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Rao F, Zhang Z, Li J. Dynamical analysis of a glucose-insulin regulatory system with insulin-degrading enzyme and multiple delays. J Math Biol 2023; 87:73. [PMID: 37856001 DOI: 10.1007/s00285-023-02003-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2021] [Revised: 12/28/2022] [Accepted: 09/18/2023] [Indexed: 10/20/2023]
Abstract
This paper investigates the dynamics of a glucose-insulin regulatory system model that incorporates: (1) insulin-degrading enzyme in the insulin equation; and (2) discrete time delays respectively in the insulin production term, hepatic glucose production term, and the insulin-degrading enzyme. We provide rigorous results of our model including the asymptotic stability of the equilibrium solution and the existence of Hopf bifurcation. We show that analytically and numerically at a certain value the time delays driven stability or instability occurs when the corresponding model has an interior equilibrium. Moreover, we illustrate the oscillatory regulation and insulin secretion via numerical simulations, which show that the model dynamics exhibit physiological observations and more information by allowing parameters to vary. Our results may provide useful biological insights into diabetes for the glucose-insulin regulatory system model.
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Affiliation(s)
- Feng Rao
- School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing, 211816, Jiangsu, China.
| | - Zhongliang Zhang
- School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing, 211816, Jiangsu, China
| | - Jiaxu Li
- Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA.
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Hannum AJ, McIlvain G, Sowinski D, McGarry MD, Johnson CL. Correlated noise in brain magnetic resonance elastography. Magn Reson Med 2022; 87:1313-1328. [PMID: 34687069 PMCID: PMC8776601 DOI: 10.1002/mrm.29050] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Revised: 09/13/2021] [Accepted: 09/28/2021] [Indexed: 12/22/2022]
Abstract
PURPOSE Magnetic resonance elastography (MRE) uses phase-contrast MRI to generate mechanical property maps of the in vivo brain through imaging of tissue deformation from induced mechanical vibration. The mechanical property estimation process in MRE can be susceptible to noise from physiological and mechanical sources encoded in the phase, which is expected to be highly correlated. This correlated noise has yet to be characterized in brain MRE, and its effects on mechanical property estimates computed using inversion algorithms are undetermined. METHODS To characterize the effects of signal noise in MRE, we conducted 3 experiments quantifying (1) physiomechanical sources of signal noise, (2) physiological noise because of cardiac-induced movement, and (3) impact of correlated noise on mechanical property estimates. We use a correlation length metric to estimate the extent that correlated signal persists in MRE images and demonstrate the effect of correlated noise on property estimates through simulations. RESULTS We found that both physiological noise and vibration noise were greater than image noise and were spatially correlated across all subjects. Added physiological and vibration noise to simulated data resulted in property maps with higher error than equivalent levels of Gaussian noise. CONCLUSION Our work provides the foundation to understand contributors to brain MRE data quality and provides recommendations for future work to correct for signal noise in MRE.
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Affiliation(s)
- Ariel J. Hannum
- Department of Biomedical Engineering, University of Delaware, Newark, DE
| | - Grace McIlvain
- Department of Biomedical Engineering, University of Delaware, Newark, DE
| | - Damian Sowinski
- Thayer School of Engineering, Dartmouth College, Hanover, NH
| | | | - Curtis L. Johnson
- Department of Biomedical Engineering, University of Delaware, Newark, DE
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Lehnertz K, Bröhl T, Rings T. The Human Organism as an Integrated Interaction Network: Recent Conceptual and Methodological Challenges. Front Physiol 2020; 11:598694. [PMID: 33408639 PMCID: PMC7779628 DOI: 10.3389/fphys.2020.598694] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Accepted: 11/30/2020] [Indexed: 12/30/2022] Open
Abstract
The field of Network Physiology aims to advance our understanding of how physiological systems and sub-systems interact to generate a variety of behaviors and distinct physiological states, to optimize the organism's functioning, and to maintain health. Within this framework, which considers the human organism as an integrated network, vertices are associated with organs while edges represent time-varying interactions between vertices. Likewise, vertices may represent networks on smaller spatial scales leading to a complex mixture of interacting homogeneous and inhomogeneous networks of networks. Lacking adequate analytic tools and a theoretical framework to probe interactions within and among diverse physiological systems, current approaches focus on inferring properties of time-varying interactions-namely strength, direction, and functional form-from time-locked recordings of physiological observables. To this end, a variety of bivariate or, in general, multivariate time-series-analysis techniques, which are derived from diverse mathematical and physical concepts, are employed and the resulting time-dependent networks can then be further characterized with methods from network theory. Despite the many promising new developments, there are still problems that evade from a satisfactory solution. Here we address several important challenges that could aid in finding new perspectives and inspire the development of theoretic and analytical concepts to deal with these challenges and in studying the complex interactions between physiological systems.
