Fluid movement in the interstitial space of the brain affects the clearance of waste products, which is an important factor in the pathophysiology of dementia. Estimating interstitial fluid (ISF) flow is critical to understanding these processes; yet, it has proven difficult to measure non-invasively. The pulsatile component of ISF flow may be particularly important for clearance, e.g. by facilitating fluid mixing. Directly measuring ISF flows is challenging due to the slow velocities and small volume fractions involved; however, pulsatile flows present a unique opportunity as their driving forces can be estimated from observations of pulsatile tissue motion. In this work, we present pressure gradient magnetic resonance imaging (pgMRI), which assimilates retrospectively gated pulsatile tissue deformations measured with a displacement encoding with stimulated echoes MRI sequence into a patient-specific poroelastic computational model by estimating the distribution of fluid sources. The new method is demonstrated to recover a spherical fluid source accurately from synthetic data with simulated noise of up to 20%, and to produce not previously reported