CNS*2020 Online

Video Conference link https://meet.google.com/ykq-pjkm-yeg

  James Henderson, Peter Robinson, Mukesh Dhamala
The relationships between brain activity and structure are of central importance to understanding how the brain carries out its functions and to interrelating and predicting different kinds of experimental measurements. The aim of this work is to describe the transfer function and its relationships to many existing forms of brain analysis. Then, to describe methods for obtaining the transfer function, with emphasis on spectral factorization using the Wilson algorithm [1,2] applied to correlations of time series measurements. The transfer function of a system contains complete information about its linear properties, responses, and dynamics. This includes relationships to impulse responses, spectra, and correlations. In the case of brain dynamics, it has been shown that the transfer function is closely related to brain connectivity, including time delays, and we note that linear coupling is widely used to model the spatial interactions of locally nonlinear dynamics. It is shown how the brain's linear transfer function provides a means of systematically analyzing brain connectivity and dynamics, providing a robust way of inferring connectivity, and activity measures such as spectra, evoked responses, coherence and causality, all of which are widely used in brain monitoring. Additionally, the eigenfunctions of the transfer function are natural modes of the system dynamics and thus underlie spatial patterns of excitation in the cortex. Thus, the transfer function is a suitable object for describing and analyzing the structure-function relationship in brains. The Wilson spectral factorization algorithm is outlined and used to efficiently obtain linear transfer functions from experimental two-point correlation functions. Criteria for time series measurements are described for the algorithm to accurately reconstruct the transfer function, including comparing the algorithm's theoretical computational complexity with empirical runtimes for systems of similar size to current experiments. The algorithm is applied to a series of examples of increasing complexity and similarity to real brain structure in order to test and verify that it is free of numerical errors and instabilities (and modifying the method where required to ensure this). The results of applying the algorithm to a 1D test case with asymmetry and time delays is shown in (Fig. 1). The method is tested on increasingly realistic structures using neural field theory, introducing time delays, asymmetry, dimensionality, and complex network connectivity to verify the algorithm's suitability for use on experimental data. Acknowledgements This work was supported by the Australian Research Council under Center of Excellence grant CE140100007 and Laureate Fellowship grant FL140100025. References 1\. Dhamala M, Rangarajan G, and Ding M: Estimating Granger causality from Fourier and wavelet transforms of time series data. Phys. Rev. Lett. 2008, 100:018701. 2\. Wilson, GT: The Factorization of Matrical Spectral Densities. SIAM J. Appl. Math. 1972, 23: 420