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

Patients with schizophrenia exhibit impairments in working memory that often appear in attenuated form in persons at high risk for the illness. The authors hypothesized that deviations in task-related brain activation and deactivation would occur in persons with an at-risk mental state performing a working memory task that entailed the maintenance and manipulation of letters. Participants at ultra high risk for developing psychosis (N=60), identified using the Comprehensive Assessment of At-Risk Mental States, and healthy comparison subjects (N=38) 14 to 29 years of age underwent functional MRI while performing a verbal working memory task. Group differences in brain activation were identified using analysis of covariance. The two groups did not show significant differences in speed or accuracy of performance, even after accounting for differences in education. Irrespective of task condition, at-risk participants exhibited significantly less activation than healthy comparison subjects in the left anterior insula. During letter manipulation, at-risk persons exhibited greater task-related deactivation within the default-mode network than comparison subjects. Region-of-interest analysis in the at-risk group revealed significantly greater right dorsolateral prefrontal cortex activation during manipulation of letters. Despite comparable behavioral performance, at-risk participants performing a verbal working memory task exhibited altered brain activation compared with healthy subjects. These findings demonstrate an altered pattern of brain activation in at-risk persons that contains elements of reduced function as well as compensation.

An Artificial Intelligence Ultrasound Platform for Screening and Staging of Thyroid Cancer

BackgroundInterpretation of high-throughput gene expression data continues to require mathematical tools in data analysis that recognizes the shape of the data in high dimensions. Topological data analysis (TDA) has recently been successful in extracting robust features in several applications dealing with high dimensional constructs. In this work, we utilize some recent developments in TDA to curate gene expression data. Our work differs from the predecessors in two aspects: (1) Traditional TDA pipelines use topological signatures called barcodes to enhance feature vectors which are used for classification. In contrast, this work involves curating relevant features to obtain somewhat better representatives with the help of TDA. This representatives of the entire data facilitates better comprehension of the phenotype labels. (2) Most of the earlier works employ barcodes obtained using topological summaries as fingerprints for the data. Even though they are stable signatures, there exists no direct mapping between the data and said barcodes.ResultsThe topology relevant curated data that we obtain provides an improvement in shallow learning as well as deep learning based supervised classifications. We further show that the representative cycles we compute have an unsupervised inclination towards phenotype labels. This work thus shows that topological signatures are able to comprehend gene expression levels and classify cohorts accordingly.ConclusionsIn this work, we engender representative persistent cycles to discern the gene expression data. These cycles allow us to directly procure genes entailed in similar processes.

A growing area of mathematics topological data analysis (TDA) uses fundamental concepts of topology to analyze complex, high-dimensional data. A topological network represents the data, and the TDA uses the network to analyze the shape of the data and identify features in the network that correspond to patterns in the data. These patterns extract knowledge from the data. TDA provides a framework to advance machine learning’s ability to understand and analyze large, complex data. This paper provides background information about TDA, TDA applications for large data sets, and details related to the investigation and implementation of existing tools and environments.

EEG-vigilance and BOLD effect during simultaneous EEG/fMRI measurement

Topological data analysis in investment decisions

Asthma is a complex respiratory disease characterised by spatial ventilation heterogeneity (VH) in the lung. Multiple breath washout (MBW) and forced oscillation technique (FOT) testing has been shown to quantify VH at the mouth. Methods to provide fresh insight into the mechanisms driving VH are urgently needed to support treatment development. Computed tomography (CT) with parametric response map (PRM) analysis provides spatial and functional lung data. Integrated data sets of imaging features and VH markers present the problem of extracting meaningful information from high dimensional objects; topological data analysis (TDA) has demonstrated recent success in solving this problem. In this thesis topological methods are applied to extract information about lung anatomy and function from imaging data to study association with VH in innately high dimensional integrated data sets. It was sought to describe the spatial distributions of voxel based metrics, visualise the lungs using TDA methods, and combine PRM with simulated airway tree models to improve computational modelling of FOT. Data was obtained from a clinical trial involving 52 subjects, 41 asthmatic (11 healthy). An algorithm was developed to quantify directional Hounsfield unit change (ΔHU) gradients. TDA was applied to integrated data sets and voxel sets with measures of airway tree depth. FOT modelling was augmented with ΔHU about simulated acinar airways.Inferior-to-superior ΔHU gradient best differentiated VH markers. Visualisations of the lungs illustrated gradient reversal and increased heterogeneity in ΔHU in asthmatics. FOT modelling using ΔHU parameterisation showed increased correlation between clinically measured and simulated FOT small airway resistance (R5-R20). In this thesis additional insight is presented into mechanisms affecting VH markers derived from MBW and FOT. Topological methods to analyse imaging data were developed and implemented, including workflows to visualise the lungs and lung function. Linking simulated airway tree geometry with ΔHU showed improvement in FOT modelling.

