Clinical Applications of Stochastic Dynamic Models of the Brain, Part I: A Primer

A Dynamical Systems View of Psychiatric Disorders-Practical Implications: A Review

Importance

Dynamical systems theory is widely used to explain tipping points, cycles, and chaos in complex systems ranging from the climate to ecosystems. It has been suggested that the same theory may be used to explain the nature and dynamics of psychiatric disorders, which may come and go with symptoms changing over a lifetime. Here we review evidence for the practical applicability of this theory and its quantitative tools in psychiatry.

Observations

Emerging results suggest that time series of mood and behavior may be used to monitor the resilience of patients using the same generic dynamical indicators that are now employed globally to monitor the risks of collapse of complex systems, such as tropical rainforest and tipping elements of the climate system. Other dynamical systems tools used in ecology and climate science open ways to infer personalized webs of causality for patients that may be used to identify targets for intervention. Meanwhile, experiences in ecological restoration help make sense of the occasional long-term success of short interventions.

Conclusions and Relevance

Those observations, while promising, evoke follow-up questions on how best to collect dynamic data, infer informative timescales, construct mechanistic models, and measure the effect of interventions on resilience. Done well, monitoring resilience to inform well-timed interventions may be integrated into approaches that give patients an active role in the lifelong challenge of managing their resilience and knowing when to seek professional help.

Dynamical noise can enhance high-order statistical structure in complex systems

Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order interdependencies constitute a powerful resource that is, however, challenging to harness and can be readily disrupted. In this paper, we contest this perspective by demonstrating that high-order interdependencies can not only exhibit robustness to stochastic perturbations, but can in fact be enhanced by them. Using elementary cellular automata as a general testbed, our results unveil the capacity of dynamical noise to enhance the statistical regularities between agents and, intriguingly, even alter the prevailing character of their interdependencies. Furthermore, our results show that these effects are related to the high-order structure of the local rules, which affect the system's susceptibility to noise and characteristic time scales. These results deepen our understanding of how high-order interdependencies may spontaneously emerge within distributed systems interacting with stochastic environments, thus providing an initial step toward elucidating their origin and function in complex systems like the human brain.

It's about time: Linking dynamical systems with human neuroimaging to understand the brain

Most human neuroscience research to date has focused on statistical approaches that describe stationary patterns of localized neural activity or blood flow. While these patterns are often interpreted in light of dynamic, information-processing concepts, the static, local, and inferential nature of the statistical approach makes it challenging to directly link neuroimaging results to plausible underlying neural mechanisms. Here, we argue that dynamical systems theory provides the crucial mechanistic framework for characterizing both the brain's time-varying quality and its partial stability in the face of perturbations, and hence, that this perspective can have a profound impact on the interpretation of human neuroimaging results and their relationship with behavior. After briefly reviewing some key terminology, we identify three key ways in which neuroimaging analyses can embrace a dynamical systems perspective: by shifting from a local to a more global perspective, by focusing on dynamics instead of static snapshots of neural activity, and by embracing modeling approaches that map neural dynamics using "forward" models. Through this approach, we envisage ample opportunities for neuroimaging researchers to enrich their understanding of the dynamic neural mechanisms that support a wide array of brain functions, both in health and in the setting of psychopathology.

Computational models link cellular mechanisms of neuromodulation to large-scale neural dynamics

Decades of neurobiological research have disclosed the diverse manners in which the response properties of neurons are dynamically modulated to support adaptive cognitive functions. This neuromodulation is achieved through alterations in the biophysical properties of the neuron. However, changes in cognitive function do not arise directly from the modulation of individual neurons, but are mediated by population dynamics in mesoscopic neural ensembles. Understanding this multiscale mapping is an important but nontrivial issue. Here, we bridge these different levels of description by showing how computational models parametrically map classic neuromodulatory processes onto systems-level models of neural activity. The ensuing critical balance of systems-level activity supports perception and action, although our knowledge of this mapping remains incomplete. In this way, quantitative models that link microscale neuronal neuromodulation to systems-level brain function highlight gaps in knowledge and suggest new directions for integrating theoretical and experimental work.

Computational approaches and machine learning for individual-level treatment predictions

RATIONALE

The impact of neuroscience-based approaches for psychiatry on pragmatic clinical decision-making has been limited. Although neuroscience has provided insights into basic mechanisms of neural function, these insights have not improved the ability to generate better assessments, prognoses, diagnoses, or treatment of psychiatric conditions.

