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Přibylová L, Ševčík J, Eclerová V, Klimeš P, Brázdil M, Meijer HGE. Weak coupling of neurons enables very high-frequency and ultra-fast oscillations through the interplay of synchronized phase shifts. Netw Neurosci 2024; 8:293-318. [PMID: 38562290 PMCID: PMC10954350 DOI: 10.1162/netn_a_00351] [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: 07/28/2023] [Accepted: 11/21/2023] [Indexed: 04/04/2024] Open
Abstract
Recently, in the past decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) were reported in epileptic patients with drug-resistant epilepsy. However, to this day, the physiological origin of these events has yet to be understood. Our study establishes a mathematical framework based on bifurcation theory for investigating the occurrence of VHFOs and UFOs in depth EEG signals of patients with focal epilepsy, focusing on the potential role of reduced connection strength between neurons in an epileptic focus. We demonstrate that synchronization of a weakly coupled network can generate very and ultra high-frequency signals detectable by nearby microelectrodes. In particular, we show that a bistability region enables the persistence of phase-shift synchronized clusters of neurons. This phenomenon is observed for different hippocampal neuron models, including Morris-Lecar, Destexhe-Paré, and an interneuron model. The mechanism seems to be robust for small coupling, and it also persists with random noise affecting the external current. Our findings suggest that weakened neuronal connections could contribute to the production of oscillations with frequencies above 1000 Hz, which could advance our understanding of epilepsy pathology and potentially improve treatment strategies. However, further exploration of various coupling types and complex network models is needed.
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Affiliation(s)
- Lenka Přibylová
- Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic
| | - Jan Ševčík
- Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic
| | - Veronika Eclerová
- Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic
| | - Petr Klimeš
- Institute of Scientific Instruments, The Czech Academy of Sciences, Brno, Czech Republic
| | - Milan Brázdil
- Brno Epilepsy Center, Dept. of Neurology, St. Anne’s Univ. Hospital and Faculty of Medicine, Masaryk University, Brno, Czech Republic, member of the ERN EpiCARE
- Behavioral and Social Neuroscience Research Group, Central European Institute of Technology, Masaryk University, Brno, Czech Republic
| | - Hil G. E. Meijer
- Department of Applied Mathematics, Techmed Centre, University of Twente, Enschede, The Netherlands
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2
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Maurya J, Blyuss KB, Misra AK. Modeling the impact of hospital beds and vaccination on the dynamics of an infectious disease. Math Biosci 2024; 368:109133. [PMID: 38145656 DOI: 10.1016/j.mbs.2023.109133] [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: 04/27/2023] [Revised: 10/26/2023] [Accepted: 12/19/2023] [Indexed: 12/27/2023]
Abstract
The unprecedented scale and rapidity of dissemination of re-emerging and emerging infectious diseases impose new challenges for regulators and health authorities. To curb the dispersal of such diseases, proper management of healthcare facilities and vaccines are core drivers. In the present work, we assess the unified impact of healthcare facilities and vaccination on the control of an infectious disease by formulating a mathematical model. To formulate the model for any region, we consider four classes of human population; namely, susceptible, infected, hospitalized, and vaccinated. It is assumed that the increment in number of beds in hospitals is continuously made in proportion to the number of infected individuals. To ensure the occurrence of transcritical, saddle-node and Hopf bifurcations, the conditions are derived. The normal form is obtained to show the existence of Bogdanov-Takens bifurcation. To validate the analytically obtained results, we have conducted some numerical simulations. These results will be useful to public health authorities for planning appropriate health care resources and vaccination programs to diminish prevalence of infectious diseases.
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Affiliation(s)
- Jyoti Maurya
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221 005, India
| | - Konstantin B Blyuss
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, United Kingdom
| | - A K Misra
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221 005, India.
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3
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Jorba-Cuscó M, Oliva-Zúniga RI, Sardanyés J, Pérez-Palau D. Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters. Theory Biosci 2024; 143:79-95. [PMID: 38383684 PMCID: PMC10904506 DOI: 10.1007/s12064-023-00411-2] [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] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2023] [Accepted: 12/26/2023] [Indexed: 02/23/2024]
Abstract
A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations. At low diffusion, the origin is a repulsor, causing the orbits to flow nearly parallel to the axes, risking stochastic extinctions. Higher diffusion turns the repeller into a saddle point. Orbits then quickly converge to the saddle's unstable manifold, reducing extinction chances. This change in the vector field enhances metapopulation robustness. On the other hand, the well-known fact that asymmetric conditions on the patches is beneficial for the total population is further investigated. This phenomenon has been studied in previous works for large enough or small enough values of the dispersal. In this work, we complete the theory for all values of the dispersal. In particular, we derive analytically a formula for the optimal value of the dispersal that maximizes the total population.
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Affiliation(s)
- Marc Jorba-Cuscó
- Centre de Recerca Matemàtica. Edifici C, Campus de Bellaterra, 08193, Cerdanyola del Vallès, Spain.
- Departament de Matemàtiques, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain.
| | - Ruth I Oliva-Zúniga
- Universidad Nacional Autónoma de Honduras en el Valle de Sula (UNAH-VS), Boulevard UNAH-VS 21102, San Pedro Sula, Honduras
| | - Josep Sardanyés
- Centre de Recerca Matemàtica. Edifici C, Campus de Bellaterra, 08193, Cerdanyola del Vallès, Spain.
| | - Daniel Pérez-Palau
- Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de la Rioja, Av. La Paz 137, 26006, Logroño, Spain
- Departament de Matemàtiques, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain
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Chen R, Singh M, Braver TS, Ching S. Dynamical models reveal anatomically reliable attractor landscapes embedded in resting state brain networks. bioRxiv 2024:2024.01.15.575745. [PMID: 38293124 PMCID: PMC10827065 DOI: 10.1101/2024.01.15.575745] [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: 02/01/2024]
Abstract
Analyses of functional connectivity (FC) in resting-state brain networks (RSNs) have generated many insights into cognition. However, the mechanistic underpinnings of FC and RSNs are still not well-understood. It remains debated whether resting state activity is best characterized as noise-driven fluctuations around a single stable state, or instead, as a nonlinear dynamical system with nontrivial attractors embedded in the RSNs. Here, we provide evidence for the latter, by constructing whole-brain dynamical systems models from individual resting-state fMRI (rfMRI) recordings, using the Mesoscale Individualized NeuroDynamic (MINDy) platform. The MINDy models consist of hundreds of neural masses representing brain parcels, connected by fully trainable, individualized weights. We found that our models manifested a diverse taxonomy of nontrivial attractor landscapes including multiple equilibria and limit cycles. However, when projected into anatomical space, these attractors mapped onto a limited set of canonical RSNs, including the default mode network (DMN) and frontoparietal control network (FPN), which were reliable at the individual level. Further, by creating convex combinations of models, bifurcations were induced that recapitulated the full spectrum of dynamics found via fitting. These findings suggest that the resting brain traverses a diverse set of dynamics, which generates several distinct but anatomically overlapping attractor landscapes. Treating rfMRI as a unimodal stationary process (i.e., conventional FC) may miss critical attractor properties and structure within the resting brain. Instead, these may be better captured through neural dynamical modeling and analytic approaches. The results provide new insights into the generative mechanisms and intrinsic spatiotemporal organization of brain networks.
