Non-destructive Determination of Disintegration Time and Dissolution in Immediate Release Tablets by Terahertz Transmission Measurements

Purpose The aim of this study was to establish the suitability of terahertz (THz) transmission measurements to accurately measure and predict the critical quality attributes of disintegration time and the amount of active pharmaceutical ingredient (API) dissolved after 15, 20 and 25 min for commercial tablets processed at production scale. Methods Samples of 18 batches of biconvex tablets from a production-scale design of experiments study into exploring the design space of a commercial tablet manufacturing process were used. The tablet production involved the process steps of high-shear wet granulation, fluid-bed drying and subsequent compaction. The 18 batches were produced using a 4 factor split plot design to study the effects of process changes on the disintegration time. Non-destructive and contactless terahertz transmission measurements of the whole tablets without prior sample preparation were performed to measure the effective refractive index and absorption coefficient of 6 tablets per batch. Results The disintegration time (R$^{2}$ = 0.86) and API dissolved after 15 min (R$^{2}$ = 0.96) linearly correlates with the effective refractive index, neff, measured at terahertz frequencies. In contrast, no such correlation could be established from conventional hardness measurements. The magnitude of neff represents the optical density of the sample and thus it reflects both changes in tablet porosity as well as granule density. For the absorption coefficient, αeff, we observed a better correlation with dissolution after 20 min (R$^{2}$ = 0.96) and a weaker correlation with disintegration (R$^{2}$ = 0.83) compared to neff. Conclusion The measurements of neff and αeff provide promising predictors for the disintegration and dissolution time of tablets. The high penetration power of terahertz radiation makes it possible to sample a significant volume proportion of a tablet without any prior sample preparation. Together with the short measurement time (seconds), the potential to measure content uniformity and the fact that the method requires no chemometric models this technology shows clear promise to be established as a process analyser to non-destructively predict critical quality attributes of tablets.We would like to thank GlaxoSmithKline for providing the sets of samples and sharing their valuable experience and advice. D.M. and J.A.Z. would like to acknowledge the the U.K. Engineering and Physical Sciences Research Council (EPSRC) for funding (EP/L019922/1). J.S. participated in this study as a undergraduate summer student visiting from the Friedrich-Schiller-University Jena and would like to thank the German Academic Exchange Service (DAAD) RISE Worldwide programme for supporting her visit (GB-PH-1870)

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Stein--Sahi complementary series and their degenerations

The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n,n).Comment: 40pp, 7fig, revised versio

Multiplicity-free theorems of the restrictions of unitary highest weight modules with respect to reductive symmetric pairs

The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known results such as the Clebsh--Gordan--Pieri formula for tensor products, the Plancherel theorem for Hermitian symmetric spaces (also for line bundle cases), the Hua--Kostant--Schmid $K$-type formula, and the canonical representations in the sense of Vershik--Gelfand--Graev. Our method works in a uniform manner for both finite and infinite dimensional cases, for both discrete and continuous spectra, and for both classical and exceptional cases

Investigating undesired spatial and temporal boundary effects of congestion charging.

Two types of reported problems are related to the existing congestion charging projects that levy traffic only in a certain area within one or a few time periods during the day. One is that travellers depart earlier or later than a charging period to avoid paying full or part of the congestion charging tolls, which creates two undesired demand peaks that are often greater than available capacity. One peak comes just before the start of congestion charging and the other follows the end of it. We term this phenomenon ‘temporal boundary effect’ of congestion charging. The other reported problem is that travellers would rather stay away from a charging zone than pay congestion charging tolls, which causes undesired congestion on those roads or paths on the edge of the charging zone. We call this phenomenon ‘spatial boundary effect’ generated by congestion charging. This research investigates these boundary effects in the context of simultaneous route and departure time choice dynamic user equilibrium (SRD-DUE) network flows with an aim to gain new insights into congestion charging design. Numerical experiments investigating constant and time-varying congestion charging toll profiles are presented in this paper. This investigation shows that congestion charging may not be able to eliminate hypercongestion efficiently if schemes are not well designed, and can unfortunately give rise to undesired boundary effects and that a simply designed congestion charging scheme with small level toll or time-varying toll profiles can reduce the magnitude of boundary effects but may not be able to fully eliminate such undesired effect