## Comparing Dynamic Causal Models (2004)

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Venue: | NEUROIMAGE |

Citations: | 80 - 33 self |

### BibTeX

@ARTICLE{Penny04comparingdynamic,

author = {W. D. Penny and K. E. Stephan and A. Mechelli and K. J. Friston},

title = {Comparing Dynamic Causal Models},

journal = {NEUROIMAGE},

year = {2004},

volume = {22},

pages = {1157--1172}

}

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### Abstract

This article describes the use of Bayes factors for comparing Dynamic Causal Models (DCMs). DCMs are used to make inferences about effective connectivity from functional Magnetic Resonance Imaging (fMRI) data. These inferences, however, are contingent upon assumptions about model structure, that is, the connectivity pattern between the regions included in the model. Given the current lack of detailed knowledge on anatomical connectivity in the human brain, there are often considerable degrees of freedom when defining the connectional structure of DCMs. In addition, many plausible scientific hypotheses may exist about which connections are changed by experimental manipulation, and a formal procedure for directly comparing these competing hypotheses is highly desirable. In this article, we show how Bayes factors can be used to guide choices about model structure, both with regard to the intrinsic connectivity pattern and the contextual modulation of individual connections. The combined use of Bayes factors and DCM thus allows one to evaluate competing scientific theories about the architecture of large-scale neural networks and the neuronal interactions that mediate perception and cognition.

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Citation Context ...an model precisely the same mechanism, at a coarser level, by allowing the V1–V5 forward connection to be modulated by attention (Fig. 1C). This approach has been applied to primate single cell data (=-=Reynolds et al., 1999-=-). The behavior of this model then corresponds to the observed neurophysiology: the magnitude of stimulus-dependent responses in V5 (i.e., the V5 responses to V1 inputs) is augmented whenever motion i... |

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Citation Context .... Keywords: Dynamic causal models; fMRI; Bayes factors Introduction Human brain mapping has been used extensively to provide functional maps showing which regions are specialized for which functions (=-=Frackowiak et al., 1997-=-). A classic example is the study by Zeki et al. (1991) who identified V4 and V5 as being specialized for the processing of color and motion, respectively. More recently, these analyses have been augm... |

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Citation Context ...ess described in the following section. 5 (9)s2.2 Hemodynamics In DCM the hemodynamics are described by the Balloon model first described by Buxton et al. [10] and developed further by Friston et al. =-=[19, 16]-=-. DCM uses a separate Balloon model for each region. For the ith region, neuronal activity zi causes an increase in vasodilatory signal si that is subject to auto-regulatory feedback. Inflow fi respon... |

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Citation Context ...ables like cognitive set or attention. The resulting neurodynamics of the modeled system then give rise to fMRI time series via local hemodynamics which are characterised by an extended Balloon model =-=[16, 10]-=-. A DCM is fitted to data by tuning the neurodynamic and hemodynamic parameters so as to minimise the discrepancy between predicted and observed fMRI time series. Importantly, however, the parameters ... |

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Citation Context ...emispheres. Recent studies have indicated, however, that asymmetries in the intra-hemispheric functional couplings may be an equally important determinant of hemispheric specialization (Friston 2003) =-=[30, 43]-=-. This section demonstrates the ability of DCM to correctly identify asymmetries of modulatory intra-hemispheric connectivity despite the presence of reciprocal inter-hemispheric connections between h... |

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Citation Context ...tell apart. 4.3 Attention to Visual Motion In previous work we have established that attention modulates connectivity in a distributed system of cortical regions mediating visual motion processing 18s=-=[8, 17]-=-. These findings were based on data acquired using the following experimental paradigm. Subjects viewed a computer screen which displayed either a fixation point, stationary dots or dots moving radial... |

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Citation Context ...ayes. We are also aware of a number of improvements to the AIC criterion [7]. Model comparison of effectivity connectivity models has previously been explored in the context of SEM by Bullmore et al. =-=[9]-=-. This work has established the usefulness of such approaches for comparing nested structural equation models which are most suitable for the analysis of PET data. In our work, we compare DCM models w... |

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Citation Context ...se processes may, at first glance, seem at odds with traditional cognitive theories that relate bottom-up processes to so-called ”forward” connections and top-down processes to ”backward” conn=-=ections [45]-=-. This paragraph therefore aims at clarifying this relationship, using some simple examples from the visual system, 7sand emphasizes the need for precise terminology when distinguishing between the le... |

