Identification and validation of effective connectivity networks in functional magnetic resonance imaging using switching linear dynamic systems

Oral Contraceptives and Cigarette Smoking: A Review of the Literature and Future Directions

INTRODUCTION

Evidence continues to mount indicating that endogenous sex hormones (eg, progesterone and estradiol) play a significant role in smoking-related outcomes. Although approximately one out of four premenopausal smokers use oral contraceptives (OCs), which significantly alter progesterone and estradiol levels, relatively little is known about how OCs may influence smoking-related outcomes. Thus, the goal of this review article is to describe the state of the literature and offer recommendations for future directions.

METHODS

In March 2017, we searched seven databases, with a restriction to articles written in English, using the following keywords: nicotine, smoker(s), smoking, tobacco, cigarettes, abstinence, withdrawal, and craving(s). We did not restrict on the publication date, type, or study design.

RESULTS

A total of 13 studies were identified. Three studies indicated faster nicotine metabolism in OC users compared to nonusers. Five of six laboratory studies that examined physiological stress response noted heightened response in OC users compared to nonusers. Three studies examined cessation-related symptomatology (eg, craving) with mixed results. One cross-sectional study observed greater odds of current smoking among OC users, and no studies have explored the relationship between OC use and cessation outcomes.

CONCLUSIONS

Relatively few studies were identified on the role of OCs in smoking-related outcomes. Future work could explore the relationship between OC use and mood, stress, weight gain, and brain function/connectivity, as well as cessation outcomes. Understanding the role of OC use in these areas may lead to the development of novel smoking cessation interventions for premenopausal women.

IMPLICATIONS

This is the first review of the relationship between oral contraceptives (OCs) and smoking-related outcomes. The existing literature suggests that the use of OCs is related to increased nicotine metabolism and physiological stress response. However, the relationship between OC use and smoking-related symptoms (eg, craving) is mixed. Further, no published data were available on OC use and smoking cessation outcomes. Therefore, we recommend additional research be conducted to characterize the relationship between OC use and smoking cessation outcomes, perhaps as a function of the effect of OC use on mood, stress, weight gain, and brain function/connectivity.

Distinct modes of functional connectivity induced by movie-watching

A fundamental question in systems neuroscience is how endogenous neuronal activity self-organizes during particular brain states. Recent neuroimaging studies have demonstrated systematic relationships between resting-state and task-induced functional connectivity (FC). In particular, continuous task studies, such as movie watching, speak to alterations in coupling among cortical regions and enhanced fluctuations in FC compared to the resting-state. This suggests that FC may reflect systematic and large-scale reorganization of functionally integrated responses while subjects are watching movies. In this study, we characterized fluctuations in FC during resting-state and movie-watching conditions. We found that the FC patterns induced systematically by movie-watching can be explained with a single principal component. These condition-specific FC fluctuations overlapped with inter-subject synchronization patterns in occipital and temporal brain regions. However, unlike inter-subject synchronization, condition-specific FC patterns were characterized by increased correlations within frontal brain regions and reduced correlations between frontal-parietal brain regions. We investigated these condition-specific functional variations as a shorter time scale, using time-resolved FC. The time-resolved FC showed condition-specificity over time; notably when subjects watched both the same and different movies. To explain self-organisation of global FC through the alterations in local dynamics, we used a large-scale computational model. We found that condition-specific reorganization of FC could be explained by local changes that engendered changes in FC among higher-order association regions, mainly in frontal and parietal cortices.

From correlation to causation: Estimating effective connectivity from zero-lag covariances of brain signals

Knowing brain connectivity is of great importance both in basic research and for clinical applications. We are proposing a method to infer directed connectivity from zero-lag covariances of neuronal activity recorded at multiple sites. This allows us to identify causal relations that are reflected in neuronal population activity. To derive our strategy, we assume a generic linear model of interacting continuous variables, the components of which represent the activity of local neuronal populations. The suggested method for inferring connectivity from recorded signals exploits the fact that the covariance matrix derived from the observed activity contains information about the existence, the direction and the sign of connections. Assuming a sparsely coupled network, we disambiguate the underlying causal structure via L¹-minimization, which is known to prefer sparse solutions. In general, this method is suited to infer effective connectivity from resting state data of various types. We show that our method is applicable over a broad range of structural parameters regarding network size and connection probability of the network. We also explored parameters affecting its activity dynamics, like the eigenvalue spectrum. Also, based on the simulation of suitable Ornstein-Uhlenbeck processes to model BOLD dynamics, we show that with our method it is possible to estimate directed connectivity from zero-lag covariances derived from such signals. In this study, we consider measurement noise and unobserved nodes as additional confounding factors. Furthermore, we investigate the amount of data required for a reliable estimate. Additionally, we apply the proposed method on full-brain resting-state fast fMRI datasets. The resulting network exhibits a tendency for close-by areas being connected as well as inter-hemispheric connections between corresponding areas. In addition, we found that a surprisingly large fraction of more than one third of all identified connections were of inhibitory nature.

