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Chung MK, Huang SG, Carroll IC, Calhoun VD, Goldsmith HH. Topological state-space estimation of functional human brain networks. PLoS Comput Biol 2024; 20:e1011869. [PMID: 38739671 PMCID: PMC11115255 DOI: 10.1371/journal.pcbi.1011869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2023] [Revised: 05/23/2024] [Accepted: 01/29/2024] [Indexed: 05/16/2024] Open
Abstract
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.
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Affiliation(s)
- Moo K. Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, Wisconsin, United States of America
| | | | - Ian C. Carroll
- Department of Child and Adolescent Psychiatry, New York University Grossman School of Medicine, New York, United States of America
| | - Vince D. Calhoun
- Tri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS), Georgia State University, Georgia Institute of Technology, Emory University, Atlanta, Georgia, United States of America
| | - H. Hill Goldsmith
- Department of Psychology & Waisman Center, University of Wisconsin, Madison, Wisconsin, United States of America
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2
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Chung MK, Azizi T, Hanson JL, Alexander AL, Pollak SD, Davidson RJ. Altered topological structure of the brain white matter in maltreated children through topological data analysis. Netw Neurosci 2024; 8:355-376. [PMID: 38711544 PMCID: PMC11073548 DOI: 10.1162/netn_a_00355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Accepted: 11/30/2023] [Indexed: 05/08/2024] Open
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.
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Affiliation(s)
- Moo K. Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin–Madison, Madison, WI, USA
| | - Tahmineh Azizi
- Department of Biostatistics and Medical Informatics, University of Wisconsin–Madison, Madison, WI, USA
| | - Jamie L. Hanson
- Department of Psychology, University of Pittsburgh, Pittsburgh, PA, USA
| | - Andrew L. Alexander
- Department of Medical Physics, University of Wisconsin–Madison, Madison, WI, USA
| | - Seth D. Pollak
- Department of Psychology, University of Wisconsin–Madison, Madison, WI, USA
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3
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Phillips JS, Adluru N, Chung MK, Radhakrishnan H, Olm CA, Cook PA, Gee JC, Cousins KAQ, Arezoumandan S, Wolk DA, McMillan CT, Grossman M, Irwin DJ. Greater white matter degeneration and lower structural connectivity in non-amnestic vs. amnestic Alzheimer's disease. Front Neurosci 2024; 18:1353306. [PMID: 38567286 PMCID: PMC10986184 DOI: 10.3389/fnins.2024.1353306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2023] [Accepted: 02/26/2024] [Indexed: 04/04/2024] Open
Abstract
Introduction Multimodal evidence indicates Alzheimer's disease (AD) is characterized by early white matter (WM) changes that precede overt cognitive impairment. WM changes have overwhelmingly been investigated in typical, amnestic mild cognitive impairment and AD; fewer studies have addressed WM change in atypical, non-amnestic syndromes. We hypothesized each non-amnestic AD syndrome would exhibit WM differences from amnestic and other non-amnestic syndromes. Materials and methods Participants included 45 cognitively normal (CN) individuals; 41 amnestic AD patients; and 67 patients with non-amnestic AD syndromes including logopenic-variant primary progressive aphasia (lvPPA, n = 32), posterior cortical atrophy (PCA, n = 17), behavioral variant AD (bvAD, n = 10), and corticobasal syndrome (CBS, n = 8). All had T1-weighted MRI and 30-direction diffusion-weighted imaging (DWI). We performed whole-brain deterministic tractography between 148 cortical and subcortical regions; connection strength was quantified by tractwise mean generalized fractional anisotropy. Regression models assessed effects of group and phenotype as well as associations with grey matter volume. Topological analyses assessed differences in persistent homology (numbers of graph components and cycles). Additionally, we tested associations of topological metrics with global cognition, disease duration, and DWI microstructural metrics. Results Both amnestic and non-amnestic patients exhibited lower WM connection strength than CN participants in corpus callosum, cingulum, and inferior and superior longitudinal fasciculi. Overall, non-amnestic patients had more WM disease than amnestic patients. LvPPA patients had left-lateralized WM degeneration; PCA patients had reductions in connections to bilateral posterior parietal, occipital, and temporal areas. Topological analysis showed the non-amnestic but not the amnestic group had more connected components than controls, indicating persistently lower connectivity. Longer disease duration and cognitive impairment were associated with more connected components and fewer cycles in individuals' brain graphs. Discussion We have previously reported syndromic differences in GM degeneration and tau accumulation between AD syndromes; here we find corresponding differences in WM tracts connecting syndrome-specific epicenters. Determining the reasons for selective WM degeneration in non-amnestic AD is a research priority that will require integration of knowledge from neuroimaging, biomarker, autopsy, and functional genetic studies. Furthermore, longitudinal studies to determine the chronology of WM vs. GM degeneration will be key to assessing evidence for WM-mediated tau spread.