OBJECTIVES

To integrate the emerging findings in machine learning and computational psychiatry to address the question: what measures that are not derived from the patient's self-assessment or the assessment by a trained professional can be used to make more precise predictions about the individual's current state, the individual's future disease trajectory, or the probability to respond to a particular intervention?

RESULTS

Currently, the ability to use individual differences to predict differential outcomes is very modest possibly related to the fact that the effect sizes of interventions are small. There is emerging evidence of genetic and neuroimaging-based heterogeneity of psychiatric disorders, which contributes to imprecise predictions. Although the use of machine learning tools to generate clinically actionable predictions is still in its infancy, these approaches may identify subgroups enabling more precise predictions. In addition, computational psychiatry might provide explanatory disease models based on faulty updating of internal values or beliefs.

CONCLUSIONS

There is a need for larger studies, clinical trials using machine learning, or computational psychiatry model parameters predictions as actionable outcomes, comparing alternative explanatory computational models, and using translational approaches that apply similar paradigms and models in humans and animals.

Computational Models of Interoception and Body Regulation

To survive, organisms must effectively respond to the challenge of maintaining their physiological integrity in the face of an ever-changing environment. Preserving this homeostasis critically relies on adaptive behavior. In this review, we consider recent frameworks that extend classical homeostatic control via reflex arcs to include more flexible forms of adaptive behavior that take interoceptive context, experiences, and expectations into account. Specifically, we define a landscape for computational models of interoception, body regulation, and forecasting, address these models' unique challenges in relation to translational research efforts, and discuss what they can teach us about cognition as well as physical and mental health.

Better Safe Than Sorry: A Common Signature of General Vulnerability for Psychopathology

Several labels, such as neuroticism, negative emotionality, and dispositional negativity, indicate a broad dimension of psychopathology. However, largely separate, often disorder-specific research lines have developed that focus on different cognitive and affective characteristics that are associated with this dimension, such as perseverative cognition (worry, rumination), reduced autobiographical memory specificity, compromised fear learning, and enhanced somatic-symptom reporting. In this article, we present a theoretical perspective within a predictive-processing framework in which we trace these phenotypically different characteristics back to a common underlying “better-safe-than-sorry” processing strategy. This implies information processing that tends to be low in sensory-perceptual detail, which allows threat-related categorical priors to dominate conscious experience and for chronic uncertainty/surprise because of a stagnated error-reduction process. This common information-processing strategy has beneficial effects in the short term but important costs in the long term. From this perspective, we suggest that the phenomenally distinct cognitive and affective psychopathological characteristics mentioned above represent the same basic processing heuristic of the brain and are only different in relation to the particular type of information involved (e.g., in working memory, in autobiographical memory, in the external and internal world). Clinical implications of this view are discussed.

Bring the Noise: Reconceptualizing Spontaneous Neural Activity

Definitions of what constitutes the 'signal of interest' in neuroscience can be controversial, due in part to continuously evolving notions regarding the significance of spontaneous neural activity. This review highlights how the challenge of separating brain signal from noise has led to new conceptualizations of brain functional organization at both the micro- and macroscopic level. Recent debates in the functional neuroimaging community surrounding artifact removal processes have revived earlier discussions surrounding how to appropriately isolate and measure neuronal signals against a background of noise from various sources. Insights from electrophysiological studies and computational modeling can inform current theory and data analytic practices in human functional neuroimaging, given that signal and noise may be inextricably linked in the brain.

Adaptive frequency-based modeling of whole-brain oscillations: Predicting regional vulnerability and hazardousness rates

Whole-brain computational modeling based on structural connectivity has shown great promise in successfully simulating fMRI BOLD signals with temporal coactivation patterns that are highly similar to empirical functional connectivity patterns during resting state. Importantly, previous studies have shown that spontaneous fluctuations in coactivation patterns of distributed brain regions have an inherent dynamic nature with regard to the frequency spectrum of intrinsic brain oscillations. In this modeling study, we introduced frequency dynamics into a system of coupled oscillators, where each oscillator represents the local mean-field model of a brain region. We first showed that the collective behavior of interacting oscillators reproduces previously shown features of brain dynamics. Second, we examined the effect of simulated lesions in gray matter by applying an in silico perturbation protocol to the brain model. We present a new approach to map the effects of vulnerability in brain networks and introduce a measure of regional hazardousness based on mapping of the degree of divergence in a feature space.