Changes in brain connectivity are considered an important biomarker for certain brain diseases. This directly raises the question of accessibility of connectivity from measured brain signals. Here we show how directed effective connectivity can be inferred from continuous brain signals, like fMRI. The main idea is to extract the connectivity from the inverse zero-lag covariance matrix of the measured signals. This is done using L¹-minimization via gradient descent algorithm on the manifold of unitary matrices. This ensures that the resulting network always fits the same covariance structure as the measured data, assuming a canonical linear model. Applying the estimation method on noise-free covariance matrices shows that the method works nicely on sparsely coupled networks with more than 40 nodes, provided network interaction is strong enough. Applying the estimation on simulated Ornstein-Uhlenbeck processes supposed to model BOLD signals demonstrates robustness against observation noise and unobserved nodes. In general, the proposed method can be applied to time-resolved covariance matrices in the frequency domain (cross-spectral densities), leading to frequency-resolved networks. We are able to demonstrate that our method leads to reliable results, if the sampled signals are long enough.

Bayesian switching factor analysis for estimating time-varying functional connectivity in fMRI

There is growing interest in understanding the dynamical properties of functional interactions between distributed brain regions. However, robust estimation of temporal dynamics from functional magnetic resonance imaging (fMRI) data remains challenging due to limitations in extant multivariate methods for modeling time-varying functional interactions between multiple brain areas. Here, we develop a Bayesian generative model for fMRI time-series within the framework of hidden Markov models (HMMs). The model is a dynamic variant of the static factor analysis model (Ghahramani and Beal, 2000). We refer to this model as Bayesian switching factor analysis (BSFA) as it integrates factor analysis into a generative HMM in a unified Bayesian framework. In BSFA, brain dynamic functional networks are represented by latent states which are learnt from the data. Crucially, BSFA is a generative model which estimates the temporal evolution of brain states and transition probabilities between states as a function of time. An attractive feature of BSFA is the automatic determination of the number of latent states via Bayesian model selection arising from penalization of excessively complex models. Key features of BSFA are validated using extensive simulations on carefully designed synthetic data. We further validate BSFA using fingerprint analysis of multisession resting-state fMRI data from the Human Connectome Project (HCP). Our results show that modeling temporal dependencies in the generative model of BSFA results in improved fingerprinting of individual participants. Finally, we apply BSFA to elucidate the dynamic functional organization of the salience, central-executive, and default mode networks-three core neurocognitive systems with central role in cognitive and affective information processing (Menon, 2011). Across two HCP sessions, we demonstrate a high level of dynamic interactions between these networks and determine that the salience network has the highest temporal flexibility among the three networks. Our proposed methods provide a novel and powerful generative model for investigating dynamic brain connectivity.

Noise concerns and post-processing procedures in cerebral blood flow (CBF) and cerebral blood volume (CBV) functional magnetic resonance imaging

Functional neuroimaging with blood oxygenation level-dependent (BOLD) contrast has emerged as the most popular method for evaluating qualitative changes in brain function in humans. At typical human field strengths (1.5-3.0T), BOLD contrast provides a measure of changes in transverse water relaxation rates in and around capillary and venous blood, and as such provides only a surrogate marker of brain function that depends on dynamic changes in hemodynamics (e.g., cerebral blood flow and volume) and metabolism (e.g., oxygen extraction fraction and the cerebral metabolic rate of oxygen consumption). Alternative functional neuroimaging methods that are specifically sensitive to these constituents of the BOLD signal are being developed and applied in a growing number of clinical and neuroscience applications of quantitative cerebral physiology. These methods require additional considerations for interpreting and quantifying their contrast responsibly. Here, an overview of two popular methods, arterial spin labeling and vascular space occupancy, is presented specifically in the context of functional neuroimaging. Appropriate post-processing and experimental acquisition strategies are summarized with the motivation of reducing sensitivity to noise and unintended signal sources and improving quantitative accuracy of cerebral hemodynamics.

A Unified Estimation Framework for State-Related Changes in Effective Brain Connectivity

OBJECTIVE

This paper addresses the critical problem of estimating time-evolving effective brain connectivity. Current approaches based on sliding window analysis or time-varying coefficient models do not simultaneously capture both slow and abrupt changes in causal interactions between different brain regions.