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Affiliation(s)
- Ruiqi Chen
- Division of Biology and Biomedical Sciences, Washington University in St. Louis, St. Louis, MO 63108
| | - Matthew Singh
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO 63108
| | - Todd S. Braver
- Department of Psychological & Brain Sciences, Washington University in St. Louis, St. Louis, MO 63108
| | - ShiNung Ching
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO 63108
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Barrio R, Jover-Galtier JA, Martínez MA, Pérez L, Serrano S. Mathematical birth of Early Afterdepolarizations in a cardiomyocyte model. Math Biosci 2023; 366:109088. [PMID: 37863283 DOI: 10.1016/j.mbs.2023.109088] [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: 04/13/2023] [Revised: 09/20/2023] [Accepted: 10/17/2023] [Indexed: 10/22/2023]
Abstract
Early Afterdepolarizations (EADs) are abnormal behaviors that can lead to cardiac failure and even cardiac death. In this paper we investigate the occurrence and development of these phenomena in a reduced Luo-Rudy cardiac model. Through a comprehensive dynamical analysis, we map out the distinct patterns observed in the parametric plane, differentiating between normal beats without EADs and pathological beats with EADs. By examining the bifurcation structure of the model, we elucidate the dynamical elements associated with these patterns and their transitions. Using a fast-slow analysis, we explore the emergence and evolution of EADs in the model. Notably, our approach combines the two commonly used fast-slow approaches (1-slow-2-fast and 2-slow-1-fast), and we show how both approaches together provide a more complete understanding of this phenomenon.
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Affiliation(s)
- R Barrio
- IUMA, CoDy and Dpto. Matemática Aplicada, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
| | - J A Jover-Galtier
- IUMA, CoDy and Dpto. Matemática Aplicada, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
| | - M A Martínez
- IUMA, CoDy and Dpto. Matemática Aplicada, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
| | - L Pérez
- Dpto. Matemáticas, University of Oviedo, Oviedo E-33007, Spain.
| | - S Serrano
- IUMA, CoDy and Dpto. Matemática Aplicada, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
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Matouk A. Applications of the generalized gamma function to a fractional-order biological system. Heliyon 2023; 9:e18645. [PMID: 37583759 PMCID: PMC10424077 DOI: 10.1016/j.heliyon.2023.e18645] [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: 05/06/2023] [Revised: 07/23/2023] [Accepted: 07/24/2023] [Indexed: 08/17/2023] Open
Abstract
In this work, variety of complex dynamics are found in a fractional-order antimicrobial resistance (AMR) model based on the generalized Gamma function. Firstly, the extended left and right Caputo fractional differential operators, respectively, ELCFDO and ERCFDO are introduced. The basic features of the ELCFDO are outlined. The ELCFDO is shown to have a new fractional parameter that affects the occurrence of the complex dynamics in the fractional AMR system. Secondly, discretization of the ELCFDO is studied using piecewise constant arguments. Then, complex dynamics of the discretized version of the fractional AMR system involving the ELCFDO are investigated such as the existence of Neimark-Sacker (NS) and flip bifurcations, the existence of closed invariant curves (CIC), the existence of strange attractors with fractal or multi-fractal structures, and chaotic attractors. Finally, an extension of the fractal-fractional operator (FFO) that combines fractal and fractional differentiation is carried out based on the generalized Gamma function. The extended FFO (EFFO) is applied to the proposed AMR system, which also generates similar complex dynamics.
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Affiliation(s)
- A.E. Matouk
- Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia
- College of Engineering, Majmaah University, Al-Majmaah, 11952, Saudi Arabia
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Apostolos A, Chlorogiannis D, Vasilagkos G, Katsanos K, Toutouzas K, Aminian A, Alexopoulos D, Davlouros P, Tsigkas G. Safety and efficacy of shortened dual antiplatelet therapy after complex percutaneous coronary intervention: A systematic review and meta-analysis. Hellenic J Cardiol 2023; 71:33-41. [PMID: 36736730 DOI: 10.1016/j.hjc.2023.01.005] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Revised: 01/07/2023] [Accepted: 01/25/2023] [Indexed: 02/04/2023] Open
Abstract
BACKGROUND Optimal duration of dual antiplatelet therapy (DAPT) in patients undergoing complex percutaneous coronary intervention (PCI) remains under investigation. Our aim is to compare shortened (≤3 months) DAPT with longer DAPT in patients undergoing complex PCIs. METHODS Three major databases (MEDLINE, Cochrane Central Register of Controlled Trials, and Scopus) were screened. The primary endpoint was major bleedings as they are defined by the Bleeding Academic Research Consortium (BARC) 3-5. The secondary endpoints were major adverse cardiovascular events, all-cause and cardiovascular mortality, myocardial infarction, stroke, and stent thrombosis. RESULTS Five studies were included in our analysis, with a total of 9,115 patients. Our meta-analysis met its primary endpoint, as abbreviated DAPT significantly reduced major bleedings by 43% (95% confidence intervals: 0.35-0.93). Ischemic events and mortality were not affected by the shortening of DAPT. CONCLUSION Shortened DAPT significantly reduced the odds of major bleedings in patients undergoing complex PCI without increasing the ischemic events or mortality. Thus, it could be considered a safe and feasible option in such patients.
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Affiliation(s)
- Anastasios Apostolos
- Department of Cardiology, Faculty of Medicine, University of Patras, University Hospital of Patras, Patras, Greece; First Department of Cardiology, Medical School, National and Kapodistrian University of Athens, Hippokration General Hospital, Athens, Greece.
| | - Dimitrios Chlorogiannis
- Department of Cardiology, Faculty of Medicine, University of Patras, University Hospital of Patras, Patras, Greece
| | - Georgios Vasilagkos
- Department of Cardiology, Faculty of Medicine, University of Patras, University Hospital of Patras, Patras, Greece
| | - Konstantinos Katsanos
- Department of Interventional Radiology, Faculty of Medicine, University of Patras, University Hospital of Patras, Patras, Greece
| | - Konstantinos Toutouzas
- First Department of Cardiology, Medical School, National and Kapodistrian University of Athens, Hippokration General Hospital, Athens, Greece
| | - Adel Aminian
- Department of Cardiology, Centre Hospitalier Universitaire de Charleroi, Charleroi, Belgium
| | - Dimitrios Alexopoulos
- Second Department of Cardiology, Medical School, National and Kapodistrian University of Athens, Attikon University Hospital, Athens, Greece
| | - Periklis Davlouros
- Department of Cardiology, Faculty of Medicine, University of Patras, University Hospital of Patras, Patras, Greece
| | - Grigorios Tsigkas
- Department of Cardiology, Faculty of Medicine, University of Patras, University Hospital of Patras, Patras, Greece.