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Affiliation(s)
- Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
- Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
| | - Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
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Madadi Asl M, Valizadeh A, Tass PA. Dendritic and Axonal Propagation Delays May Shape Neuronal Networks With Plastic Synapses. Front Physiol 2018; 9:1849. [PMID: 30618847 PMCID: PMC6307091 DOI: 10.3389/fphys.2018.01849] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2018] [Accepted: 12/07/2018] [Indexed: 12/27/2022] Open
Abstract
Biological neuronal networks are highly adaptive and plastic. For instance, spike-timing-dependent plasticity (STDP) is a core mechanism which adapts the synaptic strengths based on the relative timing of pre- and postsynaptic spikes. In various fields of physiology, time delays cause a plethora of biologically relevant dynamical phenomena. However, time delays increase the complexity of model systems together with the computational and theoretical analysis burden. Accordingly, in computational neuronal network studies propagation delays were often neglected. As a downside, a classic STDP rule in oscillatory neurons without propagation delays is unable to give rise to bidirectional synaptic couplings, i.e., loops or uncoupled states. This is at variance with basic experimental results. In this mini review, we focus on recent theoretical studies focusing on how things change in the presence of propagation delays. Realistic propagation delays may lead to the emergence of neuronal activity and synaptic connectivity patterns, which cannot be captured by classic STDP models. In fact, propagation delays determine the inventory of attractor states and shape their basins of attractions. The results reviewed here enable to overcome fundamental discrepancies between theory and experiments. Furthermore, these findings are relevant for the development of therapeutic brain stimulation techniques aiming at shifting the diseased brain to more favorable attractor states.
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Affiliation(s)
- Mojtaba Madadi Asl
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran
| | - Alireza Valizadeh
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran.,School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
| | - Peter A Tass
- Department of Neurosurgery, Stanford University School of Medicine, Stanford, CA, United States
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Bistable emergence of oscillations in growing Bacillus subtilis biofilms. Proc Natl Acad Sci U S A 2018; 115:E8333-E8340. [PMID: 30127028 DOI: 10.1073/pnas.1805004115] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
Biofilm communities of Bacillus subtilis bacteria have recently been shown to exhibit collective growth-rate oscillations mediated by electrochemical signaling to cope with nutrient starvation. These oscillations emerge once the colony reaches a large enough number of cells. However, it remains unclear whether the amplitude of the oscillations, and thus their effectiveness, builds up over time gradually or if they can emerge instantly with a nonzero amplitude. Here we address this question by combining microfluidics-based time-lapse microscopy experiments with a minimal theoretical description of the system in the form of a delay-differential equation model. Analytical and numerical methods reveal that oscillations arise through a subcritical Hopf bifurcation, which enables instant high-amplitude oscillations. Consequently, the model predicts a bistable regime where an oscillating and a nonoscillating attractor coexist in phase space. We experimentally validate this prediction by showing that oscillations can be triggered by perturbing the media conditions, provided the biofilm size lies within an appropriate range. The model also predicts that the minimum size at which oscillations start decreases with stress, a fact that we also verify experimentally. Taken together, our results show that collective oscillations in cell populations can emerge suddenly with nonzero amplitude via a discontinuous transition.
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Hermand E, Lhuissier FJ, Voituron N, Richalet JP. Ventilatory oscillations at exercise in hypoxia: A mathematical model. J Theor Biol 2016; 411:92-101. [PMID: 27743839 DOI: 10.1016/j.jtbi.2016.10.002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2016] [Revised: 09/01/2016] [Accepted: 10/04/2016] [Indexed: 10/20/2022]
Abstract
We evaluated the mechanisms responsible for the instability of ventilation control system under simultaneous metabolic (exercise) and environmental (hypoxia) stresses, promoting the genesis of periodic breathing. A model following the main concepts of ventilatory control has been tested, including cardiovascular and respiratory parameters, characteristics of peripheral and central chemoreceptors, at mild exercise in hypoxia (FIO2=0.145). Interaction between O2 and CO2 sensing was introduced following three different modalities. A sensitivity and multivariate regression analyses closely matched with physiological data for magnitude and period of oscillations. Low FIO2 and long circulatory delay from lungs to peripheral chemoreceptors (DeltaTp) lengthen the period of oscillations, while high peripheral and central chemoresponses to O2 and CO2, low FIO2 and high DeltaTp increased their magnitude. Peripheral and central O2/CO2 interactions highlight the role of CO2 on peripheral gain to O2 and the contribution of peripheral afferences on central gain to CO2. Our model supports the key role of peripheral chemoreceptors in the genesis of ventilatory oscillations. Differences in the dynamics of central and peripheral components might be determinant for the system stability.
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Affiliation(s)
- Eric Hermand
- Université Paris 13, Sorbonne Paris Cité, Laboratoire "Hypoxie et poumons", EA2363, 74 rue Marcel Cachin, 93017 Bobigny Cedex, France.
| | - François J Lhuissier
- Université Paris 13, Sorbonne Paris Cité, Laboratoire "Hypoxie et poumons", EA2363, 74 rue Marcel Cachin, 93017 Bobigny Cedex, France
| | - Nicolas Voituron
- Université Paris 13, Sorbonne Paris Cité, Laboratoire "Hypoxie et poumons", EA2363, 74 rue Marcel Cachin, 93017 Bobigny Cedex, France
| | - Jean-Paul Richalet
- Université Paris 13, Sorbonne Paris Cité, Laboratoire "Hypoxie et poumons", EA2363, 74 rue Marcel Cachin, 93017 Bobigny Cedex, France.
