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.

对流增强型药物递送 (CED) 是一种用于使治疗剂通过导管到达难以进入的部位的技术。这种技术的名称来自于导管尖端引起的压力梯度产生的对流。这种流动增强了被动扩散，并允许目标部位更有效地传播药剂。CED 在治疗影响中枢神经系统的疾病方面特别有用，在这种疾病中，血脑屏障阻止了大多数治疗药物从脑血管扩散到脑间质空间。

在这项工作中，我们处理偏微分方程耦合系统的数值分析，该系统可用于模拟脑组织等弹性介质中的 CED。模型变量是流体速度、压力、组织变形和药剂浓度。我们证明了耦合问题的稳定性，并从数值角度提出了一种完全离散的分段线性有限元方法 (FEM)。收敛性分析表明，该方法对压力、位移和浓度均具有二阶收敛性。还给出了说明理论收敛速度和系统行为的数值实验。