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Athanasouli C, Kalmbach K, Booth V, Diniz Behn CG. NREM-REM alternation complicates transitions from napping to non-napping behavior in a three-state model of sleep-wake regulation. Math Biosci 2023; 355:108929. [PMID: 36448821 DOI: 10.1016/j.mbs.2022.108929] [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] [Received: 06/12/2022] [Revised: 10/23/2022] [Accepted: 10/24/2022] [Indexed: 11/06/2022]
Abstract
The temporal structure of human sleep changes across development as it consolidates from the polyphasic sleep of infants to the single nighttime sleep episode typical in adults. Experimental studies have shown that changes in the dynamics of sleep need may mediate this developmental transition in sleep patterning, however, it is unknown how sleep architecture interacts with these changes. We employ a physiologically-based mathematical model that generates wake, rapid eye movement (REM) and non-REM (NREM) sleep states to investigate how NREM-REM alternation affects the transition in sleep patterns as the dynamics of the homeostatic sleep drive are varied. To study the mechanisms producing these transitions, we analyze the bifurcations of numerically-computed circle maps that represent key dynamics of the full sleep-wake network model by tracking the evolution of sleep onsets across different circadian (∼ 24 h) phases. The maps are non-monotonic and discontinuous, being composed of branches that correspond to sleep-wake cycles containing distinct numbers of REM bouts. As the rates of accumulation and decay of the homeostatic sleep drive are varied, we identify the bifurcations that disrupt a period-adding-like behavior of sleep patterns in the transition between biphasic and monophasic sleep. These bifurcations include border collision and saddle-node bifurcations that initiate new sleep patterns, period-doubling bifurcations leading to higher-order patterns of NREM-REM alternation, and intervals of bistability of sleep patterns with different NREM-REM alternations. Furthermore, patterns of NREM-REM alternation exhibit variable behaviors in different regimes of constant sleep-wake patterns. Overall, the sequence of sleep-wake behaviors, and underlying bifurcations, in the transition from biphasic to monophasic sleep in this three-state model is more complex than behavior observed in models of sleep-wake regulation that do not consider the dynamics of NREM-REM alternation. These results suggest that interactions between the dynamics of the homeostatic sleep drive and the dynamics of NREM-REM alternation may contribute to the wide interindividual variation observed when young children transition from napping to non-napping behavior.
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Affiliation(s)
- Christina Athanasouli
- Department of Mathematics University of Michigan, 530 Church Street, Ann Arbor, MI, 48109, USA.
| | - Kelsey Kalmbach
- Department of Applied Mathematics and Statistics Colorado School of Mines, 1500 Illinois Street, Golden, 80401, CO, USA.
| | - Victoria Booth
- Department of Mathematics University of Michigan, 530 Church Street, Ann Arbor, MI, 48109, USA; Department of Anesthesiology, University of Michigan, 1500 E Medical Center Drive, Ann Arbor, 48109-5048, MI, USA.
| | - Cecilia G Diniz Behn
- Department of Applied Mathematics and Statistics Colorado School of Mines, 1500 Illinois Street, Golden, 80401, CO, USA; Department of Pediatrics, University of Colorado Anschutz Medical Campus, 13001 East 17th Place, Aurora, 80045, CO, USA.
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Phogat R, Parmananda P, Prasad A. Intensity dependence of sub-harmonics in cortical response to photic stimulation. J Neural Eng 2022; 19. [PMID: 35839731 DOI: 10.1088/1741-2552/ac817f] [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] [Received: 03/25/2022] [Accepted: 07/15/2022] [Indexed: 11/11/2022]
Abstract
Objective. Periodic photic stimulation of human volunteers at 10 Hz is known to entrain their Electroencephalography (EEG) signals. This entrainment manifests as an increment in power at 10, 20, 30 Hz. We observed that this entrainment is accompanied by the emergence of sub-harmonics, but only at specific frequencies and higher intensities of the stimulating signal. Thereafter, we describe our results and explain them using the physiologically inspired Jansen and Rit Neural Mass Model (NMM).Approach. Four human volunteers were separately exposed to both high and low intensity 10 Hz and 6 Hz stimulation. A total of 4 experiments per subject were therefore performed. Simulations and bifurcation analysis of the NMM were carried out and compared with the experimental findings. <i> Main results. High intensity 10 Hz stimulation led to an increment in power at 5 Hz across all the 4 subjects. No increment of power was observed with low intensity stimulation. However, when the same protocol was repeated with a 6 Hz photic stimulation, neither high nor low intensity stimulation were found to cause a discernible change in power at 3 Hz. We found that the NMM was able to recapitulate these results. A further numerical analysis indicated that this arises from the underlying bifurcation structure of the NMM. <i> Significance. The excellent match between theory and experiment suggest that the bifurcation properties of the NMM are mirroring similar features possessed by the actual neural masses producing the EEG dynamics. Neural Mass Models could thus be valuable for understanding properties and pathologies of EEG dynamics, and may contribute to the engineering of brain-computer interface technologies.
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Affiliation(s)
- Richa Phogat
- Indian Institute of Technology Bombay, Department of Physics, Indian Institute of Technology - Bombay, Mumbai, 400076, INDIA
| | - P Parmananda
- Indian Institute of Technology Bombay, Department of Physics, Indian Institute of Technology - Bombay, Mumbai, Maharashtra, 400076, INDIA
| | - Ashok Prasad
- Colorado State University, Department of Chemical and Biological Engineering and School of Biomedical Engineering, Colorado State University, Fort Collins, Colorado, 80523-1019, UNITED STATES
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Depannemaecker D, Ivanov A, Lillo D, Spek L, Bernard C, Jirsa V. A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level. J Comput Neurosci 2022. [PMID: 35031915 DOI: 10.1007/s10827-022-00811-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2021] [Revised: 11/10/2021] [Accepted: 01/03/2022] [Indexed: 10/29/2022]
Abstract
The majority of seizures recorded in humans and experimental animal models can be described by a generic phenomenological mathematical model, the Epileptor. In this model, seizure-like events (SLEs) are driven by a slow variable and occur via saddle node (SN) and homoclinic bifurcations at seizure onset and offset, respectively. Here we investigated SLEs at the single cell level using a biophysically relevant neuron model including a slow/fast system of four equations. The two equations for the slow subsystem describe ion concentration variations and the two equations of the fast subsystem delineate the electrophysiological activities of the neuron. Using extracellular K+ as a slow variable, we report that SLEs with SN/homoclinic bifurcations can readily occur at the single cell level when extracellular K+ reaches a critical value. In patients and experimental models, seizures can also evolve into sustained ictal activity (SIA) and depolarization block (DB), activities which are also parts of the dynamic repertoire of the Epileptor. Increasing extracellular concentration of K+ in the model to values found during experimental status epilepticus and DB, we show that SIA and DB can also occur at the single cell level. Thus, seizures, SIA, and DB, which have been first identified as network events, can exist in a unified framework of a biophysical model at the single neuron level and exhibit similar dynamics as observed in the Epileptor.Author Summary: Epilepsy is a neurological disorder characterized by the occurrence of seizures. Seizures have been characterized in patients in experimental models at both macroscopic and microscopic scales using electrophysiological recordings. Experimental works allowed the establishment of a detailed taxonomy of seizures, which can be described by mathematical models. We can distinguish two main types of models. Phenomenological (generic) models have few parameters and variables and permit detailed dynamical studies often capturing a majority of activities observed in experimental conditions. But they also have abstract parameters, making biological interpretation difficult. Biophysical models, on the other hand, use a large number of variables and parameters due to the complexity of the biological systems they represent. Because of the multiplicity of solutions, it is difficult to extract general dynamical rules. In the present work, we integrate both approaches and reduce a detailed biophysical model to sufficiently low-dimensional equations, and thus maintaining the advantages of a generic model. We propose, at the single cell level, a unified framework of different pathological activities that are seizures, depolarization block, and sustained ictal activity.
