Precision dynamical mapping using topological data analysis reveals a hub-like transition state at rest

Deconstructing the Mapper algorithm to extract richer topological and temporal features from functional neuroimaging data

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.

Impaired brain ability of older adults to transit and persist to latent states with well-organized structures at wakeful rest

The intrinsic brain functional network organization continuously changes with aging. By integrating spatial and temporal information, the process of how brain networks temporally reconfigure and remain well-organized spatial structure largely reflects the brain function, thereby holds the potential to capture its age-related declines. In this study, we examined the spatiotemporal brain dynamics from resting-state functional Magnetic Resonance Imaging (fMRI) data of healthy young and older adults using a Hidden Markov Model (HMM). Six brain states were generated by HMM, with the young group showing higher fractional occupancy and mean dwell time in states 1, 3, and 4 (SY1, SY2 and SY3), and the older group in states 2, 5, and 6 (SO1, SO2 and SO3). Importantly, comparisons of transition probabilities revealed that the older group showed a reduced brain ability to transition into states dominated by the younger group, as well as a diminished capacity to persist in them. Moreover, graph analysis revealed that these young-specific states exhibited higher modularity and k-coreness. Collectively, these findings suggested that the older group showed impaired brain ability of both transition into and sustain well spatially organized states. This emphasized that the temporal changes in brain state organization, rather than its static mode, could be a key biomarker for detecting age-related functional decline. These insights may pave the way for targeted interventions aimed at mitigating cognitive decline in the aging population.

Dissecting glial scar formation by spatial point pattern and topological data analysis

Glial scar formation represents a fundamental response to central nervous system (CNS) injuries. It is mainly characterized by a well-defined spatial rearrangement of reactive astrocytes and microglia. The mechanisms underlying glial scar formation have been extensively studied, yet quantitative descriptors of the spatial arrangement of reactive glial cells remain limited. Here, we present a novel approach using point pattern analysis (PPA) and topological data analysis (TDA) to quantify spatial patterns of reactive glial cells after experimental ischemic stroke in mice. We provide open and reproducible tools using R and Julia to quantify spatial intensity, cell covariance and conditional distribution, cell-to-cell interactions, and short/long-scale arrangement, which collectively disentangle the arrangement patterns of the glial scar. This approach unravels a substantial divergence in the distribution of GFAP+ and IBA1+ cells after injury that conventional analysis methods cannot fully characterize. PPA and TDA are valuable tools for studying the complex spatial arrangement of reactive glia and other nervous cells following CNS injuries and have potential applications for evaluating glial-targeted restorative therapies.

Dynamic medial parietal and hippocampal deactivations under DMT relate to sympathetic output and altered sense of time, space, and the self

N,N-Dimethyltryptamine (DMT) is a serotonergic psychedelic, known to rapidly induce short-lasting alterations in conscious experience, characterized by a profound and immersive sense of physical transcendence alongside rich and vivid auditory distortions and visual imagery. Multimodal neuroimaging data paired with dynamic analysis techniques offer a valuable approach for identifying unique signatures of brain activity - and linked autonomic physiology - naturally unfolding during the altered state of consciousness induced by DMT. We leveraged simultaneous fMRI and EKG data acquired in 14 healthy volunteers prior to, during, and after intravenous administration of DMT, and, separately, placebo. fMRI data was preprocessed to derive individual dynamic activity matrices, reflecting the similarity of brain activity in time, and community detection algorithms were applied on these matrices to identify brain activity substates; EKG data was used to derive continuous heart rate. We identified a brain substate occurring immediately after DMT injection, characterized by hippocampal and medial parietal deactivations and increased superior temporal lobe activity under DMT. Deactivations in the hippocampus and medial parietal cortex correlated with alterations in the usual sense of time, space and self-referential processes, reflecting a deconstruction of essential features of ordinary consciousness. Superior lobe activations instead correlated with audio/visual hallucinations and experience of "entities", reflecting the emergence of altered sensory experiences under DMT. Finally, increased heart rate under DMT correlated positively with hippocampus/medial parietal deactivation and the experience of "entities", and negatively with altered self-referential processes. These results suggest a chain of influence linking sympathetic regulation to hippocampal and medial parietal deactivations under DMT, which combined, may contribute to positive mental health outcomes related to self-referential processing following psychedelic administration.

