Finding Nonlinear Relationships in fMRI Time Series with Symbolic Regression

The brain is an intrinsically nonlinear system, yet the dominant methods used to generate network models of functional connectivity from fMRI data use linear methods. Although these approaches have been used successfully, they are limited in that they can find only linear relations within a system we know to be nonlinear. This study employs a highly specialized genetic programming system which incorporates multiple enhancements to perform symbolic regression, a type of regression analysis that searches for declarative mathematical expressions to describe relationships in observed data. Publicly available fMRI data from the Human Connectome Project were segmented into meaningful regions of interest and highly nonlinear mathematical expressions describing functional connectivity were generated. These nonlinear expressions exceed the explanatory power of traditional linear models and allow for more accurate investigation of the underlying physiological connectivities.