Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Development and characterization of lipid-based nanosystems for controlled release of bioactive compounds

Tese de Doutoramento em Engenharia Química e Biológica.

Influence of chitosan coating on protein-based nanohydrogels properties and in vitro gastric digestibility

Chitosan coating was applied in Lactoferrin (Lf)-Glycomacropeptide (GMP) nanohydrogels by layer-by-layer coating process. A volume ratio of 0.1 of Lf-GMP nanohydrogels (0.2 mg.mL-1, at pH 5.0) to chitosan (1 mg.mL-1, at pH 3) demonstrated to be the optimal condition to obtain stable nanohydrogels with size of 230 ± 12 nm, a PdI of 0.22 ± 0.02 and a -potential of 30.0 ± 0.15 mV. Transmission electron microscopy (TEM) images showed that the application of chitosan coating in Lf-GMP did not affect the spherical shape of nanohydrogels and confirmed the low aggregation of nanohydrogels in solution. The analysis of chemical interactions between chitosan and Lf-GMP nanohydrogels were performed by Fourier transform infrared spectroscopy (FTIR) and by circular dichroism (CD) that revealed that a specific chemical interaction occurring between functional groups of protein-based nanohydrogels and active groups of the chitosan was established. The effect of chitosan coating on release mechanisms of Lf-GMP nanohydrogels at acid conditions (pH 2, 37 ºC) was evaluated by the encapsulation of a model compound (caffeine) in these systems. Linear Superposition Model was used to fit the experimental data and revealed that Fick and relaxation mechanisms are involved in caffeine release. It was also observed that the Fick contribution increase with the application of chitosan coating. In vitro gastric digestion was performed with Lf-GMP nanohydrogels and Lf-GMP nanohydrogels with chitosan coating and it was observed that the presence of chitosan improve the stability of Lf and GMP (proteins were hydrolysed at a slower rate and were present in solution by longer time). Native electrophoreses revealed that the nanohydrogels without coating remained intact in solution until 15 min and with chitosan coating remained intact until 60 min, during gastric digestion.