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

Advancing functional connectivity research from association to causation

Cognition and behavior emerge from brain network interactions, such that investigating causal interactions should be central to the study of brain function. Approaches that characterize statistical associations among neural time series-functional connectivity (FC) methods-are likely a good starting point for estimating brain network interactions. Yet only a subset of FC methods ('effective connectivity') is explicitly designed to infer causal interactions from statistical associations. Here we incorporate best practices from diverse areas of FC research to illustrate how FC methods can be refined to improve inferences about neural mechanisms, with properties of causal neural interactions as a common ontology to facilitate cumulative progress across FC approaches. We further demonstrate how the most common FC measures (correlation and coherence) reduce the set of likely causal models, facilitating causal inferences despite major limitations. Alternative FC measures are suggested to immediately start improving causal inferences beyond these common FC measures

Impaired Cerebral Perfusion in Multiple Sclerosis: Relevance of Endothelial Factors.

Magnetic resonance imaging techniques measuring in vivo brain perfusion and integrity of the blood-brain barrier have developed rapidly in the past decade, resulting in a wide range of available methods. This review first discusses their principles, possible pitfalls, and potential for quantification and outlines clinical application in neurological disorders. Then, we focus on the endothelial cells of the blood-brain barrier, pointing out their contribution in regulating vascular tone by production of vasoactive substances. Finally, the role of these substances in brain hypoperfusion in multiple sclerosis is discussed

Physiological Gaussian Process Priors for the Hemodynamics in fMRI Analysis

Background: Inference from fMRI data faces the challenge that the hemodynamic system that relates neural activity to the observed BOLD fMRI signal is unknown. New Method: We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modeled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD response, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way, and simultaneously gives us the nonparametric flexibility of the GP. Results: Results on simulated data show that the proposed model is able to discriminate between active and non-active voxels also when the GP prior deviates from the true hemodynamics. Our model finds time varying dynamics when applied to real fMRI data. Comparison with Existing Method(s): The proposed model is better at detecting activity in simulated data than standard models, without inflating the false positive rate. When applied to real fMRI data, our GP model in several cases finds brain activity where previously proposed LTI models does not. Conclusions: We have proposed a new non-linear model for the hemodynamics in task fMRI, that is able to detect active voxels, and gives the opportunity to ask new kinds of questions related to hemodynamics.Comment: 18 pages, 14 figure

The connected brain: Causality, models and intrinsic dynamics

Recently, there have been several concerted international efforts - the BRAIN initiative, European Human Brain Project and the Human Connectome Project, to name a few - that hope to revolutionize our understanding of the connected brain. Over the past two decades, functional neuroimaging has emerged as the predominant technique in systems neuroscience. This is foreshadowed by an ever increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. In this article, we summarize pedagogically the (deep) history of brain mapping. We will highlight the theoretical advances made in the (dynamic) causal modelling of brain function - that may have escaped the wider audience of this article - and provide a brief overview of recent developments and interesting clinical applications. We hope that this article will engage the signal processing community by showcasing the inherently multidisciplinary nature of this important topic and the intriguing questions that are being addressed

Understanding DCM: ten simple rules for the clinician.

Despite almost a decade since the introduction of Dynamic Causal Modelling (DCM), there remains some confusion within the wider neuroimaging, neuroscience and clinical communities as to what DCM studies are probing, and what all the jargon means. We provide ten simple rules, and a theoretical example to gently introduce the reader to the rationale behind DCM analyses, and how one should consider neuroimaging data and experiments that use DCM. It is deliberately written as a primer or orientation for non-technical imaging neuroscientists or clinicians who have had to contend with the technical intricacies of understanding DCM

Development and application of model selection methods for investigating brain function

