Capturing and tracking large-scale brain activity dynamics holds the potential to deepen our understanding of cognition. Previously, tools from topological data analysis, especially Mapper, have been successfully used to mine brain activity dynamics at the highest spatiotemporal resolutions. Even though it is a relatively established tool within the field of topological data analysis, Mapper results are highly impacted by parameter selection. Given that noninvasive human neuroimaging data (e.g., from fMRI) is typically fraught with artifacts and no gold standards exist regarding “true” state transitions, we argue for a thorough examination of Mapper parameter choices to better reveal their impact. Using synthetic data (with known transition structure) and real fMRI data, we explore a variety of parameter choices for each Mapper step, thereby providing guidance and heuristics for the field. We also release our parameter exploration toolbox as a software package to make it easier for scientists to investigate and apply Mapper to any dataset.

Characterizing large-scale dynamic organization of the brain relies on both data-driven and mechanistic modeling, which demands a low versus high level of prior knowledge and assumptions about how constituents of the brain interact. However, the conceptual translation between the two is not straightforward. The present work aims to provide a bridge between data-driven and mechanistic modeling. We conceptualize brain dynamics as a complex landscape that is continuously modulated by internal and external changes. The modulation can induce transitions between one stable brain state (attractor) to another. Here, we provide a novel method—Temporal Mapper—built upon established tools from the field of topological data analysis to retrieve the network of attractor transitions from time series data alone. For theoretical validation, we use a biophysical network model to induce transitions in a controlled manner, which provides simulated time series equipped with a ground-truth attractor transition network. Our approach reconstructs the ground-truth transition network from simulated time series data better than existing time-varying approaches. For empirical relevance, we apply our approach to fMRI data gathered during a continuous multitask experiment. We found that occupancy of the high-degree nodes and cycles of the transition network was significantly associated with subjects’ behavioral performance. Taken together, we provide an important first step toward integrating data-driven and mechanistic modeling of brain dynamics. Author Summary Brain dynamics are often described by data-driven models or mechanistic dynamical systems models to understand how specific brain states persist or change (transition). However, there lacks a computational framework that explicitly connects states/transitions discovered by data-driven methods to those of mechanistic models, leading to a disconnection between data analysis and theoretical modeling. To begin bridging this gap, we develop a data-driven method, the Temporal Mapper, to extract dynamical systems features from time series and represent them as attractor transition networks. The Temporal Mapper can reconstruct ground-truth transition networks of mechanistic models. When applied to human fMRI data, the method helps predict behavioral performance from the topology of transition networks. Potential applications include characterizing brain dynamic organization in health and diseases and designing brain stimulation protocols.

Author Summary Modern neuroimaging promises to transform how we understand human brain function, as well as how we diagnose and treat mental disorders. However, this promise hinges on the development of computational tools for distilling complex, high-dimensional neuroimaging data into simple representations that can be explored in research or clinical settings. The Mapper approach from topological data analysis (TDA) can be used to generate such representations. Here, we introduce several improvements to the underlying algorithm to aid scalability and parameter selection for high-dimensional neuroimaging data. We also provide new analytical tools for annotating and extracting neurobiological and behavioral insights from the generated representations. We hope this new framework will help facilitate translational applications of precision neuroimaging in clinical settings. Abstract For better translational outcomes, researchers and clinicians alike demand novel tools to distill complex neuroimaging data into simple yet behaviorally relevant representations at the single-participant level. Recently, the Mapper approach from topological data analysis (TDA) has been successfully applied on noninvasive human neuroimaging data to characterize the entire dynamical landscape of whole-brain configurations at the individual level without requiring any spatiotemporal averaging at the outset. Despite promising results, initial applications of Mapper to neuroimaging data were constrained by (1) the need for dimensionality reduction and (2) lack of a biologically grounded heuristic for efficiently exploring the vast parameter space. Here, we present a novel computational framework for Mapper—designed specifically for neuroimaging data—that removes limitations and reduces computational costs associated with dimensionality reduction and parameter exploration. We also introduce new meta-analytic approaches to better anchor Mapper-generated representations to neuroanatomy and behavior. Our new NeuMapper framework was developed and validated using multiple fMRI datasets where participants engaged in continuous multitask experiments that mimic “ongoing” cognition. Looking forward, we hope our framework will help researchers push the boundaries of psychiatric neuroimaging toward generating insights at the single-participant level across consortium-size datasets.