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Title: "Magnetic Resonance Elastography of the Brain" Committee: Paul Barbone, ME (Co-Advisor, Chair) Samuel Patz, BWH Radioloy (Co-Advisor) Dimitrije Stamenovic, BME Bela Suki, BME Katherine Zhang, ME Abstract: Magnetic Resonance Elastography (MRE) is a non-invasive imaging technique that maps and quantifies the mechanical properties of soft tissue as related to properties such as propagation speed and attenuation of shear waves. There is considerable interest in whether MRE can bring new insight into brain pathologies. Brain tumors, Alzheimer's disease, and Multiple Sclerosis have all been subjects of MRE studies. This thesis addresses four aspects of brain MRE, ranging from novel applications, to physiological interpretation of the measured mechanical properties, to improvements in MRE technology. The first aim measures the longitudinal progression of mechanical properties of glioblastoma tumorigenesis in a mouse model.A second aim addresses contradictory results in the literature regarding the effects of vascular pressure on shear wave speed in soft tissues. To reconcile these observations, a novel analytical approach based on poro-hyperelasticity will be used. Part of MRE requires inferring mechanical properties from MR measurements of vibration patterns in tissue. A third aim is to improve the MRE reconstruction by leveraging advanced computational methods to solve this inverse problem. Finally, we will apply the new inversion approach to an exciting new finding from our group called Mechanical-Stimulus Response (MSR). MSR refers to a localized change in mechanical properties of neural tissue when stimulated. It is potentially important because it seems to measure primary neuronal activity compared to the current state-of-the-art fMRI, which is based on an indirect blood-oxygen level dependent effect.