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The Blood-Oxygen-Level-Dependent (BOLD) signal that is measured by functional magnetic resonance imaging (fMRI) has been the subject of extensive research since the development of the first balloon model. While there are definite benefits to moving from the Canonical Hemodynamic Response function to a physiologically inspired BOLD model, significant barriers remain. Optimizing the simplest balloon model requires searching within 7 dimensions, and even more complex models exist. Additionally, the nonlinear nature of these models make them difficult to analyze; therefore, this work uses a particle filter to regresses a simple form of the BOLD model. Whereas traditional methods of analyzing fMRI aims to determine where activation occurs, BOLD model regression seeks a parametric representation of the signal. The results show that the particle filter attains a good fit but that the system of equations are not observable, leading to a large range of parameters that are consistent with the measurements.