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Affiliation(s)
- Jeffrey S. Phillips
- Penn Frontotemporal Degeneration Center, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
| | - Nagesh Adluru
- Waisman Center, University of Wisconsin-Madison, Madison, WI, United States
- Department of Radiology, University of Wisconsin-Madison, Madison, WI, United States
| | - Moo K. Chung
- Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin-Madison, Madison, WI, United States
| | - Hamsanandini Radhakrishnan
- Penn Frontotemporal Degeneration Center, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
| | - Christopher A. Olm
- Penn Frontotemporal Degeneration Center, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
| | - Philip A. Cook
- Penn Image Computing and Science Laboratory, Department of Radiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
| | - James C. Gee
- Penn Image Computing and Science Laboratory, Department of Radiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
| | - Katheryn A. Q. Cousins
- Penn Frontotemporal Degeneration Center, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
| | - Sanaz Arezoumandan
- Penn Frontotemporal Degeneration Center, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
| | - David A. Wolk
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
- Penn Memory Center, University of Pennsylvania Health System, Philadelphia, PA, United States
| | - Corey T. McMillan
- Penn Frontotemporal Degeneration Center, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
| | - Murray Grossman
- Penn Frontotemporal Degeneration Center, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
| | - David J. Irwin
- Penn Frontotemporal Degeneration Center, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, United States
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Köry J, Narain V, Stolz BJ, Kaeppler J, Markelc B, Muschel RJ, Maini PK, Pitt-Francis JM, Byrne HM. Enhanced perfusion following exposure to radiotherapy: A theoretical investigation. PLoS Comput Biol 2024; 20:e1011252. [PMID: 38363799 PMCID: PMC10903964 DOI: 10.1371/journal.pcbi.1011252] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Revised: 02/29/2024] [Accepted: 01/23/2024] [Indexed: 02/18/2024] Open
Abstract
Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumour's response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies. In this work, we first identify vascular architectural features that correlate with enhanced perfusion following radiotherapy, using in vivo imaging data from vascular tumours. Then, we present a novel computational model to determine the relationship between these architectural features and blood perfusion in silico. If perfusion is defined to be the proportion of vessels that support blood flow, we find that vascular networks with small mean diameters and large numbers of angiogenic sprouts show the largest increases in perfusion post-irradiation for both biological and synthetic tumours. We also identify cases where perfusion increases due to the pruning of hypoperfused vessels, rather than blood being rerouted. These results indicate the importance of considering network composition when determining the optimal irradiation strategy. In the future, we aim to use our findings to identify tumours that are good candidates for perfusion enhancement and to improve the efficacy of combination therapies.
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Affiliation(s)
- Jakub Köry
- School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Vedang Narain
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Bernadette J. Stolz
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
- Laboratory for Topology and Neuroscience, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Jakob Kaeppler
- Cancer Research UK and MRC Oxford Institute for Radiation Oncology, Department of Oncology, University of Oxford, Oxford, United Kingdom
| | - Bostjan Markelc
- Cancer Research UK and MRC Oxford Institute for Radiation Oncology, Department of Oncology, University of Oxford, Oxford, United Kingdom
- Department of Experimental Oncology, Institute of Oncology Ljubljana, Ljubljana, Slovenia
| | - Ruth J. Muschel
- Cancer Research UK and MRC Oxford Institute for Radiation Oncology, Department of Oncology, University of Oxford, Oxford, United Kingdom
| | - Philip K. Maini
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Joe M. Pitt-Francis
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Helen M. Byrne
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
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5
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Ohki T, Kunii N, Chao ZC. Efficient, continual, and generalized learning in the brain - neural mechanism of Mental Schema 2.0. Rev Neurosci 2023; 34:839-868. [PMID: 36960579 DOI: 10.1515/revneuro-2022-0137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 02/26/2023] [Indexed: 03/25/2023]
Abstract
There has been tremendous progress in artificial neural networks (ANNs) over the past decade; however, the gap between ANNs and the biological brain as a learning device remains large. With the goal of closing this gap, this paper reviews learning mechanisms in the brain by focusing on three important issues in ANN research: efficiency, continuity, and generalization. We first discuss the method by which the brain utilizes a variety of self-organizing mechanisms to maximize learning efficiency, with a focus on the role of spontaneous activity of the brain in shaping synaptic connections to facilitate spatiotemporal learning and numerical processing. Then, we examined the neuronal mechanisms that enable lifelong continual learning, with a focus on memory replay during sleep and its implementation in brain-inspired ANNs. Finally, we explored the method by which the brain generalizes learned knowledge in new situations, particularly from the mathematical generalization perspective of topology. Besides a systematic comparison in learning mechanisms between the brain and ANNs, we propose "Mental Schema 2.0," a new computational property underlying the brain's unique learning ability that can be implemented in ANNs.