Higher-order functional connectivity analysis of resting-state functional magnetic resonance imaging data using multivariate cumulants

Blood-level oxygenation-dependent (BOLD) functional magnetic resonance imaging (fMRI) is the most common modality to study functional connectivity in the human brain. Most research to date has focused on connectivity between pairs of brain regions. However, attention has recently turned towards connectivity involving more than two regions, that is, higher-order connectivity. It is not yet clear how higher-order connectivity can best be quantified. The measures that are currently in use cannot distinguish between pairwise (i.e., second-order) and higher-order connectivity. We show that genuine higher-order connectivity can be quantified by using multivariate cumulants. We explore the use of multivariate cumulants for quantifying higher-order connectivity and the performance of block bootstrapping for statistical inference. In particular, we formulate a generative model for fMRI signals exhibiting higher-order connectivity and use it to assess bias, standard errors, and detection probabilities. Application to resting-state fMRI data from the Human Connectome Project demonstrates that spontaneous fMRI signals are organized into higher-order networks that are distinct from second-order resting-state networks. Application to a clinical cohort of patients with multiple sclerosis further demonstrates that cumulants can be used to classify disease groups and explain behavioral variability. Hence, we present a novel framework to reliably estimate genuine higher-order connectivity in fMRI data which can be used for constructing hyperedges, and finally, which can readily be applied to fMRI data from populations with neuropsychiatric disease or cognitive neuroscientific experiments.

Psilocybin enhances insightfulness in meditation: a perspective on the global topology of brain imaging during meditation

In this study, for the first time, we explored a dataset of functional magnetic resonance images collected during focused attention and open monitoring meditation before and after a five-day psilocybin-assisted meditation retreat using a recently established approach, based on the Mapper algorithm from topological data analysis. After generating subject-specific maps for two groups (psilocybin vs. placebo, 18 subjects/group) of experienced meditators, organizational principles were uncovered using graph topological tools, including the optimal transport (OT) distance, a geometrically rich measure of similarity between brain activity patterns. This revealed characteristics of the topology (i.e. shape) in space (i.e. abstract space of voxels) and time dimension of whole-brain activity patterns during different styles of meditation and psilocybin-induced alterations. Most interestingly, we found that (psilocybin-induced) positive derealization, which fosters insightfulness specifically when accompanied by enhanced open-monitoring meditation, was linked to the OT distance between open-monitoring and resting state. Our findings suggest that enhanced meta-awareness through meditation practice in experienced meditators combined with potential psilocybin-induced positive alterations in perception mediate insightfulness. Together, these findings provide a novel perspective on meditation and psychedelics that may reveal potential novel brain markers for positive synergistic effects between mindfulness practices and psilocybin.

Topological Data Analysis Captures Task-Driven fMRI Profiles in Individual Participants: A Classification Pipeline Based on Persistence

BOLD-based fMRI is the most widely used method for studying brain function. The BOLD signal while valuable, is beset with unique vulnerabilities. The most notable of these is the modest signal to noise ratio, and the relatively low temporal and spatial resolution. However, the high dimensional complexity of the BOLD signal also presents unique opportunities for functional discovery. Topological Data Analyses (TDA), a branch of mathematics optimized to search for specific classes of structure within high dimensional data may provide particularly valuable applications. In this investigation, we acquired fMRI data in the anterior cingulate cortex (ACC) using a basic motor control paradigm. Then, for each participant and each of three task conditions, fMRI signals in the ACC were summarized using two methods: a) TDA based methods of persistent homology and persistence landscapes and b) non-TDA based methods using a standard vectorization scheme. Finally, using machine learning (with support vector classifiers), classification accuracy of TDA and non-TDA vectorized data was tested across participants. In each participant, TDA-based classification out-performed the non-TDA based counterpart, suggesting that our TDA analytic pipeline better characterized task- and condition-induced structure in fMRI data in the ACC. Our results emphasize the value of TDA in characterizing task- and condition-induced structure in regional fMRI signals. In addition to providing our analytical tools for other users to emulate, we also discuss the unique role that TDA-based methods can play in the study of individual differences in the structure of functional brain signals in the healthy and the clinical brain.

Framewise multi-echo distortion correction for superior functional MRI

Functional MRI (fMRI) data are severely distorted by magnetic field (B0) inhomogeneities which currently must be corrected using separately acquired field map data. However, changes in the head position of a scanning participant across fMRI frames can cause changes in the B0 field, preventing accurate correction of geometric distortions. Additionally, field maps can be corrupted by movement during their acquisition, preventing distortion correction altogether. In this study, we use phase information from multi-echo (ME) fMRI data to dynamically sample distortion due to fluctuating B0 field inhomogeneity across frames by acquiring multiple echoes during a single EPI readout. Our distortion correction approach, MEDIC (Multi-Echo DIstortion Correction), accurately estimates B0 related distortions for each frame of multi-echo fMRI data. Here, we demonstrate that MEDIC's framewise distortion correction produces improved alignment to anatomy and decreases the impact of head motion on resting-state functional connectivity (RSFC) maps, in higher motion data, when compared to the prior gold standard approach (i.e., TOPUP). Enhanced framewise distortion correction with MEDIC, without the requirement for field map collection, furthers the advantage of multi-echo over single-echo fMRI.

Deconstructing the Mapper algorithm to extract richer topological and temporal features from functional neuroimaging data

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 non-invasive 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 on any dataset.

