Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of (ie, hypotheses about) network architectures and implicit coupling functions in terms of their Bayesian model evidence. These methods are collectively referred to as dynamical casual modelling (DCM). We focus on a relatively new approach that is proving remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems

Multimodal imaging of human brain activity: rational, biophysical aspects and modes of integration

Until relatively recently the vast majority of imaging and electrophysiological studies of human brain activity have relied on single-modality measurements usually correlated with readily observable or experimentally modified behavioural or brain state patterns. Multi-modal imaging is the concept of bringing together observations or measurements from different instruments. We discuss the aims of multi-modal imaging and the ways in which it can be accomplished using representative applications. Given the importance of haemodynamic and electrophysiological signals in current multi-modal imaging applications, we also review some of the basic physiology relevant to understanding their relationship

MEG and fMRI Fusion for Non-Linear Estimation of Neural and BOLD Signal Changes

The combined analysis of magnetoencephalography (MEG)/electroencephalography and functional magnetic resonance imaging (fMRI) measurements can lead to improvement in the description of the dynamical and spatial properties of brain activity. In this paper we empirically demonstrate this improvement using simulated and recorded task related MEG and fMRI activity. Neural activity estimates were derived using a dynamic Bayesian network with continuous real valued parameters by means of a sequential Monte Carlo technique. In synthetic data, we show that MEG and fMRI fusion improves estimation of the indirectly observed neural activity and smooths tracking of the blood oxygenation level dependent (BOLD) response. In recordings of task related neural activity the combination of MEG and fMRI produces a result with greater signal-to-noise ratio, that confirms the expectation arising from the nature of the experiment. The highly non-linear model of the BOLD response poses a difficult inference problem for neural activity estimation; computational requirements are also high due to the time and space complexity. We show that joint analysis of the data improves the system's behavior by stabilizing the differential equations system and by requiring fewer computational resources

Simultaneous EEG-fMRI Analysis with Application to Detection of Seizure Signal Sources

Non

Bayesian multi-modal model comparison: a case study on the generators of the spike and the wave in generalized spike–wave complexes

We present a novel approach to assess the networks involved in the generation of spontaneous pathological brain activity based on multi-modal imaging data. We propose to use probabilistic fMRI-constrained EEG source reconstruction as a complement to EEG-correlated fMRI analysis to disambiguate between networks that co-occur at the fMRI time resolution. The method is based on Bayesian model comparison, where the different models correspond to different combinations of fMRI-activated (or deactivated) cortical clusters. By computing the model evidence (or marginal likelihood) of each and every candidate source space partition, we can infer the most probable set of fMRI regions that has generated a given EEG scalp data window. We illustrate the method using EEG-correlated fMRI data acquired in a patient with ictal generalized spike–wave (GSW) discharges, to examine whether different networks are involved in the generation of the spike and the wave components, respectively. To this effect, we compared a family of 128 EEG source models, based on the combinations of seven regions haemodynamically involved (deactivated) during a prolonged ictal GSW discharge, namely: bilateral precuneus, bilateral medial frontal gyrus, bilateral middle temporal gyrus, and right cuneus. Bayesian model comparison has revealed the most likely model associated with the spike component to consist of a prefrontal region and bilateral temporal–parietal regions and the most likely model associated with the wave component to comprise the same temporal–parietal regions only. The result supports the hypothesis of different neurophysiological mechanisms underlying the generation of the spike versus wave components of GSW discharges

The relationship between MEG and fMRI

In recent years functional neuroimaging techniques such as fMRI, MEG, EEG and PET have provided researchers with a wealth of information on human brain function. However none of these modalities can measure directly either the neuro-electrical or neuro-chemical processes that mediate brain function. This means that metrics directly reflecting brain ‘activity’ must be inferred from other metrics (e.g. magnetic fields (MEG) or haemodynamics (fMRI)). To overcome this limitation, many studies seek to combine multiple complementary modalities and an excellent example of this is the combination of MEG (which has high temporal resolution) with fMRI (which has high spatial resolution). However, the full potential of multi-modal approaches can only be truly realised in cases where the relationship between metrics is known. In this paper, we explore the relationship between measurements made using fMRI and MEG. We describe the origins of the two signals as well as their relationship to electrophysiology. We review multiple studies that have attempted to characterise the spatial relationship between fMRI and MEG, and we also describe studies that exploit the rich information content of MEG to explore differing relationships between MEG and fMRI across neural oscillatory frequency bands. Monitoring the brain at “rest” has become of significant recent interest to the neuroimaging community and we review recent evidence comparing MEG and fMRI metrics of functional connectivity. A brief discussion of the use of magnetic resonance spectroscopy (MRS) to probe the relationship between MEG/fMRI and neurochemistry is also given. Finally, we highlight future areas of interest and offer some recommendations for the parallel use of fMRI and MEG

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE