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Mijangos M, Pacheco L, Bravetti A, González-García N, Padilla P, Velasco-Segura R. Persistent homology reveals robustness loss in inhaled substance abuse rs-fMRI networks. PLoS One 2024; 19:e0310165. [PMID: 39283839 PMCID: PMC11404802 DOI: 10.1371/journal.pone.0310165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2024] [Accepted: 08/26/2024] [Indexed: 09/20/2024] Open
Abstract
Analyzing functional brain activity through functional magnetic resonance imaging (fMRI) is commonly done using tools from graph theory for the analysis of the correlation matrices. A drawback of these methods is that the networks must be restricted to values of the weights of the edges within certain thresholds and there is no consensus about the best choice of such thresholds. Topological data analysis (TDA) is a recently-developed tool in algebraic topology which allows us to analyze networks through combinatorial spaces obtained from them, with the advantage that all the possible thresholds can be considered at once. In this paper we applied TDA, in particular persistent homology, to study correlation matrices from rs-fMRI, and through statistical analysis, we detected significant differences between the topological structures of adolescents with inhaled substance abuse disorder (ISAD) and healthy controls. We interpreted the topological differences as indicative of a loss of robustness in the functional brain networks of the ISAD population.
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Affiliation(s)
- Martin Mijangos
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Lucero Pacheco
- Facultad de Medicina, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Alessandro Bravetti
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Nadia González-García
- Laboratorio de Neurociencias, Hospital Infantil de México Federico Gómez, Mexico City, Mexico
| | - Pablo Padilla
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Roberto Velasco-Segura
- Instituto de Ciencias Aplicadas y Tecnología, Universidad Nacional Autónoma de México, Mexico City, Mexico
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2
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Siva NK, Singh Y, Hathaway QA, Sengupta PP, Yanamala N. A novel multi-task machine learning classifier for rare disease patterning using cardiac strain imaging data. Sci Rep 2024; 14:10672. [PMID: 38724564 PMCID: PMC11082231 DOI: 10.1038/s41598-024-61201-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 05/02/2024] [Indexed: 05/12/2024] Open
Abstract
To provide accurate predictions, current machine learning-based solutions require large, manually labeled training datasets. We implement persistent homology (PH), a topological tool for studying the pattern of data, to analyze echocardiography-based strain data and differentiate between rare diseases like constrictive pericarditis (CP) and restrictive cardiomyopathy (RCM). Patient population (retrospectively registered) included those presenting with heart failure due to CP (n = 51), RCM (n = 47), and patients without heart failure symptoms (n = 53). Longitudinal, radial, and circumferential strains/strain rates for left ventricular segments were processed into topological feature vectors using Machine learning PH workflow. In differentiating CP and RCM, the PH workflow model had a ROC AUC of 0.94 (Sensitivity = 92%, Specificity = 81%), compared with the GLS model AUC of 0.69 (Sensitivity = 65%, Specificity = 66%). In differentiating between all three conditions, the PH workflow model had an AUC of 0.83 (Sensitivity = 68%, Specificity = 84%), compared with the GLS model AUC of 0.68 (Sensitivity = 52% and Specificity = 76%). By employing persistent homology to differentiate the "pattern" of cardiac deformations, our machine-learning approach provides reasonable accuracy when evaluating small datasets and aids in understanding and visualizing patterns of cardiac imaging data in clinically challenging disease states.
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Affiliation(s)
- Nanda K Siva
- School of Medicine, West Virginia University, Morgantown, WV, USA
- Division of Cardiology, Heart and Vascular Institute, West Virginia University, Morgantown, WV, USA
| | - Yashbir Singh
- Division of Cardiology, Heart and Vascular Institute, West Virginia University, Morgantown, WV, USA
- Department of Radiology, Mayo Clinic, Rochester, MN, USA
| | - Quincy A Hathaway
- School of Medicine, West Virginia University, Morgantown, WV, USA
- Division of Cardiology, Heart and Vascular Institute, West Virginia University, Morgantown, WV, USA
| | - Partho P Sengupta
- Division of Cardiovascular Disease and Hypertension, Rutgers Robert Wood Johnson Medical School, 125 Patterson St, New Brunswick, NJ, 08901, USA.
| | - Naveena Yanamala
- Division of Cardiovascular Disease and Hypertension, Rutgers Robert Wood Johnson Medical School, 125 Patterson St, New Brunswick, NJ, 08901, USA.
- Institute for Software Research, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA.
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Zabaleta-Ortega A, Masoller C, Guzmán-Vargas L. Topological data analysis of the synchronization of a network of Rössler chaotic electronic oscillators. CHAOS (WOODBURY, N.Y.) 2023; 33:113110. [PMID: 37921586 DOI: 10.1063/5.0167523] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Accepted: 10/13/2023] [Indexed: 11/04/2023]
Abstract
Synchronization study allows a better understanding of the exchange of information among systems. In this work, we study experimental data recorded from a set of Rössler-like chaotic electronic oscillators arranged in a complex network, where the interactions between the oscillators are given in terms of a connectivity matrix, and their intensity is controlled by a global coupling parameter. We use the zero and one persistent homology groups to characterize the point clouds obtained from the signals recorded in pairs of oscillators. We show that the normalized persistent entropy (NPE) allows us to characterize the effective coupling between pairs of oscillators because it tends to increase with the coupling strength and to decrease with the distance between the oscillators. We also observed that pairs of oscillators that have similar degrees and are nearest neighbors tend to have higher NPE values than pairs with different degrees. However, large variability is found in the NPE values. Comparing the NPE behavior with that of the phase-locking value (PLV, commonly used to evaluate the synchronization of phase oscillators), we find that for large enough coupling, PLV only displays a monotonic increase, while NPE shows a richer behavior that captures variations in the behavior of the oscillators. This is due to the fact that PLV only captures coupling-induced phase changes, while NPE also captures amplitude changes. Moreover, when we consider the same network but with Kuramoto phase oscillators, we also find that NPE captures the transition to synchronization (as it increases with the coupling strength), and it also decreases with the distance between the oscillators. Therefore, we propose NPE as a data analysis technique to try to differentiate pairs of oscillators that have strong effective coupling because they are first or near neighbors, from those that have weaker coupling because they are distant neighbors.
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Affiliation(s)
- A Zabaleta-Ortega
- Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, 07340 Ciudad de México, Mexico
| | - C Masoller
- Departament de Física, Universitat Politècnica de Catalunya, Rambla St. Nebridi 22, 08222 Terrassa, Spain
| | - L Guzmán-Vargas
- Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, 07340 Ciudad de México, Mexico
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4
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Harvey J, Chan B, Srivastava T, Zarebski AE, Dłotko P, Błaszczyk P, Parkinson RH, White LJ, Aguas R, Mahdi A. Epidemiological waves - Types, drivers and modulators in the COVID-19 pandemic. Heliyon 2023; 9:e16015. [PMID: 37197148 PMCID: PMC10154246 DOI: 10.1016/j.heliyon.2023.e16015] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2022] [Revised: 04/21/2023] [Accepted: 04/28/2023] [Indexed: 05/19/2023] Open
Abstract
Introduction A discussion of 'waves' of the COVID-19 epidemic in different countries is a part of the national conversation for many, but there is no hard and fast means of delineating these waves in the available data and their connection to waves in the sense of mathematical epidemiology is only tenuous. Methods We present an algorithm which processes a general time series to identify substantial, significant and sustained periods of increase in the value of the time series, which could reasonably be described as 'observed waves'. This provides an objective means of describing observed waves in time series. We use this method to synthesize evidence across different countries to study types, drivers and modulators of waves. Results The output of the algorithm as applied to epidemiological time series related to COVID-19 corresponds to visual intuition and expert opinion. Inspecting the results of individual countries shows how consecutive observed waves can differ greatly with respect to the case fatality ratio. Furthermore, in large countries, a more detailed analysis shows that consecutive observed waves have different geographical ranges. We also show how waves can be modulated by government interventions and find that early implementation of NPIs correlates with a reduced number of observed waves and reduced mortality burden in those waves. Conclusion It is possible to identify observed waves of disease by algorithmic methods and the results can be fruitfully used to analyse the progression of the epidemic.
