On the Search for Brain Bifurcation Parameters: Lessons From FMRI Studies on Visual Illusions

Data from three functional magnetic resonance imaging (fMRI) studies that involved in total about 100 participants and showed that the strength of several visual illusions such as the Ebbinghaus, Ponzo, and Muller-Lyer illusions depends on neuroanatomical subject measures such as visual cortex surface area and parahippocampal cortex gray matter volume were evaluated using a dynamical systems perspective to determine brain bifurcation parameters. Bifurcation parameters that involved power laws and captured relational dependencies were fitted separately to the three fMRI studies. The bifurcation parameter hypothesis that states that such parameters show unique quantities and are no longer correlated to structural systems properties was tested. The power law exponents and mean bifurcation parameter values were determined. For all three studies and three illusion types, the bifurcation parameter hypothesis was supported. Accordingly, the constructed parameters characterized the reactions of the participants under the Ebbinghaus, Ponzo, and Muller-Lyer illusions in terms of unique threshold values that no longer depended on neuroanatomical subject measures. Power law exponents in the range from 1 to 7 were found. The fMRI data describing gray matter volume of certain active regions in the parahippocampal cortex showed some interesting relationship between the mean bifurcation parameter values.