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Abstract
Circadian clocks are autonomous systems able to oscillate in a self-sustained manner in the absence of external cues, although such Zeitgebers are typically present. At the cellular level, the molecular clockwork consists of a complex network of interlocked feedback loops. This chapter discusses self-sustained circadian oscillators in the context of nonlinear dynamics theory. We suggest basic steps that can help in constructing a mathematical model and introduce how self-sustained generations can be modeled using ordinary differential equations. Moreover, we discuss how coupled oscillators synchronize among themselves or entrain to periodic signals. The development of mathematical models over the last years has helped to understand such complex network systems and to highlight the basic building blocks in which oscillating systems are built upon. We argue that, through theoretical predictions, the use of simple models can guide experimental research and is thus suitable to model biological systems qualitatively.
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Affiliation(s)
- Marta Del Olmo
- Institute for Theoretical Biology, Charité and Humboldt Universität zu Berlin, Berlin, Germany.
| | - Saskia Grabe
- Institute for Theoretical Biology, Charité and Humboldt Universität zu Berlin, Berlin, Germany
| | - Hanspeter Herzel
- Institute for Theoretical Biology, Charité and Humboldt Universität zu Berlin, Berlin, Germany
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John YJ, Sawyer KS, Srinivasan K, Müller EJ, Munn BR, Shine JM. It's about time: Linking dynamical systems with human neuroimaging to understand the brain. Netw Neurosci 2022; 6:960-979. [PMID: 36875012 PMCID: PMC9976648 DOI: 10.1162/netn_a_00230] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Accepted: 01/04/2022] [Indexed: 11/04/2022] Open
Abstract
Most human neuroscience research to date has focused on statistical approaches that describe stationary patterns of localized neural activity or blood flow. While these patterns are often interpreted in light of dynamic, information-processing concepts, the static, local, and inferential nature of the statistical approach makes it challenging to directly link neuroimaging results to plausible underlying neural mechanisms. Here, we argue that dynamical systems theory provides the crucial mechanistic framework for characterizing both the brain's time-varying quality and its partial stability in the face of perturbations, and hence, that this perspective can have a profound impact on the interpretation of human neuroimaging results and their relationship with behavior. After briefly reviewing some key terminology, we identify three key ways in which neuroimaging analyses can embrace a dynamical systems perspective: by shifting from a local to a more global perspective, by focusing on dynamics instead of static snapshots of neural activity, and by embracing modeling approaches that map neural dynamics using "forward" models. Through this approach, we envisage ample opportunities for neuroimaging researchers to enrich their understanding of the dynamic neural mechanisms that support a wide array of brain functions, both in health and in the setting of psychopathology.
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Affiliation(s)
- Yohan J John
- Neural Systems Laboratory, Department of Health Sciences, Boston University, Boston, MA, USA
| | - Kayle S Sawyer
- Departments of Anatomy and Neurobiology, Boston University, Boston University, Boston, MA, USA.,Department of Radiology, Massachusetts General Hospital, Boston, MA, USA.,Boston VA Healthcare System, Boston, MA, USA.,Sawyer Scientific, LLC, Boston, MA, USA
| | - Karthik Srinivasan
- McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Eli J Müller
- Brain and Mind Center, University of Sydney, Sydney, NSW, Australia
| | - Brandon R Munn
- Brain and Mind Center, University of Sydney, Sydney, NSW, Australia
| | - James M Shine
- Brain and Mind Center, University of Sydney, Sydney, NSW, Australia
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Madeo D, Mocenni C. Evolutionary Game Theoretic Insights on the SIRS Model of the COVID-19 Pandemic. IFAC Pap OnLine 2021; 54:1-6. [PMID: 38620939 PMCID: PMC8603029 DOI: 10.1016/j.ifacol.2021.11.016] [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] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The effectiveness of control measures against the diffusion of the COVID-19 pandemic is grounded on the assumption that people are prepared and disposed to cooperate. From a strategic decision point of view, cooperation is the unreachable strategy of the prisoner's dilemma game, where the temptation to exploit the others and the fear to be betrayed by them drives the people behavior, which eventually results fully defective. In this work, we integrate the SIRS epidemic model with the replicator equation of evolutionary games in order to study the interplay between the infection spreading and the propensity of people to become cooperative under the pressure of the epidemic. We find that the developed model possesses several steady states, including fully or partially cooperative ones and that the presence of such states allows to take the disease under control. Moreover, assuming a seasonal variation of the infection rate, the system presents rich dynamics, including chaotic behavior and epidemic extinction.
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Affiliation(s)
- D Madeo
- Department of Information Engineering and Mathematics University of Siena Via Roma, 56, 53100 Siena Italy
| | - C Mocenni
- Department of Information Engineering and Mathematics University of Siena Via Roma, 56, 53100 Siena Italy
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14
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Rukhlenko OS, Kholodenko BN. Modeling the Nonlinear Dynamics of Intracellular Signaling Networks. Bio Protoc 2021; 11:e4089. [PMID: 34395728 PMCID: PMC8329461 DOI: 10.21769/bioprotoc.4089] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [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: 12/20/2020] [Revised: 04/09/2021] [Accepted: 05/28/2021] [Indexed: 11/17/2022] Open
Abstract
This protocol illustrates a pipeline for modeling the nonlinear behavior of intracellular signaling pathways. At fixed spatial points, nonlinear signaling dynamics are described by ordinary differential equations (ODEs). At constant parameters, these ODEs may have multiple attractors, such as multiple steady states or limit cycles. Standard optimization procedures fine-tune the parameters for the system trajectories localized within the basin of attraction of only one attractor, usually a stable steady state. The suggested protocol samples the parameter space and captures the overall dynamic behavior by analyzing the number and stability of steady states and the shapes of the assembly of nullclines, which are determined as projections of quasi-steady-state trajectories into different 2D spaces of system variables. Our pipeline allows identifying main qualitative features of the model behavior, perform bifurcation analysis, and determine the borders separating the different dynamical regimes within the assembly of 2D parametric planes. Partial differential equation (PDE) systems describing the nonlinear spatiotemporal behavior are derived by coupling fixed point dynamics with species diffusion.
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Affiliation(s)
- Oleksii S Rukhlenko
- Systems Biology Ireland, School of Medicine and Medical Science, University College Dublin, Belfield, Dublin 4, Ireland
| | - Boris N Kholodenko
- Systems Biology Ireland, School of Medicine and Medical Science, University College Dublin, Belfield, Dublin 4, Ireland.,Conway Institute of Biomolecular & Biomedical Research, University College Dublin, Belfield, Dublin 4, Ireland.,Department of Pharmacology, Yale University School of Medicine, New Haven, USA
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15
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Vranckx M, Geerinckx H, Gaêta-Araujo H, Leite AF, Politis C, Jacobs R. Do anatomical variations of the mandibular canal pose an increased risk of inferior alveolar nerve injury after third molar removal? Clin Oral Investig 2021; 26:931-937. [PMID: 34279700 DOI: 10.1007/s00784-021-04076-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [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: 04/14/2021] [Accepted: 07/08/2021] [Indexed: 11/25/2022]
Abstract
OBJECTIVES The present study aimed to assess whether anatomical variations of the mandibular canal are associated with neurosensory disturbances of the inferior alveolar nerve (IAN) following mandibular third molar removal. METHODS Two observers compared the detection of third molar root-nerve relations and bifurcations of the mandibular canal on panoramic radiographs and CBCT images of 201 patients undergoing removal of 357 mandibular third molars. Potential neurosensory disturbances of the IAN were surveyed ten days after surgery. Fisher's Exact was performed to correlate presence of canal variations to postoperative neurosensory disturbances. Positive and negative predictive values (PPV, NPV) and likelihood ratios (LR + , LR-) were calculated. RESULTS Thirteen patients reported postoperative altered sensation of the lower lip, with 2 of them having mandibular canal bifurcations on the ipsilateral side of the injury. Fisher's Exact showed that the studied mandibular canal variations were not related to postoperative neurosensory disturbances. CBCT was superior in visualization of anatomical variations of the mandibular canal. Prevalence of bifurcations was 14% on CBCT and 7% on panoramic radiographs. In both imaging modalities and for all parameters, PPVs were low (0.04 - 0.06) and NPVs were high (0.92 - 0.98), with LR ranging around 1. CONCLUSION In the present study, the assessed mandibular canal variations had limited predictive value for IAN neurosensory disturbances following third molar removal. CLINICAL RELEVANCE While a close relation between the third molar and the mandibular canal remains a high risk factor, mandibular canal variations did not pose an increased risk of postoperative IAN injury after third molar removal.