We examined neural activity, in the frontal lobes, associated with speech production during affective states. Using functional magnetic resonance imaging (fMRI), the blood oxygen level-dependent (BOLD) response to the overt reading of emotionally neutral sentences was measured before and after a happy or sad mood induction. There was no explicit demand to produce affect-congruent speech and a cover story was used to de-emphasize the significance of the speech task in light of our experimental aims. Each fMRI measurement was acquired 6 s after the onset of sentence presentation so that speech could be recorded while the scanner noise was minimal; speech parameters (e.g. pitch variation) were extracted from the sentences and regressed against fMRI data. In the sad group we found the predicted changes in affect and pitch variation. Further, the fMRI data confirmed our hypothesis in that the 'reading effect' (i.e. the BOLD response to reading minus the BOLD response to baseline stimuli) in the supracallosal anterior cingulate cortex covaried negatively with both pitch variation and affect. Our results suggest that the anterior cingulate cortex modulates paralinguistic features of speech during affective states, thus placing this neural structure at the interface between action and emotions.

Topological Data Analysis (TDA) and its mainstay computational device, persistent homology (PH), has established a strong track record of providing researchers across the data-driven sciences with new insights and methodologies by characterizing low-dimensional geometric structures in high-dimensional data. When combined with machine learning (ML) methods, PH is valued as a discriminating-feature extraction tool. This work highlights many of the recent successes at the intersection of TDA and ML, introduces some of the foundational mathematics underpinning TDA, and summarizes the efforts to strengthen the bridge between TDA and ML. Thus, this document is a launching point for experimentalists and theoreticians to consider what can be learned from the shape of their data.

Persistence landscapes (PL) have emerged as a transformative tool in topological data analysis (TDA), a rapidly advancing field in the current era of data-driven research. In this study, we propose a machine learning model that leverages persistence landscapes to analyse and classify time series data. We apply this model to the problem of Alzheimer's disease detection, using electroencephalogram (EEG) time series data to differentiate between a group of Alzheimer's patients and a control group of unaffected individuals. Our results demonstrate the potential of PL-based models in supporting effective classification in biomedical applications.

Traditional deep learning methods for histopathological analysis suffer from a lack of interpretability, which limits their use in the clinic despite their high accuracy. This paper proposes a Topological Data Analysis (TDA) framework for interpretable colorectal cancer tissue classification. We used persistent homology to extract topological features from 5000 histological images representing eight tissue classes, combining persistence landscapes with Support Vector Machine (SVM) classification. This method achieved an overall accuracy rate of 82.70%, while providing biologically interpretable features that are directly related to tissue morphology. Topological features successfully represented cellular connectivity as well as structural patterns, enabling perfect classification of morphologically distinct tissue pairs. This research demonstrates that topological data analysis (TDA) represents a promising alternative to non-transparent methods, offering competitive efficiency while ensuring interpretability, a crucial aspect for its clinical integration in computational pathology.

Most of the currently used methods for functional brain imaging do not visualize neuronal activity directly but rather rely on the elicited hemodynamic and/or metabolic responses. Glutamate, the major excitatory neurotransmitter, plays an important role in the neurovascular/neurometabolic coupling, but the specific mechanisms are still poorly understood. To investigate the role of the two major ionotropic glutamate receptors [NMDA receptors (NMDA-Rs) and AMPA receptors (AMPA-Rs)] for the generation of functional magnetic resonance imaging (fMRI) signals, we used fMRI [measurements of blood oxygenation level-dependent (BOLD), perfusion-weighted imaging (PWI), and cerebral blood volume (CBV)] together with recordings of somatosensory evoked potentials (SEPs) during electrical forepaw stimulation in the alpha-chloralose anesthetized rat. Intravenous injection of the NMDA-R antagonist MK-801 [(+)-5-methyl-10,11-dihydro-5H-dibenzo [a,d] cyclohepten-5,10-imine maleate] (0.06 mg/kg plus 3.6 microg x kg(-1) x h(-1)) significantly decreased BOLD (-51 +/- 19%; n = 5) and PWI (-57 +/- 26%; n = 5) responses but reduced the SEPs only mildly (approximately -10%). Systemic application of the AMPA-R antagonist GYKI-53655 [1-(4-aminophenyl)-3-methylcarbamyl-4-methyl-7,8-methylenedioxy-3,4-dihydro-5H-2,3-benzodiazepine] significantly decreased both the hemodynamic response (BOLD, -49 +/- 13 and -65 +/- 15%; PWI, -22 +/- 48 and -68 +/- 4% for 5 and 7 mg/kg, i.v., respectively; CBV, -80 +/- 7% for 7 mg/kg; n = 4) and the SEPs (up to -60%). These data indicate that the interaction of glutamate with its postsynaptic and/or glial receptors is necessary for the generation of blood flow and BOLD responses and illustrate the differential role of NMDA-Rs and AMPA-Rs in the signaling chain leading from increased neuronal activity to the hemodynamic response in the somatosensory cortex.