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Affiliation(s)
- John Harvey
- Department of Mathematics, Swansea University, Swansea, UK
- School of Mathematics, Cardiff University, UK
| | - Bryan Chan
- Department of Economics, London School of Economics and Political Science, London, UK
| | - Tarun Srivastava
- Department of Engineering Science, University of Oxford, Oxford, UK
| | | | - Paweł Dłotko
- Dioscuri Centre in Topological Data Analysis, Mathematical Institute, Polish Academy of Sciences, Warsaw, Poland
| | - Piotr Błaszczyk
- Faculty of Computer Science, Electronics and Telecommunications, AGH University of Science and Technology, Krakow, Poland
- Oxford Internet Institute, University of Oxford, Oxford, UK
| | | | - Lisa J. White
- Li Ka Shing Centre for Health Information and Discovery, Big Data Institute, University of Oxford, Oxford, UK
| | - Ricardo Aguas
- Nuffield Department of Medicine, Mahidol-Oxford Tropical Medicine Research Unit, University of Oxford, Oxford, UK
| | - Adam Mahdi
- Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford, UK
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Ji J, Venderley J, Zhang H, Lei M, Ruan G, Patel N, Chung YM, Giesting R, Miller L. Assessing nocturnal scratch with actigraphy in atopic dermatitis patients. NPJ Digit Med 2023; 6:72. [PMID: 37100893 PMCID: PMC10133290 DOI: 10.1038/s41746-023-00821-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Accepted: 04/04/2023] [Indexed: 04/28/2023] Open
Abstract
Nocturnal scratch is one major factor leading to impaired quality of life in atopic dermatitis (AD) patients. Therefore, objectively quantifying nocturnal scratch events aids in assessing the disease state, treatment effect, and AD patients' quality of life. In this paper, we describe the use of actigraphy, highly predictive topological features, and a model-ensembling approach to develop an assessment of nocturnal scratch events by measuring scratch duration and intensity. Our assessment is tested in a clinical setting against the ground truth obtained from video recordings. The new approach addresses unmet challenges in existing studies, such as the lack of generalizability to real-world applications, the failure to capture finger scratches, and the limitations in the evaluation due to imbalanced data in the current literature. Furthermore, the performance evaluation shows agreement between derived digital endpoints and the video annotation ground truth, as well as patient-reported outcomes, which demonstrated the validity of the new assessment of nocturnal scratch.
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Affiliation(s)
- Ju Ji
- Eli Lilly & Company, INc., Indianapolis, IN, USA.
| | | | - Hui Zhang
- Eli Lilly & Company, INc., Indianapolis, IN, USA
| | - Mengjue Lei
- Eli Lilly & Company, INc., Indianapolis, IN, USA
| | | | - Neel Patel
- Eli Lilly & Company, INc., Indianapolis, IN, USA
| | - Yu-Min Chung
- Eli Lilly & Company, INc., Indianapolis, IN, USA
| | | | - Leah Miller
- Eli Lilly & Company, INc., Indianapolis, IN, USA
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Ren Y, Liu F, Xia S, Shi S, Chen L, Wang Z. Dynamic ECG signal quality evaluation based on persistent homology and GoogLeNet method. Front Neurosci 2023; 17:1153386. [PMID: 36968492 PMCID: PMC10030713 DOI: 10.3389/fnins.2023.1153386] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2023] [Accepted: 02/20/2023] [Indexed: 03/29/2023] Open
Abstract
Cardiovascular disease is a serious health problem. Continuous Electrocardiograph (ECG) monitoring plays a vital role in the early detection of cardiovascular disease. As the Internet of Things technology continues to mature, wearable ECG signal monitors have been widely used. However, dynamic ECG signals are extremely susceptible to contamination. Therefore, it is necessary to evaluate the quality of wearable dynamic ECG signals. The topological data analysis method (TDA) with persistent homology, which can effectively capture the topological information of high-dimensional data space, has been widely studied. In this study, a brand-new quality assessment method of wearable dynamic ECG signals was proposed based on the TDA with persistent homology method. The point cloud of an ECG signal was constructed, and then the complex sequence was generated and displayed as a persistent barcode. Finally, GoogLeNet based on the transfer learning model with a 10-fold cross-validation method was used to train the classification model. A total of 12-leads ECGs Dataset and single-lead ECGs Dataset, established based on the 2011 PhysioNet/CinC challenge dataset, were both used to verify the performance of this method. In the study, 773 "acceptable" and 225 "unacceptable" signals were used as 12-leads ECGs Dataset. We relabeled 12,000 ECG signals in the challenge dataset, and treated them as single-lead ECGs Dataset after empty lead detection and balance datasets. Compared with the traditional ECG signal quality assessment method mainly based on waveform characteristics and time-frequency characteristics, the performance of the quality assessment method proposed. In this study, the classification performance of the proposed method are fairly great, mAcc = 98.04%, F1 = 98.40%, Se = 97.15%, Sp = 98.93% for 12-leads ECGs Dataset and mAcc = 98.55%, F1 = 98.62%, Se = 98.37%, Sp = 98.85% for single-lead ECGs Dataset.