METHODS

To overcome these limitations, we develop a unified framework based on a switching vector autoregressive (SVAR) model. Here, the dynamic connectivity regimes are uniquely characterized by distinct vector autoregressive (VAR) processes and allowed to switch between quasi-stationary brain states. The state evolution and the associated directed dependencies are defined by a Markov process and the SVAR parameters. We develop a three-stage estimation algorithm for the SVAR model: 1) feature extraction using time-varying VAR (TV-VAR) coefficients, 2) preliminary regime identification via clustering of the TV-VAR coefficients, 3) refined regime segmentation by Kalman smoothing and parameter estimation via expectation-maximization algorithm under a state-space formulation, using initial estimates from the previous two stages.

RESULTS

The proposed framework is adaptive to state-related changes and gives reliable estimates of effective connectivity. Simulation results show that our method provides accurate regime change-point detection and connectivity estimates. In real applications to brain signals, the approach was able to capture directed connectivity state changes in functional magnetic resonance imaging data linked with changes in stimulus conditions, and in epileptic electroencephalograms, differentiating ictal from nonictal periods.

CONCLUSION

The proposed framework accurately identifies state-dependent changes in brain network and provides estimates of connectivity strength and directionality.

SIGNIFICANCE

The proposed approach is useful in neuroscience studies that investigate the dynamics of underlying brain states.

Multivariate dynamical systems-based estimation of causal brain interactions in fMRI: Group-level validation using benchmark data, neurophysiological models and human connectome project data

BACKGROUND

Causal estimation methods are increasingly being used to investigate functional brain networks in fMRI, but there are continuing concerns about the validity of these methods.

NEW METHOD

Multivariate dynamical systems (MDS) is a state-space method for estimating dynamic causal interactions in fMRI data. Here we validate MDS using benchmark simulations as well as simulations from a more realistic stochastic neurophysiological model. Finally, we applied MDS to investigate dynamic casual interactions in a fronto-cingulate-parietal control network using human connectome project (HCP) data acquired during performance of a working memory task. Crucially, since the ground truth in experimental data is unknown, we conducted novel stability analysis to determine robust causal interactions within this network.

RESULTS

MDS accurately recovered dynamic causal interactions with an area under receiver operating characteristic (AUC) above 0.7 for benchmark datasets and AUC above 0.9 for datasets generated using the neurophysiological model. In experimental fMRI data, bootstrap procedures revealed a stable pattern of causal influences from the anterior insula to other nodes of the fronto-cingulate-parietal network.

COMPARISON WITH EXISTING METHODS

MDS is effective in estimating dynamic causal interactions in both the benchmark and neurophysiological model based datasets in terms of AUC, sensitivity and false positive rates.

CONCLUSIONS

Our findings demonstrate that MDS can accurately estimate causal interactions in fMRI data. Neurophysiological models and stability analysis provide a general framework for validating computational methods designed to estimate causal interactions in fMRI. The right anterior insula functions as a causal hub during working memory.

Combining optogenetic stimulation and fMRI to validate a multivariate dynamical systems model for estimating causal brain interactions

State-space multivariate dynamical systems (MDS) (Ryali et al. 2011) and other causal estimation models are being increasingly used to identify directed functional interactions between brain regions. However, the validity and accuracy of such methods are poorly understood. Performance evaluation based on computer simulations of small artificial causal networks can address this problem to some extent, but they often involve simplifying assumptions that reduce biological validity of the resulting data. Here, we use a novel approach taking advantage of recently developed optogenetic fMRI (ofMRI) techniques to selectively stimulate brain regions while simultaneously recording high-resolution whole-brain fMRI data. ofMRI allows for a more direct investigation of causal influences from the stimulated site to brain regions activated downstream and is therefore ideal for evaluating causal estimation methods in vivo. We used ofMRI to investigate whether MDS models for fMRI can accurately estimate causal functional interactions between brain regions. Two cohorts of ofMRI data were acquired, one at Stanford University and the University of California Los Angeles (Cohort 1) and the other at the University of North Carolina Chapel Hill (Cohort 2). In each cohort, optical stimulation was delivered to the right primary motor cortex (M1). General linear model analysis revealed prominent downstream thalamic activation in Cohort 1, and caudate-putamen (CPu) activation in Cohort 2. MDS accurately estimated causal interactions from M1 to thalamus and from M1 to CPu in Cohort 1 and Cohort 2, respectively. As predicted, no causal influences were found in the reverse direction. Additional control analyses demonstrated the specificity of causal interactions between stimulated and target sites. Our findings suggest that MDS state-space models can accurately and reliably estimate causal interactions in ofMRI data and further validate their use for estimating causal interactions in fMRI. More generally, our study demonstrates that the combined use of optogenetics and fMRI provides a powerful new tool for evaluating computational methods designed to estimate causal interactions between distributed brain regions.