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Affiliation(s)
- Takefumi Ohki
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo 113-0033, Japan
| | - Naoto Kunii
- Department of Neurosurgery, The University of Tokyo, Tokyo 113-0033, Japan
| | - Zenas C Chao
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo 113-0033, Japan
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6
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Chung MK, Ramos CG, De Paiva FB, Mathis J, Prabhakaran V, Nair VA, Meyerand ME, Hermann BP, Binder JR, Struck AF. Unified topological inference for brain networks in temporal lobe epilepsy using the Wasserstein distance. Neuroimage 2023; 284:120436. [PMID: 37931870 PMCID: PMC11074922 DOI: 10.1016/j.neuroimage.2023.120436] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Revised: 09/14/2023] [Accepted: 10/30/2023] [Indexed: 11/08/2023] Open
Abstract
Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological features that persist over these scales. These features are summarized in persistence diagrams, and their dissimilarity is quantified using the Wasserstein distance. However, the Wasserstein distance does not follow a known distribution, posing challenges for the application of existing parametric statistical models. To tackle this issue, we introduce a unified topological inference framework centered on the Wasserstein distance. Our approach has no explicit model and distributional assumptions. The inference is performed in a completely data driven fashion. We apply this method to resting-state functional magnetic resonance images (rs-fMRI) of temporal lobe epilepsy patients collected from two different sites: the University of Wisconsin-Madison and the Medical College of Wisconsin. Importantly, our topological method is robust to variations due to sex and image acquisition, obviating the need to account for these variables as nuisance covariates. We successfully localize the brain regions that contribute the most to topological differences. A MATLAB package used for all analyses in this study is available at https://github.com/laplcebeltrami/PH-STAT.
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Affiliation(s)
- Moo K Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, USA.
| | | | | | | | | | - Veena A Nair
- Department of Radiology, University of Wisconsin-Madison, USA.
| | - Mary E Meyerand
- Departments of Medical Physics & Biomedical Engineering, University of Wisconsin-Madison, USA.
| | - Bruce P Hermann
- Department of Neurology, University of Wisconsin-Madison, USA.
| | | | - Aaron F Struck
- Department of Neurology, University of Wisconsin-Madison, USA.
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7
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Chung MK, Azizi T, Hanson JL, Alexander AL, Davidson RJ, Pollak SD. Altered Topological Structure of the Brain White Matter in Maltreated Children through Topological Data Analysis. ArXiv 2023:arXiv:2304.05908v3. [PMID: 37090232 PMCID: PMC10120754] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 04/25/2023]
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 (MRI) and diffusion tensor imaging (DTI). 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 to 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.
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Affiliation(s)
- Moo K. Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, USA
| | - Tahmineh Azizi
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, USA
| | | | | | | | - Seth D. Pollak
- Department of Psychology, University of Wisconsin-Madison, USA
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8
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Wang Y, Yin J, Desai RH. Topological inference on brain networks across subtypes of post-stroke aphasia. ArXiv 2023:arXiv:2311.01625v1. [PMID: 37961747 PMCID: PMC10635302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Subscribe] [Scholar Register] [Indexed: 11/15/2023]
Abstract
Persistent homology (PH) characterizes the shape of brain networks through the persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space representation of persistence diagram (PD) through heat diffusion reparameterizes using the finite number of Fourier coefficients with respect to the Laplace-Beltrami (LB) eigenfunction expansion of the domain, which provides a powerful vectorized algebraic representation for group comparisons of PDs. In this study, we advance a transposition-based permutation test for comparing multiple groups of PDs through the heat-diffusion estimates of the PDs. We evaluate the empirical performance of the spectral transposition test in capturing within- and between-group similarity and dissimilarity with respect to statistical variation of topological noise and hole location. We also illustrate how the method extends naturally into a clustering scheme by subtyping individuals with post-stroke aphasia through the PDs of their resting-state functional brain networks.
