Modelling and analysis of time-variant directed interrelations between brain regions based on BOLD-signals

doi:10.1016/j.neuroimage.2008.12.065

NeuroImage

Volume 45, Issue 3, 15 April 2009, Pages 722-737

https://doi.org/10.1016/j.neuroimage.2008.12.065 Get rights and content

Abstract

Time-variant Granger Causality Index (tvGCI) was applied to simulated and measured BOLD signals to investigate the reliability of time-variant analysis approaches for the identification of directed interrelations between brain areas on the basis of fMRI data.

Single-shot fMRI data of a single image slice with short repetition times (200 ms, 16000 frames/subject, 64 × 64 voxels) were acquired from 5 healthy subjects during an externally-driven, self-paced finger-tapping paradigm (57–59 single taps for each subject). BOLD signals were derived from the pre-supplementary motor area (preSMA), the supplementary motor area (SMA), and the primary motor cortex (M1).

The simulations were carried out by means of a Dynamic Causal Modelling (DCM) approach. The tvGCI as well as time-variant Partial Directed Coherence (tvPDC) were used to identify the modelled connectivity network (connectivity structure – CS – of the DCM). Different CSs were applied by using dynamic systems (Generalized Dynamic Neural Network — GDNN) and trivariate autoregressive (AR) processes. The influence of the low-pass characteristics of the simulated hemodynamic response (Balloon model) and of the measuring noise was tested. Additionally, our modelling strategy considered “spontaneous” BOLD fluctuations before, during, and after the appearance of the event-related BOLD component. Couplings which were extracted from the simulated signals were statistically evaluated (tvGCI for shuffled data, confidence tubes for tvGCI courses). We demonstrate that connections of our CS models can be correctly identified during the event-related BOLD component and with signal-to-noise-ratios corresponding to those of the measured data. The results based on simulations can be used to examine the reliability of connectivity identification based on BOLD signals by means of time-variant as well as time-invariant connectivity measures and enable a better interpretation of the analysis results using fMRI data.

A readiness-BOLD response was only detected in one subject. However, in two subjects a strong time-variant connection (tvGCI) from preSMA to SMA was observed 3 s before the tapping was executed. This connection was accompanied by a weaker rise of the tvGCI from preSMA to M1. These preceding interrelations were confirmed in the other subjects by the dynamics of tvGCI courses. Based on the results of tvGCI analysis, the time-evolution of an individual connectivity network is shown for each subject.

Introduction

The investigation of directed information transfer (interrelations, connections) between brain regions is one of the most important aims of current functional magnetic resonance imaging (fMRI) analysis. New time-variant methods are required for the identification, quantification, and modelling of the spatiotemporal dynamics of these brain interrelations.

Following studies by K. Friston, B. Horwitz and R. McIntosh, who successfully applied concepts of functional and effective connectivity to PET and fMRI data in the 90ies, a multitude of connectivity measures have been developed in which the mathematical basis depends on the particular measurement or imaging modality. The linear correlation analysis between two time-series (random variables) may be generalized (e.g. “mutual information”) and transferred to the frequency domain (coherence and partial coherence). The “mutual information” of two processes does not contain any directional sense, because it measures only the deviation from the erroneous assumption, that two systems are independent. Mutual information can be given a directional sense by introducing a time lag in one or both of the two processes (“transfer entropy”; Schreiber, 2000). With such an approach, the direction of information transfer and asymmetries of interrelations may be detected. Chavez et al. (2003) and Hinrichs et al. (2006) considered the “transfer entropy” from the perspective of Granger Causality (GC), and applied connectivity analysis to EEG and fMRI data. In this context, the “transfer entropy” represents a kind of non-linear GC, measuring the deviation from an assumed independency of two systems. With linearity assumptions, interrelations in the sense of GC may be investigated on the basis of multivariate autoregressive (AR) models. Thereby, it is either investigated whether certain bilinear terms of the model vanish, or whether the knowledge of the past of one process significantly improves the predictability of the other process (Geweke, 1982). Vanishing bilinear terms in the first approach imply missing interrelations. Basically, the second approach may be applied to all models which provide a prediction error (Leistritz et al., 2006a).

The extraction of directional information is aimed at the analysis of effective connectivity. Based on multivariate AR models, connectivity measures for the directed information transfer may be estimated in a frequency-dependent manner: Partial Directed Coherence (PDC) (Baccala and Sameshima, 2001), and Directed Transfer Function (DTF) (Kaminski et al., 2001). The PDC may be interpreted as linear GC in the frequency domain. The coherence spectrum with its corresponding phase spectrum, the partial coherence, the PDC, and DTF may be estimated using a time-variant AR model (Winterhalder et al., 2005). All these approaches allow a successful analysis of “dynamic connectivity” (Breakspear, 2004). Time-variant estimations of GC for event-related potentials (Hesse et al., 2003, Weiss et al., 2008) and fMRI data (Leistritz et al., 2006b) have been introduced (Goebel et al., 2003), and in Roebroeck et al. (2005) the authors used a time-invariant estimation of GC in fMRI data analysis.

