## Dynamic causal modelling of induced responses (2008)

Venue: | NeuroImage |

Citations: | 13 - 4 self |

### BibTeX

@ARTICLE{Chen08dynamiccausal,

author = {C. C. Chen and S. J. Kiebel and K. J. Friston},

title = {Dynamic causal modelling of induced responses},

journal = {NeuroImage},

year = {2008},

pages = {1293--1312}

}

### OpenURL

### Abstract

This paper describes a dynamic causal model (DCM) for induced or spectral responses as measured with the electroencephalogram (EEG) or the magnetoencephalogram (MEG). We model the time-varying power, over a range of frequencies, as the response of a distributed system of coupled electromagnetic sources to a spectral perturbation. The model parameters encode the frequency response to exogenous input and coupling among sources and different frequencies. The Bayesian inversion of this model, given data enables inferences about the parameters of a particular model and allows us to compare different models, or hypotheses. One key aspect of the model is that it differentiates between linear and non-linear coupling; which correspond to within and betweenfrequency coupling respectively. To establish the face validity of our approach, we generate synthetic data and test the identifiability of various parameters to ensure they can be estimated accurately, under different levels of noise. We then apply our model to EEG data from a faceperception experiment, to ask whether there is evidence for non-linear coupling between early visual cortex and fusiform areas.

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Citation Context ...one has to show that the statistical dependencies are significant. This entails, in its most general formulation, measuring the mutual information among two or more time-series (Roulston, 1999; Quian =-=Quiroga et al., 2002-=-). There are several approaches to assessing mutual information, which divide broadly into linear and non-linear. The most common approach uses linear systems theory and measures the correlation or co... |

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Citation Context ...We will exploit this below (see also Friston (2000)). The same non-linear crossfrequency coupling is seen in phase-synchrony; two principal forms of cross-frequency phase interactions are recognized (=-=Palva et al., 2005-=-): n:m phase-synchrony, which indicates amplitudeindependent phase locking of n cycles of one oscillation to m cycles of another (Tass et al., 1998), and nested oscillations, which reflect the locking... |

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Citation Context ...inearities in neuronal activity are an important aspect of processing in large-scale neuronal networks and have led to many different proposals of how to best characterise them given some data (e.g., =-=David et al., 2004-=-). As we have illustrated above, linear coupling is mediated by first-order transfer functions that transfer energy in the source to the target, while non-linear mechanisms express themselves as cross... |

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Citation Context ...inguish between changes in linear and non-linear coupling in the brain. This work represents a further extension of dynamic causal modelling to cover spectral responses as measured by the EEG or MEG (=-=David et al., 2006a-=-; Kiebel et al., 2006; Moran et al., 2007). There are many approaches to detecting and estimating neuronal coupling using frequency-based analyses of electrophysiological recordings. These can be divi... |

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Citation Context ...es in linear and non-linear coupling in the brain. This work represents a further extension of dynamic causal modelling to cover spectral responses as measured by the EEG or MEG (David et al., 2006a; =-=Kiebel et al., 2006-=-; Moran et al., 2007). There are many approaches to detecting and estimating neuronal coupling using frequency-based analyses of electrophysiological recordings. These can be divided into descriptive ... |

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Citation Context ...etwork, based on prior knowledge or beliefs about the functional anatomy of the paradigm. For source locations, one can employ conventional source-reconstruction methods; for example, source imaging (=-=Mattout et al., 2006-=-) or equivalent current dipole (ECD) models (Kiebel et al., 2006, 2008). In terms of the network architecture, one needs to specify whether directed connections exist and whether they are linear or no... |

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Citation Context ...nctional connectivity one has to show that the statistical dependencies are significant. This entails, in its most general formulation, measuring the mutual information among two or more time-series (=-=Roulston, 1999-=-; Quian Quiroga et al., 2002). There are several approaches to assessing mutual information, which divide broadly into linear and non-linear. The most common approach uses linear systems theory and me... |