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Affiliation(s)
- Yuan Wang
- Department of Epidemiology and Biostatistics University of South Carolina U.S.A
| | - Jian Yin
- Department of Biostatistics Nanjing Medical University China
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9
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Chung MK, Ramos CG, De Paiva FB, Mathis J, Prabharakaren V, Nair VA, Meyerand E, Hermann BP, Binder JR, Struck AF. Unified Topological Inference for Brain Networks in Temporal Lobe Epilepsy Using the Wasserstein Distance. ArXiv 2023:arXiv:2302.06673v3. [PMID: 36824424 PMCID: PMC9949148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
Abstract
Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological features that persist over these scales. These features are summarized in persistence diagrams, and their dissimilarity is quantified using the Wasserstein distance. However, the Wasserstein distance does not follow a known distribution, posing challenges for the application of existing parametric statistical models. To tackle this issue, we introduce a unified topological inference framework centered on the Wasserstein distance. Our approach has no explicit model and distributional assumptions. The inference is performed in a completely data driven fashion. We apply this method to resting-state functional magnetic resonance images (rs-fMRI) of temporal lobe epilepsy patients collected from two different sites: the University of Wisconsin-Madison and the Medical College of Wisconsin. Importantly, our topological method is robust to variations due to sex and image acquisition, obviating the need to account for these variables as nuisance covariates. We successfully localize the brain regions that contribute the most to topological differences. A MATLAB package used for all analyses in this study is available at https://github.com/laplcebeltrami/PH-STAT.
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Affiliation(s)
- Moo K Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, USA
| | | | | | | | | | - Veena A Nair
- Department of Radiology, University of Wisconsin-Madison, USA
| | - Elizabeth Meyerand
- Departments of Medical Physics & Biomedical Engineering, University of Wisconsin-Madison, USA
| | - Bruce P Hermann
- Department of Neurology, University of Wisconsin-Madison, USA
| | | | - Aaron F Struck
- Department of Neurology, University of Wisconsin-Madison, USA
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10
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Anand DV, Chung MK. Hodge Laplacian of Brain Networks. IEEE Trans Med Imaging 2023; 42:1563-1573. [PMID: 37018280 PMCID: PMC10909176 DOI: 10.1109/tmi.2022.3233876] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain. In this work, we propose an efficient algorithm for systematic identification and modeling of cycles using persistent homology and the Hodge Laplacian. Various statistical inference procedures on cycles are developed. We validate the our methods on simulations and apply to brain networks obtained through the resting state functional magnetic resonance imaging. The computer codes for the Hodge Laplacian are given in https://github.com/laplcebeltrami/hodge.
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11
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Das S, Anand DV, Chung MK. Topological data analysis of human brain networks through order statistics. PLoS One 2023; 18:e0276419. [PMID: 36913351 PMCID: PMC10010566 DOI: 10.1371/journal.pone.0276419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 09/21/2022] [Indexed: 03/14/2023] Open
Abstract
Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the topological properties of the brain network. The development of group-level statistical inference procedures in brain graphs while accounting for the heterogeneity and randomness still remains a difficult task. In this study, we develop a robust statistical framework based on persistent homology using the order statistics for analyzing brain networks. The use of order statistics greatly simplifies the computation of the persistent barcodes. We validate the proposed methods using comprehensive simulation studies and subsequently apply to the resting-state functional magnetic resonance images. We found a statistically significant topological difference between the male and female brain networks.
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Affiliation(s)
- Soumya Das
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, United States of America
| | - D. Vijay Anand
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, United States of America
| | - Moo K. Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, United States of America
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12
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Songdechakraiwut T, Chung MK. TOPOLOGICAL LEARNING FOR BRAIN NETWORKS. Ann Appl Stat 2023; 17:403-433. [PMID: 36911168 PMCID: PMC9997114 DOI: 10.1214/22-aoas1633] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient topological loss. The use of the proposed loss bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations to assess its effectiveness when discriminating networks with different topology. The method is further demonstrated in a twin brain imaging study where we determine if brain networks are genetically heritable. The challenge here is due to the difficulty of overlaying the topologically different functional brain networks obtained from resting-state functional MRI onto the template structural brain network obtained through diffusion MRI.
