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Mathematics of aging: Diseases of the posterior segment of the eye
Ferreira, José Augusto; Oliveira, Paula de; Silva, Pascoal; Silva, RufinoThe changes caused by aging affect all body tissues. The vitreous humor, which fills the space between the lens and the retina, progressively liquefies and shrinks, eventually causing a posterior vitreous detachment. Retinal disorders caused by the breakdown of the blood retinal barrier are also associated with physiological aging. In this work a mathematical model of the pharmacokinetics of a drug eluted from ...
Iontophoretic transdermal drug delivery: a multi-layered approach
Pontrelli, Giuseppe; Lauricella, Marco; Ferreira, José Augusto; Pena, GonçaloWe present a multi-layer mathematical model to describe the the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describe the basic convection-diffusion process, with the electric potential obtained by Laplace equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in dif...
The influence of atherosclerotic plaques on the pharmacokinetics of a drug elut...
Ferreira, José Augusto; Gonçalves, Lino; Naghipoor, Jahed; Oliveira, Paula de; Rabczuk, TimonIn this paper the effect of plaque composition, on the accumulation of drug released by a drug eluting stent, is analyzed. The mathematical model is represented by two coupled systems of partial differential equations that describe the pharmacokinetics of drug in the stent coating and in the arterial wall. The influence of the stiffness and porosity of soft and hard plaques is studied. A case study based on opt...
Second order approximations for kinetic and potential energies in Maxwell's wav...
Ferreira, José Augusto; Jordão, Daniela; Pinto, LuísIn this paper we propose a numerical scheme for wave type equations with damping and space variable coefficients. Relevant equations of this kind arise for instance in the context of Maxwell's equations, namely, the electric potential equation and the electric field equation. The main motivation to study such class of equations is the crucial role played by the electric potential or the electric field in enhanc...
Transdermal iontophoresis—A quantitative and qualitative study
Ferreira, José Augusto; Oliveira, Paula de; Pena, GonçaloThe use of enhancers to increase the drug molecules penetration into target tissues is a usual technique in drug delivery. In transdermal drug delivery, electric fields are often used to increase the drug transport through the skin. In this paper we study a drug delivery mechanism from a reservoir which is in contact with the skin. We assume that the drug transport in the coupled system is enhanced by a small e...
On the exponential decay of waves with memory
Ferreira, José Augusto; Oliveira, Paula de; Pena, GonçaloIn this paper we consider general linear damped wave equations with memory. We establish energy estimates that under the assumption of exponentially bounded kernels, induce exponential decaying solutions. Numerical waves that mimic their continuous counterpart are also introduced using a finite element approach.
Non-Fickian convection–diffusion models in porous media
Barbeiro, Sílvia; Bardeji, Somayeh Gh.; Ferreira, José Augusto; Pinto, LuísIn this paper we propose a numerical scheme to approximate the solution of a non-Fickian coupled model that describes, e.g., miscible transport in porous media. The model is defined by a system of a quasilinear elliptic equation, which governs the fluid pressure, and a quasilinear integro-differential equation, which models the convection–diffusion transport process. The numerical scheme is based on a conformin...
An integro-differential model for non-Fickian tracer transport in porous media:...
Ferreira, José Augusto; Pinto, LuísDiffusion processes have traditionally been modeled using the classical parabolic advection-diffusion equation. However, as in the case of tracer transport in porous media, significant discrepancies between experimental results and numerical simulations have been reported in the literature. Therefore, in order to describe such anomalous behavior, known as non-Fickian diffusion, some authors have replaced the pa...
A coupled non-Fickian model of a cardiovascular drug delivery system
Ferreira, José Augusto; Naghipoor, Jahed; Oliveira, Paula deA coupled non-Fickian model of a cardiovascular drug delivery system using a biodegradable drug-eluting stent is proposed. The numerical results are obtained using an implicit-explicit finite-element method. The influence of vessel stiffness on the transport of drug eluted from the stent is analysed. The results presented in this paper suggest new perspectives to adapt the drug delivery profile to the needs of ...
Tuning polymeric and drug properties in a drug eluting stent: A numerical study
Naghipoor, Jahed; Ferreira, José Augusto; Oliveira, Paula de; Rabczuk, TimonA two dimensional coupled nonlinear non-Fickian model for drug release from a biodegradable drug eluting stent into the arterial wall is studied. The influence of porosity and degradation of the polymer as well as the dissolution rate of the drug are analyzed. Numerical simulations that illustrate the kind of dependence of drug profiles on these properties are included.