Exploring dynamical whole-brain models in high-dimensional parameter spaces.

Personalized modeling of the resting-state brain activity implies the usage of dynamical whole-brain models with high-dimensional model parameter spaces. However, the practical benefits and mathematical challenges originating from such approaches have not been thoroughly documented, leaving the question of the value and utility of high-dimensional approaches unanswered. Studying a whole-brain model of coupled phase oscillators, we proceeded from low-dimensional scenarios featuring 2-3 global model parameters only to high-dimensional cases, where we additionally equipped every brain region with a specific local model parameter. To enable the parameter optimizations for the high-dimensional model fitting to empirical data, we applied two dedicated mathematical optimization algorithms (Bayesian Optimization, Covariance Matrix Adaptation Evolution Strategy). We thereby optimized up to 103 parameters simultaneously with the aim to maximize the correlation between simulated and empirical functional connectivity separately for 272 subjects. The obtained model parameters demonstrated increased variability within subjects and reduced reliability across repeated optimization runs in high-dimensional spaces. Nevertheless, the quality of the model validation (goodness-of-fit, GoF) improved considerably and remained very stable and reliable together with the simulated functional connectivity. Applying the modeling results to phenotypical data, we found significantly higher prediction accuracies for sex classification when the GoF or coupling parameter values optimized in the high-dimensional spaces were considered as features. Our results elucidate the model fitting in high-dimensional parameter spaces and can contribute to an improved dynamical brain modeling as well as its application to the frameworks of inter-individual variability and brain-behavior relationships.