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A dynamical systems approach for estimating phase interactions between rhythms of different frequencies from experimental data.

ABSTRACT: Synchronization of neural oscillations as a mechanism of brain function is attracting increasing attention. Neural oscillation is a rhythmic neural activity that can be easily observed by noninvasive electroencephalography (EEG). Neural oscillations show the same frequency and cross-frequency synchronization for various cognitive and perceptual functions. However, it is unclear how this neural synchronization is achieved by a dynamical system. If neural oscillations are weakly coupled oscillators, the dynamics of neural synchronization can be described theoretically using a phase oscillator model. We propose an estimation method to identify the phase oscillator model from real data of cross-frequency synchronized activities. The proposed method can estimate the coupling function governing the properties of synchronization. Furthermore, we examine the reliability of the proposed method using time-series data obtained from numerical simulation and an electronic circuit experiment, and show that our method can estimate the coupling function correctly. Finally, we estimate the coupling function between EEG oscillation and the speech sound envelope, and discuss the validity of these results.

SUBMITTER: Onojima T

PROVIDER: S-EPMC5770039 | biostudies-literature | 2018 Jan

REPOSITORIES: biostudies-literature

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A dynamical systems approach for estimating phase interactions between rhythms of different frequencies from experimental data.

Onojima Takayuki T Goto Takahiro T Mizuhara Hiroaki H Aoyagi Toshio T

PLoS computational biology 20180116 1

Synchronization of neural oscillations as a mechanism of brain function is attracting increasing attention. Neural oscillation is a rhythmic neural activity that can be easily observed by noninvasive electroencephalography (EEG). Neural oscillations show the same frequency and cross-frequency synchronization for various cognitive and perceptual functions. However, it is unclear how this neural synchronization is achieved by a dynamical system. If neural oscillations are weakly coupled oscillator ...[more]

PMID: 29337999

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Project description:Analysis of dynamical interactions between distributed brain areas is of fundamental importance for understanding cognitive information processing. However, estimating dynamic causal interactions between brain regions using functional magnetic resonance imaging (fMRI) poses several unique challenges. For one, fMRI measures Blood Oxygenation Level Dependent (BOLD) signals, rather than the underlying latent neuronal activity. Second, regional variations in the hemodynamic response function (HRF) can significantly influence estimation of causal interactions between them. Third, causal interactions between brain regions can change with experimental context over time. To overcome these problems, we developed a novel state-space Multivariate Dynamical Systems (MDS) model to estimate intrinsic and experimentally-induced modulatory causal interactions between multiple brain regions. A probabilistic graphical framework is then used to estimate the parameters of MDS as applied to fMRI data. We show that MDS accurately takes into account regional variations in the HRF and estimates dynamic causal interactions at the level of latent signals. We develop and compare two estimation procedures using maximum likelihood estimation (MLE) and variational Bayesian (VB) approaches for inferring model parameters. Using extensive computer simulations, we demonstrate that, compared to Granger causal analysis (GCA), MDS exhibits superior performance for a wide range of signal to noise ratios (SNRs), sample length and network size. Our simulations also suggest that GCA fails to uncover causal interactions when there is a conflict between the direction of intrinsic and modulatory influences. Furthermore, we show that MDS estimation using VB methods is more robust and performs significantly better at low SNRs and shorter time series than MDS with MLE. Our study suggests that VB estimation of MDS provides a robust method for estimating and interpreting causal network interactions in fMRI data.

Project description:State-space multivariate dynamical systems (MDS) (Ryali et al. 2011) and other causal estimation models are being increasingly used to identify directed functional interactions between brain regions. However, the validity and accuracy of such methods are poorly understood. Performance evaluation based on computer simulations of small artificial causal networks can address this problem to some extent, but they often involve simplifying assumptions that reduce biological validity of the resulting data. Here, we use a novel approach taking advantage of recently developed optogenetic fMRI (ofMRI) techniques to selectively stimulate brain regions while simultaneously recording high-resolution whole-brain fMRI data. ofMRI allows for a more direct investigation of causal influences from the stimulated site to brain regions activated downstream and is therefore ideal for evaluating causal estimation methods in vivo. We used ofMRI to investigate whether MDS models for fMRI can accurately estimate causal functional interactions between brain regions. Two cohorts of ofMRI data were acquired, one at Stanford University and the University of California Los Angeles (Cohort 1) and the other at the University of North Carolina Chapel Hill (Cohort 2). In each cohort, optical stimulation was delivered to the right primary motor cortex (M1). General linear model analysis revealed prominent downstream thalamic activation in Cohort 1, and caudate-putamen (CPu) activation in Cohort 2. MDS accurately estimated causal interactions from M1 to thalamus and from M1 to CPu in Cohort 1 and Cohort 2, respectively. As predicted, no causal influences were found in the reverse direction. Additional control analyses demonstrated the specificity of causal interactions between stimulated and target sites. Our findings suggest that MDS state-space models can accurately and reliably estimate causal interactions in ofMRI data and further validate their use for estimating causal interactions in fMRI. More generally, our study demonstrates that the combined use of optogenetics and fMRI provides a powerful new tool for evaluating computational methods designed to estimate causal interactions between distributed brain regions.

Project description:MotivationWhile biological systems operated from a common genome can be conserved in various ways, they can also manifest highly diverse dynamics and functions. This is because the same set of genes can interact differentially across specific molecular contexts. For example, differential gene interactions give rise to various stages of morphogenesis during cerebellar development. However, after over a decade of efforts toward reverse engineering biological networks from high-throughput omic data, gene networks of most organisms remain sketchy. This hindrance has motivated us to develop comparative modeling to highlight conserved and differential gene interactions across experimental conditions, without reconstructing complete gene networks first.ResultsWe established a comparative dynamical system modeling (CDSM) approach to identify conserved and differential interactions across molecular contexts. In CDSM, interactions are represented by ordinary differential equations and compared across conditions through statistical heterogeneity and homogeneity tests. CDSM demonstrated a consistent superiority over differential correlation and reconstruct-then-compare in simulation studies. We exploited CDSM to elucidate gene interactions important for cellular processes poorly understood during mouse cerebellar development. We generated hypotheses on 66 differential genetic interactions involved in expansion of the external granule layer. These interactions are implicated in cell cycle, differentiation, apoptosis and morphogenesis. Additional 1639 differential interactions among gene clusters were also identified when we compared gene interactions during the presence of Rhombic lip versus the presence of distinct internal granule layer. Moreover, compared with differential correlation and reconstruct-then-compare, CDSM makes fewer assumptions on data and thus is applicable to a wider range of biological assays.AvailabilitySource code in C++ and R is available for non-commercial organizations upon request from the corresponding author. The cerebellum gene expression dataset used in this article is available upon request from the Goldowitz lab (dang@cmmt.ubc.ca, http://grits.dglab.org/).Contactjoemsong@cs.nmsu.eduSupplementary informationSupplementary data are available at Bioinformatics online.

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A dynamical systems approach for estimating phase interactions between rhythms of different frequencies from experimental data.

Publications

A dynamical systems approach for estimating phase interactions between rhythms of different frequencies from experimental data.

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