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Citation Context ...about the intrinsic connectivity of DCMs are therefore usually based on inferring connections from supposedly equivalent areas in the Macaque brain for which the anatomical connectivity is well known =-=[42]-=-. This procedure has many pitfalls, however, including a multitude of incompatible parcellation schemes and frequent uncertainties about the homology and functional equivalence of areas in the brains ... |

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Citation Context ...of several alternative models is optimal given the data. Such decisions are of great practical relevance because we still lack detailed knowledge about the anatomical connectivity of the human brain (=-=Passingham et al., 2002-=-). Decisions about the intrinsic connectivity of DCMs are therefore usually based on inferring connections from supposedly equivalent areas in the Macaque brain for which the anatomical connectivity i... |

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Citation Context ...quivalence of areas in the brains of man and monkey. This problem may be less severe in sensory systems, but is of particular importance for areas involved in higher cognitive processes like language =-=[1]-=-. Thus, there are often considerable degrees of freedom when defining the connectional structure of DCMs of the human brain. We show how Bayes factors can be used to guide the modeller in making such ... |

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Citation Context ...nections [5, 24], such that (ii) the responsiveness of these V5 neurons to simultaneous inputs from V1 is enhanced, possibly through interactions between dendritic and somatic postsynaptic potentials =-=[41]-=- (see Fig. 3D). Although this level of detail cannot currently be modeled in DCMs, we can describe precisely the same mechanism at a coarser level by allowing the V1 V5 forward connection 8sto be modu... |

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Citation Context ...lved in the processing of various stimulus attributes, but is particularly sensitive to motion information, i.e. V5 shows increased responses to inputs from V1 whenever the applied stimulus is moving =-=[4]-=- (Fig. 3B). In DCM, this bottom-up process would be modeled by modulating the V1 V5 forward connection by a vector that indicates when the stimuli were moving (MOT, Fig. 3A). Importantly, however, not... |

13 |
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Citation Context ...here Λ is an L × L diagonal matrix with Λii denoting error variance in the ith region. 2.4 Modelling bottom-up and top-down effects Many applications of DCM, both in this article and in previous wo=-=rk [18, 31], refer -=-to ”bottom-up” and ”top-down” processes in the visual system, and we envisage that a large number of future applications of DCM will address the same issue. Some of the possible DCM architectu... |

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Citation Context ... is mediated neurophysiologically by feedback connections from higher areas (represented by ”X” in Fig. 3D) that (i) influence those neurons in V5 which receive inputs from V1 via forward connecti=-=ons [5, 24]-=-, such that (ii) the responsiveness of these V5 neurons to simultaneous inputs from V1 is enhanced, possibly through interactions between dendritic and somatic postsynaptic potentials [41] (see Fig. 3... |

8 |
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Citation Context ...emispheres. Recent studies have indicated, however, that asymmetries in the intra-hemispheric functional couplings may be an equally important determinant of hemispheric specialization (Friston 2003) =-=[30, 43]-=-. This section demonstrates the ability of DCM to correctly identify asymmetries of modulatory intra-hemispheric connectivity despite the presence of reciprocal inter-hemispheric connections between h... |

6 |
The anatomical basis of functional localization
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(Show Context)
Citation Context ... of several alternative models is optimal given the data. Such decisions are of great practical relevance because we still lack detailed knowledge about the anatomical connectivity of the human brain =-=[34]-=-. Decisions about the intrinsic connectivity of DCMs are therefore usually based on inferring connections from supposedly equivalent areas in the Macaque brain for which the anatomical connectivity is... |

3 |
A neural system for human visual working
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(Show Context)
Citation Context ...ocesses may, at first glance, seem at odds with traditional cognitive theories that relate bottom-up processes to so-called ‘‘forward’’ connections and top-down processes to ‘‘backward’’ connections (=-=Ungerleider et al., 1998-=-). Here we try to clarify this relationship using some simple examples from the visual system and emphasize the need for precise terminology when distinguishing between the levels of anatomical connec... |

2 |
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Citation Context ...s in 12sclassical statistics (eg. p < 0.05), so one has developed around the use of Bayes factors. Raftery [36], for example, presents an interpretation of Bayes factors as shown in Table 1. Jefferys =-=[23]-=- presents a similar grading for the comparison of scientific theories. These partitionings are somewhat arbitrary but do provide rough descriptive statements. Bayes factors can also be directly interp... |