We construct a Brownian motion in a medium with a semi-permeable barrier. For this, we paste in a suitable way two elastic Brownian motions. This process is the limit of a diffusion process moving in a media with a thin layer of low diffusivity. A simulation algorithm is then given. The mean residence time in cells surrounded by such semi-permeable barriers is computed. Provided as a benchmark test, this problem is a simplified form of a real-life problem coming from brain imaging techniques. We also refine the ways to compute the exponential decaying rate from the distribution function of some random variables estimated through Monte Carlo techniques.