Categorical laterality indices in fMRI: a parallel with classic similarity indices

FMRI-based laterality index (LI) is widely used to assess relative left-right differences in brain function. Here we investigated objective ways to generate categorical LI. By defining left and right hemisphere contributions as discrete random variables, it was possible to depict the probability mass function of LI. Its distribution has a shape of a symmetrical truncated exponential function. We demonstrate that LI = ± 0.2 is an objective cut-off to categorize classification of hemispheric dominance. We then searched for parallels between LI and classic similarity or association indices. A parallel between LI and Sorensen-Dice index can be established under maximal voxel-wise overlap between left and right hemispheres. To redefine LI as a proper distance metric, we suggest instead to relate LI to Jaccard-Tanimoto similarity index. Accordingly, a new LI formula can be derived: LI_new = LH-RH/max(LH,RH). Using this new formula, all LI_new values follow a uniform-like distribution, and optimal categorization of hemispheric dominance can be achieved at cut-off LI_new = ± 1/3. Overall, this study investigated some statistical properties of LI and revealed interesting parallels with classic similarity indices in taxonomy. The theoretical distribution of LI should be taken into account when quantifying any existing bias in empirical distributions of lateralization in healthy or clinical populations.