Comments and Controversies The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution Alard Roebroeck ���, Elia Formisano, Rainer Goebel Department of Cognitive Neuroscience, Faculty of Psychology and Neuroscience, Maastricht University, Postbus 616, 6200MD Maastricht, The Netherlands a b s t r a c t a r t i c l e i n f o Article history: Received 8 June 2009 Revised 24 August 2009 Accepted 17 September 2009 Available online xxxx Functional magnetic resonance imaging (fMRI) is increasingly used to study functional connectivity in large- scale brain networks that support cognitive and perceptual processes. We face serious conceptual, statistical and data analysis challenges when addressing the combinatorial explosion of possible interactions within high-dimensional fMRI data. Moreover, we need to know, and account for, the physiological mechanisms underlying our signals. We argue here that (i) model selection procedures for connectivity should include consideration of more than just a few brain structures, (ii) temporal precedence ��� and causality concepts based on it ��� are essential in dynamic models of connectivity and (iii) undoing the effect of hemodynamics on fMRI data (by deconvolution) can be an important tool. However, it is crucially dependent upon assumptions that need to be verified. �� 2009 Elsevier Inc. All rights reserved. Introduction Understanding how interactions between brain structures (���func- tional and effective connectivity���) support the performance of specific cognitive tasks or perceptual processes is a prominent goal in cognitive neuroscience. Neuroimaging methods, such as electroen- cephalography (EEG), magnetoencephalography (MEG) and func- tional magnetic resonance imaging (fMRI), are employed more and more to address questions of functional connectivity, inter-region coupling and networked computation that go beyond the ���where��� and ���when��� of task-related activity (McIntosh, 2004 Valdes-Sosa et al., 2005a Salmelin and Kujala, 2006 Horwitz and Smith, 2008). A network perspective onto the parallel and distributed processing in the brain ��� even on the large scale accessible by neuroimaging methods ��� is a promising approach to enlarge our understanding of perceptual, cognitive and motor functions. However, we face serious conceptual, statistical and data analysis challenges when addressing the combinatorial explosion of possible interactions within high- dimensional neuroimaging data sets. Moreover, we need to know, and take account of, the actual physiological mechanisms underlying our signals (e.g., Logothetis, 2008). Functional magnetic resonance imaging (fMRI) in particular is increasingly used not only to localize structures involved in cognitive and perceptual processes but also to study the connectivity in large- scale brain networks that support these functions. Two fMRI-based connectivity methods have gained increasing popularity in recent years: Granger causality analysis (GCA Goebel et al., 2003 Valdes- Sosa, 2004 Roebroeck et al., 2005) and dynamic causal modeling (DCM Friston et al., 2003). Both techniques aim to estimate directed influences between brain structures making use of the temporal dynamics in the fMRI signal. Despite the common goal, there are also differences between the two methods. Whereas GCA explicitly models temporal precedence and uses the concept of Granger causality (or G-causality), DCM employs a biophysically motivated generative model of neuronal population dynamics and hemody- namic processes. A recent article (David et al., 2008) has compared the two techniques in a rat model of absence epilepsy. Simultaneous fMRI and EEG and separate intracranial EEG (iEEG) were measured in six rats during epileptic episodes in which spike-and-wave discharges (SWDs) spread through the brain. These authors and a related commentary (Friston, 2009) concluded that (i) the concepts of temporal precedence and G-causality should not be used in fMRI connectivity analysis and (ii) explicit biophysically motivated models, such as DCM, model true causality in fMRI data, because they account for the hemodynamic processes that intervene between neural activity and fMRI signals. We show here that these conclusions are not unequivocally supported by the actual results of David et al. (2008) and that they give only a partial view onto the important considerations in modeling brain connectivity. More specifically, we argue that the results of David et al., along with general considerations in system identification theory and neuroscience, lead to three crucial points about brain connectivity modeling: (i) model selection procedures for connectivity should include consideration of more than just a few brain structures, NeuroImage xxx (2009) xxx���xxx YNIMG-06585 No. of pages: 7 4C: 1053-8119/$ ��� see front matter �� 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2009.09.036 ��� Corresponding author. Fax: +31 43 3884125. E-mail address: a.roebroeck@maastrichtuniversity.nl (A. Roebroeck). Contents lists available at ScienceDirect NeuroImage journal homepage: www.elsevier.com/locate/ynimg Please cite this article as: Roebroeck, A., et al., The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution, NeuroImage (2009), doi:10.1016/j.neuroimage.2009.09.036

