  Because LFPs arise from multiple sources in different spatial locations, they
do not easily reveal coordinated activity across neural populations on a
trial-to-trial basis. As we show here, however, once disparate source signals
are decoupled, their trial-to-trial fluctuations become more accessible, and
cross-population correlations become more apparent. To decouple sources we
introduce a general framework for estimation of current source densities
(CSDs). In this framework, the set of LFPs result from noise being added to the
transform of the CSD by a biophysical forward model, while the CSD is
considered to be the sum of a zero-mean, stationary, spatiotemporal Gaussian
process, having fast and slow components, and a mean function, which is the sum
of multiple time-varying functions distributed across space, each varying
across trials. We derived biophysical forward models relevant to the data we
analyzed. In simulation studies this approach improved identification of source
signals compared to existing CSD estimation methods. Using data recorded from
primate auditory cortex, we analyzed trial-to-trial fluctuations in both
steady-state and task-evoked signals. We found cortical layer-specific phase
coupling between two probes and showed that the same analysis applied directly
to LFPs did not recover these patterns. We also found task-evoked CSDs to be
correlated across probes, at specific cortical depths. Using data from
Neuropixels probes in mouse visual areas, we again found evidence for
depth-specific phase coupling of areas V1 and LM based on the CSDs.