Neural correlates of gratitude

Gratitude is an important aspect of human sociality, and is valued by religions and moral philosophies. It has been established that gratitude leads to benefits for both mental health and interpersonal relationships. It is thus important to elucidate the neurobiological correlates of gratitude, which are only now beginning to be investigated. To this end, we conducted an experiment during which we induced gratitude in participants while they underwent functional magnetic resonance imaging. We hypothesized that gratitude ratings would correlate with activity in brain regions associated with moral cognition, value judgment and theory of mind. The stimuli used to elicit gratitude were drawn from stories of survivors of the Holocaust, as many survivors report being sheltered by strangers or receiving lifesaving food and clothing, and having strong feelings of gratitude for such gifts. The participants were asked to place themselves in the context of the Holocaust and imagine what their own experience would feel like if they received such gifts. For each gift, they rated how grateful they felt. The results revealed that ratings of gratitude correlated with brain activity in the anterior cingulate cortex and medial prefrontal cortex, in support of our hypotheses. The results provide a window into the brain circuitry for moral cognition and positive emotion that accompanies the experience of benefitting from the goodwill of others.

Functional Magnetic Resonance Imaging Methods

Since its inception in 1992, Functional Magnetic Resonance Imaging (fMRI) has become an indispensible tool for studying cognition in both the healthy and dysfunctional brain. FMRI monitors changes in the oxygenation of brain tissue resulting from altered metabolism consequent to a task-based evoked neural response or from spontaneous fluctuations in neural activity in the absence of conscious mentation (the "resting state"). Task-based studies have revealed neural correlates of a large number of important cognitive processes, while fMRI studies performed in the resting state have demonstrated brain-wide networks that result from brain regions with synchronized, apparently spontaneous activity. In this article, we review the methods used to acquire and analyze fMRI signals.

Oppositional COMT Val158Met effects on resting state functional connectivity in adolescents and adults

Prefrontal dopamine levels are relatively increased in adolescence compared to adulthood. Genetic variation of COMT (COMT Val158Met) results in lower enzymatic activity and higher dopamine availability in Met carriers. Given the dramatic changes of synaptic dopamine during adolescence, it has been suggested that effects of COMT Val158Met genotypes might have oppositional effects in adolescents and adults. The present study aims to identify such oppositional COMT Val158Met effects in adolescents and adults in prefrontal brain networks at rest. Resting state functional connectivity data were collected from cross-sectional and multicenter study sites involving 106 healthy young adults (mean age 24 ± 2.6 years), gender matched to 106 randomly chosen 14-year-olds. We selected the anterior medial prefrontal cortex (amPFC) as seed due to its important role as nexus of the executive control and default mode network. We observed a significant age-dependent reversal of COMT Val158Met effects on resting state functional connectivity between amPFC and ventrolateral as well as dorsolateral prefrontal cortex, and parahippocampal gyrus. Val homozygous adults exhibited increased and adolescents decreased connectivity compared to Met homozygotes for all reported regions. Network analyses underscored the importance of the parahippocampal gyrus as mediator of observed effects. Results of this study demonstrate that adolescent and adult resting state networks are dose-dependently and diametrically affected by COMT genotypes following a hypothetical model of dopamine function that follows an inverted U-shaped curve. This study might provide cues for the understanding of disease onset or dopaminergic treatment mechanisms in major neuropsychiatric disorders such as schizophrenia and attention deficit hyperactivity disorder.

Adolescent risk-taking and resting state functional connectivity

The existing literature on the role of emotion regulation circuits (amygdala-prefrontal cortex) in the adolescent brain yields mixed results, particularly on the role of these regions in the context of reward sensitivity and risk-taking behavior sensitivity and risk-taking behavior. Here, we examined functional connectivity in the resting state in 18 risk-taking (RT) adolescents compared with 18 non-risk-taking (NRT) adolescents as defined by the Youth Risk Behavior Surveillance Survey. Separate seed-based correlations with bilateral amygdala and bilateral nucleus accumbens used as the seed were performed to determine functional connectivity using functional magnetic resonance imaging (fMRI). The results showed greater connectivity between the amygdala (seed region) and the right middle frontal gyrus, left cingulate gyrus, left precuneus and right inferior parietal lobule in RT adolescents than in NRT adolescents. Likewise, there was greater connectivity between the nucleus accumbens (seed region) and the right middle frontal gyrus in RT adolescents compared with NRT adolescents. These findings suggest that risk-taking behavior in adolescents is associated with hyperconnectivity during the resting state in networks associated with emotion regulation, reward sensitivity, executive control, and the default mode.

