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Positron Emission Tomography (PET) has been of utmost importance for helping the diagnostics of neurodegenerative diseases, such as Alzheimer's disease(AD). Radiolabeled drugs help quantifying the amount of deposition of beta-amyloid in the brain which can be a strong indication for AD. In this work, using data coming from an experiment at the Brain Institute with Pittsburgh Compound-B (11C-PIB) as a marker, we propose a two-tissue reversible compartment model as a mathematical modeling in the quantitative analysis of the 11C-PIB. Laplace Transform is applied to solve the corresponding system of differential equations for CILAMCE 2017