Bioequivalence of two tablet formulations of capecitabine and exploration of age, gender, body surface area, and creatinine clearance as factors influencing systemic exposure in cancer patients

Purpose: The objective of the study was to assess the bioequivalence of two tablet formulations of capecitabine and to explore the effect of age, gender, body surface area and creatinine clearance on the systemic exposure to capecitabine and its metabolites. Methods: The study was designed as an open, randomized two-way crossover trial. A single oral dose of 2000 mg capecitabine was administered on two separate days to 25 patients with solid tumors. On one day, the patients received four 500-mg tablets of formulation B (test formulation) and on the other day, four 500-mg tablets of formulation A (reference formulation). The washout period between the two administrations was between 2 and 8 days. After each administration, serial blood and urine samples were collected for up to 12 and 24 h, respectively. Unchanged capecitabine and its metabolites were determined in plasma using LC/MS-MS and in urine by NMRS. Results: Based on the primary pharmacokinetic parameter, AUC(0-∞) of 5'-DFUR, equivalence was concluded for the two formulations, since the 90% confidence interval of the estimate of formulation B relative to formulation A of 97% to 107% was within the acceptance region 80% to 125%. There was no clinically significant difference between the t(max) for the two formulations (median 2.1 versus 2.0 h). The estimate for C(max) was 111% for formulation B compared to formulation A and the 90% confidence interval of 95% to 136% was within the reference region 70% to 143%. Overall, these results suggest no relevant difference between the two formulations regarding the extent to which 5'-DFUR reached the systemic circulation and the rate at which 5'-DFUR appeared in the systemic circulation. The overall urinary excretions were 86.0% and 86.5% of the dose, respectively, and the proportion recovered as each metabolite was similar for the two formulations. The majority of the dose was excreted as FBAL (61.5% and 60.3%), all other chemical species making a minor contribution. Univariate and multivariate regression analysis to explore the influence of age, gender, body surface area and creatinine clearance on the log-transformed pharmacokinetic parameters AUC(0-∞) and C(max) of capecitabine and its metabolites revealed no clinically significant effects. The only statistically significant results were obtained for AUC(0-∞) and C(max) of intact drug and for C(max) of FBAL, which were higher in females than in males. Conclusion: The bioavailability of 5'-DFUR in the systemic circulation was practically identical after administration of the two tablet formulations. Therefore, the two formulations can be regarded as bioequivalent. The variables investigated (age, gender, body surface area, and creatinine clearance) had no clinically significant effect on the pharmacokinetics of capecitabine or its metabolites.

The Tarim picrite-basalt-rhyolite suite, a Permian flood basalt from Northwest China with contrasting rhyolites produced by fractional crystallization and anatexis

We report major and trace element composition, Sr–Nd isotopic and seismological data for a picrite–basalt–rhyolite suite from the northern Tarim uplift (NTU), northwest China. The samples were recovered from 13 boreholes at depths between 5,166 and 6,333 m. The picritic samples have high MgO (14.5–16.8 wt%, volatiles included) enriched in incompatible element and have high 87Sr/86Sr and low 143Nd/144Nd isotopic ratios (εNd (t) = −5.3; Sri = 0.707), resembling the Karoo high-Ti picrites. All the basaltic samples are enriched in TiO2 (2.1–3.2 wt%, volatiles free), have high FeOt abundances (11.27–15.75 wt%, volatiles free), are enriched in incompatible elements and have high Sr and low Nd isotopic ratios (Sri = 0.7049–0.7065; εNd (t) = −4.1 to −0.4). High Nb/La ratios (0.91–1.34) of basalts attest that they are mantle-derived magma with negligible crustal contamination. The rhyolite samples can be subdivided into two coeval groups with overlapping U–Pb zircon ages between 291 ± 4 and 272 ± 2 Ma. Group 1 rhyolites are enriched in Nb and Ta, have similar Nb/La, Nb/U, and Sr–Nd isotopic compositions to the associated basalts, implying that they are formed by fractional crystallization of the basalts. Group 2 rhyolites are depleted in Nb and Ta, have low Nb/La ratios, and have very high Sr and low Nd isotopic ratios, implying that crustal materials have been extensively, if not exclusively, involved in their source. The picrite–basalt–rhyolite suite from the NTU, together with Permian volcanic rocks from elsewhere Tarim basin, constitute a Large Igneous Province (LIP) that is characterized by large areal extent, rapid eruption, OIB-type chemical composition, and eruption of high temperature picritic magma. The Early Permian magmatism, which covered an area >300,000 km2, is therefore named the Tarim Flood Basalt.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Traffic incident clearance time and arrival time prediction based on hazard models

Accurate prediction of incident duration is not only important information of Traffic Incident Management System, but also an ffective input for travel time prediction. In this paper, the hazard based prediction odels are developed for both incident clearance time and arrival time. The data are obtained from the Queensland Department of Transport and Main Roads’ STREAMS Incident Management System (SIMS) for one year ending in November 2010. The best fitting distributions are drawn for both clearance and arrival time for 3 types of incident: crash, stationary vehicle, and hazard. The results show that Gamma, Log-logistic, and Weibull are the best fit for crash, stationary vehicle, and hazard incident, respectively. The obvious impact factors are given for crash clearance time and arrival time. The quantitative influences for crash and hazard incident are presented for both clearance and arrival. The model accuracy is analyzed at the end.

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Fractional differential equations have been increasingly used as a powerful tool to model the non-locality and spatial heterogeneity inherent in many real-world problems. However, a constant challenge faced by researchers in this area is the high computational expense of obtaining numerical solutions of these fractional models, owing to the non-local nature of fractional derivatives. In this paper, we introduce a finite volume scheme with preconditioned Lanczos method as an attractive and high-efficiency approach for solving two-dimensional space-fractional reaction–diffusion equations. The computational heart of this approach is the efficient computation of a matrix-function-vector product f(A)bf(A)b, where A A is the matrix representation of the Laplacian obtained from the finite volume method and is non-symmetric. A key aspect of our proposed approach is that the popular Lanczos method for symmetric matrices is applied to this non-symmetric problem, after a suitable transformation. Furthermore, the convergence of the Lanczos method is greatly improved by incorporating a preconditioner. Our approach is show-cased by solving the fractional Fisher equation including a validation of the solution and an analysis of the behaviour of the model.

Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.