Variational Bayesian causal connectivity analysis for fMRI

The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience. We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data. The method uses a vector autoregressive model for the latent variables describing neuronal activity in combination with a linear observation model based on a convolution with a hemodynamic response function. Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm. The computational efficiency of the method enables us to apply it to large scale problems with high sampling rates and several hundred regions of interest. We use a comprehensive empirical evaluation with synthetic and real fMRI data to evaluate the performance of our method under various conditions.

Interpreting the effects of altered brain anatomical connectivity on fMRI functional connectivity: a role for computational neural modeling

Recently, there have been a large number of studies using resting state fMRI to characterize abnormal brain connectivity in patients with a variety of neurological, psychiatric, and developmental disorders. However, interpreting what the differences in resting state fMRI functional connectivity (rsfMRI-FC) actually reflect in terms of the underlying neural pathology has proved to be elusive because of the complexity of brain anatomical connectivity. The same is the case for task-based fMRI studies. In the last few years, several groups have used large-scale neural modeling to help provide some insight into the relationship between brain anatomical connectivity and the corresponding patterns of fMRI-FC. In this paper we review several efforts at using large-scale neural modeling to investigate the relationship between structural connectivity and functional/effective connectivity to determine how alterations in structural connectivity are manifested in altered patterns of functional/effective connectivity. Because the alterations made in the anatomical connectivity between specific brain regions in the model are known in detail, one can use the results of these simulations to determine the corresponding alterations in rsfMRI-FC. Many of these simulation studies found that structural connectivity changes do not necessarily result in matching changes in functional/effective connectivity in the areas of structural modification. Often, it was observed that increases in functional/effective connectivity in the altered brain did not necessarily correspond to increases in the strength of the anatomical connection weights. Note that increases in rsfMRI-FC in patients have been interpreted in some cases as resulting from neural plasticity. These results suggest that this interpretation can be mistaken. The relevance of these simulation findings to the use of functional/effective fMRI connectivity as biomarkers for brain disorders is also discussed.

Identifying effective connectivity parameters in simulated fMRI: a direct comparison of switching linear dynamic system, stochastic dynamic causal, and multivariate autoregressive models

The number and variety of connectivity estimation methods is likely to continue to grow over the coming decade. Comparisons between methods are necessary to prune this growth to only the most accurate and robust methods. However, the nature of connectivity is elusive with different methods potentially attempting to identify different aspects of connectivity. Commonalities of connectivity definitions across methods upon which base direct comparisons can be difficult to derive. Here, we explicitly define "effective connectivity" using a common set of observation and state equations that are appropriate for three connectivity methods: dynamic causal modeling (DCM), multivariate autoregressive modeling (MAR), and switching linear dynamic systems for fMRI (sLDSf). In addition while deriving this set, we show how many other popular functional and effective connectivity methods are actually simplifications of these equations. We discuss implications of these connections for the practice of using one method to simulate data for another method. After mathematically connecting the three effective connectivity methods, simulated fMRI data with varying numbers of regions and task conditions is generated from the common equation. This simulated data explicitly contains the type of the connectivity that the three models were intended to identify. Each method is applied to the simulated data sets and the accuracy of parameter identification is analyzed. All methods perform above chance levels at identifying correct connectivity parameters. The sLDSf method was superior in parameter estimation accuracy to both DCM and MAR for all types of comparisons.

Hippocampal-prefrontal engagement and dynamic causal interactions in the maturation of children's fact retrieval