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Affiliation(s)
- Myrthel Vranckx
- OMFS-IMPATH Research Group, , Department of Imaging and Pathology, Faculty of Medicine, University of Leuven, and Department of Oral and Maxillofacial Surgery, University Hospitals Leuven, Kapucijnenvoer 7 blok a, 3000, Leuven, Belgium.
| | - Hannah Geerinckx
- OMFS-IMPATH Research Group, , Department of Imaging and Pathology, Faculty of Medicine, University of Leuven, and Department of Oral and Maxillofacial Surgery, University Hospitals Leuven, Kapucijnenvoer 7 blok a, 3000, Leuven, Belgium
| | - Hugo Gaêta-Araujo
- OMFS-IMPATH Research Group, , Department of Imaging and Pathology, Faculty of Medicine, University of Leuven, and Department of Oral and Maxillofacial Surgery, University Hospitals Leuven, Kapucijnenvoer 7 blok a, 3000, Leuven, Belgium
- Department of Oral Diagnosis, Division of Oral Radiology, Piracicaba Dental School, University of Campinas (UNICAMP), Piracicaba, Brazil
| | - Andre Ferreira Leite
- OMFS-IMPATH Research Group, , Department of Imaging and Pathology, Faculty of Medicine, University of Leuven, and Department of Oral and Maxillofacial Surgery, University Hospitals Leuven, Kapucijnenvoer 7 blok a, 3000, Leuven, Belgium
- Department of Dentistry, Faculty of Health Sciences, University of Brasília, Brasília, Brazil
| | - Constantinus Politis
- OMFS-IMPATH Research Group, , Department of Imaging and Pathology, Faculty of Medicine, University of Leuven, and Department of Oral and Maxillofacial Surgery, University Hospitals Leuven, Kapucijnenvoer 7 blok a, 3000, Leuven, Belgium
| | - Reinhilde Jacobs
- OMFS-IMPATH Research Group, , Department of Imaging and Pathology, Faculty of Medicine, University of Leuven, and Department of Oral and Maxillofacial Surgery, University Hospitals Leuven, Kapucijnenvoer 7 blok a, 3000, Leuven, Belgium
- Department of Dental Medicine, Karolinska Institutet, Stockholm, Sweden
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16
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Abstract
Recently, considering the susceptible population size-guided implementations of control measures, several modelling studies investigated the global dynamics and bifurcation phenomena of the state-dependent impulsive SIR models. In this study, we propose a state-dependent impulsive model based on the SIS model. We firstly recall the complicated dynamics of the ODE system with saturated treatment. Based on the dynamics of the ODE system, we firstly discuss the existence and the stability of the semi-trivial periodic solution. Then, based on the definition of the Poincaré map and its properties, we systematically investigate the bifurcations near the semi-trivial periodic solution with all the key control parameters; consequently, we prove the existence and stability of the positive periodic solutions.
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Affiliation(s)
- Jinyan Wang
- School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021 P.R. China
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17
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Lucci G, Giverso C, Preziosi L. Cell orientation under stretch: Stability of a linear viscoelastic model. Math Biosci 2021; 337:108630. [PMID: 34015301 DOI: 10.1016/j.mbs.2021.108630] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Revised: 05/13/2021] [Accepted: 05/13/2021] [Indexed: 10/21/2022]
Abstract
The sensitivity of cells to alterations in the microenvironment and in particular to external mechanical stimuli is significant in many biological and physiological circumstances. In this regard, experimental assays demonstrated that, when a monolayer of cells cultured on an elastic substrate is subject to an external cyclic stretch with a sufficiently high frequency, a reorganization of actin stress fibres and focal adhesions happens in order to reach a stable equilibrium orientation, characterized by a precise angle between the cell major axis and the largest strain direction. To examine the frequency effect on the orientation dynamics, we propose a linear viscoelastic model that describes the coupled evolution of the cellular stress and the orientation angle. We find that cell orientation oscillates tending to an angle that is predicted by the minimization of a very general orthotropic elastic energy, as confirmed by a bifurcation analysis. Moreover, simulations show that the speed of convergence towards the predicted equilibrium orientation presents a changeover related to the viscous-elastic transition for viscoelastic materials. In particular, when the imposed oscillation period is lower than the characteristic turnover rate of the cytoskeleton and of adhesion molecules such as integrins, reorientation is significantly faster.
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Affiliation(s)
- Giulio Lucci
- Department of Mathematical Sciences "G.L. Lagrange" Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy; Department of Mathematics "G. Peano", Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Turin, Italy.
| | - Chiara Giverso
- Department of Mathematical Sciences "G.L. Lagrange" Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy.
| | - Luigi Preziosi
- Department of Mathematical Sciences "G.L. Lagrange" Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy.
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18
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Watanabe Y, Mitomo S, Demir OM, Liu KL, Tung YC, Chieffo A, Montorfano M, Chang CJ, Nakamura S, Colombo A. Clinical Outcomes of Dialysis Patients Treated with Drug-Eluting Stent for Left Main Distal Bifurcation Lesions. Cardiorenal Med 2021; 11:99-108. [PMID: 33657556 DOI: 10.1159/000510731] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 07/27/2020] [Indexed: 11/19/2022] Open
Abstract
AIMS We assessed clinical outcomes after percutaneous coronary intervention (PCI) for unprotected left main coronary artery (ULMCA) distal bifurcation lesions using drug-eluting stents (DES) in hemodialysis (HD) patients compared to non-HD patients. METHODS AND RESULTS We identified 1,858 consecutive patients who underwent PCI for ULMCA distal bifurcation lesions at 4 high-volume centers in Japan, Italy, and Taiwan between January 2005 and December 2015. Of them, 1,416 patients were treated with DES including 113 HD patients and 1,303 non-HD patients. The primary end point was target lesion failure (TLF) defined as a composite of cardiac death, target lesion revascularization (TLR), and myocardial infarction. HD patients were more likely to be younger and have diabetes mellitus, dyslipidemia, peripheral artery disease, lower ejection fraction, and higher EuroSCORE. TLF rate at 3 years was significantly higher in HD group than in non-HD group (adjusted hazard ratio [HR] 2.43 [1.75-3.38], p < 0.001). Cardiac mortality and TLR rate were also significantly higher in HD group than in non-HD group (adjusted HR 3.85 [2.34-6.34], p < 0.001, and HR 2.10 [1.41-3.14], p < 0.001, respectively). CONCLUSIONS HD was strongly associated with adverse cardiac events after PCI for ULMCA distal bifurcation lesions with DES.
