Higuchi Fractal Dimension with Fréchet Distance (HFDf) to Assess Cortical Neurodynamics

The temporal course of neuronal electric activity within brain networks, or neurodynamics, reflects the structural and functional properties of the neuronal populations that generate it. Using intracranial stereo-electroencephalography (sEEG) recordings from the public Montreal Neurological Institute (MNI) atlas, we investigated neurodynamics in the primary motor (M1), somatosensory (S1), and auditory (A1) cortices. We tested whether modifying the Higuchi fractal dimension (HFD) by replacing the Euclidean distance with the Fréchet distance could improve sensitivity to local neurodynamics by incorporating trajectory-based similarities in signal evolution. Using a conservative within-subject approach established in the previous literature, we compared signals recorded from different cortical areas within the same individuals (M1 vs. S1: # of people = 16; M1 vs. A1: # = 9; S1 vs. A1: # = 6). To delve deeper into the new measure’s meaning, it was tested on sequences with known fractal properties, the Brownian motion and the Weierstrass function. Results showed that the newly introduced Fréchet-based HFD (HFDf), similarly to standard HFD, consistently discriminated cortical areas at the intra-subject level, confirming the robustness of fractal dimension as a descriptor of region-specific neurodynamics. Contrary to our hypothesis, HFDf did not provide additional sensitivity across areas and notably, it displayed less evident reduction of values in sleep than awake. While cortical regions may share common governing principles across spatiotemporal scales, these do not necessarily translate into strict similarity in temporal signal morphology. We suggest that these findings support that the free-scale nature of neurodynamics is not a self-similar one. This refinement of quantitative tools for cortical neurodynamic mapping paves the way towards novel tools for neuroimaging-informed neuromodulation strategies.