An official website of the United States government
Topological data analysis (TDA) has proven to be a potent approach for extracting intricate topological structures from complex and high-dimensional data. In this paper, we propose a TDA-based processing pipeline for analyzing multi-channel scalp EEG data. The pipeline starts with extracting both frequency and temporal information from the signals via the Hilbert–Huang Transform. The sequences of instantaneous frequency and instantaneous amplitude across all electrode channels are treated as approximations of curves in the high-dimensional space. TDA features, which represent the local topological structure of the curves, are further extracted and used in the classification models. Three sets of scalp EEG data, including one collected in a lab and two Brain–computer Interface (BCI) competition data, were used to validate the proposed methods, and compare with other state-of-art TDA methods. The proposed TDA-based approach shows superior performance and outperform the winner of the BCI competition. Besides BCI, the proposed method can also be applied to spatial and temporal data in other domains such as computer vision, remote sensing, and medical imaging.
more »
« less
Altered topological structure of the brain white matter in maltreated children through topological data analysis
Abstract Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in the global topology of the brain white matter structural covariance network among children. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging and diffusion tensor imaging. We develop a novel framework for statistical inference based on the Wasserstein distance to assess the significance of the observed topological differences. Using these methods in comparing maltreated children with a typically developing control group, we find that maltreatment may increase homogeneity in white matter structures and thus induce higher correlations in the structural covariance; this is reflected in the topological profile. Our findings strongly suggest that TDA can be a valuable framework to model altered topological structures of the brain. The MATLAB codes and processed data used in this study can be found at https://github.com/laplcebeltrami/maltreated.
more »
« less
- Award ID(s):
- 2010778
- PAR ID:
- 10480049
- Publisher / Repository:
- DOI PREFIX: 10.1162
- Date Published:
- Journal Name:
- Network Neuroscience
- Volume:
- 8
- Issue:
- 1
- ISSN:
- 2472-1751
- Format(s):
- Medium: X Size: p. 355-376
- Size(s):
- p. 355-376
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Neural oscillations may be sensitive to aspects of brain maturation such as myelination and synaptic density changes. Better characterization of developmental trajectories and reliability is necessary for understanding typical and atypical neurodevelopment. Here, we examined reliability in 110 typically developing children and adolescents (aged 9–17 years) across 2.25 years. From 10 min of magnetoencephalography resting-state data, normalized source spectral power and intraclass correlation coefficients were calculated. We found sex-specific differences in global normalized power, with males showing age-related decreases in delta and theta, along with age-related increases in beta and gamma. Females had fewer significant age-related changes. Structural magnetic resonance imaging revealed that males had more total gray, subcortical gray, and cortical white matter volume. There were significant age-related changes in total gray matter volume with sex-specific and frequency-specific correlations to normalized power. In males, increased total gray matter volume correlated with increased theta and alpha, along with decreased gamma. Split-half reliability was excellent in all frequency bands and source regions. Test–retest reliability ranged from good (alpha) to fair (theta) to poor (remaining bands). While resting-state neural oscillations can have fingerprint-like quality in adults, we show here that neural oscillations continue to evolve in children and adolescents due to brain maturation and neurodevelopmental change.more » « less
-
Abstract Research using functional and structural magnetic resonance imaging has identified areas of reduced brain activation and gray matter volume in children and adults with reading disability, but associations between cortical structure and individual differences in reading in typically developing children remain underexplored. Furthermore, the majority of research linking gray matter structure to reading ability quantifies gray matter in terms of volume, and cannot specify unique contributions of cortical surface area and thickness to these relationships. Here, we applied a continuous analytic approach to investigate associations between distinct surface-based properties of cortical structure and individual differences in reading-related skills in a sample of typically developing young children. Correlations between cortical structure and reading-related skills were conducted using a surface-based vertex-wise approach. Cortical thickness in the left superior temporal cortex was positively correlated with word and pseudoword reading performance. The observed positive correlation between cortical thickness in the left superior temporal cortex and reading may have implications for the patterns of brain activation that support reading.more » « less
-
Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach that can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent homology (PH), which can extract topological properties from data at various scales. The aim of this article is to introduce TDA concepts to a statistical audience and provide an approach to analyzing multivariate time series data. The application’s focus will be on multivariate brain signals and brain connectivity networks. Finally, this paper concludes with an overview of some open problems and potential application of TDA to modeling directionality in a brain network, as well as the casting of TDA in the context of mixed effect models to capture variations in the topological properties of data collected from multiple subjects.more » « less
-
Wang, Yalin (Ed.)We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure topological differences, enabling the clustering of brain networks into distinct topological states. This technique outperforms the commonly used k-means clustering in identifying brain network state spaces by effectively incorporating the temporal dynamics of the data without the need for explicit model specification. We further investigate the genetic underpinnings of these topological features using a twin study design, examining the heritability of such state changes. Our findings suggest that the topology of brain networks, particularly in their dynamic state changes, may hold significant hidden genetic information.more » « less