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Affiliation(s)
| | - Moo K Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison
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13
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Brown EL, Lefebvre TL, Sweeney PW, Stolz BJ, Gröhl J, Hacker L, Huang Z, Couturier DL, Harrington HA, Byrne HM, Bohndiek SE. Quantification of vascular networks in photoacoustic mesoscopy. Photoacoustics 2022; 26:100357. [PMID: 35574188 PMCID: PMC9095888 DOI: 10.1016/j.pacs.2022.100357] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Mesoscopic photoacoustic imaging (PAI) enables non-invasive visualisation of tumour vasculature. The visual or semi-quantitative 2D measurements typically applied to mesoscopic PAI data fail to capture the 3D vessel network complexity and lack robust ground truths for assessment of accuracy. Here, we developed a pipeline for quantifying 3D vascular networks captured using mesoscopic PAI and tested the preservation of blood volume and network structure with topological data analysis. Ground truth data of in silico synthetic vasculatures and a string phantom indicated that learning-based segmentation best preserves vessel diameter and blood volume at depth, while rule-based segmentation with vesselness image filtering accurately preserved network structure in superficial vessels. Segmentation of vessels in breast cancer patient-derived xenografts (PDXs) compared favourably to ex vivo immunohistochemistry. Furthermore, our findings underscore the importance of validating segmentation methods when applying mesoscopic PAI as a tool to evaluate vascular networks in vivo.
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Affiliation(s)
- Emma L. Brown
- Department of Physics, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Cancer Research UK Cambridge Institute, University of Cambridge, Robinson Way, Cambridge CB2 0RE, UK
| | - Thierry L. Lefebvre
- Department of Physics, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Cancer Research UK Cambridge Institute, University of Cambridge, Robinson Way, Cambridge CB2 0RE, UK
| | - Paul W. Sweeney
- Department of Physics, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Cancer Research UK Cambridge Institute, University of Cambridge, Robinson Way, Cambridge CB2 0RE, UK
| | - Bernadette J. Stolz
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
| | - Janek Gröhl
- Department of Physics, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Cancer Research UK Cambridge Institute, University of Cambridge, Robinson Way, Cambridge CB2 0RE, UK
| | - Lina Hacker
- Department of Physics, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Cancer Research UK Cambridge Institute, University of Cambridge, Robinson Way, Cambridge CB2 0RE, UK
| | - Ziqiang Huang
- Cancer Research UK Cambridge Institute, University of Cambridge, Robinson Way, Cambridge CB2 0RE, UK
| | | | | | - Helen M. Byrne
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
| | - Sarah E. Bohndiek
- Department of Physics, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Cancer Research UK Cambridge Institute, University of Cambridge, Robinson Way, Cambridge CB2 0RE, UK
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14
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Choe S, Ramanna S. Cubical Homology-Based Machine Learning: An Application in Image Classification. Axioms 2022; 11:112. [DOI: 10.3390/axioms11030112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Persistent homology is a powerful tool in topological data analysis (TDA) to compute, study, and encode efficiently multi-scale topological features and is being increasingly used in digital image classification. The topological features represent a number of connected components, cycles, and voids that describe the shape of data. Persistent homology extracts the birth and death of these topological features through a filtration process. The lifespan of these features can be represented using persistent diagrams (topological signatures). Cubical homology is a more efficient method for extracting topological features from a 2D image and uses a collection of cubes to compute the homology, which fits the digital image structure of grids. In this research, we propose a cubical homology-based algorithm for extracting topological features from 2D images to generate their topological signatures. Additionally, we propose a novel score measure, which measures the significance of each of the sub-simplices in terms of persistence. In addition, gray-level co-occurrence matrix (GLCM) and contrast limited adapting histogram equalization (CLAHE) are used as supplementary methods for extracting features. Supervised machine learning models are trained on selected image datasets to study the efficacy of the extracted topological features. Among the eight tested models with six published image datasets of varying pixel sizes, classes, and distributions, our experiments demonstrate that cubical homology-based machine learning with the deep residual network (ResNet 1D) and Light Gradient Boosting Machine (lightGBM) shows promise with the extracted topological features.
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15
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Casanova R, Lyday RG, Bahrami M, Burdette JH, Simpson SL, Laurienti PJ. Embedding Functional Brain Networks in Low Dimensional Spaces Using Manifold Learning Techniques. Front Neuroinform 2022; 15:740143. [PMID: 35002665 PMCID: PMC8739961 DOI: 10.3389/fninf.2021.740143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 11/19/2021] [Indexed: 11/13/2022] Open
Abstract
Background: fMRI data is inherently high-dimensional and difficult to visualize. A recent trend has been to find spaces of lower dimensionality where functional brain networks can be projected onto manifolds as individual data points, leading to new ways to analyze and interpret the data. Here, we investigate the potential of two powerful non-linear manifold learning techniques for functional brain networks representation: (1) T-stochastic neighbor embedding (t-SNE) and (2) Uniform Manifold Approximation Projection (UMAP) a recent breakthrough in manifold learning. Methods: fMRI data from the Human Connectome Project (HCP) and an independent study of aging were used to generate functional brain networks. We used fMRI data collected during resting state data and during a working memory task. The relative performance of t-SNE and UMAP were investigated by projecting the networks from each study onto 2D manifolds. The levels of discrimination between different tasks and the preservation of the topology were evaluated using different metrics. Results: Both methods effectively discriminated the resting state from the memory task in the embedding space. UMAP discriminated with a higher classification accuracy. However, t-SNE appeared to better preserve the topology of the high-dimensional space. When networks from the HCP and aging studies were combined, the resting state and memory networks in general aligned correctly. Discussion: Our results suggest that UMAP, a more recent development in manifold learning, is an excellent tool to visualize functional brain networks. Despite dramatic differences in data collection and protocols, networks from different studies aligned correctly in the embedding space.
