Two-dimensional transport analysis of transdermal drug absorption with a non-perfect sink boundary condition at the skin-capillary interface

Simon, Laurent; Ospina, Juan

doi:10.1016/j.mbs.2013.04.004

Cited by 15 publications

(7 citation statements)

References 16 publications

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“…of SPIE Vol. 9108 91080N-5 (10) The temperature profile for the cylindrical potato in the temporal domain is given by (11) where δ n are the roots of (12)…”

Section: Results When the Thermal Conductivity Is Constantmentioning

confidence: 99%

“…The first goal consist in to re-derive the analytical results of [1] using computer algebra software [5], specifically Maple [6] ; and then to compute the effective time constant [7,10,11] for the drying process. The second goal consist is to solve, by the first time, the drying problem assuming that the thermal conductivity of the cylindrical food is radially modulated.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical model for solar drying of potato cylinders with thermal conductivity radially modulated

Arredondo

2014

Sensing for Agriculture and Food Quality and Safety VI

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A mathematical model for drying potato cylinders using solar radiation is proposed and solved analytically. The model incorporates the energy balance for the heat capacity of the potato, the radiation heat transfer from the potato toward the drying chamber and the solar radiation absorbed by the potato during the drying process. Potato cylinders are assumed to exhibit a thermal conductivity which is radially modulated. The method of the Laplace transform, with integral Bromwich and residue theorem will be applied and the analytic solutions for the temperature profiles in the potato cylinder will be derived in the form of an infinite series of Bessel functions, when the thermal conductivity is constant; and in the form of an infinite series of Heun functions, when the thermal conductivity has a linear radial modulation. All computations are performed using computer algebra, specifically Maple. It is expected that the analytical results obtained will be useful in food engineering and industry. Our results suggest some lines for future investigations such as the adoption of more general forms of radial modulation for the thermal conductivity of potato cylinders; and possible applications of other computer algebra software such as Maxima and Mathematica.

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“…of SPIE Vol. 9108 91080N-5 (10) The temperature profile for the cylindrical potato in the temporal domain is given by (11) where δ n are the roots of (12)…”

Section: Results When the Thermal Conductivity Is Constantmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical model for solar drying of potato cylinders with thermal conductivity radially modulated

Arredondo

2014

Sensing for Agriculture and Food Quality and Safety VI

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“…Clearly, however, local tissue architecture could create spatially heterogeneous xenobiotic profiles within the tissue and, to enable capture of such spatial profiles, these local tissue features therefore should be incorporated into the PBPK framework. Mathematical modelling of these features in relation to transdermal drug transport has been a major area of research [62]. Seminal work by Higuchi (1960) [63], based on Fick's law for transport processes, laid the foundation of current theories of skin penetration.…”

Section: Potential To Elicit Toxicitymentioning

confidence: 99%

In silico prediction of skin metabolism and its implication in toxicity assessment

Madden

Webb

Enoch

et al. 2017

Computational Toxicology

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Skin, being the largest organ of the body, represents an important route of exposure, not only for the abundance of chemicals present in the environment, but also for products designed for topical application such as drugs and personal care products. Determining whether such incidental or intentional exposure poses a risk to human health requires consideration of temporal concentration, both externally and internally, in addition to assessing the chemical's intrinsic hazard. In order to elicit a toxic response in vivo the chemical must reach its site of action in sufficient concentration, as determined by its absorption, distribution, metabolism and elimination (ADME) profile. Whilst absorption and distribution into and through skin layers have been studied for decades, only more recently has skin metabolism become a subject of intense research, now recognised as playing a key role in both toxification and detoxification processes. The majority of information on metabolic processes, however, has generally been acquired via studies performed on the liver. This paper outlines strategies that may be used to leverage current knowledge, gained from liver metabolism studies, to inform predictions for skin metabolism through understanding the differences in the enzymatic landscapes between skin and liver. The strategies outlined demonstrate how an array of in silico tools may be used in concert to resolve a significant challenge in predicting toxicity following dermal exposure. The use of in vitro methods for determining skin metabolism, both to provide further experimental data for modelling and to verify predictions is also discussed. Herein, information on skin metabolism is placed within the context of toxicity prediction for risk assessment, which requires consideration of both exposure and hazard of parent chemicals and their metabolites.

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“…The explicit form of the output current for the biosensor is computed analytically both in the Laplace domain as in the temporal domain. Also, the effective time constant [8,11,12] for the biosensor is analytically computed and its algebraic form will be an important tool for designing a biosensor. All the computations will be performed using computer algebra software [9], specifically Maple [10].…”

Section: Introductionmentioning

confidence: 99%

Analytical solution using computer algebra of a biosensor for detecting toxic substances in water

Taborda

2014

SPIE Proceedings

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In a relatively recent paper an electrochemical biosensor for water toxicity detection based on a bio-chip as a whole cell was proposed and numerically solved and analyzed. In such paper the kinetic processes in a miniaturized electrochemical biosensor system was described using the equations for specific enzymatic reaction and the diffusion equation. The numerical solution shown excellent agreement with the measured data but such numerical solution is not enough to design efficiently the corresponding bio-chip. For this reason an analytical solution is demanded. The object of the present work is to provide such analytical solution and then to give algebraic guides to design the bio-sensor. The analytical solution is obtained using computer algebra software, specifically Maple. The method of solution is the Laplace transform, with Bromwich integral and residue theorem. The final solution is given as a series of Bessel functions and the effective time for the bio-sensor is computed. It is claimed that the analytical solutions that were obtained will be very useful to predict further current variations in similar systems with different geometries, materials and biological components. Beside of this the analytical solution that we provide is very useful to investigate the relationship between different chamber parameters such as cell radius and height; and electrode radius.

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Two-dimensional transport analysis of transdermal drug absorption with a non-perfect sink boundary condition at the skin-capillary interface

Cited by 15 publications

References 16 publications

Mathematical model for solar drying of potato cylinders with thermal conductivity radially modulated

Mathematical model for solar drying of potato cylinders with thermal conductivity radially modulated

In silico prediction of skin metabolism and its implication in toxicity assessment

Analytical solution using computer algebra of a biosensor for detecting toxic substances in water

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