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Affiliation(s)
- Yonglian Ren
- School of Science, Shandong Jianzhu University, Jinan, China
| | - Feifei Liu
- School of Science, Shandong Jianzhu University, Jinan, China
- Center for Engineering Computation and Software Development, Shandong Jianzhu University, Jinan, China
- *Correspondence: Feifei Liu,
| | - Shengxiang Xia
- School of Science, Shandong Jianzhu University, Jinan, China
- Shengxiang Xia,
| | - Shuhua Shi
- School of Science, Shandong Jianzhu University, Jinan, China
| | - Lei Chen
- School of Science and Technology, Shandong University of Traditional Chinese Medicine, Jinan, China
| | - Ziyu Wang
- School of Science, Shandong Jianzhu University, Jinan, China
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7
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Singh Y, Jons WA, Eaton JE, Vesterhus M, Karlsen T, Bjoerk I, Abildgaard A, Jorgensen KK, Folseraas T, Little D, Gulamhusein AF, Petrovic K, Negard A, Conte GM, Sobek JD, Jagtap J, Venkatesh SK, Gores GJ, LaRusso NF, Lazaridis KN, Erickson BJ. Algebraic topology-based machine learning using MRI predicts outcomes in primary sclerosing cholangitis. Eur Radiol Exp 2022; 6:58. [PMID: 36396865 PMCID: PMC9672219 DOI: 10.1186/s41747-022-00312-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Accepted: 10/25/2022] [Indexed: 11/19/2022] Open
Abstract
BACKGROUND Primary sclerosing cholangitis (PSC) is a chronic cholestatic liver disease that can lead to cirrhosis and hepatic decompensation. However, predicting future outcomes in patients with PSC is challenging. Our aim was to extract magnetic resonance imaging (MRI) features that predict the development of hepatic decompensation by applying algebraic topology-based machine learning (ML). METHODS We conducted a retrospective multicenter study among adults with large duct PSC who underwent MRI. A topological data analysis-inspired nonlinear framework was used to predict the risk of hepatic decompensation, which was motivated by algebraic topology theory-based ML. The topological representations (persistence images) were employed as input for classification to predict who developed early hepatic decompensation within one year after their baseline MRI. RESULTS We reviewed 590 patients; 298 were excluded due to poor image quality or inadequate liver coverage, leaving 292 potentially eligible subjects, of which 169 subjects were included in the study. We trained our model using contrast-enhanced delayed phase T1-weighted images on a single center derivation cohort consisting of 54 patients (hepatic decompensation, n = 21; no hepatic decompensation, n = 33) and a multicenter independent validation cohort of 115 individuals (hepatic decompensation, n = 31; no hepatic decompensation, n = 84). When our model was applied in the independent validation cohort, it remained predictive of early hepatic decompensation (area under the receiver operating characteristic curve = 0.84). CONCLUSIONS Algebraic topology-based ML is a methodological approach that can predict outcomes in patients with PSC and has the potential for application in other chronic liver diseases.
