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• Study of a system of quasilinear PDEs that can be used to model drug release from a polymeric structure enhanced by light. • A numerical scheme to compute the numerical solution of the IBVP based on the system of PDEs is proposed. • The theoretical support (stability and convergence) under weaker assumptions than those usually used is developed. • Numerical results illustrating the theoretical results established are provided. • A comparation between experimental data and simulation results is also presented. In this paper, we analyze a numerical scheme for a nonlinear coupled system of partial differential equations. Our study is motivated by the mathematical modeling of light-triggered drug delivery, a technique that can have a significant impact on cancer treatment. The numerical scheme combines a finite difference method (FDM) in space with an implicit-explicit (IMEX) method in time. For the main variable of interest - free drug concentration - we prove that the scheme is second-order supraconvergent in space in a discrete H 1 -norm and first-order convergent in time in a discrete L 2 -norm. We give numerical results illustrating the theoretical findings and computational simulations based on a laboratory experiment concerned with light-triggered drug delivery. [ABSTRACT FROM AUTHOR]

Convection enhanced drug delivery (CED) is a technique used to make therapeutic agents reach, through a catheter, sites of difficult access. The name of this technique comes from the convective flow originated by a pressure gradient induced at the tip of the catheter. This flow enhances passive diffusion and allows a more efficient spread of the agents by the target site. CED is particularly useful in the treatment of diseases that affect the central nervous system, where the blood–brain barrier prevents the diffusion of most therapeutic agents from the cerebral blood vessels to the brain interstitial space. In this work we deal with the numerical analysis of a coupled system of partial differential equations that can be used to simulate CED in an elastic medium like brain tissue. The model variables are the fluid velocity, the pressure, the tissue deformation, and the agents concentration. We prove the stability of the coupled problem and from the numerical point of view we propose a fully discrete piecewise linear finite element method (FEM). The convergence analysis shows that the method has second order convergence for the pressure, displacement, and concentration. Numerical experiments illustrating the theoretical convergence rates and the behavior of the system are also given. [ABSTRACT FROM AUTHOR]

• A mathematical methodology to find the optimal NIR light protocol in transdermal drug delivery; • Strategy based on an optimization problem minimizing the difference between target and simulated drug absorption profile; • The optimization problem relies on a 2D mathematical model for NIR light controlled transdermal drug delivery; • Validation of the transdermal model against laboratory data; • Convergence and stability analysis of a finite difference spatial scheme for a generalization of the transdermal model. Near-infrared light-controlled transdermal drug delivery (NIRTDD) has several advantages over traditional delivery methods, and it is now undergoing extensive research. One prominent aspect of NIRTDD is the possibility of keeping the drug concentration in its optimal therapeutic window using a suitable near-infrared light protocol. The problem is that this ideal protocol is usually unknown. In this paper, we propose a computational tool that aims at solving this issue. The computational tool relies on an optimization problem involving the numerical simulation of a two-dimensional mathematical model for NIRTDD. We also analyze the convergence and stability of a finite difference spatial scheme for a generalized version of this mathematical model. [ABSTRACT FROM AUTHOR]