My research interests focus on modeling contrast agent and nanoparticle flow through cancerous tissue for treatment of glioblastoma multiforme (GBM). GBM is an aggressive brain cancer, notoriously difficult to treat due to its high recurrence rate and low mean survival time. Thus, new methods for treating GBM are desperately needed. One promising therapy uses 186Re-infused liposomal carriers, injected directly into the tumor and irradiating the cancerous tissue with a high dose of β-radiation. One of the implementation challenges is selecting an injection site to best distribute the liposomes within the brain. Using quantitative MRI, PET, and SPECT imaging, my goal is to accurately model the dispersion of radioactive liposomes in patients, with the goal of mathematically choosing the optimal delivery site for this therapy. To this end, I am also improving the current model of MR contrast agent perfusion in cancerous tissue. Current models of dynamic contrast-enhanced MRI do not account for diffusion of the contrast agent, and thus do not accurately model edematous or necrotic tissue accurately. Using FEM of histology, my goal is to improve the standard models of contrast agent perfusion, explicitly including a diffusive term and developing an inversion methodology for the new model.