Meshfree methods are attractive for simulating transport phenomena in biological tissues due to their flexibility in handling complex geometries and evolving microstructures [1][2]. However, accurately capturing cellular-scale features within tissue-scale domains remains challenging because of the high computational cost. To address this issue, multi-resolution techniques that enable local refinement while maintaining numerical consistency are essential. This study aims to develop a local-refinement framework based on the mesh-constrained discrete point (MCD) method [3][4] to enable its application to substance transport phenomena involving membrane permeation in the brain parenchyma. The MCD method employs a background structured grid to constrain the placement of discrete points while allowing meshfree spatial discretization using the moving least squares method [5]. A tree-based data structure is introduced to locally refine the background grid near membranes. Discrete points are redistributed according to the refined background grid, and stencil constructions corresponding to different resolution levels are assigned for spatial derivative evaluation. A membrane-permeation model is incorporated by imposing interface conditions based on membrane permeability. Numerical verification is first performed using test problems to evaluate the accuracy of spatial derivatives in domains containing different resolution levels. The results demonstrate that the proposed multi-resolution formulation preserves stable convergence behaviour and maintains accuracy comparable to that of uniformly refined discretization [6]. The method is then applied to a two-dimensional diffusion problem with membrane permeation, which mimics substance transport in the brain parenchyma. The computed concentration fields show good agreement with reference solutions obtained on uniformly fine discretization, while the total number of discrete points is significantly reduced. By combining meshfree discretization with adaptive local refinement, the proposed formulation effectively balances accuracy and computational cost and is promising for simulating more complex mass-transfer problems in the brain parenchyma.