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In contrast to functional connectivity approaches, effective connectivity analyses promise extended insight, referring explicitly to the influence that one neuronal system exerts over another, and may be used to better explain integration within a distributed neural system. Models employed in analyzing imaging data to uncover effective connectivity are based on regression models, or structural equation models, and these models may be linear or nonlinear. Dynamic causal modeling (DCM) is a type of effective connectivity analysis that yields directional, pathway information and allows for a quantification of the influence of a given neural region over another.57,58 DCM analysis, introduced in 2003 for fMRI data, is a Bayesian framework for inferring hidden neuronal states from measurements of brain activity; it is a hypothesisdriven approach, requiring an a priori definition of a set of interconnected neural areas that mediate a given function of interest.59 DCMs are generative models of brain responses, which provide estimates of neurobiologically interpretable quantities including strength of synaptic connections among neuronal populations and their context-dependent modulation.60 Causality in DCM is based on control theory, ie, causal interactions among hidden state variables that are expressed by differential equations that describe how the present state of one neuronal population causes dynamics in another via synaptic connection, and how these interactions change under the influence of external perturbations (eg, experimental manipulations) or brain activity. DCM tests hypotheses about neuronal mechanisms, allowing one to specify a generative model of measured brain data, which is a probabilistic mapping from experimentally controlled manipulations to observed data, via neuronal dynamics.
DCM has begun to be applied to imaging genetics. Using a DCM approach, distributed circuits that putatively underlie working memory — prefrontal-parietal and prefrontal-striatal circuits — were identified in healthy, normal subjects, and COMT, DRD2, and AKT1 functional variants were associated with the circuits.61 The goal of the study was to engage a hypothesis-driven strategy to study component dopamine signaling processes, both D2-mediated and non-D2-mediated aspects of dopamine signaling. The investigators developed a working memory task that allowed dissociation of working memory into sub-processes, specifically maintenance of information and manipulation of information. In accordance with the DCM approach, models of prefrontal-subcortical-parietal networks were generated (each model's nodes, connections, and inputs were generated) during working memory maintenance and manipulation events, and the optimal model with the highest group Bayes factor was determined. The best DCMs for maintenance were primarily prefrontal-parietal connections, while for manipulation, the circuit that best fit the data was a prefrontalstriatal network. These results fit remarkably well with data from nonhuman primates about subprocesses in working memory and the principal networks engaged. The cortical network engaged during maintenance is presumed to be a non-D2 dominated network, and indeed, only COMT showed association with activity in this network. In contrast, the cortical-striatal network is expected to be D2-dominated, and all three genes showed effects on this network. This study illustrates the greater fidelity of genetic association based on more realistic models of brain information processing.
In a study using nonlinear DCM, subjects at high familial risk of schizophrenia performed a sentence completion task, and the connection strength of the mediodorsal (MD) thalamus and inferior frontal gyrus (IFG) was investigated, revealing lower connection strength in the at-risk subjects.62 Bayesian Model Selection was used to compare the optimal bilinear and nonlinear models, and Bayesian Model Averaging was used to assess the connection strengths with the gating from the MD thalamus and the IFG, with nonlinear models providing better explanation of the data. In another study, dynamic causal models were applied to fMRI data to investigate how brain connectivity during an associative emotional learning task is affected by different PPPIRIB variants (DARPP32-encoding), in healthy subjects.63 A PPPIRIB variant was associated with increased connectivity between the inferior frontal gyrus (IFG), amygdala and parahippocampal gyrus (PHG), with directionality of the connectivity determined to be from the IFG to the PHG. In addition to emerging effective connectivity analyses by DCM, connectivity is being explored from a more systems-level, hierarchical perspective, using graph theory metrics to describe the structural and functional composition of neural circuits. In graph theory, the correlated activity across multiple, distributed preselected brain regions can be expressed in terms of a graph, having various quantitative parameters, such as nodes, hubs, edges, pathway length, and connectivity strength.64,65 The “hubs” of these networks correspond to the most highly interconnected neural regions, which typically map to the association cortices of the human brain. The strength of each node is defined as its average connectivity with all other nodes, and the graph's size is defined by the number of nodes in the largest connected component; a larger graph size indicates fewer disconnected nodes.66,67
Accumulating evidence suggests that the small-world topological properties of brain functional networks are altered in patients with schizophrenia. In one study, in 31 patients with schizophrenia compared with 31 healthy controls, functional connectivity between 90 cortical and subcortical regions was estimated by partial correlation analysis and thresholded to construct a set of unidirected graphs.68 The healthy subjects demonstrated efficient small-world properties, whereas topological parameters of brain networks — strength and degree of connectivity — were decreased in patients with schizophrenia, especially in the prefrontal, parietal, and temporal lobes, consistent with a hypothesis of dysfunctional integration. In another study, in a sample of 203 patients with schizophrenia, compared with 259 healthy controls, multimodal network organization was noted to be abnormal, as measured by topological and distance metrics of anatomical network organization, abstracted from fMRI data.69 Patients with schizophrenia, compared with controls, demonstrated reduced hierarchy throughout the small-world regime, and increased connection distance in the multimodal cortical network. The loss of frontal hubs and the emergence of nonfrontal hubs was also noted, supporting the hypothesis of schizophrenia as a dysconnectivity syndrome, impacting the efficiency of a frontally dominated hierarchical network of multimodal cortical connections. Though the impact of genetic variation on network topology based on graph analyses has not yet been reported, moderate levels of heritability have been found for brain graph topology measured in a twin study using EEG, suggesting that genetic variation may Impact small-world organization and brain graph metrics.70
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