From Mathematics to Medicine: A Practical Primer on Topological Data Analysis (TDA) and the Development of Related Analytic Tools for the Functional Discovery of Latent Structure in fMRI Data

fMRI is the preeminent method for collecting signals from the human brain in vivo, for using these signals in the service of functional discovery, and relating these discoveries to anatomical structure. Numerous computational and mathematical techniques have been deployed to extract information from the fMRI signal. Yet, the application of Topological Data Analyses (TDA) remain limited to certain sub-areas such as connectomics (that is, with summarized versions of fMRI data). While connectomics is a natural and important area of application of TDA, applications of TDA in the service of extracting structure from the (non-summarized) fMRI data itself are heretofore nonexistent. “Structure” within fMRI data is determined by dynamic fluctuations in spatially distributed signals over time, and TDA is well positioned to help researchers better characterize mass dynamics of the signal by rigorously capturing shape within it. To accurately motivate this idea, we a) survey an established method in TDA (“persistent homology”) to reveal and describe how complex structures can be extracted from data sets generally, and b) describe how persistent homology can be applied specifically to fMRI data. We provide explanations for some of the mathematical underpinnings of TDA (with expository figures), building ideas in the following sequence: a) fMRI researchers can and should use TDA to extract structure from their data; b) this extraction serves an important role in the endeavor of functional discovery, and c) TDA approaches can complement other established approaches toward fMRI analyses (for which we provide examples). We also provide detailed applications of TDA to fMRI data collected using established paradigms, and offer our software pipeline for readers interested in emulating our methods. This working overview is both an inter-disciplinary synthesis of ideas (to draw researchers in TDA and fMRI toward each other) and a detailed description of methods that can motivate collaborative research

Dorsal anterior cingulate cortex modulates supplementary motor area in coordinated unimanual motor behavior

Motor control is integral to all types of human behavior, and the dorsal Anterior Cingulate Cortex (dACC) is thought to play an important role in the brain network underlying motor control. Yet the role of the dACC in motor control is under-characterized. Here we aimed to characterize the dACC’s role in adolescent brain network interactions during a simple motor control task involving visually coordinated unimanual finger movements. Network interactions were assessed using both undirected and directed functional connectivity analysis of fMRI BOLD signals, comparing the task with a rest condition. The relation between the dACC and Supplementary Motor Area (SMA) was compared to that between the dACC and Primary Motor Cortex (M1). The directed signal from dACC to SMA was significantly elevated during motor control in the task. By contrast, the directed signal from SMA to dACC, both directed signals between dACC and M1, and the undirected functional connections of dACC with SMA and M1, all did not differ between task and rest. Undirected coupling of dACC with both SMA and dACC, and only the dACC-to-SMA directed signal, were significantly greater for a proactive than a reactive task condition, suggesting that dACC plays a role in motor control by maintaining stimulus timing expectancy. Overall, these results suggest that the dACC selectively modulates the SMA during visually coordinated unimanual behavior in adolescence. The role of the dACC as an important brain area for the mediation of task-related motor control may be in place in adolescence, continuing into adulthood. The task and analytic approach described here should be extended to the study of healthy adults to examine network profiles of the dACC during basic motor behavior

Attempts at memory control induce dysfunctional brain activation profiles in Generalized Anxiety Disorder: An exploratory fMRI study

Suppression of aversive memories through memory control has historically been proposed as a central psychological defense mechanism. Inability to suppress memories is considered a central psychological trait in several psychiatric disorders, including Generalized Anxiety Disorder (GAD). Yet, few studies have attempted the focused identification of dysfunctional brain activation profiles when patients with Generalized Anxiety Disorders attempt memory control. Using a well-characterized behavioral paradigm we studied brain activation profiles in a group of adult GAD patients and well-matched healthy controls (HC). Participants learned word-association pairs before imaging. During fMRI when presented with one word of the pair, they were instructed to either suppress memory of, or retrieve the paired word. Subsequent behavioral testing indicated both GAD and HC were able to engage in the task, but attempts at memory control (suppression or retrieval) during fMRI revealed vastly different activation profiles. GAD were characterized by substantive hypo-activation signatures during both types of memory control, with effects particularly strong during suppression in brain regions including the dorsal anterior cingulate and the ventral prefrontal cortex. Attempts at memory control in GAD fail to engage brain regions to the same extent HC, providing a putative neuronal signature for a well-established psychological characteristic of the illness

Inefficient white matter activity in Schizophrenia evoked during intra and inter-hemispheric communication

