Sleep spindles are bursts of 11-15 Hz that occur during non-rapid eye movement sleep. Spindles are highly synchronous across the scalp in the electroencephalogram (EEG) but have low spatial coherence and exhibit low correlation with the EEG when simultaneously measured in the magnetoencephalogram (MEG). We developed a computational model to explore the hypothesis that the spatial coherence spindles in the EEG is a consequence of diffuse matrix projections of the thalamus to layer 1 compared with the focal projections of the core pathway to layer 4 recorded in the MEG. Increasing the fanout of thalamocortical connectivity in the matrix pathway while keeping the core pathway fixed led to increased synchrony of the spindle activity in the superficial cortical layers in the model. In agreement with cortical recordings, the latency for spindles to spread from the core to the matrix was independent of the thalamocortical fanout but highly dependent on the probability of connections between cortical areas.