Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Single line for assembly just-in-sequence multiple models

Programa Doutoral em Líderes para as Indústrias Tecnológicas

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Development of computational and experimental methods for biomass composition and evaluation of its impact in genome-scale models prediction

The use of genome-scale metabolic models has been rapidly increasing in fields such as metabolic engineering. An important part of a metabolic model is the biomass equation since this reaction will ultimately determine the predictive capacity of the model in terms of essentiality and flux distributions. Thus, in order to obtain a reliable metabolic model the biomass precursors and their coefficients must be as precise as possible. Ideally, determination of the biomass composition would be performed experimentally, but when no experimental data are available this is established by approximation to closely related organisms. Computational methods however, can extract some information from the genome such as amino acid and nucleotide compositions. The main objectives of this study were to compare the biomass composition of several organisms and to evaluate how biomass precursor coefficients affected the predictability of several genome-scale metabolic models by comparing predictions with experimental data in literature. For that, the biomass macromolecular composition was experimentally determined and the amino acid composition was both experimentally and computationally estimated for several organisms. Sensitivity analysis studies were also performed with the Escherichia coli iAF1260 metabolic model concerning specific growth rates and flux distributions. The results obtained suggest that the macromolecular composition is conserved among related organisms. Contrasting, experimental data for amino acid composition seem to have no similarities for related organisms. It was also observed that the impact of macromolecular composition on specific growth rates and flux distributions is larger than the impact of amino acid composition, even when data from closely related organisms are used.

Fundamental studies on natural deep eutectic solvents: physico-chemical, thermal and rheological properties

When combined at particular molar fractions, sugars, aminoacids or organic acids a present a high melting point depression, becoming liquids at room temperature. These are called Natural Deep Eutectic Solvents – NADES and are envisaged to play a major role on the chemical engineering processes of the future. Nonetheless, there is a significant lack of knowledge of its fundamental and basic properties, which is hindering their industrial applications. For this reason it is important to extend the knowledge on these systems, boosting their application development [1]. In this work, we have developed and characterized NADES based on choline chloride, organic acids, amino acids and sugars. Their density, thermal behavior, conductivity and polarity were assessed for different compositions. The conductivity was measured from 0 to 40 °C and the temperature effect was well described by the Vogel-Fulcher-Tammann equation. The morphological characterization of the crystallizable materials was done by polarized optical microscopy that provided also evidence of homogeneity/phase separation. Additionally, the rheological and thermodynamic properties of the NADES and the effect of water content were also studied. The results show these systems have Newtonian behavior and present significant viscosity decrease with temperature and water content, due to increase on the molecular mobility. The anhydrous systems present viscosities that range from higher than 1000Pa.s at 20°C to less than 1Pa.s at 70°C. DSC characterization confirms that for water content as high as 1:1:1 molar ratio, the mixture retains its single phase behavior. The results obtained demonstrate that the NADES properties can be finely tunned by careful selection of its constituents. NADES present the necessary properties for use as extraction solvents. They can be prepared from inexpensive raw materials and tailored for the selective extraction of target molecules. The data produced in this work is hereafter importance for the selection of the most promising candidates avoiding a time consuming and expensive trial and error phase providing also data for the development of models able to predict their properties and the mechanisms that allow the formation of the deep eutectic mixtures.