Intensive cognitive tasks induce inefficient regional and network responses in schizophrenia (SCZ). fMRI-based studies have naturally focused on gray matter, but appropriately titrated visuo-motor integration tasks reliably activate inter- and intra-hemispheric white matter pathways. Such tasks can assess network inefficiency without demanding intensive cognitive effort. Here, we provide the first application of this framework to the study of white matter functional responses in SCZ. Event-related fMRI data were acquired from 28 patients (nine females, mean age 43.3, ±11.7) and 28 age- and gender-comparable controls (nine females, mean age 42.1 ± 10.1), using the Poffenberger paradigm, a rapid visual detection task used to induce intra- (ipsi-lateral visual and motor cortex) or inter-hemispheric (contra-lateral visual and motor cortex) transfer. fMRI data were pre- and post-processed to reliably isolate activations in white matter, using probabilistic tractography-based white matter tracts. For intra- and inter-hemispheric transfer conditions, SCZ evinced hyper-activations in longitudinal and transverse white matter tracts, with hyper-activation in sub-regions of the corpus callosum primarily observed during inter-hemispheric transfer. Evidence for the functional inefficiency of white matter was observed in conjunction with small (~50 ms) but significant increases in response times. Functional inefficiencies in SCZ are (1) observable in white matter, with the degree of inefficiency contextually related to task-conditions, and (2) are evoked by simple detection tasks without intense cognitive processing. These cumulative results while expanding our understanding of this dys-connection syndrome, also extend the search of biomarkers beyond the traditional realm of fMRI studies of gray matter

Activations in gray and white matter are modulated by uni-manual responses during within and inter-hemispheric transfer: effects of response hand and right-handedness

Because the visual cortices are contra-laterally organized, inter-hemispheric transfer tasks have been used to behaviorally probe how information briefly presented to one hemisphere of the visual cortex is integrated with responses resulting from the ipsi- or contra-lateral motor cortex. By forcing rapid information exchange across diverse regions, these tasks robustly activate not only gray matter regions, but also white matter tracts. It is likely that the response hand itself (dominant or non-dominant) modulates gray and white matter activations during within and inter-hemispheric transfer. Yet the role of uni-manual responses and/or right hand dominance in modulating brain activations during such basic tasks is unclear. Here we investigated how uni-manual responses with either hand modulated activations during a basic visuo-motor task (the established Poffenberger paradigm) alternating between inter- and within-hemispheric transfer conditions. In a large sample of strongly right-handed adults (n = 49), we used a factorial combination of transfer condition [Inter vs. Within] and response hand [Dominant(Right) vs. Non-Dominant (Left)] to discover fMRI-based activations in gray matter, and in narrowly defined white matter tracts. These tracts were identified using a priori probabilistic white matter atlases. Uni-manual responses with the right hand strongly modulated activations in gray matter, and notably in white matter. Furthermore, when responding with the left hand, activations during inter-hemispheric transfer were strongly predicted by the degree of right-hand dominance, with increased right-handedness predicting decreased fMRI activation. Finally, increasing age within the middle-aged sample was associated with a decrease in activations. These results provide novel evidence of complex relationships between uni-manual responses in right-handed subjects, and activations during within- and inter-hemispheric transfer suggest that the organization of the motor system exerts sophisticated functional effects. Moreover, our evidence of activation in white matter tracts is consistent with prior studies, confirming fMRI-detectable white matter activations which are systematically modulated by experimental condition

Sexual regional dimorphism of post-adolescent and middle age brain maturation. A multi-center 3T MRI study

Sex-related differences are tied into neurodevelopmental and lifespan processes, beginning early in the perinatal and developmental phases and continue into adulthood. The present study was designed to investigate sexual dimorphism of changes in gray matter (GM) volume in post-adolescence, with a focus on early and middle-adulthood using a structural magnetic resonance imaging (MRI) dataset of healthy controls from the European Network on Psychosis, Affective disorders and Cognitive Trajectory (ENPACT). Three hundred and seventy three subjects underwent a 3.0 T MRI session across four European Centers. Age by sex effects on GM volumes were investigated using voxel-based morphometry (VBM) and the Automated Anatomical Labeling atlas regions (ROI). Females and males showed overlapping and non-overlapping patterns of GM volume changes during aging. Overlapping age-related changes emerged in bilateral frontal and temporal cortices, insula and thalamus. Both VBM and ROI analyses revealed non-overlapping changes in multiple regions, including cerebellum and vermis, bilateral mid frontal, mid occipital cortices, left inferior temporal and precentral gyri. These findings highlight the importance of accounting for sex differences in cross-sectional analyses, not only in the study of normative changes, but particularly in the context of psychiatric and neurologic disorders, wherein sex effects may be confounded with disease-related changes