The goal of any scientific discipline is to learn about nature, usually through the process of evaluating competing hypotheses for explaining observations. Brain research is no exception. Investigating brain function usually entails comparing models, expressed as mathematical equations, of how the brain works. The aim of this thesis is to provide and evaluate new model comparison techniques that facilitate this research. In addition, it applies existing comparison methods to disambiguate between hypotheses of how neuronal activity relates to blood ow, a topic known as neurovascular coupling. In neuroimaging, techniques such as functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) allow to routinely image the brain, whilst statistical frameworks, such as statistical parametric mapping (SPM), allow to identify regionally specific responses, or brain activations. In this thesis, SPM is first used to address the problem of neurovascular coupling, and compare different putative coupling functions, which relate fMRI signals to different features of the EEG power spectrum. These inferences are made using linear models and a model selection approach based on F-tests. Although valid, this approach is restricted to nested models. This thesis then focuses on the development of a Bayesian technique, to construct posterior model probability maps (PPMs) for group studies. PPMs are analogous to F-tests but not limited to nested hypotheses. The work presented here then focuses again on neurovascular coupling, this time from a mechanistic perspective, not afforded by linear models. For this purpose, a detailed biophysical framework is used to explore the contribution of synaptic and spiking activity in the generation of hemodynamic signals in visual cortex, using simultaneous EEG-fMRI. This approach is a special case of brain connectivity models. Finally, using fMRI data, this thesis validates a recently proposed Bayesian approach for quickly comparing large numbers of connectivity models based on inverting a single model

Towards clinical assessment of cerebral blood flow regulation using ultrasonography : model applicability in clinical studies

