Ju M, Gaussier P. A model of path integration and representation of spatial context in the retrosplenial cortex. Biological Cybernetics. 2020 Apr;114(2):303-313. DOI: 10.1007/s00422-020-00833-x.

Abstract
“Inspired by recent biological experiments, we simulate animals moving in different environments (open space, spiral mazes and on a treadmill) to test the performances of a simple model of the retrosplenial cortex (RSC) acting as a path integration (PI) and as a categorization mechanism. The connection between the hippocampus, RSC and the entorhinal cortex is revealed through a novel perspective. We suppose that the path integration is performed by the information coming from RSC. Grid cells in the entorhinal cortex then can be built as the result of a modulo projection of RSC activity. In our model, PI is performed by a 1D field of neurons acting as a simple low-pass filter of head direction (HD) cells modulated by the linear velocity of the animal. Our paper focuses on the constraints on the HD cells shape for a good approximation of PI. Recording of neurons on our 1D PI field shows these neurons would not be intuitively interpreted as performing PI. Using inputs coming from a narrow neighbouring projection of our PI field creates place cell-like activities in the RSC when the mouse runs on the treadmill. This can be the result of local self-organizing maps representing blobs of neurons in the RSC (e.g. cortical columns). Other simulations show that accessing the whole PI field would induce place cells whatever the environment is. Since this property is not observed, we conclude that the categorization neurons in the RSC should have access to only a small fraction of the PI field.”

Ju M, Gaussier P. A model of path integration and representation of spatial context in the retrosplenial cortex. Biological Cybernetics. 2020 Apr;114(2):303-313. DOI: 10.1007/s00422-020-00833-x.