kCSD-python, a tool for reliable current source density estimation

Kernel Current Source Density (kCSD), which we introduced in 2012, is a kernel-based method to estimate current source density (CSD) from extracellular potentials recorded with arbitrarily placed electrodes. Estimating reconstruction errors in CSD has been an outstanding challenge. To address it, here we revisit kCSD and explore its mathematical underpinnings. First, we quantify the information that can be recovered from extracellular recordings for a given setup, by introducing eigensources — a set of basic CSD profiles, which form the basis of estimation space. Next, we investigate the effect of relative placement of basis sources and electrodes on the reconstruction fidelity. We show that the correct distribution of sources is crucial for the reconstruction, in particular, CSD reconstruction is possible even for badly misplaced electrodes. We also introduce L-curve, a new method for choosing reconstruction parameters, in addition to the previously used cross-validation. Finally, we propose two types of diagnostics of reconstruction veracity, error propagation map and reliability map. For any given setup, the error propagation map indicates how the electrode noise propagates to the reconstructed CSD and the reliability map illustrates the point-wise reliability of kCSD estimation. The kCSD method and the additional techniques introduced here are implemented in kCSD-python, a new Python package provided under an open license. kCSD-python’s features and usage are highlighted with a jupyter notebook tutorial. This new tool can perform CSD estimations for 1D, 2D, and 3D electrode setups, assuming distributions of sources in a tissue, a slice, or in a single cell.