The introduction of the glymphatic system in 2012 unleashed a massive research interest in the fluid-mechanical aspects of the brain. Much of the research stems from medical imaging data of solute transport in alive brains in both animals and humans. Yet, the underlying physics of the fundamental processes are not fully understood. In this chapter, we utilize cerebrospinal fluid contrast-enhanced magnetic resonance (MR) imaging (MRI) data to test if a physical model including diffusion and reaction can explain how molecules are distributed brain-wide in humans. We apply two different methods, namely, physics-informed neural networks and an adjoint-based finite element method approach, to determine unknown model parameters from the MRI data. By incorporating executable code snippets, this chapter allows the reader to carry out and understand the implementation of these two approaches on their own machine using the associated publicly available MRI data.