(ii) temporal precedence ��� and causality concepts based on it ��� are essential in dynamic models of brain connectivity and (iii) undoing the effect of hemodynamics on fMRI data (by deconvolution) can be an important tool. However, it is crucially dependent upon assumptions that need to be verified. Structural model selection for brain connectivity Brain connectivity modeling of neuroimaging data entails the estimation of multivariate mathematical models and inference on parameters that quantify the directed influence between brain structures. The estimation mathematical models from time series data generally has two important aspects: model selection and model identification (Ljung, 1999). In the model selection stage a class of models is chosen by the researcher that is deemed suitable for the problem at hand. In the model identification stage the parameters in the chosen model class are estimated from the observed data record. In practice, model selection and identification often occur in a somewhat interactive fashion where, for instance, model selection can be informed by the fit of different models to the data achieved in an identification step. The important point is that model selection involves a mixture of choices and assumptions on the part of the researcher and the information gained from the data record itself. We can usefully partition brain connectivity models into two parts, each necessitating choices and assumptions: the structural model and the dynamical model (see Fig. 1). The structural model contains (i) a selection of the regions of interest (ROIs) in the brain that are assumed to be of importance in the cognitive process or task under investigation, (ii) the possible interactions between those structures and (iii) the possible effects of exogenous inputs onto the network. The exogenous inputs may be under control of the experimenter and often have the form of a simple indicator function that can represent, for instance, the presence or absence of a visual stimulus. The dynamical model consists of parameterized equations that relate the signals of the selected structures and exogenous inputs to each other. The functional form of these equations can embed assumptions on signal dynamics, temporal precedence or physiological processes from which signals originate. Connectivity modeling involves the estimation of (and inference on) the parameters in the dynamical model from actual measurements and possibly exogenous inputs. The number of parameters to be estimated (i.e., the total model complexity) is directly dependent on the complexity of the structural model (i.e., how many ROIs are included) and the complexity of the dynamical model. The bias/variance trade-off in model fitting dictates that overfitting a finite data set with too many parameters will lead to poor generalization of model fit to other data sets. Therefore, clear justifiable choices must be made both in the structural model and in the dynamical model to keep the number of estimated parameters in a suitable range. Applications of DCM invariably use very simple structural models (typically employing three to six ROIs) in combination with a complex parameter-rich dynamical model that we discuss below. The clear danger with overly simple structural models is that of spurious influence: an erroneous influence found between two selected regions that in reality is due to interactions with additional regions which have been ignored. Prototypical examples of spurious influence, of relevance in brain connectivity, are those between unconnected structures A and B that receive common input from, or are intervened by, an unmodeled region C. Early applications of G-causality to fMRI data were aimed at counteracting the problems with overly restrictive structural models by employing more permissive structural models in combination with a simple dynamical model (Goebel et al., 2003 Valdes-Sosa, 2004 Roebroeck et al., 2005). We developed the technique of Granger causality mapping (GCM1) to explore all regions in the brain that interact with a single selected reference region using GCA of fMRI time series. By employing a simple bivariate model containing the reference region and, in turn, every other voxel in the brain, the sources and targets of influence for the reference region can be mapped. We showed that such an ���exploratory��� mapping approach can form an important tool in structural model selection (Roebroeck et al., 2005). Although a bivariate model does not discern direct from indirect influences, the mapping approach locates potential sources of common input and areas that could act as intervening network nodes. Other applications of GCA to fMRI data have considered full multivariate models on large sets of selected brain regions that can model indirect influences within those sets. Valdes-Sosa et al. (2004, 2005b) applied these models to parcellations of the entire cortex in Fig. 1. A partitioning of brain connectivity models. Models to estimate connectivity from data (e.g. fMRI) can partitioned into a structural (or anatomical) model and a dynamical (or mathematical) model (Buchel and Friston, 2000). The structural model contains a selection of the structures in the brain that are assumed to be of importance in the cognitive process or task under investigation. Specifically, it specifies which regions of interest (ROIs) in the spatially rich high-dimensional fMRI data set will be considered for further analysis, as illustrated by the selection of the red boxes y1���y4. The structural model can also define the possible interactions between the ROIs in the form of one or more directed graph models that might be compared in a later model selection step. Finally the structural model also defines where exogenous inputs (that may be under control of the experimenter) can exert effects onto the network. The dynamical model embeds the structural model assumptions into parameterized equations that relate the selected measurements and inputs to each other. Connectivity modeling involves the estimation of the parameters in the dynamical model from actual measurements yj and, possibly, inputs uk. 1 It is unfortunate and confusing that our original definition of the acronym GCM as Granger causality mapping (Goebel et al., 2003 Roebroeck et al., 2005) is used in the discussed comment (Friston, 2009) as Granger causality modeling, since ���mapping��� expresses a fundamental and distinguishing characteristic of the way we apply Granger causality without employing a restrictive structural model. 2 A. Roebroeck et al. / NeuroImage xxx (2009) xxx���xxx Please cite this article as: Roebroeck, A., et al., The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution, NeuroImage (2009), doi:10.1016/j.neuroimage.2009.09.036