Comparative Analysis of Linear and Nonlinear Methods of Estimating the Pseudo-Second-Order Kinetic Parameters for Sorption of Malachite Green onto Pretreated Rice Husk

Batch sorption experiments were carried out for removal of malachite green from aqueous solution using pretreated rice husk. The equilibrium kinetic data were analyzed using pseudo-second-order kinetic model. A comparison between linear and nonlinear methods of estimating the kinetic parameters was carried out. Four pseudo-second-order kinetic linear equations were discussed. The coefficient of determination (r ²) and chi-square (χ²) test were employed as error analysis methods to determine the best-fitting equation. The results show that nonlinear method is a better alternative to obtain the kinetic parameters. In addition, the chi-square test was a better method to determine the best-fitting model.     

Linear and Nonlinear Regression Analyses for Binary Sorption Kinetics of Methylene Blue and Safranin onto Pretreated Rice Husk

This article extends the study of the comparison between linear and nonlinear forms of the two widely used kinetic models, namely, pseudo-first-order and pseudo-second-order, by considering the binary biosorption of the basic dyes methylene blue and safranin onto pretreated rice husk in a batch system. The present investigation showed that nonlinear forms of pseudo-first-order and pseudo-second-order models were more suitable than the linear forms for fitting the experimental data. The sorption process was found to follow the pseudo-second-order kinetics. The results suggest that it is not appropriate to use the linear method in determining the kinetic parameters of a particular kinetic model. The nonlinear method is a better way to obtain the kinetic parameters than the linear method and thus it should be primarily adopted to determine the kinetic parameters.     

Optimum Sorption Isotherm by Linear and Nonlinear Methods for Safranin onto Alkali-Treated Rice Husk

Rice husk, a lignocellulosic by-product of the agroindustry, was treated with alkali and used as a low-cost adsorbent for the removal of safranin from aqueous solution in batch adsorption procedure. In order to estimate the equilibrium parameters, the equilibrium adsorption data were analyzed using the following two-parameter isotherms: Freundlich, Langmuir, and Temkin. A comparison of linear and nonlinear regression methods in selecting the optimum adsorption isotherm was applied on the experimental data. Six linearized isotherm models (including four linearized Langmuir models) and three nonlinear isotherm models are thus discussed in this paper. In order to determine the best-fit isotherm predicted by each method, seven error functions namely, coefficient of determination (r ²), the sum of the squares of the errors (SSE), sum of the absolute errors (SAE), average relative error (ARE), hybrid fractional error-function (HYBRID), Marquardt's percent standard deviation (MPSD), and the chi-square test (χ²) were used. It was concluded that the nonlinear method is a better way to obtain the isotherm parameters and the data were in good agreement with the Langmuir isotherm model.     

Comparison of the Neutral Red and Methylene Blue Assays to Study Cell Growth in Culture

The neutral red and methylene blue in vitro cytotoxicity assays were compared under a variety of conditions using normal human ovarian epithelial cells to determine whether either assay is superior for studying cell growth. The results were standardized against a DNA spectrofluorometric assay. Although the assays were equivalent in reflecting cell number, each has specific advantages: while neutral red discriminates between viable and dead cells, the methylene blue assay is more sensitive and easier to perform.     

Comparison of Linear,Nonlinear and Semiparametric Mixed‐effects Models for Estimating HIV Dynamic Parameters

The potency of antiretroviral agents in AIDS clinical trials can be assessed on the basis of an early viral response such as viral decay rate or change in viral load (number of copies of HIV RNA) of the plasma. Linear, parametric nonlinear, and semiparametric nonlinear mixed‐effects models have been proposed to estimate viral decay rates in viral dynamic models. However, before applying these models to clinical data, a critical question that remains to be addressed is whether these models produce coherent estimates of viral decay rates, and if not, which model is appropriate and should be used in practice. In this paper, we applied these models to data from an AIDS clinical trial of potent antiviral treatments and found significant incongruity in the estimated rates of reduction in viral load. Simulation studies indicated that reliable estimates of viral decay rate were obtained by using the parametric and semiparametric nonlinear mixed‐effects models. Our analysis also indicated that the decay rates estimated by using linear mixed‐effects models should be interpreted differently from those estimated by using nonlinear mixed‐effects models. The semiparametric nonlinear mixed‐effects model is preferred to other models because arbitrary data truncation is not needed. Based on real data analysis and simulation studies, we provide guidelines for estimating viral decay rates from clinical data. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)