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Affiliation(s)
| | - William A Jons
- Radiology, Mayo Clinic, Rochester, MN, USA
- Biomedical Engineering and Physiology Graduate Program, Mayo Clinic Graduate School of Biomedical Sciences, Rochester, USA
| | - John E Eaton
- Division of Gastroenterology & Hepatology, Mayo Clinic, Rochester, MN, USA
| | - Mette Vesterhus
- Department of Medicine, Haraldsplass Deaconess Hospital, and Department of Clinical Science, University of Bergen, Bergen, Norway
- Norwegian PSC Research Center, Department of Transplantation Medicine, Division of Surgery, Inflammatory Medicine and Transplantation, Oslo University Hospital Rikshospitalet, Oslo, Norway
| | - Tom Karlsen
- Norwegian PSC Research Center, Department of Transplantation Medicine, Division of Surgery, Inflammatory Medicine and Transplantation, Oslo University Hospital Rikshospitalet, Oslo, Norway
| | - Ida Bjoerk
- Department of Radiology, Oslo University Hospital, Oslo, Norway
| | | | - Kristin Kaasen Jorgensen
- Norwegian PSC Research Center, Department of Transplantation Medicine, Division of Surgery, Inflammatory Medicine and Transplantation, Oslo University Hospital Rikshospitalet, Oslo, Norway
- Department of Gastroenterology, Akershus University Hospital, Nordbyhagen, Norway
| | - Trine Folseraas
- Norwegian PSC Research Center, Department of Transplantation Medicine, Division of Surgery, Inflammatory Medicine and Transplantation, Oslo University Hospital Rikshospitalet, Oslo, Norway
| | - Derek Little
- Toronto Centre for Liver Disease, University Health Network and Department of Medicine, University of Toronto, Toronto, Ontario, Canada
| | - Aliya F Gulamhusein
- Toronto Centre for Liver Disease, University Health Network and Department of Medicine, University of Toronto, Toronto, Ontario, Canada
| | - Kosta Petrovic
- Department of Radiology, Haukeland University Hospital, Bergen, Norway
| | - Anne Negard
- Institute of Clinical Medicine, University of Oslo, Oslo, Norway
- Department of Diagnostic Imaging, Akershus University Hospital, Lørenskog, Norway
| | | | | | | | | | - Gregory J Gores
- Division of Gastroenterology & Hepatology, Mayo Clinic, Rochester, MN, USA
| | - Nicholas F LaRusso
- Division of Gastroenterology & Hepatology, Mayo Clinic, Rochester, MN, USA
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8
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Hayashi S, Koseki J, Shimamura T. Bayesian statistical method for detecting structural and topological diversity in polymorphic proteins. Comput Struct Biotechnol J 2022; 20:6519-6525. [DOI: 10.1016/j.csbj.2022.11.038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Revised: 11/17/2022] [Accepted: 11/18/2022] [Indexed: 11/22/2022] Open
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9
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Güzel İ, Munch E, Khasawneh FA. Detecting bifurcations in dynamical systems with CROCKER plots. CHAOS (WOODBURY, N.Y.) 2022; 32:093111. [PMID: 36182371 DOI: 10.1063/5.0102421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2022] [Accepted: 08/05/2022] [Indexed: 06/16/2023]
Abstract
Existing tools for bifurcation detection from signals of dynamical systems typically are either limited to a special class of systems or they require carefully chosen input parameters and a significant expertise to interpret the results. Therefore, we describe an alternative method based on persistent homology-a tool from topological data analysis-that utilizes Betti numbers and CROCKER plots. Betti numbers are topological invariants of topological spaces, while the CROCKER plot is a coarsened but easy to visualize data representation of a one-parameter varying family of persistence barcodes. The specific bifurcations we investigate are transitions from periodic to chaotic behavior or vice versa in a one-parameter collection of differential equations. We validate our methods using numerical experiments on ten dynamical systems and contrast the results with existing tools that use the maximum Lyapunov exponent. We further prove the relationship between the Wasserstein distance to the empty diagram and the norm of the Betti vector, which shows that an even more simplified version of the information has the potential to provide insight into the bifurcation parameter. The results show that our approach reveals more information about the shape of the periodic attractor than standard tools, and it has more favorable computational time in comparison with the Rösenstein algorithm for computing the maximum Lyapunov exponent.