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Pikovsky A, Rosenblum M. Dynamics of globally coupled oscillators: Progress and perspectives. CHAOS (WOODBURY, N.Y.) 2015; 25:097616. [PMID: 26428569 DOI: 10.1063/1.4922971] [Citation(s) in RCA: 94] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches.
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Affiliation(s)
- Arkady Pikovsky
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
| | - Michael Rosenblum
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
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Dickten H, Lehnertz K. Identifying delayed directional couplings with symbolic transfer entropy. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062706. [PMID: 25615128 DOI: 10.1103/physreve.90.062706] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2014] [Indexed: 06/04/2023]
Abstract
We propose a straightforward extension of symbolic transfer entropy to enable the investigation of delayed directional relationships between coupled dynamical systems from time series. Analyzing time series from chaotic model systems, we demonstrate the applicability and limitations of our approach. Our findings obtained from applying our method to infer delayed directed interactions in the human epileptic brain underline the importance of our approach for improving the construction of functional network structures from data.
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Affiliation(s)
- Henning Dickten
- Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn, Germany and Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn, Germany and Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany
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Yeldesbay A, Pikovsky A, Rosenblum M. Chimeralike states in an ensemble of globally coupled oscillators. PHYSICAL REVIEW LETTERS 2014; 112:144103. [PMID: 24765969 DOI: 10.1103/physrevlett.112.144103] [Citation(s) in RCA: 93] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2014] [Indexed: 06/03/2023]
Abstract
We demonstrate the emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in nonlocally coupled oscillator lattices. In this regime some part of the ensemble forms a regularly evolving cluster, while all other units irregularly oscillate and remain asynchronous. We argue that the chimera emerges because of effective bistability, which dynamically appears in the originally monostable system due to internal delayed feedback in individual units. Additionally, we present two examples of chimeras in bistable systems with frequency-dependent phase shift in the global coupling.
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Affiliation(s)
- Azamat Yeldesbay
- Institute for Physics and Astronomy, University of Potsdam, Karl-Libknecht-Strasse 24/25, 14476 Potsdam-Golm, Germany
| | - Arkady Pikovsky
- Institute for Physics and Astronomy, University of Potsdam, Karl-Libknecht-Strasse 24/25, 14476 Potsdam-Golm, Germany and Department of Control Theory, Nizhni Novgorod State University, Gagarin Avenue 23, 606950 Nizhni Novgorod, Russia
| | - Michael Rosenblum
- Institute for Physics and Astronomy, University of Potsdam, Karl-Libknecht-Strasse 24/25, 14476 Potsdam-Golm, Germany
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Adimy M, Angulo O, Marquet C, Sebaa L. A mathematical model of multistage hematopoietic cell lineages. ACTA ACUST UNITED AC 2014. [DOI: 10.3934/dcdsb.2014.19.1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Keith Sharp M, Batzel JJ, Montani JP. Space physiology IV: mathematical modeling of the cardiovascular system in space exploration. Eur J Appl Physiol 2013; 113:1919-37. [PMID: 23539439 DOI: 10.1007/s00421-013-2623-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2012] [Accepted: 03/03/2013] [Indexed: 01/03/2023]
Abstract
Mathematical modeling represents an important tool for analyzing cardiovascular function during spaceflight. This review describes how modeling of the cardiovascular system can contribute to space life science research and illustrates this process via modeling efforts to study postflight orthostatic intolerance (POI), a key issue for spaceflight. Examining this application also provides a context for considering broader applications of modeling techniques to the challenges of bioastronautics. POI, which affects a large fraction of astronauts in stand tests upon return to Earth, presents as dizziness, fainting and other symptoms, which can diminish crew performance and cause safety hazards. POI on the Moon or Mars could be more critical. In the field of bioastronautics, POI has been the dominant application of cardiovascular modeling for more than a decade, and a number of mechanisms for POI have been investigated. Modeling approaches include computational models with a range of incorporated factors and hemodynamic sophistication, and also physical models tested in parabolic and orbital flight. Mathematical methods such as parameter sensitivity analysis can help identify key system mechanisms. In the case of POI, this could lead to more effective countermeasures. Validation is a persistent issue in modeling efforts, and key considerations and needs for experimental data to synergistically improve understanding of cardiovascular responses are outlined. Future directions in cardiovascular modeling include subject-specific assessment of system status, as well as research on integrated physiological responses, leading, for instance, to assessment of subject-specific susceptibility to POI or effects of cardiovascular alterations on muscular, vision and cognitive function.
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Affiliation(s)
- M Keith Sharp
- Biofluid Mechanics Laboratory, Department of Mechanical Engineering, University of Louisville, Louisville, KY, USA
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