Children's gains in problem-solving skills during the elementary school years are characterized by shifts in the mix of problem-solving approaches, with inefficient procedural strategies being gradually replaced with direct retrieval of domain-relevant facts. We used a well-established procedure for strategy assessment during arithmetic problem solving to investigate the neural basis of this critical transition. We indexed behavioral strategy use by focusing on the retrieval frequency and examined changes in brain activity and connectivity associated with retrieval fluency during arithmetic problem solving in second- and third-grade (7- to 9-year-old) children. Children with higher retrieval fluency showed elevated signal in the right hippocampus, parahippocampal gyrus (PHG), lingual gyrus (LG), fusiform gyrus (FG), left ventrolateral PFC (VLPFC), bilateral dorsolateral PFC (DLPFC), and posterior angular gyrus. Critically, these effects were not confounded by individual differences in problem-solving speed or accuracy. Psychophysiological interaction analysis revealed significant effective connectivity of the right hippocampus with bilateral VLPFC and DLPFC during arithmetic problem solving. Dynamic causal modeling analysis revealed strong bidirectional interactions between the hippocampus and the left VLPFC and DLPFC. Furthermore, causal influences from the left VLPFC to the hippocampus served as the main top-down component, whereas causal influences from the hippocampus to the left DLPFC served as the main bottom-up component of this retrieval network. Our study highlights the contribution of hippocampal-prefrontal circuits to the early development of retrieval fluency in arithmetic problem solving and provides a novel framework for studying dynamic developmental processes that accompany children's development of problem-solving skills.

Effective Connectivity Modeling for fMRI: Six Issues and Possible Solutions Using Linear Dynamic Systems

Analysis of directionally specific or causal interactions between regions in functional magnetic resonance imaging (fMRI) data has proliferated. Here we identify six issues with existing effective connectivity methods that need to be addressed. The issues are discussed within the framework of linear dynamic systems for fMRI (LDSf). The first concerns the use of deterministic models to identify inter-regional effective connectivity. We show that deterministic dynamics are incapable of identifying the trial-to-trial variability typically investigated as the marker of connectivity while stochastic models can capture this variability. The second concerns the simplistic (constant) connectivity modeled by most methods. Connectivity parameters of the LDSf model can vary at the same timescale as the input data. Further, extending LDSf to mixtures of multiple models provides more robust connectivity variation. The third concerns the correct identification of the network itself including the number and anatomical origin of the network nodes. Augmentation of the LDSf state space can identify additional nodes of a network. The fourth concerns the locus of the signal used as a "node" in a network. A novel extension LDSf incorporating sparse canonical correlations can select most relevant voxels from an anatomically defined region based on connectivity. The fifth concerns connection interpretation. Individual parameter differences have received most attention. We present alternative network descriptors of connectivity changes which consider the whole network. The sixth concerns the temporal resolution of fMRI data relative to the timescale of the inter-regional interactions in the brain. LDSf includes an "instantaneous" connection term to capture connectivity occurring at timescales faster than the data resolution. The LDS framework can also be extended to statistically combine fMRI and EEG data. The LDSf framework is a promising foundation for effective connectivity analysis.

The future of FMRI connectivity

"FMRI connectivity" encompasses many areas of research, including resting-state networks, biophysical modelling of task-FMRI data and bottom-up simulation of multiple individual neurons interacting with each other. In this brief paper I discuss several outstanding areas that I believe will see exciting developments in the next few years, in particular concentrating on how I think the currently separate approaches will increasingly need to take advantage of each others' respective complementarities.

A short history of causal modeling of fMRI data

Twenty years ago, the discovery of the blood oxygen level dependent (BOLD) contrast and invention of functional magnetic resonance imaging (MRI) not only allowed for enhanced analyses of regional brain activity, but also laid the foundation for novel approaches to studying effective connectivity, which is essential for mechanistically interpretable accounts of neuronal systems. Dynamic causal modeling (DCM) and Granger causality (G-causality) modeling have since become the most frequently used techniques for inferring effective connectivity from fMRI data. In this paper, we provide a short historical overview of these approaches, describing milestones of their development from our subjective perspectives.

Using large-scale neural models to interpret connectivity measures of cortico-cortical dynamics at millisecond temporal resolution

Over the last two decades numerous functional imaging studies have shown that higher order cognitive functions are crucially dependent on the formation of distributed, large-scale neuronal assemblies (neurocognitive networks), often for very short durations. This has fueled the development of a vast number of functional connectivity measures that attempt to capture the spatiotemporal evolution of neurocognitive networks. Unfortunately, interpreting the neural basis of goal directed behavior using connectivity measures on neuroimaging data are highly dependent on the assumptions underlying the development of the measure, the nature of the task, and the modality of the neuroimaging technique that was used. This paper has two main purposes. The first is to provide an overview of some of the different measures of functional/effective connectivity that deal with high temporal resolution neuroimaging data. We will include some results that come from a recent approach that we have developed to identify the formation and extinction of task-specific, large-scale neuronal assemblies from electrophysiological recordings at a ms-by-ms temporal resolution. The second purpose of this paper is to indicate how to partially validate the interpretations drawn from this (or any other) connectivity technique by using simulated data from large-scale, neurobiologically realistic models. Specifically, we applied our recently developed method to realistic simulations of MEG data during a delayed match-to-sample (DMS) task condition and a passive viewing of stimuli condition using a large-scale neural model of the ventral visual processing pathway. Simulated MEG data using simple head models were generated from sources placed in V1, V4, IT, and prefrontal cortex (PFC) for the passive viewing condition. The results show how closely the conclusions obtained from the functional connectivity method match with what actually occurred at the neuronal network level.

