Validation of dynamical whole-brain models in high-dimensional parameter spaces
Creators: name: Wischnewski, Kevin
name: Eickhoff, Simon
name: Popovych, Oleksandr
Publisher: name: Forschungzentrum Jülich
Year: 2023

description: The 29th Annual Meeting of the Organization for Human Brain Mapping (OHBM2023), Montréal, HHU Düsseldorf, Canada, 22 Jul 2023 - 26 Jul 2023
description: INTRODUCTIONSimulating the resting-state brain dynamics via mathematical whole-brain models allows for describing a subject’s brain activity by a set of interpretable model parameters. In this setting, increased efforts are currently devoted to personalized simulations, which require a rising number of optimally selected model parameters [1]. However, a dense grid search is computationally unfeasible and constrains the studies of high-dimensional models. In our work, we apply mathematical optimization algorithms to explore low- and high-dimensional parameter spaces at moderate computational costs. We analyze the results in terms of fit to empirical data and required computation time as well as the impact of the number of optimized model parameters on the differentiability between males and females based on simulated data.METHODSWe used neuroimaging data of 272 healthy subjects (128 males) of the Human Connectome Project [2]. Working with an ensemble of coupled phase oscillators [3] built upon individual empirical structural connectivity (SC), we aimed at replicating the empirical functional connectivity (FC) of every subject. We considered Schaefer’s functional brain atlas (100 regions, [4]) and the anatomical Harvard-Oxford parcellation (96 regions, [5]) as well as 2 optimization schemes based on Covariance Matrix Adaptation Evolution Strategy (CMAES, [6]) and Bayesian Optimization (BO, [7]). Both algorithms represent global stochastic search methods and were applied to detect the optimal model parameters which maximize the correlation between empirical FC (eFC) and simulated FC (sFC). The optimized parameters included the global coupling and delay (2D parameter space), the noise intensity (3D parameter space), and the oscillation frequencies of individual brain regions (99D or 103D parameter space). By optimizing between 2 and 103 free parameters simultaneously, we generated whole-brain models of an improved fitting to empirical data of individual subjects and thus enhanced model personalization, which we compared across subjects and brain atlases. Particular focus was set on the optimal model parameters and sFC as well as on their reliability and subject-specificity.RESULTSWhen increasing the number of optimized model parameters, we observed an enhancement of the quality of the model validation, i.e. the similarity between eFC and sFC (goodness-of-fit, GoF), for both atlases and optimization algorithms. While the improvement from 2 to 3 variables ranges around 12%, the transition to the high-dimensional cases is sharp and can double the GoF. Also the computational demands increased, but remain within a tractable extent: For CMAES, the requirements were doubled, and for BO around 12 times more resources were needed. The reliability of the optimal parameters drops in higher dimensions, and several constellations of parameter values appear to generate comparably high GoF values. However, we also observed high correlations (positive and negative) between individual solutions. This hints at the presence of a manifold in the model parameter space, where the optimal values may be located. Additionally, we observed higher GoF values for males than for females, with the differentiation between these subject groups being enhanced for the model optimization in high-dimensional parameter spaces.CONCLUSIONSOur results provide an insight into the model validation in high-dimensional parameter spaces, which has been made possible by mathematical optimization schemes. In particular, we have shown that more optimized parameters lead to a much higher GoF that can be obtained for several configurations of model parameters. The fact that phenotypical differences were more pronounced in the data derived from high-dimensional simulations implies a great potential for model-based, personalized studies with application to the investigation of inter-individual variability.REFERENCES[1] Hashemi, M., Vattikonda, A. N., Sip, V., Diaz-Pier, S., Peyser, A., Wang, H., Guye, M., Bartolomei, F., Woodman, M. M., &amp; Jirsa, V. K. (2021). On the influence of prior information evaluated by fully Bayesian criteria in a personalized whole-brain model of epilepsy spread. PLoS computational biology, 17(7), e1009129. https://doi.org/10.1371/journal.pcbi.1009129[2] Van Essen, D. C., Smith, S. M., Barch, D. M., Behrens, T. E., Yacoub, E., Ugurbil, K., &amp; WU-Minn HCP Consortium (2013). The WU-Minn Human Connectome Project: an overview. NeuroImage, 80, 62–79. https://doi.org/10.1016/j.neuroimage.2013.05.041[3] Cabral, J., Hugues, E., Sporns, O., &amp; Deco, G. (2011). Role of local network oscillations in resting-state functional connectivity. NeuroImage, 57(1), 130–139. https://doi.org/10.1016/j.neuroimage.2011.04.010[4] Schaefer, A., Kong, R., Gordon, E. M., Laumann, T. O., Zuo, X. N., Holmes, A. J., Eickhoff, S. B., &amp; Yeo, B. T. T. (2018). Local-Global Parcellation of the Human Cerebral Cortex from Intrinsic Functional Connectivity MRI. Cerebral cortex (New York, N.Y. : 1991), 28(9), 3095–3114. https://doi.org/10.1093/cercor/bhx179[5] Desikan, R. S., Ségonne, F., Fischl, B., Quinn, B. T., Dickerson, B. C., Blacker, D., Buckner, R. L., Dale, A. M., Maguire, R. P., Hyman, B. T., Albert, M. S., &amp; Killiany, R. J. (2006). An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. NeuroImage, 31(3), 968–980. https://doi.org/10.1016/j.neuroimage.2006.01.021[6] Hansen, N. (2006). The CMA Evolution Strategy: A Comparing Review. In: Lozano, J.A., Larrañaga, P., Inza, I., Bengoetxea, E. (eds) Towards a New Evolutionary Computation. Studies in Fuzziness and Soft Computing, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32494-1_4[7] Martinez-Cantin, R. (2014). BayesOpt: A Bayesian Optimization Library for Nonlinear Optimization, Experimental Design and Bandits. Journal of Machine Learning Research, 15, 3735-3739.[8] Rosenthal, R., &amp; Rosnow, R. L. (1991). Essentials of behavioral research: Methods and data analysis (2nd ed.). New York: McGraw Hill.