Dynamic causal modeling for calcium imaging: Exploration of differential effective connectivity for sensory processing in a barrel cortical column

Multi-photon calcium imaging (CaI) is an important tool to assess activities of neural populations within a column in the sensory cortex. However, the complex asymmetrical interactions among neural populations, termed effective connectivity, cannot be directly assessed by measuring the activity of each neuron or neural population using CaI but calls for computational modeling. To estimate effective connectivity among neural populations, we proposed a dynamic causal model (DCM) for CaI by combining a convolution-based dynamic neural state model and a dynamic calcium ion concentration model for CaI signals. After conducting a simulation study to evaluate DCM for CaI, we applied it to an experimental CaI signals measured at the layer 2/3 of a barrel cortical column that differentially responds to hit and error whisking trials in mice. We first identified neural populations and constructed computational models with intrinsic connectivity of neural populations within the layer 2/3 of the barrel cortex and extrinsic connectivity with latent external modes. Bayesian model inversion and comparison shows that interactions with latent inhibitory and excitatory external modes explain the observed CaI signals within the barrel cortical column better than any other tested models, with a single external mode or without any latent modes. The best model also showed differential intrinsic and extrinsic effective connectivity between hit and error trials in the functional hierarchy. Both simulation and experimental results suggest the usefulness of DCM for CaI in terms of exploration of hierarchical interactions among neural populations observed in CaI.