Abstract
Simulating the resting-state brain dynamics via mathematical whole-brain models requires an optimal selection of parameters, which determine the model’s capability to replicate empirical data. Since the parameter optimization via a grid search (GS) becomes unfeasible for high-dimensional models, we evaluate several alternative approaches to maximize the correspondence between simulated and empirical functional connectivity. A dense GS serves as a benchmark to assess the performance of four optimization schemes: Nelder-Mead Algorithm (NMA), Particle Swarm Optimization (PSO), Covariance Matrix Adaptation Evolution Strategy (CMAES) and Bayesian Optimization (BO). To compare them, we employ an ensemble of coupled phase oscillators built upon individual empirical structural connectivity of 105 healthy subjects. We determine optimal model parameters from two- and three-dimensional parameter spaces and show that the overall fitting quality of the tested methods can compete with the GS. There are, however, marked differences in the required computational resources and stability properties, which we also investigate before proposing CMAES and BO as efficient alternatives to a high-dimensional GS. For the three-dimensional case, these methods generated similar results as the GS, but within less than 6% of the computation time. Our results contribute to an efficient validation of models for personalized simulations of brain dynamics.
Highlights
Analyzing the discussed parameter distributions with the help of the cost function’s respective component, we found that the performance of both Particle Swarm Optimization (PSO) and Covariance Matrix Adaptation Evolution Strategy (CMAES) remains comparable in the 2Dim case, where the former gains more recommendations (Fig. 6J; Supplementary Table S1), and the latter demonstrates a lower median in the cost distributions (Fig. 6E; Supplementary Table S1)
To evaluate the quality of the algorithms’ output, we compared their performance on a phase oscillator model with one another as well as with a parameter space exploration on a dense grid
The results of the grid search served as an approximation of the ground truth with respect to the highest possible fit and the location of the corresponding optimal model parameters
Summary
Schaefer’s a tlas[56] with N = 100 cortical regions was employed as a brain parcellation for the calculation of an atlas-based SC The latter served as a basis for the underlying network in the dynamical model and was used to determine the coupling weights and delays between individual network nodes (brain regions or parcels). The model was deployed to simulate the resting-state brain dynamics and eventually generate simulated FC (simFC). This in turn was fitted to the empirical FC (empFC) by adjusting up to three model parameters simultaneously: global coupling and delay in a two-dimensional parameter space (see Cabral et al.57,58) and the noise intensity when a three-dimensional scenario was considered (see Deco et al.[14])
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