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Affiliation(s)
- Ramon Casanova
- Department of Biostatistics and Data Science, Wake Forest School of Medicine, Winston-Salem, NC, United States
| | - Robert G Lyday
- Laboratory for Complex Brain Networks, Wake Forest School of Medicine, Winston-Salem, NC, United States.,Department of Radiology, Wake Forest School of Medicine, Winston-Salem, NC, United States
| | - Mohsen Bahrami
- Laboratory for Complex Brain Networks, Wake Forest School of Medicine, Winston-Salem, NC, United States.,Department of Radiology, Wake Forest School of Medicine, Winston-Salem, NC, United States
| | - Jonathan H Burdette
- Laboratory for Complex Brain Networks, Wake Forest School of Medicine, Winston-Salem, NC, United States.,Department of Radiology, Wake Forest School of Medicine, Winston-Salem, NC, United States
| | - Sean L Simpson
- Department of Biostatistics and Data Science, Wake Forest School of Medicine, Winston-Salem, NC, United States.,Laboratory for Complex Brain Networks, Wake Forest School of Medicine, Winston-Salem, NC, United States
| | - Paul J Laurienti
- Laboratory for Complex Brain Networks, Wake Forest School of Medicine, Winston-Salem, NC, United States.,Department of Radiology, Wake Forest School of Medicine, Winston-Salem, NC, United States
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16
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Chung MK, Ombao H. Discussion of 'Event history and topological data analysis'. Biometrika 2021; 108:775-778. [PMID: 34937951 PMCID: PMC8689579 DOI: 10.1093/biomet/asab023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Affiliation(s)
- Moo K Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Medical Science Center 4725, 1300 University Avenue, Madison, Wisconsin 53706, U.S.A
| | - Hernando Ombao
- Statistics Program, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
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18
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Abstract
Persistent homology has undergone significant development in recent years. However, one outstanding challenge is to build a coherent statistical inference procedure on persistent diagrams. In this paper, we first present a new lattice path representation for persistent diagrams. We then develop a new exact statistical inference procedure for lattice paths via combinatorial enumerations. The lattice path method is applied to the topological characterization of the protein structures of the COVID-19 virus. We demonstrate that there are topological changes during the conformational change of spike proteins.
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Affiliation(s)
| | - Hernando Ombao
- King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
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19
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Songdechakraiwut T, Shen L, Chung M. Topological Learning and Its Application to Multimodal Brain Network Integration. Med Image Comput Comput Assist Interv 2021; 12902:166-176. [PMID: 35098263 PMCID: PMC8797159 DOI: 10.1007/978-3-030-87196-3_16] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
A long-standing challenge in multimodal brain network analyses is to integrate topologically different brain networks obtained from diffusion and functional MRI in a coherent statistical framework. Existing multimodal frameworks will inevitably destroy the topological difference of the networks. In this paper, we propose a novel topological learning framework that integrates networks of different topology through persistent homology. Such challenging task is made possible through the introduction of a new topological loss that bypasses intrinsic computational bottlenecks and thus enables us to perform various topological computations and optimizations with ease. We validate the topological loss in extensive statistical simulations with ground truth to assess its effectiveness of discriminating networks. Among many possible applications, we demonstrate the versatility of topological loss in the twin imaging study where we determine the extend to which brain networks are genetically heritable.
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Affiliation(s)
- Tananun Songdechakraiwut
- University of Wisconsin–Madison, USA
- Correspondence should be addressed to Tananun Songdechakraiwut ()
| | - Li Shen
- University of Pennsylvania, USA
| | - Moo Chung
- University of Wisconsin–Madison, USA
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20
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Salch A, Regalski A, Abdallah H, Suryadevara R, Catanzaro MJ, Diwadkar VA. 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. PLoS One 2021; 16:e0255859. [PMID: 34383838 PMCID: PMC8360597 DOI: 10.1371/journal.pone.0255859] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2021] [Accepted: 07/23/2021] [Indexed: 11/19/2022] Open
Abstract
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.