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Citation Context ...easures of linear dependencies can be generalised to multivariate time-series to furnish interesting formulations in terms of directed transfer functions and Granger causality (Brovelli et al., 2004; =-=Bernasconi and Konig, 1999-=-). Non-linear methods In terms of non-linear approaches; the most general approach relies upon the notion of generalised synchrony (Rulkov et al., 1995; Schiff et al., 1996), which posits a mapping be... |

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Citation Context ...text-sensitive (non-linear or bilinear) changes in that coupling. Overview This paper comprises four sections. In the first, we reprise, briefly, a generalised convolution model of neuronal coupling (=-=Friston, 2000-=-) to demonstrate the link between cross-frequency coupling and non-linear mechanisms. We illustrate these phenomena using a neural-mass model that is the basis of biophysical DCMs for ERPs (David et a... |

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Citation Context ...EG sources (Pikovsky et al., 2001). Time– frequency analysis of phase-synchronisation is popular in current research on cortical networks (David et al., 2003; Engel et al., 2001; Varela et al., 2001; =-=Lee et al., 2003-=-). Establishing phasesynchronisation proceeds in two steps; estimation of instantaneous phase and the quantification of the phase locking. This quantification uses the distribution of phase difference... |

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Citation Context ...e framed using, at most, eight sources. Note that the generalised inverse of the lead-field in Eq. (16) is one of many inversion schemes that one can use to project data from channel to source space (=-=Darvas et al., 2004-=-; Michel et al., 2004; Friston et al., 2008; Kiebel et al., 2008). The generalised inverse is an appropriate projector if one knows a priori where the sources are located. In other words, when there i... |

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Citation Context ... (MEG). Induced oscillations are a hallmark of many neuronal systems (Gray et al., 1989; Tiitinen et al., 1993; Tass et al., 1998; Singer, 1999; Tallon-Baudry and Bertrand, 1999; Varela et al., 2001; =-=Singh et al., 2002-=-; TallonBaudry et al., 1997; Pantev, 1995). They are ubiquitous in both the sensory and motor systems and may play an important role in the ⁎ Corresponding author. Wellcome Trust Centre for Neuroimagi... |

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Citation Context ...id; i.e., exp(jωt) 2 = exp(j2ωt) (see Friston (2001)). Biological evidence speaks to the prevalence of non-linear interactions among cortical areas during cognitive tasks (e.g., Bullock et al., 1997; =-=Schack et al., 2002-=-). We have shown that second-order features of the data (i.e., the spectrum) can be modelled by DCM for induced responses in aC.C. Chen et al. / NeuroImage 41 (2008) 1293–1312 1309 Fig. 11. Upper pan... |

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Citation Context ....sciencedirect.com). functional integration of distributed brain systems. Induced responses represent a stimulus- or task-related increase in frequency-specific power recorded electrophysiologically (=-=Kilner et al., 2005-=-). It had been shown that the modulation of frequencyspecific dynamics, reflecting functional integration within or between neuronal sources, can be used to characterise neuronal coupling and address ... |

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Citation Context ...linear coupling in the brain. This work represents a further extension of dynamic causal modelling to cover spectral responses as measured by the EEG or MEG (David et al., 2006a; Kiebel et al., 2006; =-=Moran et al., 2007-=-). There are many approaches to detecting and estimating neuronal coupling using frequency-based analyses of electrophysiological recordings. These can be divided into descriptive and 1053-8119/$ - se... |

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Citation Context ...e oscillation to m cycles of another (Tass et al., 1998), and nested oscillations, which reflect the locking of the amplitude fluctuations of faster oscillations to the phase of a slower oscillation (=-=Vanhatalo et al., 2004-=-). These forms of phase-synchronisation can be used to disclose nonlinear coupling, in which a slower frequency comes to entrain or be entrained by a faster frequency. In summary, there are several wa... |