Functional biomarkers for neurodegenerative disorders based on the network paradigm

This commentary provides a brief introduction to the various uses that functional neuroimaging biomarkers can play in detecting, diagnosing, assessing treatment response and investigating neurodegenerative disorders. It then goes on to explain why the emphasis of much recent work has shifted to network-based biomarkers, as opposed to those that examine individual brain regions. A number of examples are referenced that illustrate the points made.

Serotonin transporter genotype modulates subgenual response to fearful faces using an incidental task

This study assessed the impact of serotonin transporter genotype (5-HTTLPR) on regional responses to emotional faces in the amygdala and subgenual cingulate cortex (sgACC), while subjects performed a gender discrimination task. Although we found no evidence for greater amygdala reactivity or reduced amygdala-sgACC coupling in short variant 5-HTTLPR homozygotes (s/s), we observed an interaction between genotype and emotion in sgACC. Only long variant homozygotes (la/la) exhibited subgenual deactivation to fearful versus neutral faces, whereas the effect in s/s subjects was in the other direction. This absence of subgenual deactivation in s/s subjects parallels a recent finding in depressed subjects [Grimm, S., Boesiger, P., Beck, J., Schuepbach, D., Bermpohl, F., Walter, M., et al. Altered negative BOLD responses in the default-mode network during emotion processing in depressed subjects. Neuropsychopharmacology, 34, 932-943, 2009]. Taken together, the findings suggest that subgenual cingulate activity may play an important role in regulating the impact of aversive stimuli, potentially conferring greater resilience to the effects of aversive stimuli in la/la subjects. Using dynamic causal modeling of functional magnetic resonance imaging data, we explored the effects of genotype on effective connectivity and emotion-specific changes in coupling across a network of regions implicated in social processing. Viewing fearful faces enhanced bidirectional excitatory coupling between the amygdala and the fusiform gyrus, and increased the inhibitory influence of the amygdala over the sgACC, although this modulation of coupling did not differ between the genotype groups. The findings are discussed in relation to the role of sgACC and serotonin in moderating responses to aversive stimuli [Dayan, P., & Huys, Q. J., Serotonin, inhibition, and negative mood. PLoS Comput Biol, 4, e4, 2008; Mayberg, H. S., Liotti, M., Brannan, S. K., McGinnis, S., Mahurin, R. K., Jerabek, P. A., et al. Reciprocal limbic-cortical function and negative mood: Converging PET findings in depression and normal sadness. Am J Psychiatry, 156, 675-682, 1999].

Tracing the route to path analysis in neuroimaging

This article provides a personal perspective of the adoption of path analysis (structural equation modeling) to neuroimaging. The paper covers the motivation stemming from the need to merge functional measures with neuroanatomy and early innovations in its application. The use of path analysis as a means to test directional hypotheses about networks is presented along with the development of the complementary method, partial least squares. A method is useful when it provides insights that were previously inaccessible, and reflecting this, the paper concludes with a synopsis of the theoretical developments that arose for the routine use of methods like path analysis.

Effective connectivity: influence, causality and biophysical modeling

This is the final paper in a Comments and Controversies series dedicated to "The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution". We argue that discovering effective connectivity depends critically on state-space models with biophysically informed observation and state equations. These models have to be endowed with priors on unknown parameters and afford checks for model Identifiability. We consider the similarities and differences among Dynamic Causal Modeling, Granger Causal Modeling and other approaches. We establish links between past and current statistical causal modeling, in terms of Bayesian dependency graphs and Wiener-Akaike-Granger-Schweder influence measures. We show that some of the challenges faced in this field have promising solutions and speculate on future developments.