For preservation of its vital functions, the brain is largely dependent of a sufficient delivery of oxygen and nutrients. Blood flow to the brain is essentially regulated by 2 control mechanisms i.e. neurovascular coupling and cerebral autoregulation. Cerebral autoregulation aims for constant adequate blood supply by compensating for blood pressure variations by dilatation or narrowing of the cerebral microvasculature. Neurovascular coupling adjusts blood supply to the local metabolic need. Cerebral perfusion and blood flow regulation are compromised in several pathological conditions. Clinical examination of cerebral blood flow and its regulation may therefore provide helpful diagnostic, predictive and therapeutic information. The work in this thesis was aimed at putting a step forward towards development of reliable and clinically usable parameters for cerebral blood flow regulation assessment using ultrasonography. Regarding early diagnostics, screening and monitoring of cerebral blood flow and its regulation, ultrasonography has major advantages over other imaging tools because of its noninvasiveness, cost-effectiveness, easy usability and its good time resolution. It allows examination of blood flow velocities at multiple locations throughout the extra- and intracranial circulation and evaluation of both control mechanisms by transfer function analysis. For evaluation of cerebral autoregulation, transcranial Doppler blood flow velocities in the large middle cerebral arteries have been recorded simultaneously with plethysmographic (finger) blood pressure. Gain and phase of the pressure-flow transfer function have been determined to obtain quantitative measures for cerebral autoregulation. Neurovascular coupling has been assessed by presenting a visual block stimulus to a subject and simultaneous measurement of the blood flow velocity in the artery exclusively supplying the visual cortex. The obtained visually-evoked blood flow response (VEFR) has been considered as the step response of a linear second order control system model providing patient-specific parameters such as gain and damping as quantitative measures for neurovascular coupling . In chapter 2, a clinical study has been described in which extra- and intracranial blood flow velocities (BFVs), measured at multiple sites in the circulation, have been compared between Alzheimer patients (AD), patients with mild cognitive impairment (MCI) and healthy aging controls (HC). BFVs of AD were significantly lowered at proximal sites but preserved at distal sites for the internal carotid artery and middle and posterior cerebral arteries as compared to those of MCI or HC. This specific pattern can presumably be ascribed to reduced distal diameters resulting from AD pathology. MCI BFV were similar to HC BFV in the extracranial and intracranial posterior circulation, whereas they were intermediate between AD and HC in the intracranial anterior circulation. This suggests that intracranial anterior vessels are most suitable for early detection of pathological alterations resulting from AD. The study findings further indicate that extensive ultrasonographic screening of intra- and extracranial arteries is useful for monitoring BFV decline in the MCI stage. Future follow-up of MCI patients may reveal the predictive value of location-specific BFV for conversion to AD. In the same study cohort, dynamic cerebral autoregulation has been studied as discussed in chapter 3. Cerebral autoregulatory gain and phase values were similar for AD, MCI and HC which implies that the cerebral autoregulatory mechanism is preserved in AD. However, the cerebrovascular resistance index i.e. the ratio between absolute time-averaged blood pressure and flow velocity, was significantly higher in AD as compared to MCI and HC indicating that vessel stiffness is increased in AD. Indeed, it appeared to be a potential biomarker for AD development of MCI. The cerebrovascular resistance increase in AD was furthermore confirmed by windkessel model findings of a significantly elevated peripheral resistance in AD. Arterial resistance and peripheral compliance were equal for all groups. From chapter 4, the focus was shifted to assessment of local blood flow regulation. Visuallyevoked blood flow responses (VEFRs) of formerly (pre-)eclamptic patients and healthy controls have been examined to evaluate neurovascular coupling first in a relative young study population. The aim of the study was to investigate whether possible local (pre)eclampsia-induced endothelial damage was reversible or not. The measured VEFRs have been fitted with the step response of a 2nd order control system model. Although inter-group differences in model parameters were not found, a trend was observed that critical damping (z>1) occurred more frequently in former patients than in controls. Critical damping reflects an atypical VEFR, which is either uncompensated (sluggish, z>1; Tv <20) or compensated by a rise in rate time (intermediate, z>1; Tv > 20). Since these abnormal VEFRs were mainly found in former patients (but not exclusively), these response types were hypothesized to result from pathological disturbances. A revised VEFR analysis procedure to account for reliability and blood pressure dynamics has been proposed in chapter 5. This revised procedure consists of the introduction of a reliability measure for model parameters and of a model extension to consider possible blood pressure contribution to the measured VEFR. The effects of these adjustments on study outcomes have been evaluated by applying both the standard VEFR analysis procedure (applied in chapter 4) and the revised procedure to the AD study cohort. Reliability consideration resulted in about 40% VEFR exclusion, mainly due to the models’ inability to fit critically damped responses. Reliability consideration reduced parameter variability substantially. Regarding the influence of blood pressure variation, a significantly increased damping was found in AD for the standard but not for the revised model. This reversed the study conclusion from altered to normal neurovascular coupling in AD. Considering their influence on obtained parameters, both aspects i.e. reliability and blood pressure variation should be included in VEFR-analysis. Regarding clinical study outcomes, neurovascular coupling seems to be unaffected in AD since the finding of an increased damping may be ascribed to ignorance of blood pressure contribution to VEFR. Study conclusions of earlier chapters (4 and 5) emphasize the need for a model incorporating physiological features. In chapter 6, preliminary results have been reported of the application of a newly developed lumped parameter model of the visual cortex vasculature to the 3 different VEFR types. In the new model, regulatory processes i.e. neurogenic, metabolic, myogenic and shear stress mechanisms, act on smooth muscle tone which inherently leads to adjustment of microcirculatory resistance and compliance. This allows the study of effects of pathological changes on the VEFR. It may be concluded that the model provides an improved link between VEFR and physiology. Preliminary results show that the physiology-based model can describe VEFR type representatives reasonably well obtaining physiologically plausible parameter values. Thus, from a clinical perspective it may be concluded that (Duplex) ultrasonography has great potential as a standard screening tool for MCI patients. It seems worthwhile to examine all future MCI patients on extra- and intracranial blood flow velocity and to determine their cerebrovascular resistance index by simultaneous blood pressure recording. Follow-up of MCI patients will reveal the predictive value of these parameters for future AD development. Furthermore, from a methodological perspective, it can be concluded that the current standard of control system analysis to assess local cerebral blood flow regulation has limitations regarding parameter reliability and VEFR interpretation. Both reliability and interpretation may be improved by optimization and control of data acquisition quality and by use of physiology-based models. Physiological mechanisms influencing VEFR establishment should be incorporated in such a model to possibly explain part of its variance. Efforts should be directed to development and validation of physiology-based models aimed at reliable description of VEFRs by physiologically meaningful parameters