Single-cell technologies have revolutionized our ability to interrogate biological systems at unprecedented resolution, revealing complex cellular heterogeneity and dynamic processes that underlie development, disease, and immune responses. However, the high dimensionality and nonlinear structure of single-cell data present substantial analytical challenges. Topological data analysis offers a powerful mathematical framework for capturing the intrinsic shape of data, providing novel insights that complement and extend traditional statistical and machine learning methods. By leveraging tools such as persistent homology and the Mapper algorithm, TDA enables the detection of subtle, multiscale patterns – including rare cell populations, transitional states, and branching trajectories – that are often obscured by conventional approaches. In this review, we explore the theoretical foundations of topological data analysis and examine its emerging applications across single-cell transcriptomics, proteomics, and spatial biology. We highlight how this approach can unveil previously unrecognized biological phenomena, from alternative differentiation paths to complex tissue architectures, and discuss the growing ecosystem of computational tools that support its use. As single-cell datasets become increasingly large and multimodal, topological data analysis stands out as a uniquely robust and interpretable approach, with the potential to deepen our understanding of cellular identity and function in health and disease. TDA is specially suited for fields such as systems immunology since it can capture the complex, nonlinear structures inherent in high-dimensional immune data helping to identify distinct immune cell states, differentiation pathways, and dynamic responses to infection or therapy. This topological perspective complements traditional statistical approaches, providing a robust, scale-invariant framework for uncovering hidden organization within the immune system’s complexity.

ABSTRACTThe increased prevalence of HIV among adults >50 years underscores the importance of improving our understanding of mechanisms causing HIV-associated neurocognitive disorders (HAND). Identifying novel and noninvasive diagnostic predictors of HAND prior to clinical manifestation is critical to ultimately identifying means of preventing progression to symptomatic HAND. Here, using a task-switching paradigm, in which subjects were cued (unpredictably) to perform a face-gender or a word-semantic task on superimposed face and word images, we examined the behavioral and neural profile of impaired cognitive control in older HIV + adults (N = 14, 9 HIV+). Functional magnetic resonance imaging (fMRI) and behavioral data were acquired while subjects were performing the face-gender or word-semantic task. We found that, despite comparable performance in standard neuropsychology tests that are designed to probe executive deficits, HIV-infected participants were significantly slower than uninfected controls in adapting to change in task demand, and the behavioral impairments can be quantitatively related to difference in fMRI signal at the dorsal anterior cingulate cortex (ACC). Due to the limited sample size of this hypothesis-generating study, we should take caution with these findings and future studies with a large and better matched sample size are needed. However, these rather novel findings in this study have a few important implications: first, the prevalence of cognitive impairments in HIV+ older adults might be even higher than previously proposed; second, ACC (in particularly its dorsal region) might be one of the key regions underlying cognitive impairments (in particularly executive functions) in HIV; and third, it might be beneficial to adopt paradigms developed and validated in cognitive neuroscience to study HAND, as these techniques might be more sensitive to some aspects of HIV-associated neurocognitive impairments than standard neuropsychology tests.

Abstract: Neurodegenerative diseases, such as Alzheimer's and Parkinson's, are characterized by progressive neuronal deterioration, leading to cognitive and motor impairments. Early detection is crucial for effective intervention and management. This study proposes a novel framework utilizing Topological Data Analysis (TDA), particularly persistent homology, to identify early biomarkers from neuroimaging and physiological data. This study explores the application of TDA techniques—specifically persistent homology and topological invariants—for the early detection of neurodegenerative diseases such as Alzheimer's. By analyzing functional brain connectivity, gait dynamics, and molecular structures associated with disease progression, the research demonstrates that TDA can capture subtle, yet critical, topological signatures indicative of early neurodegenerative changes. Layer-wise topological complexity in neural networks and persistent homology in clinical datasets reveal distinct structural degradation patterns. The integration of TDA with machine learning models enhances diagnostic accuracy, interpretability, and generalization, offering a promising direction for non-invasive, data-driven diagnostics in neurology.By capturing the intrinsic topological features of brain networks, the framework aims to distinguish between healthy and early-stage neurodegenerative conditions, offering a robust tool for early diagnosis.Topological Data Analysis (TDA) offers a robust mathematical framework for extracting shape-based features from high-dimensional and noisy biomedical data. Keywords: Topological Data Analysis, Persistent Homology, Neurodegenerative Disease, Alzheimer's, Brain Connectivity, Early Diagnosis, Betti Numbers, Gait Analysis, Functional Networks, Machine Learning, Biomedical Data