E. Ritter, L. Puskar, E.F. Aziz, U. Schade, Optical Constants of Harmful and Highly Energetic Liquids for Application to THz Screening Systems, IEEE Trans. Terahertz Sci. Technol. 6 (2016) 396–407. doi: https://doi.org/10.1109/TTHZ.2016.2547319.CrossRefGoogle Scholar
- 3.N. Krumbholz, C. Jansen, M. Scheller, T. Müller-Wirts, S. Lübbecke, R. Holzwarth, R. Scheunemann, R. Wilk, B. Sartorius, H. Roehle, D. Stanze, J. Beckmann, L.S. von Chrzanowski, U. Ewert, M. Koch, Handheld terahertz spectrometer for detection of liquid explosives, Proc. SPIE. 7485 (2009) 748504–748504–12. doi: https://doi.org/10.1117/12.830381.
- 4.Y. Dong, J. Zhang, Y. Shen, K. Su, J.A. Zeitler, Noninvasive Characterization of Automobile Car Paints using Terahertz Pulsed Imaging and Infrared Optical Coherence Tomography, in: 40th Int. Conf. Infrared, Millimeter, Terahertz Waves, 2014: p. 2015.Google Scholar
- 5.J.S. Dodge, P. Mousavi, I. Bushfiel, S. Savard, D. Jez, F. Haran, Paper Parameter Estimation Using Time-Domain Terahertz Spectroscopy, in: IEEE 2014 Int. Symp. Optomechatronic Technol. Pap., IEEE, 2014: pp. 119–120. doi: https://doi.org/10.1109/ISOT.2014.36.
- 19.J.A. Zeitler, D. a Newnham, P.F. Taday, T.L. Threlfall, R.W. Lancaster, R.W. Berg, C.J. Strachan, M. Pepper, K.C. Gordon, T. Rades, Characterization of temperature-induced phase transitions in five polymorphic forms of sulfathiazole by terahertz pulsed spectroscopy and differential scanning calorimetry., J. Pharm. Sci. 95 (2006) 2486–98. doi: https://doi.org/10.1002/jps.20719.CrossRefGoogle Scholar
- 21.E.P.J. Parrott, K.L. Nguyen, T. Friscic, J.A. Zeitler, M. Pepper, W. Jones, L.F. Gladden, Using terahertz time-domain spectroscopy to identify pharmaceutical cocrystals, in: Jt. 32nd Int. Conf. Infrared Millim. Waves/15th Int. Conf. Terahertz Electron., 2007: pp. 660–661. https://doi.org/10.1109/ICIMW.2007.4516670.
- 22.E.P.J. Parrott, J.A. Zeitler, T. Friščić, M. Pepper, W. Jones, G.M. Day, L.F. Gladden, 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. https://doi.org/10.1021/cg8008893.CrossRefGoogle Scholar
- 26.K.C. Gordon, P. Kleinebudde, M. Pepper, L. Ho, R. Mu, R. Müller, K.C. Gordon, P. Kleinebudde, M. Pepper, T. Rades, Y. Shen, P.F. Taday, J.A. Zeitler, Monitoring the film coating unit operation and predicting drug dissolution using terahertz pulsed imaging., J. Pharm. Sci. 98 (2009) 4866–76. https://doi.org/10.1002/jps.21766.CrossRefGoogle Scholar
- 33.L. Ho, R. Müller, K.C. Gordon, P. Kleinebudde, M. Pepper, T. Rades, Y. Shen, P.F. Taday, J.A. Zeitler, Applications of terahertz pulsed imaging to sustained-release tablet film coating quality assessment and dissolution performance., J. Control. Release. 127 (2008) 79–87. doi: https://doi.org/10.1016/j.jconrel.2008.01.002.CrossRefGoogle Scholar
