Numerical analysis of a porous-elastic model for convection enhanced drug delivery (Preprint)

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Type: Preprint
National /International: International
Title: Numerical analysis of a porous-elastic model for convection enhanced drug delivery
Publication Date: 2020-01-27
Authors: - José Augusto Ferreira
- Luís Miguel Dias Pinto
- Rafael F. Santos
Abstract: 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 ow originated by a pressure gradient induced at the tip of the catheter. This ow 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 bloodbrain 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 uid velocity, pressure, tissue deformation, and 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.
Institution: DMUC 20-05
Online version: http://www.mat.uc.pt...prints/eng_2020.html
Download: Not available
 
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