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Affiliation(s)
- Yusuke Watanabe
- Interventional Cardiology Unit, San Raffaele Scientific Institute, Milan, Italy, .,Interventional Cardiology Unit, New Tokyo Hospital, Chiba, Japan,
| | - Satoru Mitomo
- Interventional Cardiology Unit, New Tokyo Hospital, Chiba, Japan
| | - Ozan M Demir
- Interventional Cardiology Unit, San Raffaele Scientific Institute, Milan, Italy
| | - Kuan-Liang Liu
- Department of Cardiology, Landseed International Hospital, Taoyuan, Taiwan
| | - Ying-Chang Tung
- Division of Cardiology, Department of Internal Medicine, Chang Gung Memorial Hospital, Chang Gung University College of Medicine, Taoyuan, Taiwan
| | - Alaide Chieffo
- Interventional Cardiology Unit, San Raffaele Scientific Institute, Milan, Italy
| | - Matteo Montorfano
- Interventional Cardiology Unit, San Raffaele Scientific Institute, Milan, Italy
| | - Chi-Jen Chang
- Division of Cardiology, Department of Internal Medicine, Chang Gung Memorial Hospital, Chang Gung University College of Medicine, Taoyuan, Taiwan
| | - Sunao Nakamura
- Interventional Cardiology Unit, New Tokyo Hospital, Chiba, Japan
| | - Antonio Colombo
- Interventional Cardiology Unit, EMO-GVM, Centro Cuore Columbus, Milan, Italy
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19
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Carvalho T, Cristiano R, Rodrigues DS, Tonon DJ. Global Analysis of a piecewise smooth epidemiological model of COVID-19. Nonlinear Dyn 2021; 105:3763-3773. [PMID: 34456509 PMCID: PMC8384106 DOI: 10.1007/s11071-021-06801-9] [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] [Received: 10/06/2020] [Accepted: 08/04/2021] [Indexed: 05/09/2023]
Abstract
Despite the huge relevance of vaccines for preventing COVID-19, physical isolation and quarantine of infected individuals are still the key strategies to fight against the COVID-19 pandemic. Based on a COVID-19 transmission epidemiological model governed by ordinary differential equations, here we propose an intermittent non-pharmacological protocol to control the fraction of infected individuals. In our approach, unlike what generically happens for numerical simulation models, we provide a global analysis of the model, giving qualitative information about every initial condition. Under some simple hypothesis and variations of parameters, we present some bifurcations and we are able to predict the minimum social distancing effort that do not collapse the health system.
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Affiliation(s)
- Tiago Carvalho
- Department of Computing and Mathematics, Faculty of Philosophy, Sciences and Letters of Ribeirão Preto, Univ. of São Paulo, 14040-901 Ribeirão Preto, SP Brazil
| | - Rony Cristiano
- Institute of Mathematics and Statistics, Federal University of Goiás, Avenida Esperança s/n, Campus Samambaia, 74690-900 Goiânia, Goiás Brazil
| | - Diego S. Rodrigues
- School of Technology, University of Campinas, R. Paschoal Marmo, 1888, 13484-332 Limeira, SP Brazil
| | - Durval J. Tonon
- Institute of Mathematics and Statistics, Federal University of Goiás, Avenida Esperança s/n, Campus Samambaia, 74690-900 Goiânia, Goiás Brazil
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20
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Osojnik A, Gaffney EA, Davies M, Yates JWT, Byrne HM. Identifying and characterising the impact of excitability in a mathematical model of tumour-immune interactions. J Theor Biol 2020; 501:110250. [PMID: 32199856 DOI: 10.1016/j.jtbi.2020.110250] [Citation(s) in RCA: 4] [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] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2019] [Revised: 02/24/2020] [Accepted: 03/17/2020] [Indexed: 02/07/2023]
Abstract
We study a five-compartment mathematical model originally proposed by Kuznetsov et al. (1994) to investigate the effect of nonlinear interactions between tumour and immune cells in the tumour microenvironment, whereby immune cells may induce tumour cell death, and tumour cells may inactivate immune cells. Exploiting a separation of timescales in the model, we use the method of matched asymptotics to derive a new two-dimensional, long-timescale, approximation of the full model, which differs from the quasi-steady-state approximation introduced by Kuznetsov et al. (1994), but is validated against numerical solutions of the full model. Through a phase-plane analysis, we show that our reduced model is excitable, a feature not traditionally associated with tumour-immune dynamics. Through a systematic parameter sensitivity analysis, we demonstrate that excitability generates complex bifurcating dynamics in the model. These are consistent with a variety of clinically observed phenomena, and suggest that excitability may underpin tumour-immune interactions. The model exhibits the three stages of immunoediting - elimination, equilibrium, and escape, via stable steady states with different tumour cell concentrations. Such heterogeneity in tumour cell numbers can stem from variability in initial conditions and/or model parameters that control the properties of the immune system and its response to the tumour. We identify different biophysical parameter targets that could be manipulated with immunotherapy in order to control tumour size, and we find that preferred strategies may differ between patients depending on the strength of their immune systems, as determined by patient-specific values of associated model parameters.
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Affiliation(s)
- Ana Osojnik
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK.
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK
| | - Michael Davies
- DMPK, Early Oncology, Oncology R&D, AstraZeneca, Chesterford Research Park, Little Chesterford, Cambridge, CB10 1XL, UK
| | - James W T Yates
- DMPK, Early Oncology, Oncology R&D, AstraZeneca, Chesterford Research Park, Little Chesterford, Cambridge, CB10 1XL, UK
| | - Helen M Byrne
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK
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21
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Sidorova A, Tverdislov V, Levashova N, Garaeva A. A model of autowave self-organization as a hierarchy of active media in the biological evolution. Biosystems 2020; 198:104234. [PMID: 32889101 DOI: 10.1016/j.biosystems.2020.104234] [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] [Received: 06/22/2020] [Revised: 08/23/2020] [Accepted: 08/24/2020] [Indexed: 11/28/2022]
Abstract
Within the framework of the active media concept, we develop a biophysical model of autowave self-organization which is treated as a hierarchy of active media in the evolution of the biosphere. We also propose a mathematical model of the autowave process of speciation in a flow of mutations for the three main taxonometric groups (prokaryotes, unicellular and multicellular eukaryotes) with a naturally determined lower boundary of living matter (the appearance of prokaryotes) and an open upper boundary for the formation of new species. It is shown that the fluctuation-bifurcation description of the evolution for the formation of new taxonometric groups as a trajectory of transformation of small fluctuations into giant ones adequately reflects the process of self-organization during the formation of taxa. The major concepts of biological evolution, conditions of hierarchy formation as a fundamental manifestation of self-organization and complexity in the evolution of biological systems are considered.
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Affiliation(s)
- Alla Sidorova
- Department of Biophysics, Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russia.
| | - Vsevolod Tverdislov
- Head of the Department of Biophysics, Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russia.
| | - Natalia Levashova
- Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russia.
| | - Anastasia Garaeva
- Postgraduate Student of the Department of Biophysics, Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russia.