Low-frequency repetitive transcranial magnetic stimulation alters the individual functional dynamical landscape

Repetitive transcranial magnetic stimulation (rTMS) is a noninvasive approach to modulate brain activity and behavior in humans. Still, how individual resting-state brain dynamics after rTMS evolves across different functional configurations is rarely studied. Here, using resting state fMRI data from healthy subjects, we aimed to examine the effects of rTMS to individual large-scale brain dynamics. Using Topological Data Analysis based Mapper approach, we construct the precise dynamic mapping (PDM) for each participant. To reveal the relationship between PDM and canonical functional representation of the resting brain, we annotated the graph using relative activation proportion of a set of large-scale resting-state networks (RSNs) and assigned the single brain volume to corresponding RSN-dominant or a hub state (not any RSN was dominant). Our results show that (i) low-frequency rTMS could induce changed temporal evolution of brain states; (ii) rTMS didn't alter the hub-periphery configurations underlined resting-state brain dynamics; and (iii) the rTMS effects on brain dynamics differ across the left frontal and occipital lobe. In conclusion, low-frequency rTMS significantly alters the individual temporo-spatial dynamics, and our finding further suggested a potential target-dependent alteration of brain dynamics. This work provides a new perspective to comprehend the heterogeneous effect of rTMS.

Topological data analysis for revealing dynamic brain reconfiguration in MEG data

In recent years, the focus of the functional connectivity community has shifted from stationary approaches to the ones that include temporal dynamics. Especially, non-invasive electrophysiological data (magnetoencephalography/electroencephalography (MEG/EEG)) with high temporal resolution and good spatial coverage have made it possible to measure the fast alterations in the neural activity in the brain during ongoing cognition. In this article, we analyze dynamic brain reconfiguration using MEG images collected from subjects during the rest and the cognitive tasks. Our proposed topological data analysis method, called Mapper, produces biomarkers that differentiate cognitive tasks without prior spatial and temporal collapse of the data. The suggested method provides an interactive visualization of the rapid fluctuations in electrophysiological data during motor and cognitive tasks; hence, it has the potential to extract clinically relevant information at an individual level without temporal and spatial collapse.

Temporal Mapper: Transition networks in simulated and real neural dynamics

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.

Persistent homology-based functional connectivity and its association with cognitive ability: Life-span study

Brain-segregation attributes in resting-state functional networks have been widely investigated to understand cognition and cognitive aging using various approaches [e.g., average connectivity within/between networks and brain system segregation (BSS)]. While these approaches have assumed that resting-state functional networks operate in a modular structure, a complementary perspective assumes that a core-periphery or rich club structure accounts for brain functions where the hubs are tightly interconnected to each other to allow for integrated processing. In this article, we apply a novel method, persistent homology (PH), to develop an alternative to standard functional connectivity by quantifying the pattern of information during the integrated processing. We also investigate whether PH-based functional connectivity explains cognitive performance and compare the amount of variability in explaining cognitive performance for three sets of independent variables: (1) PH-based functional connectivity, (2) graph theory-based measures, and (3) BSS. Resting-state functional connectivity data were extracted from 279 healthy participants, and cognitive ability scores were generated in four domains (fluid reasoning, episodic memory, vocabulary, and processing speed). The results first highlight the pattern of brain-information flow over whole brain regions (i.e., integrated processing) accounts for more variance of cognitive abilities than other methods. The results also show that fluid reasoning and vocabulary performance significantly decrease as the strength of the additional information flow on functional connectivity with the shortest path increases. While PH has been applied to functional connectivity analysis in recent studies, our results demonstrate potential utility of PH-based functional connectivity in understanding cognitive function.

Neural resources shift under Methylphenidate: A computational approach to examine anxiety-cognition interplay

The reciprocal interplay between anxiety and cognition is well documented. Anxiety negatively impacts cognition, while cognitive engagement can down-regulate anxiety. The brain mechanisms and dynamics underlying such interplay are not fully understood. To study this question, we experimentally and orthogonally manipulated anxiety (using a threat of shock paradigm) and cognition (using methylphenidate; MPH). The effects of these manipulations on the brain and behavior were evaluated in 50 healthy participants (25 MPH, 25 placebo), using an n-back working memory fMRI task (with low and high load conditions). Behaviorally, improved response accuracy was observed as a main effect of the drug across all conditions. We employed two approaches to understand the neural mechanisms underlying MPH-based cognitive enhancement in safe and threat conditions. First, we performed a hypothesis-driven computational analysis using a mathematical framework to examine how MPH putatively affects cognitive enhancement in the face of induced anxiety across two levels of cognitive load. Second, we performed an exploratory data analysis using Topological Data Analysis (TDA)-based Mapper to examine changes in spatiotemporal brain activity across the entire cortex. Both approaches provided converging evidence that MPH facilitated greater differential engagement of neural resources (brain activity) across low and high working memory load conditions. Furthermore, load-based differential management of neural resources reflects enhanced efficiency that is most powerful during higher load and induced anxiety conditions. Overall, our results provide novel insights regarding brain mechanisms that facilitate cognitive enhancement under MPH and, in future research, may be used to help mitigate anxiety-related cognitive underperformance.

NeuMapper: A scalable computational framework for multiscale exploration of the brain's dynamical organization

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.