Multivariate dynamical systems models for estimating causal interactions in fMRI

Analysis of dynamical interactions between distributed brain areas is of fundamental importance for understanding cognitive information processing. However, estimating dynamic causal interactions between brain regions using functional magnetic resonance imaging (fMRI) poses several unique challenges. For one, fMRI measures Blood Oxygenation Level Dependent (BOLD) signals, rather than the underlying latent neuronal activity. Second, regional variations in the hemodynamic response function (HRF) can significantly influence estimation of causal interactions between them. Third, causal interactions between brain regions can change with experimental context over time. To overcome these problems, we developed a novel state-space Multivariate Dynamical Systems (MDS) model to estimate intrinsic and experimentally-induced modulatory causal interactions between multiple brain regions. A probabilistic graphical framework is then used to estimate the parameters of MDS as applied to fMRI data. We show that MDS accurately takes into account regional variations in the HRF and estimates dynamic causal interactions at the level of latent signals. We develop and compare two estimation procedures using maximum likelihood estimation (MLE) and variational Bayesian (VB) approaches for inferring model parameters. Using extensive computer simulations, we demonstrate that, compared to Granger causal analysis (GCA), MDS exhibits superior performance for a wide range of signal to noise ratios (SNRs), sample length and network size. Our simulations also suggest that GCA fails to uncover causal interactions when there is a conflict between the direction of intrinsic and modulatory influences. Furthermore, we show that MDS estimation using VB methods is more robust and performs significantly better at low SNRs and shorter time series than MDS with MLE. Our study suggests that VB estimation of MDS provides a robust method for estimating and interpreting causal network interactions in fMRI data.

Connectivity Analysis is Essential to Understand Neurological Disorders

Neurological and neuropsychiatric disorders are major causes of morbidity worldwide. A systems level analysis including functional and structural neuroimaging is particularly useful when the pathology leads to disorders of higher order cognitive functions in human patients. However, an analysis that is restricted to regional effects is impoverished and insensitive, compared to the analysis of distributed brain networks. We discuss the issues to consider when choosing an appropriate connectivity method, and compare the results from several different methods that are relevant to fMRI and PET data. These include psychophysiological interactions in general linear models, structural equation modeling, dynamic causal modeling, and independent components analysis. The advantages of connectivity analysis are illustrated with a range of structural and neurodegenerative brain disorders. We illustrate the sensitivity of these methods to the presence or severity of disease and/or treatment, even where analyses of voxel-wise activations are insensitive. However, functional and structural connectivity methods should be seen as complementary to, not a substitute for, other imaging and behavioral approaches. The functional relevance of changes in connectivity, to motor or cognitive performance, are considered alongside the complex relationship between structural and functional changes and neuropathology. Finally some of the problems associated with connectivity analysis are discussed. We suggest that the analysis of brain connectivity is an essential complement to the analysis of regionally specific dysfunction, in order to understand neurological and neuropsychiatric disease, and to evaluate the mechanisms of effective therapies.

Identifying abnormal connectivity in patients using dynamic causal modeling of FMRI responses

Functional imaging studies of brain damaged patients offer a unique opportunity to understand how sensorimotor and cognitive tasks can be carried out when parts of the neural system that support normal performance are no longer available. In addition to knowing which regions a patient activates, we also need to know how these regions interact with one another, and how these inter-regional interactions deviate from normal. Dynamic causal modeling (DCM) offers the opportunity to assess task-dependent interactions within a set of regions. Here we review its use in patients when the question of interest concerns the characterization of abnormal connectivity for a given pathology. We describe the currently available implementations of DCM for fMRI responses, varying from the deterministic bilinear models with one-state equation to the stochastic non-linear models with two-state equations. We also highlight the importance of the new Bayesian model selection and averaging tools that allow different plausible models to be compared at the single subject and group level. These procedures allow inferences to be made at different levels of model selection, from features (model families) to connectivity parameters. Following a critical review of previous DCM studies that investigated abnormal connectivity we propose a systematic procedure that will ensure more flexibility and efficiency when using DCM in patients. Finally, some practical and methodological issues crucial for interpreting or generalizing DCM findings in patients are discussed.

Using Granger-Geweke causality model to evaluate the effective connectivity of primary motor cortex (M1), supplementary motor area (SMA) and cerebellum

Currently, Granger-Geweke causality models have been widely applied to investigate the dynamic direction relationships among brain regions. In a previous study, we have found that the right hand finger-tapping task can produce relatively reliable brain response. As an extension of our previous study, we developed an algorithm based on the classical Granger-Geweke causality model to further investigate the effective connectivity of three brain regions (left primary motor cortex (M1), supplementary motor area (SMA) and right cerebellum) that showed the most robust brain activations. Our computational results not only confirm the strong linear feedback among SMA, M1 and right cerebellum, but also demonstrate that M1 is the hub of these three regions indicated by the anatomy research. Moreover, the model predicts the high intermediate node density existing in the area between SMA and M1, which will stimulate the imaging experimentalists to carry out new experiments to validate this postulation.