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22
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Rigatelli G, Zuin M, Chiastra C, Burzotta F. Biomechanical Evaluation of Different Balloon Positions for Proximal Optimization Technique in Left Main Bifurcation Stenting. Cardiovasc Revasc Med 2020; 21:1533-1538. [PMID: 32473906 DOI: 10.1016/j.carrev.2020.05.028] [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] [Received: 04/17/2020] [Revised: 05/19/2020] [Accepted: 05/19/2020] [Indexed: 11/25/2022]
Abstract
BACKGROUND Proximal optimization technique (POT) is a key step during left main (LM) bifurcation stenting. However, after crossover stenting, the ideal position of POT balloon is unclear. We sought to evaluate the biomechanical impact of different POT balloon positions during LM cross-over stenting procedure. METHODS We reconstructed the patient-specific LM bifurcation anatomy, using coronary computed tomography angiography data of 5 consecutive patients (3 males, mean age 66.3 ± 21.6 years) with complex LM bifurcation disease, defined as Medina 1,1,1, evaluated between 1st January 2018 to 1st June 2018 at our center. Finite element analyses were carried out to virtually perform the stenting procedure. POT was virtually performed in a mid (marker just at the carina cut plane), proximal (distal marker 1 mm before the carina) and distal (distal marker 1 mm after the carina) position in each investigated case. Final left circumflex obstruction (SBO%), strut malapposition, elliptical ratio and stent malapposition were evaluated. RESULTS The use of both proximal and distal POT resulted in a smaller LM diameter compared to the mid POT. SBO was significantly higher in both proximal and distal configurations compared to mid POT: 38.3 ± 5.1 and 29.3 ± 3.1 versus 18.3 ± 3.6%, respectively. Similarly stent malapposition was higher in both proximal and distal configurations compared to mid POT: 1.3 ± 0.4 and 0.82 ± 1.8 versus 0.78 ± 1.2, respectively. CONCLUSIONS Mid POT offers the best results in terms of LCx opening maintaining slightly smaller but still acceptable LM and LAD diameters compared to alternative POT configuration.
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Affiliation(s)
- Gianluca Rigatelli
- Cardiovascular Diagnosis and Endoluminal Interventions Unit, Rovigo General Hospital, Rovigo, Italy.
| | - Marco Zuin
- Cardiovascular Diagnosis and Endoluminal Interventions Unit, Rovigo General Hospital, Rovigo, Italy; University of Ferrara, School of Medicine, Ferrara, Italy
| | - Claudio Chiastra
- PoliTo(BIO)Med Lab, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Turin, Italy
| | - Francesco Burzotta
- Fondazione Policlinico Universitario A, Gemelli IRCCS, Università Cattolica del Sacro Cuore, Rome, Italy
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23
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Hervella ÁS, Rouco J, Novo J, Penedo MG, Ortega M. Deep multi-instance heatmap regression for the detection of retinal vessel crossings and bifurcations in eye fundus images. Comput Methods Programs Biomed 2020; 186:105201. [PMID: 31783244 DOI: 10.1016/j.cmpb.2019.105201] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2019] [Revised: 10/09/2019] [Accepted: 11/11/2019] [Indexed: 06/10/2023]
Abstract
BACKGROUND AND OBJECTIVES The analysis of the retinal vasculature plays an important role in the diagnosis of many ocular and systemic diseases. In this context, the accurate detection of the vessel crossings and bifurcations is an important requirement for the automated extraction of relevant biomarkers. In that regard, we propose a novel approach that addresses the simultaneous detection of vessel crossings and bifurcations in eye fundus images. METHOD We propose to formulate the detection of vessel crossings and bifurcations in eye fundus images as a multi-instance heatmap regression. In particular, a deep neural network is trained in the prediction of multi-instance heatmaps that model the likelihood of a pixel being a landmark location. This novel approach allows to make predictions using full images and integrates into a single step the detection and distinction of the vascular landmarks. RESULTS The proposed method is validated on two public datasets of reference that include detailed annotations for vessel crossings and bifurcations in eye fundus images. The conducted experiments evidence that the proposed method offers a satisfactory performance. In particular, the proposed method achieves 74.23% and 70.90% F-score for the detection of crossings and bifurcations, respectively, in color fundus images. Furthermore, the proposed method outperforms previous works by a significant margin. CONCLUSIONS The proposed multi-instance heatmap regression allows to successfully exploit the potential of modern deep learning algorithms for the simultaneous detection of retinal vessel crossings and bifurcations. Consequently, this results in a significant improvement over previous methods, which will further facilitate the automated analysis of the retinal vasculature in many pathological conditions.
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Affiliation(s)
- Álvaro S Hervella
- CITIC-Research Center of Information and Communication Technologies, Universidade da Coruña, A Coruña, Spain; Department of Computer Science, Universidade da Coruña, A Coruña, Spain.
| | - José Rouco
- CITIC-Research Center of Information and Communication Technologies, Universidade da Coruña, A Coruña, Spain; Department of Computer Science, Universidade da Coruña, A Coruña, Spain
| | - Jorge Novo
- CITIC-Research Center of Information and Communication Technologies, Universidade da Coruña, A Coruña, Spain; Department of Computer Science, Universidade da Coruña, A Coruña, Spain
| | - Manuel G Penedo
- CITIC-Research Center of Information and Communication Technologies, Universidade da Coruña, A Coruña, Spain; Department of Computer Science, Universidade da Coruña, A Coruña, Spain
| | - Marcos Ortega
- CITIC-Research Center of Information and Communication Technologies, Universidade da Coruña, A Coruña, Spain; Department of Computer Science, Universidade da Coruña, A Coruña, Spain
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24
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Kumar A, Kumar M, Nilam. A study on the stability behavior of an epidemic model with ratio-dependent incidence and saturated treatment. Theory Biosci 2020; 139:225-34. [PMID: 32232649 DOI: 10.1007/s12064-020-00314-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Accepted: 03/07/2020] [Indexed: 10/24/2022]
Abstract
In the present article, the dynamics of a novel combination of ratio-dependent incidence rate and saturated treatment rate in susceptible-infected-recovered disease compartmental model has been presented. The ratio-dependent incidence rate has been incorporated into the model to monitor the situation when ratio of the number of infectives to that of the susceptibles is getting higher. The saturated treatment rate of the infected population has been considered as Holling type II functional, which explains the limitation in treatment availability. From the mathematical analysis of the model, two types of equilibria of the model have been obtained, which are named as disease-free equilibrium (DFE) and endemic equilibrium (EE). The local stability behavior of equilibria has been investigated by the basic reproduction number [Formula: see text], center manifold theory and Routh-Hurwitz criterion. It has been investigated that the DFE is locally asymptotically stable when [Formula: see text], and when [Formula: see text], the DFE exhibits either a forward bifurcation or a backward bifurcation under some conditions. The local stability behavior of the EE has also been analyzed, and some conditions are obtained for the same. Finally, some numerical computations have been performed in support of our theoretical results.
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25
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Paquin-Lefebvre F, Xu B, DiPietro KL, Lindsay AE, Jilkine A. Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations. J Theor Biol 2020; 497:110242. [PMID: 32179107 DOI: 10.1016/j.jtbi.2020.110242] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Revised: 03/02/2020] [Accepted: 03/05/2020] [Indexed: 01/19/2023]
Abstract
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov-Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in mass-conserved cell polarity models.
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Affiliation(s)
- Frédéric Paquin-Lefebvre
- Department of Mathematics and Institute of Applied Mathematics, University of British Columbia, Vancouver, Canada
| | - Bin Xu
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Kelsey L DiPietro
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA; Sandia National Laboratories, NM, 46556, USA
| | - Alan E Lindsay
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Alexandra Jilkine
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA.