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Affiliation(s)
- Andrew Salch
- Department of Mathematics, Wayne State University, Detroit, Michigan, United States of America
- * E-mail: (AS); (AR); (HA)
| | - Adam Regalski
- Department of Mathematics, Wayne State University, Detroit, Michigan, United States of America
- * E-mail: (AS); (AR); (HA)
| | - Hassan Abdallah
- Department of Mathematics, Wayne State University, Detroit, Michigan, United States of America
- * E-mail: (AS); (AR); (HA)
| | - Raviteja Suryadevara
- Department of Mathematics, Wayne State University, Detroit, Michigan, United States of America
- Department of Psychiatry & Behavioral Neuroscience, Wayne State University, Detroit, Michigan, United States of America
| | - Michael J. Catanzaro
- Department of Mathematics, Iowa State University, Ames, Iowa, United States of America
| | - Vaibhav A. Diwadkar
- Department of Psychiatry & Behavioral Neuroscience, Wayne State University, Detroit, Michigan, United States of America
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21
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Billings J, Saggar M, Hlinka J, Keilholz S, Petri G. Simplicial and topological descriptions of human brain dynamics. Netw Neurosci 2021; 5:549-568. [PMID: 34189377 PMCID: PMC8233107 DOI: 10.1162/netn_a_00190] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Accepted: 02/11/2021] [Indexed: 11/06/2022] Open
Abstract
While brain imaging tools like functional magnetic resonance imaging (fMRI) afford measurements of whole-brain activity, it remains unclear how best to interpret patterns found amid the data’s apparent self-organization. To clarify how patterns of brain activity support brain function, one might identify metric spaces that optimally distinguish brain states across experimentally defined conditions. Therefore, the present study considers the relative capacities of several metric spaces to disambiguate experimentally defined brain states. One fundamental metric space interprets fMRI data topographically, that is, as the vector of amplitudes of a multivariate signal, changing with time. Another perspective compares the brain’s functional connectivity, that is, the similarity matrix computed between signals from different brain regions. More recently, metric spaces that consider the data’s topology have become available. Such methods treat data as a sample drawn from an abstract geometric object. To recover the structure of that object, topological data analysis detects features that are invariant under continuous deformations (such as coordinate rotation and nodal misalignment). Moreover, the methods explicitly consider features that persist across multiple geometric scales. While, certainly, there are strengths and weaknesses of each brain dynamics metric space, wefind that those that track topological features optimally distinguish experimentally defined brain states. Time-varying functional connectivity interprets brain function as time-varying patterns of coordinated brain activity. While many questions remain regarding how brain function emerges from multiregional interactions, advances in the mathematics of topological data analysis (TDA) may provide new insights. One tool from TDA, “persistent homology,” observes the occurrence and persistence of n-dimensional holes in a sequence of simplicial complexes extracted from a weighted graph. In the present study, we compare the use of persistent homology versus more traditional metrics at the task of segmenting brain states that differ across experimental conditions. We find that the structures identified by persistent homology more accurately segment the stimuli, more accurately segment high versus low performance levels under common stimuli, and generalize better across volunteers.
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Affiliation(s)
- Jacob Billings
- Mathematics and Complex Systems Research Area, ISI Foundation, Turin, Italy
| | - Manish Saggar
- Department of Psychiatry & Behavioral Sciences, Stanford University School of Medicine, Stanford, CA, USA
| | - Jaroslav Hlinka
- Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic
| | - Shella Keilholz
- Coulter Department of Biomedical Engineering, Emory University and Georgia Institute of Technology, Atlanta, GA, USA
| | - Giovanni Petri
- Mathematics and Complex Systems Research Area, ISI Foundation, Turin, Italy
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22
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Chung MK, Ombao H. Lattice Paths for Persistent Diagrams. ArXiv 2021:arXiv:2105.00351v5. [PMID: 34159224 PMCID: PMC8219103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Revised: 07/31/2021] [Indexed: 12/04/2022]
Abstract
Persistent homology has undergone significant development in recent years. However, one outstanding challenge is to build a coherent statistical inference procedure on persistent diagrams. In this paper, we first present a new lattice path representation for persistent diagrams. We then develop a new exact statistical inference procedure for lattice paths via combinatorial enumerations. The lattice path method is applied to the topological characterization of the protein structures of the COVID-19 virus. We demonstrate that there are topological changes during the conformational change of spike proteins.