The major aim of our present methodological study was to investigate the reliability and with it the practicability of time-variant analysis approaches for the identification of directed interrelations between brain areas on the basis of fMRI data (one single image slice, 200 ms repetition time). This technique provides BOLD signals from which the time evolution of directed interrelations can be studied within the time range of a single-trial (inter-trial interval is about 25 s) with high time-resolution. Our time-variant Granger Causality Index (tvGCI) approach (Hesse et al., 2003) is based on a time-variant multivariate autoregressive model whose parameters are adapted by a recursive least square algorithm (Möller et al., 2001). In a preliminary study this strategy was successfully evaluated (Leistritz et al., 2006b).

In a preceding step, the reliability of the tvGCI approach was evaluated by means of simulated BOLD signals which were generated by a specific Dynamic Causal Modelling (DCM) approach. DCM approaches are used to make inferences about effective connectivity (Penny et al., 2004). By means of our DCM approach a nonlinear neuronal connectivity model with directed interrelations can be constructed which is able to show nonlinearities of neuronal mass activity. The influence of the extrinsic input to the coupling-model was reduced and unified to increase the influence of different interrelations to the simulated event-related BOLD signal output.

The new strategy for identifying directed interrelations between activated brain areas on the basis of BOLD signals opens new perspectives for fMRI analysis. However, our methodological study also includes a critical analysis of the method-inherent drawbacks based on the analysis of DCM simulations. The disadvantages of the single shot fMRI acquisition as well as of the analysis and modelling methods are discussed. The use of faster fMRI acquisition techniques (e.g. 50–150 ms repetition time for one slice), the optimization of the position fitting of the slice(s), and the gain of the signal-to-noise-ratio (SNR) by using MRI at higher field strengths (i.e., 3 T), are crucial objectives to improve and optimize our methodological strategy. The computer programme descriptions (MATLAB®) are available for anyone who is interested in the use of these algorithms for other applications and to further develop and discuss our methodological approaches (www.imsid.uniklinikum-jena.de).

Section snippets

fMRI data acquisition and subjects

Single slice fMRI data of five healthy subjects (mean age: 22.3 ± 1.7) were acquired by using single shot gradient echo EPI with an short repetition time on a 1.5 T MRI system (TR = 200 ms, TE = 40 ms, flip angle = 36°, matrix = 64 × 64, voxel size 3.1 × 3.1 × 10 mm, number of repetitive slice acquisitions = 16000). The task (stimulus) consisted of an externally-driven, self-paced finger tapping. The volunteers were requested to perform a single finger-tap after the occurrence of a green light (maximal 5 s

Objective

It is known that connections can be correctly identified on the basis of a connectivity structure represented by a multivariate AR model (Baccala and Sameshima, 2001, Winterhalder et al., 2005). The AR modelling simulates spontaneous BOLD fluctuations without an event-related component. Noise was subsequently added and investigated to determine its influence. The variance of the measuring noise was adjusted to SNRs from 0.5 to 4.

Results

The simulated connections could be correctly identified in the

Discussion

The reliability of CS identification was studied on the basis of simulated BOLD signals by using time-variant Granger Causality approaches. As described in the simulation section, the correct identification of the connectivity can be achieved under specific preconditions. The combination of the low-pass characteristics (Balloon model) with measuring noise limits the capability of CS identification. On the basis of our results using simulations we would recommend an application of both tvGCI and

Acknowledgments

This interdisciplinary study was supported by the DFG (W.H., LE 2025/1-3), the Marie Curie Programme (M.U. was supported by the MC-Intra-European exchange programme, project 041452, NADIBA) and the BMBF (Bernstein-Group for Computational Neuroscience Jena; 01GQ0703) and the Interdisciplinary Centre for Clinical Research Jena (IZKF grant for D.H.).

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¹: These authors contribute equally to the study.

²: Fax: +49 03641 933200.

³: All authors from the Friedrich Schiller University Jena are members of the Bernstein Group for Computational Neuroscience Jena.

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Modelling and analysis of time-variant directed interrelations between brain regions based on BOLD-signals

Abstract

Introduction

Section snippets

fMRI data acquisition and subjects

Objective

Results

Discussion

Acknowledgments

NeuroImage

NeuroImage

NeuroImage

J. Neurosci. Methods

NeuroImage

NeuroImage

Hum. Mov. Sci.

NeuroImage

NeuroImage

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Magn. Reson. Imaging

J. Neurosci. Methods

NeuroImage

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J. Neurosci. Methods

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