This chapter discusses the application of the derived methods to the simulation of tau propagation in Alzheimer’s disease. The objective is to test the applicability of the methods to real world, large scale data. The main ideas of the Global Brainsphere Model and the representation of the brain as a metric graph are introduced. Numerical experiments on the solution of IBVPs governed by linear reaction-diffusion equations are carried out using the finite element discretization from Chap. 3 . The eigenvalue algorithm from Sect. 5.3 is applied to compute eigenvalues of metric graphs modeling the brain.