Efficient visually-guided behavior depends on our ability to form, retain, and compare visual representations that may be separated in space and time. This ability relies on visual working memory (VWM). Here, we describe a layered neural architecture that captures the cortical population dynamics that underlie VWM. We then test this model using functional neuroimaging. Recent work has shown that the BOLD response is strongly correlated with local field potentials (LFPs). An analog of LFPs can be estimated from dynamic neural field (DNF) models. This estimate can be convolved with an impulse response function to yield time-dependent hemodynamic predictions. Using this approach, we show that the DFN model quantitatively captures fMRI data from recent studies probing changes in the BOLD response in the intraparietal sulcus (IPS) as set size increases in change detection. We also test a novel prediction of the model that BOLD responses should be greater on false alarms versus misses. These data run counter to common explanations of the origin of errors in change detection.