- 35.M. Juuti, H. Tuononen, T. Prykäri, V. Kontturi, M. Kuosmanen, E. Alarousu, J. Ketolainen, R. Myllylä, K.-E. Peiponen, 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. doi: https://doi.org/10.1088/0957-0233/20/1/015301.CrossRefGoogle Scholar
- 38.O.H. Wiener, Die Theorie des Mischkörpers für das Feld der stationären Strömung. 1 Die Mittelwertsätze für Kraft, Polarisation und Energie, B.G. Teubner, Leipzig, 1912.Google Scholar
- 39.D. Markl, P. Bawuah, C. Ridgway, S. van den Ban, D.J. Goodwin, J. Ketolainen, P. Gane, K.-E. Peiponen, J.A. Zeitler, Fast and Non-destructive Pore Structure Analysis using Terahertz Time-Domain Spectroscopy, Int. J. Pharm. 537 (2017) 102–110. doi: https://doi.org/10.1016/j.ijpharm.2017.12.029.CrossRefGoogle Scholar
- 40.P. Bawuah, A. Pierotic Mendia, P. Silfsten, P. Pääkkönen, T. Ervasti, J. Ketolainen, J.A. Zeitler, K.-E. Peiponen, Detection of porosity of pharmaceutical compacts by terahertz radiation transmission and light reflection measurement techniques, Int. J. Pharm. 465 (2014) 70–76. doi: https://doi.org/10.1016/j.ijpharm.2014.02.011.CrossRefGoogle Scholar
- 41.P. Bawuah, N. Tan, S.N.A. Tweneboah, T. Ervasti, J. Axel Zeitler, J. Ketolainen, K.-E. Peiponen, Terahertz study on porosity and mass fraction of active pharmaceutical ingredient of pharmaceutical tablets, Eur. J. Pharm. Biopharm. 105 (2016) 122–133. doi: https://doi.org/10.1016/j.ejpb.2016.06.007.CrossRefGoogle Scholar
- 42.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. doi: https://doi.org/10.1016/j.ijpharm.2014.09.027.CrossRefGoogle Scholar
- 44.D. Markl, P. Wang, C. Ridgway, A.-P. Karttunen, M. Chakraborty, P. Bawuah, P. Pääkkönen, P. Gane, J. Ketolainen, K.-E. Peiponen, J.A. Zeitler, Characterization of the Pore Structure of Functionalized Calcium Carbonate Tablets by Terahertz Time-Domain Spectroscopy and X-Ray Computed Microtomography, J. Pharm. Sci. 106 (2017) 1586–1595. doi: https://doi.org/10.1016/j.xphs.2017.02.028.CrossRefGoogle Scholar
- 45.C. Ridgway, P. Bawuah, D. Markl, J.A.A. Zeitler, J. Ketolainen, K.-E.K.-E. Peiponen, P. Gane, On the role of API in determining porosity, pore structure and bulk modulus of the skeletal material in pharmaceutical tablets formed with MCC excipient, Int. J. Pharm. 526 (2017) 321–331. doi: https://doi.org/10.1016/j.ijpharm.2017.04.038.CrossRefGoogle Scholar
- 46.D. Markl, A. Strobel, R. Schlossnikl, J. Bøtker, P. Bawuah, C. Ridgway, J. Rantanen, T. Rades, P. Gane, K.-E. Peiponen, J.A. Zeitler, Characterisation of Pore Structures of Pharmaceutical Tablets: A Review, Int. J. Pharm. 538 (2018) 188–214. doi: https://doi.org/10.1016/j.ijpharm.2018.01.017.CrossRefGoogle Scholar
- 58.M. Kawase, K. Yamamoto, K. Takagi, R. Yasuda, M. Ogawa, Y. Hatsuda, S. Kawanishi, Y. Hirotani, M. Myotoku, Y. Urashima, K. Nagai, K. Ikeda, H. Konishi, J. Yamakawa, M. Tani, 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. doi: https://doi.org/10.1007/s10762-013-9994-2.CrossRefGoogle Scholar
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.