Space-time recurrences for functional connectivity evaluation and feature extraction in motor imagery brain-computer interfaces

This work presents a classification performance comparison between different frameworks for functional connectivity evaluation and complex network feature extraction aiming to distinguish motor imagery classes in electroencephalography (EEG)-based brain-computer interfaces (BCIs). The analysis was performed in two online datasets: (1) a classical benchmark-the BCI competition IV dataset 2a-allowing a comparison with a representative set of strategies previously employed in this BCI paradigm and (2) a statistically representative dataset for signal processing technique comparisons over 52 subjects. Besides exploring three classical similarity measures-Pearson correlation, Spearman correlation, and mean phase coherence-this work also proposes a recurrence-based alternative for estimating EEG brain functional connectivity, which takes into account the recurrence density between pairwise electrodes over a time window. These strategies were followed by graph feature evaluation considering clustering coefficient, degree, betweenness centrality, and eigenvector centrality. The features were selected by Fisher's discriminating ratio and classification was performed by a least squares classifier in agreement with classical and online BCI processing strategies. The results revealed that the recurrence-based approach for functional connectivity evaluation was significantly better than the other frameworks, which is probably associated with the use of higher order statistics underlying the electrode joint probability estimation and a higher capability of capturing nonlinear inter-relations. There were no significant differences in performance among the evaluated graph features, but the eigenvector centrality was the best feature regarding processing time. Finally, the best ranked graph-based attributes were found in classical EEG motor cortex positions for the subjects with best performances, relating functional organization and motor activity. Graphical Abstract Evaluating functional connectivity based on Space-Time Recurrence Counting for motor imagery classification in brain-computer interfaces. Recurrences are evaluated between electrodes over a time window, and, after a density threshold, the electrodes adjacency matrix is stablish, leading to a graph. Graph-based topological measures are used for motor imagery classification.

The role that choice of model plays in predictions for epilepsy surgery

Mathematical modelling has been widely used to predict the effects of perturbations to brain networks. An important example is epilepsy surgery, where the perturbation in question is the removal of brain tissue in order to render the patient free of seizures. Different dynamical models have been proposed to represent transitions to ictal states in this context. However, our choice of which mathematical model to use to address this question relies on making assumptions regarding the mechanism that defines the transition from background to the seizure state. Since these mechanisms are unknown, it is important to understand how predictions from alternative dynamical descriptions compare. Herein we evaluate to what extent three different dynamical models provide consistent predictions for the effect of removing nodes from networks. We show that for small, directed, connected networks the three considered models provide consistent predictions. For larger networks, predictions are shown to be less consistent. However consistency is higher in networks that have sufficiently large differences in ictogenicity between nodes. We further demonstrate that heterogeneity in ictogenicity across nodes correlates with variability in the number of connections for each node.

Metastable brain waves

Traveling patterns of neuronal activity-brain waves-have been observed across a breadth of neuronal recordings, states of awareness, and species, but their emergence in the human brain lacks a firm understanding. Here we analyze the complex nonlinear dynamics that emerge from modeling large-scale spontaneous neural activity on a whole-brain network derived from human tractography. We find a rich array of three-dimensional wave patterns, including traveling waves, spiral waves, sources, and sinks. These patterns are metastable, such that multiple spatiotemporal wave patterns are visited in sequence. Transitions between states correspond to reconfigurations of underlying phase flows, characterized by nonlinear instabilities. These metastable dynamics accord with empirical data from multiple imaging modalities, including electrical waves in cortical tissue, sequential spatiotemporal patterns in resting-state MEG data, and large-scale waves in human electrocorticography. By moving the study of functional networks from a spatially static to an inherently dynamic (wave-like) frame, our work unifies apparently diverse phenomena across functional neuroimaging modalities and makes specific predictions for further experimentation.

Putting the "dynamic" back into dynamic functional connectivity

The study of fluctuations in time-resolved functional connectivity is a topic of substantial current interest. As the term "dynamic functional connectivity" implies, such fluctuations are believed to arise from dynamics in the neuronal systems generating these signals. While considerable activity currently attends to methodological and statistical issues regarding dynamic functional connectivity, less attention has been paid toward its candidate causes. Here, we review candidate scenarios for dynamic (functional) connectivity that arise in dynamical systems with two or more subsystems; generalized synchronization, itinerancy (a form of metastability), and multistability. Each of these scenarios arises under different configurations of local dynamics and intersystem coupling: We show how they generate time series data with nonlinear and/or nonstationary multivariate statistics. The key issue is that time series generated by coupled nonlinear systems contain a richer temporal structure than matched multivariate (linear) stochastic processes. In turn, this temporal structure yields many of the phenomena proposed as important to large-scale communication and computation in the brain, such as phase-amplitude coupling, complexity, and flexibility. The code for simulating these dynamics is available in a freeware software platform, the Brain Dynamics Toolbox.