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Affiliation(s)
| | - Hernando Ombao
- King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
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23
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Lovato I, Pini A, Stamm A, Taquet M, Vantini S. Multiscale null hypothesis testing for network‐valued data: Analysis of brain networks of patients with autism. J R Stat Soc Ser C Appl Stat 2021. [DOI: 10.1111/rssc.12463] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ilenia Lovato
- Department of Mathematics Università di Pavia Pavia MI Italy
| | - Alessia Pini
- Department of Statistical Sciences Università Cattolica del Sacro Cuore Milan MI Italy
| | - Aymeric Stamm
- Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629 Nantes Pays de la Loire France
| | - Maxime Taquet
- Department of Psychiatry University of Oxford Oxford UK
| | - Simone Vantini
- Department of Mathematics Politecnico di Milano Milan MI Italy
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24
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Don APH, Peters JF, Ramanna S, Tozzi A. Topological View of Flows Inside the BOLD Spontaneous Activity of the Human Brain. Front Comput Neurosci 2020; 14:34. [PMID: 32390820 PMCID: PMC7189216 DOI: 10.3389/fncom.2020.00034] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2019] [Accepted: 03/30/2020] [Indexed: 01/21/2023] Open
Abstract
Spatio-temporal brain activities with variable delay detectable in resting-state functional magnetic resonance imaging (rs-fMRI) give rise to highly reproducible structures, termed cortical lag threads, that propagate from one brain region to another. Using a computational topology of data approach, we found that persistent, recurring blood oxygen level dependent (BOLD) signals in triangulated rs-fMRI videoframes display previously undetected topological findings, i.e., vortex structures that cover brain activated regions. Measure of persistence of vortex shapes in BOLD signal propagation is carried out in terms of Betti numbers that rise and fall over time during spontaneous activity of the brain. Importantly, a topology of data given in terms of geometric shapes of BOLD signal propagation offers a practical approach in coping with and sidestepping massive noise in neurodata, such as unwanted dark (low intensity) regions in the neighborhood of non-zero BOLD signals. Our findings have been codified and visualized in plots able to track the non-trivial BOLD signals that appear intermittently in a sequence of rs-fMRI videoframes. The end result of this tracking of changing lag structures is a so-called persistent barcode, which is a pictograph that offers a convenient visual means of exhibiting, comparing, and classifying brain activation patterns.
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Affiliation(s)
- Arjuna P. H. Don
- Computational Intelligence Laboratory, University of Manitoba, Winnipeg, MB, Canada
| | - James F. Peters
- Computational Intelligence Laboratory, University of Manitoba, Winnipeg, MB, Canada
| | - Sheela Ramanna
- Applied Computer Science, University of Winnipeg, Winnipeg, MB, Canada
| | - Arturo Tozzi
- Computational Intelligence Laboratory, University of Manitoba, Winnipeg, MB, Canada
- Department of Physics, University of North Texas, Denton, TX, United States
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25
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Abstract
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees yield insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies at different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and real world networks. We put forward a multi-scale picture of graph structure wherein we study the effect of global and local structures on changes in distance measures. We make recommendations on the applicability of different distance measures to the analysis of empirical graph data based on this multi-scale view. Finally, we introduce the Python library NetComp that implements the graph distances used in this work.
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Affiliation(s)
- Peter Wills
- Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO, United States of America
| | - François G. Meyer
- Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO, United States of America
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Abstract
Topology, in its many forms, describes relations. It has thus long been a central concept in neuroscience, capturing structural and functional aspects of the organization of the nervous system and their links to cognition. Recent advances in computational topology have extended the breadth and depth of topological descriptions. This Focus Feature offers a unified overview of the emerging field of topological neuroscience and of its applications across the many scales of the nervous system from macro-, over meso-, to microscales.
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Affiliation(s)
- Paul Expert
- Department of Mathematics, Imperial College London, London, UK
- EPSRC Centre for Mathematics of Precision Healthcare, Imperial College London, London, UK
- Department of Neuroimaging, Institute of Psychiatry, Psychology and Neuroscience, Kings College London, London, UK
- Global Digital Health Unit, School of Public Health, Faculty of Medicine, Imperial College London, London, UK
| | | | - Morten L. Kringelbach
- Department of Psychiatry, University of Oxford, Oxford, UK
- Center for Music in the Brain, Aarhus University, Aarhus, Denmark
| | - Giovanni Petri
- ISI Foundation, Turin, Italy
- ISI Global Science Foundation, New York, New York, USA
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