Estimating neuronal firing density: A quantitative analysis of firing rate map algorithms

The analysis of neurons that exhibit receptive fields dependent on an organism’s spatial location, such as grid, place or boundary cells typically begins by mapping their activity in space using firing rate maps. However, mapping approaches are varied and depend on multiple tuning parameters that are usually chosen qualitatively by the experimenter and thus vary significantly across studies. Small changes in parameters such as these can impact results significantly, yet, to date a quantitative investigation of firing rate maps has not been attempted. Using simulated datasets, we examined how tuning parameters, recording duration and firing field size affect the accuracy of spatial maps generated using the most widely used approaches. For each approach we found a clear subset of parameters which yielded low-error firing rate maps and isolated the parameters yielding 1) the least error possible and 2) the Pareto-optimal parameter set which balanced error, computation time, place field detection accuracy and the extrapolation of missing values. Smoothed bivariate histograms and averaged shifted histograms were consistently associated with the fastest computation times while still providing accurate maps. Adaptive smoothing and binning approaches were found to compensate for low positional sampling the most effectively. Kernel smoothed density estimation also compensated for low sampling well and resulted in accurate maps, but it was also among the slowest methods tested. Overall, the bivariate histogram, coupled with spatial smoothing, is likely the most desirable method in the majority of cases.Author summary: Spatially modulated neurons in the brain increase their activity when an animal visits specific regions of its environment. Studying these neurons often begins with the creation of a firing rate map: a statistical representation of the cell’s activity in space. Different methods, relying on different parameters, are commonly used to generate these maps. These parameters can have a huge impact on the maps created and, in turn, any results derived from them. Yet, very little quantification of these parameters has been attempted and they are almost universally chosen based on qualitative, study-dependent assessments. In this paper we quantify the ‘best’ combinations of parameters for each method and provide a way for researchers to calculate these for their own data. Using parameters that are both consistent across studies and quantifiably demonstrated to be the most accurate will reduce the variability between future studies while improving the validity of their results.