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Affiliation(s)
- İsmail Güzel
- Department of Mathematics Engineering, İstanbul Technical University, Maslak, İstanbul 34469, Turkey
| | - Elizabeth Munch
- Department of Computational Mathematics, Science and Engineering and Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
| | - Firas A Khasawneh
- Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824, USA
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10
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Personalized Medicine for the Critically Ill Patient: A Narrative Review. Processes (Basel) 2022. [DOI: 10.3390/pr10061200] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Personalized Medicine (PM) is rapidly advancing in everyday medical practice. Technological advances allow researchers to reach patients more than ever with their discoveries. The critically ill patient is probably the most complex of all, and personalized medicine must make serious efforts to fulfill the desire to “treat the individual, not the disease”. The complexity of critically ill pathologies arises from the severe state these patients and from the deranged pathways of their diseases. PM constitutes the integration of basic research into clinical practice; however, to make this possible complex and voluminous data require processing through even more complex mathematical models. The result of processing biodata is a digitized individual, from which fragments of information can be extracted for specific purposes. With this review, we aim to describe the current state of PM technologies and methods and explore its application in critically ill patients, as well as some of the challenges associated with PM in intensive care from the perspective of economic, approval, and ethical issues. This review can help in understanding the complexity of, P.M.; the complex processes needed for its application in critically ill patients, the benefits that make the effort of implementation worthwhile, and the current challenges of PM.
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11
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Skaf Y, Laubenbacher R. Topological data analysis in biomedicine: A review. J Biomed Inform 2022; 130:104082. [PMID: 35508272 DOI: 10.1016/j.jbi.2022.104082] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Revised: 03/20/2022] [Accepted: 04/23/2022] [Indexed: 01/22/2023]
Abstract
Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the widespread use of electronic health records to improved medical imaging capabilities and the rising ubiquity of genomic sequencing contribute to a "digitization" of biomedical research and clinical care. With this shift toward computerized tools comes a dramatic increase in the amount of available data, and current tools for data analysis capable of extracting meaningful knowledge from this wealth of information have yet to catch up. This article seeks to provide an overview of emerging mathematical methods with the potential to improve the abilities of clinicians and researchers to analyze biomedical data, but may be hindered from doing so by a lack of conceptual accessibility and awareness in the life sciences research community. In particular, we focus on topological data analysis (TDA), a set of methods grounded in the mathematical field of algebraic topology that seeks to describe and harness features related to the "shape" of data. We aim to make such techniques more approachable to non-mathematicians by providing a conceptual discussion of their theoretical foundations followed by a survey of their published applications to scientific research. Finally, we discuss the limitations of these methods and suggest potential avenues for future work integrating mathematical tools into clinical care and biomedical informatics.
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Affiliation(s)
- Yara Skaf
- University of Florida, Department of Mathematics, Gainesville, FL, USA; University of Florida, Department of Medicine, Division of Pulmonary, Critical Care, & Sleep Medicine, Gainesville, FL, USA.
| | - Reinhard Laubenbacher
- University of Florida, Department of Mathematics, Gainesville, FL, USA; University of Florida, Department of Medicine, Division of Pulmonary, Critical Care, & Sleep Medicine, Gainesville, FL, USA.
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12
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Dee Algar S, Corrêa DC, Walker DM. On detecting dynamical regime change using a transformation cost metric between persistent homology diagrams. CHAOS (WOODBURY, N.Y.) 2021; 31:123117. [PMID: 34972347 DOI: 10.1063/5.0073247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2021] [Accepted: 11/26/2021] [Indexed: 06/14/2023]
Abstract
This work outlines a pipeline for time series analysis that incorporates a measure of similarity not previously applied between homological summaries. Specifically, the well-established, but disparate, methods of persistent homology and TrAnsformation Cost Time Series (TACTS) are combined to provide a metric for tracking dynamics via changing homological features. TACTS allows subtle changes in dynamics to be accounted for, gives a quantitative output that can be directly interpreted, and is tunable to provide several complementary perspectives simultaneously. Our method is demonstrated first with known dynamical systems and then with a real-world electrocardiogram dataset. This paper highlights inadequacies in existing persistent homology metrics and describes circumstances where TACTS can be more sensitive and better suited to detecting a variety of regime changes.
