Ms. Isabel Montoya Arroyave Profile

Isabel Montoya Arroyave

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Proceedings Article | 28 May 2014 Paper

Analytical model of contamination during the drying of cylinders of jamonable muscle

Isabel Montoya Arroyave

Proceedings Volume 9108, 91080K (2014) https://doi.org/10.1117/12.2048858

KEYWORDS: Contamination, Diffusion, Pathogens, Resistance, Bessel functions, Modulation, Integral transforms, Bacteria, Humidity, Analytical research

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For a cylinder of jamonable muscle of radius R and length much greater than R; considering that the internal resistance to the transfer of water is much greater than the external and that the internal resistance is one certain function of the distance to the axis; the distribution of the punctual moisture in the jamonable cylinder is analytically computed in terms of the Bessel’s functions. During the process of drying and salted the jamonable cylinder is sensitive to contaminate with bacterium and protozoa that come from the environment. An analytical model of contamination is presents using the diffusion equation with sources and sinks, which is solve by the method of the Laplace transform, the Bromwich integral, the residue theorem and some special functions like Bessel and Heun. The critical times intervals of drying and salted are computed in order to obtain the minimum possible contamination. It is assumed that both external moisture and contaminants decrease exponentially with time. Contaminants profiles are plotted and discussed some possible techniques of contaminants detection. All computations are executed using Computer Algebra, specifically Maple. It is said that the results are important for the food industry and it is suggested some future research lines.

Proceedings Article | 22 May 2014 Paper

Drug diffusion across skin with diffusivity spatially modulated

Isabel Montoya Arroyave

Proceedings Volume 9107, 91071F (2014) https://doi.org/10.1117/12.2049766

KEYWORDS: Skin, Diffusion, Modulation, Mathematical modeling, Capillaries, Bessel functions, Integral transforms, Analytical research, Molecules, Blood circulation

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A diffusion and delivery model of a drug across the skin with diffusivity spatially modulated is formulated and solved analytically using computer algebra. The model is developed using one-dimensional diffusion equation with a diffusivity which is a function of position in the skin; with an initial condition which is describing that the drug is initially contained inside a therapeutic patch; with a boundary condition according to which the change in concentration in the patch is minimal, such that assumption of zero flux at the patch-skin interface is valid; and with other boundary condition according to which the microcirculation in the capillaries just below the dermis carries the drug molecules away from the site at a very fast rate, maintaining the inner concentration at 0. The model is solved analytically by the method of the Laplace transform, with Bromwich integral and residue theorem. The concentration profile of the drug in the skin is expressed as an infinite series of Bessel functions. The corresponding total amount of delivered drug is expressed as an infinite series of decreasing exponentials. Also, the corresponding effective time for the therapeutic patch is determined. All computations were performed using computer algebra software, specifically Maple. The analytical results obtained are important for understanding and improving currentapplications of therapeutic patches. For future research it is interesting to consider more general models of spatial modulation of the diffusivity and the possible application of other computer algebra software such as Mathematica and Maxima.

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