The topology, stability, and instability of learning-induced brain network repertoires in schizophrenia

AbstractThere is a paucity of graph theoretic methods applied to task-based data in schizophrenia (SCZ). Tasks are useful for modulating brain network dynamics, and topology. Understanding how changes in task conditions impact inter-group differences in topology can elucidate unstable network characteristics in SCZ. Here, in a group of patients and healthy controls (n = 59 total, 32 SCZ), we used an associative learning task with four distinct conditions (Memory Formation, Post-Encoding Consolidation, Memory Retrieval, and Post-Retrieval Consolidation) to induce network dynamics. From the acquired fMRI time series data, betweenness centrality (BC), a metric of a node’s integrative value was used to summarize network topology in each condition. Patients showed (a) differences in BC across multiple nodes and conditions; (b) decreased BC in more integrative nodes, but increased BC in less integrative nodes; (c) discordant node ranks in each of the conditions; and (d) complex patterns of stability and instability of node ranks across conditions. These analyses reveal that task conditions induce highly variegated patterns of network dys-organization in SCZ. We suggest that the dys-connection syndrome that is schizophrenia, is a contextually evoked process, and that the tools of network neuroscience should be oriented toward elucidating the limits of this dys-connection

Stability of Satellite Planes in M31 II: Effects of the Dark Subhalo Population

The planar arrangement of nearly half the satellite galaxies of M31 has been a source of mystery and speculation since it was discovered. With a growing number of other host galaxies showing these satellite galaxy planes, their stability and longevity have become central to the debate on whether the presence of satellite planes are a natural consequence of prevailing cosmological models, or represent a challenge. Given the dependence of their stability on host halo shape, we look into how a galaxy plane's dark matter environment influences its longevity. An increased number of dark matter subhalos results in increased interactions that hasten the deterioration of an already-formed plane of satellite galaxies in spherical dark halos. The role of total dark matter mass fraction held in subhalos in dispersing a plane of galaxies present non trivial effects on plane longevity as well. But any misalignments of plane inclines to major axes of flattened dark matter halos lead to their lifetimes being reduced to < 3 Gyrs. Distributing > 40% of total dark mass in subhalos in the overall dark matter distribution results in a plane of satellite galaxies that is prone to change through the 5 Gyr integration time period.Comment: 11 pages, 9 figures, accepted to MNRAS September 22 201

Reading related white matter structures in adolescents are influenced more by dysregulation of emotion than behavior

Mood disorders and behavioral are broad psychiatric diagnostic categories that have different symptoms and neurobiological mechanisms, but share some neurocognitive similarities, one of which is an elevated risk for reading deficit. Our aim was to determine the influence of mood versus behavioral dysregulation on reading ability and neural correlates supporting these skills in youth, using diffusion tensor imaging in 11- to 17-year-old children and youths with mood disorders or behavioral disorders and age-matched healthy controls. The three groups differed only in phonological processing and passage comprehension. Youth with mood disorders scored higher on the phonological test but had lower comprehension scores than children with behavioral disorders and controls; control participants scored the highest. Correlations between fractional anisotropy and phonological processing in the left Arcuate Fasciculus showed a significant difference between groups and were strongest in behavioral disorders, intermediate in mood disorders, and lowest in controls. Correlations between these measures in the left Inferior Longitudinal Fasciculus were significantly greater than in controls for mood but not for behavioral disorders. Youth with mood disorders share a deficit in the executive-limbic pathway (Arcuate Fasciculus) with behavioral-disordered youth, suggesting reduced capacity for engaging frontal regions for phonological processing or passage comprehension tasks and increased reliance on the ventral tract (e.g., the Inferior Longitudinal Fasciculus). The low passage comprehension scores in mood disorder may result from engaging the left hemisphere. Neural pathways for reading differ mainly in executive-limbic circuitry. This new insight may aid clinicians in providing appropriate intervention for each disorder

Can Emotional and Behavioral Dysregulation in Youth Be Decoded from Functional Neuroimaging?

High comorbidity among pediatric disorders characterized by behavioral and emotional dysregulation poses problems for diagnosis and treatment, and suggests that these disorders may be better conceptualized as dimensions of abnormal behaviors. Furthermore, identifying neuroimaging biomarkers related to dimensional measures of behavior may provide targets to guide individualized treatment. We aimed to use functional neuroimaging and pattern regression techniques to determine whether patterns of brain activity could accurately decode individual-level severity on a dimensional scale measuring behavioural and emotional dysregulation at two different time points