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Affiliation(s)
- Shannon Dee Algar
- Department of Mathematics and Statistics, University of Western Australia, Crawley 6009, Australia
| | - Débora C Corrêa
- Department of Mathematics and Statistics, University of Western Australia, Crawley 6009, Australia
| | - David M Walker
- Department of Mathematics and Statistics, University of Western Australia, Crawley 6009, Australia
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13
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Tan E, Corrêa D, Stemler T, Small M. Grading your models: Assessing dynamics learning of models using persistent homology. CHAOS (WOODBURY, N.Y.) 2021; 31:123109. [PMID: 34972316 DOI: 10.1063/5.0073722] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2021] [Accepted: 11/18/2021] [Indexed: 06/14/2023]
Abstract
Assessing model accuracy for complex and chaotic systems is a non-trivial task that often relies on the calculation of dynamical invariants, such as Lyapunov exponents and correlation dimensions. Well-performing models are able to replicate the long-term dynamics and ergodic properties of the desired system. We term this phenomenon "dynamics learning." However, existing estimates based on dynamical invariants, such as Lyapunov exponents and correlation dimensions, are not unique to each system, not necessarily robust to noise, and struggle with detecting pathological errors, such as errors in the manifold density distribution. This can make meaningful and accurate model assessment difficult. We explore the use of a topological data analysis technique, persistent homology, applied to uniformly sampled trajectories from constructed reservoir models of the Lorenz system to assess the learning quality of a model. A proposed persistent homology point summary, conformance, was able to identify models with successful dynamics learning and detect discrepancies in the manifold density distribution.
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Affiliation(s)
- Eugene Tan
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Débora Corrêa
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Thomas Stemler
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Michael Small
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
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TopoResNet: A Hybrid Deep Learning Architecture and Its Application to Skin Lesion Classification. MATHEMATICS 2021. [DOI: 10.3390/math9222924] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
The application of artificial intelligence (AI) to various medical subfields has been a popular topic of research in recent years. In particular, deep learning has been widely used and has proven effective in many cases. Topological data analysis (TDA)—a rising field at the intersection of mathematics, statistics, and computer science—offers new insights into data. In this work, we develop a novel deep learning architecture that we call TopoResNet that integrates topological information into the residual neural network architecture. To demonstrate TopoResNet, we apply it to a skin lesion classification problem. We find that TopoResNet improves the accuracy and the stability of the training process.
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Graff G, Graff B, Pilarczyk P, Jabłoński G, Gąsecki D, Narkiewicz K. Persistent homology as a new method of the assessment of heart rate variability. PLoS One 2021; 16:e0253851. [PMID: 34292957 PMCID: PMC8297888 DOI: 10.1371/journal.pone.0253851] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2020] [Accepted: 06/15/2021] [Indexed: 11/22/2022] Open
Abstract
Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode.
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Affiliation(s)
- Grzegorz Graff
- Faculty of Applied Physics and Mathematics & BioTechMed Center, Gdańsk University of Technology, Gdańsk, Poland
| | - Beata Graff
- Department of Hypertension and Diabetology, Medical University of Gdańsk, Gdańsk, Poland
| | - Paweł Pilarczyk
- Faculty of Applied Physics and Mathematics & Digital Technologies Center, Gdańsk University of Technology, Gdańsk, Poland
| | | | - Dariusz Gąsecki
- Department of Neurology for Adults, Medical University of Gdańsk, Gdańsk, Poland
| | - Krzysztof Narkiewicz
- Department of Hypertension and Diabetology, Medical University of Gdańsk, Gdańsk, Poland
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