Detecting and Quantifying Topography in Neural Maps

Topographic maps are an often-encountered feature in the brains of many species, yet there are no standard, objective procedures for quantifying topography. Topographic maps are typically identified and described subjectively, but in cases where the scale of the map is close to the resolution limit of the measurement technique, identifying the presence of a topographic map can be a challenging subjective task. In such cases, an objective topography detection test would be advantageous. To address these issues, we assessed seven measures (Pearson distance correlation, Spearman distance correlation, Zrehen's measure, topographic product, topological correlation, path length and wiring length) by quantifying topography in three classes of cortical map model: linear, orientation-like, and clusters. We found that all but one of these measures were effective at detecting statistically significant topography even in weakly-ordered maps, based on simulated noisy measurements of neuronal selectivity and sparse sampling of the maps. We demonstrate the practical applicability of these measures by using them to examine the arrangement of spatial cue selectivity in pallid bat A1. This analysis shows that significantly topographic arrangements of interaural intensity difference and azimuth selectivity exist at the scale of individual binaural clusters.