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WIREs Cogn Sci
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Analyzing effective connectivity with functional magnetic resonance imaging

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Abstract Functional neuroimaging techniques are used widely in cognitive neuroscience to investigate aspects of functional specialization and functional integration in the human brain. Functional integration can be characterized in two ways, functional connectivity and effective connectivity. While functional connectivity describes statistical dependencies between data, effective connectivity rests on a mechanistic model of the causal effects that generated the data. This review addresses the conceptual and methodological basis of established techniques for characterizing effective connectivity using functional magnetic resonance imaging (fMRI) data. In particular, we focus on dynamic causal modeling (DCM) of fMRI data and emphasize the importance of model selection procedures and nonlinear mechanisms for context‐dependent changes in connection strengths. Copyright © 2010 John Wiley & Sons, Ltd. This article is categorized under: Neuroscience > Cognition

Application of nonlinear dynamic causal model to single‐subject functional magnetic resonance imaging data from an attention to motion paradigm.17 (a) Maximum a posteriori estimates of all parameters. PPC, posterior parietal cortex. (b) Posterior density of the estimate for the nonlinear modulation parameter for the V1 → V5 connection. Given the mean and variance of this posterior density, we have 99.1% confidence that the true parameter value is larger than zero or, in other words, that there is an increase in gain of V5 responses to V1 inputs that is mediated by PPC activity. (Reproduced with permission from Ref 30. Copyright 2008).

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An example of the neuronal and hemodynamic parameters that can be accounted for by nonlinear dynamic causal models (DCMs). The right panel shows synthetic neuronal and BOLD time series that were generated using the nonlinear DCM shown on the left. In this model, neuronal population activity x1 (blue) is driven by irregularly spaced random events (delta‐functions). Activity in x2 (green) is driven through a connection from x1; critically, the strength of this connection depends on activity in a third population, x3 (red), which receives a connection from x2 but also receives a direct input from a box‐car input. The effect of nonlinear modulation can be seen easily: responses of x2 to x1 become negligible when x3 activity is low. Conversely, x2 responds vigorously to x1 inputs when the x1 → x2 connection is gated by x3 activity. Strengths of connections are indicated by symbols (–: negative; +: weakly positive; + + +: strongly positive). (Reproduced with permission from Ref 30. Copyright 2008).

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This figure shows an example of a single‐subject dynamic causal model that was used to study asymmetries in interhemispheric connections during a letter decision task. LG, lingual gyrus; FG, fusiform gyrus; LD, letter decisions; LD|VF, letter decisions conditional on the visual field of stimulus presentation. (a) The values denote the maximum a posteriori (MAP) estimates of the parameters ( ± square root of the posterior variances; units: 1/s = Hz). For clarity, only the parameters of interest, i.e., the modulatory parameters of inter‐ and intra‐hemispheric connections, are shown. (b) Asymmetry of callosal connections with regard to contextual modulation. The plots show the probability (98.7%) that the modulation of the right LG → left LG connection is stronger than the modulation of the left LG → right LG connection. (Adapted with permission from Ref 36. Copyright 2005).

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Schematic summary of the conceptual basis of dynamic causal model. The dynamics in a system of interacting neuronal populations (left lower panel), which are not directly observable by functional magnetic resonance imaging, is modeled using a bilinear state equation (right upper panel). Integrating the state equation gives predicted neural dynamics (z) that enter a model of the hemodynamic response (λ) to give predicted BOLD responses (y) (right lower panel). The parameters at both neural and hemodynamic levels are adjusted such that the differences between predicted and measured BOLD series are minimized. Critically, the neural dynamics are determined by experimental manipulations. These enter the model in the form of external inputs (left upper panel). Driving inputs (u1; e.g., sensory stimuli) elicit local responses directly which are propagated through the system according to the intrinsic connections. The strengths of these connections can be changed by modulatory inputs (u2; e.g., changes in cognitive set, attention, or learning). In this figure, the structure of the system and the scaling of the inputs are arbitrary. Note that state variables are denoted by z in this figure (as opposed to the main text where state variables are referred to as x). (Reproduced with permission from Ref 36. Copyright 2005).

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Fit of the nonlinear model in Figure 9 to the binocular rivalry data. Dotted lines represent the observed data, solid lines the responses predicted by the nonlinear dynamic causal model. The upper panel shows the entire time series. The lower panel zooms in on the first half of the data (dotted box). One can see that the functional coupling between fusiform face area (FFA) (blue) and parahippocampal place area (PPA) (green) depends on the activity level in middle frontal gyrus (MFG) (red): when MFG activity is high during binocular rivalry blocks (BR; short black arrows), FFA and PPA are strongly coupled and their responses are difficult to disambiguate. In contrast, when MFG activity is low, during non‐rivalry blocks (nBR; long gray arrows), FFA and PPA are less coupled, and their activities evolve more independently. (Reproduced with permission from Ref 30. Copyright 2008).

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Application of nonlinear dynamic causal model (DCM) to single‐subject functional magnetic resonance imaging data from a binocular rivalry paradigm. (a) The structure of the nonlinear DCM fitted to the binocular rivalry data, along with the maximum a posteriori estimates of all parameters. The intrinsic connections between fusiform face area (FFA) and parahippocampal place area (PPA) are negative in both directions; i.e., FFA and PPA mutually inhibited each other. This may be seen as an expression, at the neurophysiological level, of the perceptual competition between the face and house stimuli. This competitive interaction between FFA and PPA is modulated nonlinearly by the activity in middle frontal gyrus (MFG), which showed higher activity during rivalry versus non‐rivalry conditions. (b) Our confidence about the presence of this nonlinear modulation is very high (99.9%), for both connections. (Reproduced with permission from Ref 30. Copyright 2008).

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Fit of the nonlinear model to the attention to motion data in Figure 5. Dotted lines represent the observed data, solid lines the responses predicted by the nonlinear dynamic causal model. The increase in the gain of V5 responses to V1 inputs during attention is clearly visible. (Reproduced with permission from Ref 30. Copyright 2008).

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Schematic summary of the neural state equation and the hemodynamic forward model in dynamic causal model; Experimentally controlled input functions u evoke neural responses x, modeled by a bilinear differential state equation, which trigger a hemodynamic cascade, modeled by four state equations with five parameters. These hemodynamic parameters comprise the rate constant of the vasodilatory signal decay (κ), the rate constant for auto‐regulatory feedback by blood flow (γ), transit time (τ), Grubb's vessel stiffness exponent (α), and capillary resting net oxygen extraction (ρ). The so‐called Balloon model consists of the two equations describing the dynamics of blood volume (v) and deoxyhemoglobin content (q) (light gray boxes). Integrating the state equations for a given set of inputs and parameters produces predicted time series for v and q which enter a BOLD signal equation λ (dark gray box) to give a predicted BOLD response. (Reproduced with permission from Ref 33. Copyright 2007).

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