Mathematics and Medicine: How mathematics, modelling and simulations can lead to better diagnosis and treatments

Starting with the discovery of X-rays by Röntgen in 1895, the progress in medical imaging has been extraordinary and immensely beneficial to diagnosis and therapy. Parallel to the increase of imaging accuracy, there is the quest of moving from qualitative to quantitative analysis and patient-tailored therapy. Mathematics, modelling and simulations are increasing their importance as tools in this quest. In this paper we give an overview of relations between mathematical modelling and imaging and focus particularly on the estimation of perfusion in the brain. In the forward model, the brain is treated as a porous medium and a two compartment model (arterial/venous) is used. Motivated by the similarity with techniques in reservoir modelling, we propose an ensemble Kalman filter to perform the parameter estimation and apply the method to a simple example as an illustrative example.acceptedVersio

Application of Factorial Design in the Analysis of Factors Influencing Textile Dye Adsorption on Activated Carbon

In this study, the use of factorial design software is applied to evaluate efficiently factors influencing the adsorption capacity of activated carbon in treating textile dyes. Activated carbon is usually used to treat wastewater effluents from textile industries in order to remove textile dyes before discharge into the environment. Most treatment facilities, particularly large industrial or wastewater treatment facilities use continuous flow reactors or packed columns to treat the dye. Due to the limited residence time in these types of reactors, adsorption equilibrium is not necessarily reached, and the absorption rate becomes an important factor in this treatment process. Other factors influencing the capacity of activated carbon used in this study included pH, ionic strength, the type of the dye and the type of carbon. In this study, we use Minitab software to design an experiment to evaluate collectively these factors, each under various levels (33 × 22 factorial design). The novelty of this study is the utilization of factorial design in the experimental approach