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Sidorova A, Levashova N, Garaeva A, Tverdislov V. A percolation model of natural selection. Biosystems 2020; 193-194:104120. [PMID: 32092352 DOI: 10.1016/j.biosystems.2020.104120] [Citation(s) in RCA: 4] [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] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Revised: 01/29/2020] [Accepted: 02/15/2020] [Indexed: 12/13/2022]
Abstract
A new approach has been proposed and developed: the selection of optimal variants in the evolutionary mutation flow is considered as an analogue of a percolation filter. Interaction of mutations in a series of generations and random processes of drift determine the collective behavior of nodes (individuals - carriers and converters of mutations) and bonds (mutations) in the space of percolation lattice. It is shown that the choice of the development trajectory at the population level depends on the spectrum of supporting and prohibiting mutations under the influence of conjugate deterministic and random factors. From the point of view of the fluctuation-bifurcation process, new concepts of the lower and upper thresholds of the percolation selection grid are defined in the hierarchical structure of speciation. The upper threshold determines the state of self-organized criticality, which, when overcome, leads to irreversible self-organization processes in the population caused by the accumulation of mutations.
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Affiliation(s)
- Alla Sidorova
- Department of Biophysics, Faculty of Physics, M.V.Lomonosov Moscow State University. Moscow, 119991, Russia.
| | - Natalia Levashova
- Department of Mathematics, Faculty of Physics, M.V.Lomonosov Moscow State University. Moscow, 119991, Russia.
| | - Anastasia Garaeva
- Department of Biophysics, Faculty of Physics, M.V.Lomonosov Moscow State University. Moscow, 119991, Russia.
| | - Vsevolod Tverdislov
- Department of Biophysics, Faculty of Physics, M.V.Lomonosov Moscow State University. Moscow, 119991, Russia.
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27
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Goel K, Kumar A. Nonlinear dynamics of a time-delayed epidemic model with two explicit aware classes, saturated incidences, and treatment. Nonlinear Dyn 2020; 101:1693-1715. [PMID: 32836810 PMCID: PMC7334637 DOI: 10.1007/s11071-020-05762-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Accepted: 06/10/2020] [Indexed: 05/10/2023]
Abstract
Whenever a disease emerges, awareness in susceptibles prompts them to take preventive measures, which influence individuals' behaviors. Therefore, we present and analyze a time-delayed epidemic model in which class of susceptible individuals is divided into three subclasses: unaware susceptibles, fully aware susceptibles, and partially aware susceptibles to the disease, respectively, which emphasizes to consider three explicit incidences. The saturated type of incidence rates and treatment rate of infectives are deliberated herein. The mathematical analysis shows that the model has two equilibria: disease-free and endemic. We derive the basic reproduction number R 0 of the model and study the stability behavior of the model at both disease-free and endemic equilibria. Through analysis, it is demonstrated that the disease-free equilibrium is locally asymptotically stable when R 0 < 1 , unstable when R 0 > 1 , and linearly neutrally stable when R 0 = 1 for the time delay ϱ > 0 . Further, an undelayed epidemic model is studied when R 0 = 1 , which reveals that the model exhibits forward and backward bifurcations under specific conditions, which also has important implications in the study of disease transmission dynamics. Moreover, we investigate the stability behavior of the endemic equilibrium and show that Hopf bifurcation occurs near endemic equilibrium when we choose time delay as a bifurcation parameter. Lastly, numerical simulations are performed in support of our analytical results.
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Affiliation(s)
- Kanica Goel
- Department of Applied Mathematics, Delhi Technological University, Delhi, 110042 India
| | - Abhishek Kumar
- Department of Mathematics, School of Basic Sciences and Research, Sharda University, Greater Noida, 201310 India
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28
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Landolff Q, Veugeois A, Godin M, Boussaada MM, Dibie A, Caussin C, Amabile N. [Hot issues in bifurcation lesions PCI in 2019]. Ann Cardiol Angeiol (Paris) 2019; 68:325-332. [PMID: 31542202 DOI: 10.1016/j.ancard.2019.08.004] [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] [Received: 07/15/2019] [Accepted: 08/28/2019] [Indexed: 11/27/2022]
Abstract
Coronary bifurcations are involved in 15-20% of all percutaneous coronary interventions (PCI) and remain one of the most challenging lesions in interventional cardiology in terms of procedural success rate as well as long-term cardiac events. The optimal management of bifurcation lesions is still debated but involves careful assessment, planning and a sequential provisional approach. The preferential strategy for PCI of bifurcation lesions remains to use main vessel (MV) stenting with a proximal optimisation technique (POT) and provisional side branch (SB) stenting as a preferred approach. Final kissing balloon inflation is not recommended in all cases. In the minority of lesions where two stents are required, careful deployment and optimal expansion are essential to achieve a long-term result. Intracoronary imaging techniques (IVUS, OCT) and FFR are useful endovascular tools to achieve optimal results.
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Affiliation(s)
- Q Landolff
- Service de cardiologie, institut mutualiste Montsouris, 42, boulevard Jourdan, 75014 Paris, France
| | - A Veugeois
- Service de cardiologie, institut mutualiste Montsouris, 42, boulevard Jourdan, 75014 Paris, France
| | - M Godin
- Service de cardiologie, clinique St-Hilaire, Rouen, France
| | - M M Boussaada
- Service de cardiologie, institut mutualiste Montsouris, 42, boulevard Jourdan, 75014 Paris, France
| | - A Dibie
- Service de cardiologie, institut mutualiste Montsouris, 42, boulevard Jourdan, 75014 Paris, France
| | - C Caussin
- Service de cardiologie, institut mutualiste Montsouris, 42, boulevard Jourdan, 75014 Paris, France
| | - N Amabile
- Service de cardiologie, institut mutualiste Montsouris, 42, boulevard Jourdan, 75014 Paris, France.
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29
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Alvarez RF, Barbuto JAM, Venegeroles R. A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity. J Theor Biol 2019; 471:42-50. [PMID: 30930063 DOI: 10.1016/j.jtbi.2019.03.025] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2018] [Revised: 03/23/2019] [Accepted: 03/28/2019] [Indexed: 01/21/2023]
Abstract
Human cancers display intra-tumor heterogeneity in many phenotypic features, such as expression of cell surface receptors, growth, and angiogenic, proliferative, and immunogenic factors, which represent obstacles to a successful immune response. In this paper, we propose a nonlinear mathematical model of cancer immunosurveillance that takes into account some of these features based on cell-mediated immune responses. The model describes phenomena that are seen in vivo, such as tumor dormancy, robustness, immunoselection over tumor heterogeneity (also called "cancer immunoediting") and strong sensitivity to initial conditions in the composition of tumor microenvironment. The results framework has as common element the tumor as an attractor for abnormal cells. Bifurcation analysis give us as tumor attractors fixed-points, limit cycles and chaotic attractors, the latter emerging from period-doubling cascade displaying Feigenbaum's universality. Finally, we simulated both elimination and escape tumor scenarios by means of a stochastic version of the model according to the Doob-Gillespie algorithm.
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30
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Kaouri K, Maini PK, Skourides PA, Christodoulou N, Chapman SJ. A simple mechanochemical model for calcium signalling in embryonic epithelial cells. J Math Biol 2019; 78:2059-92. [PMID: 30826846 DOI: 10.1007/s00285-019-01333-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2018] [Revised: 11/14/2018] [Indexed: 12/17/2022]
Abstract
Calcium signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between calcium signalling and mechanical forces is critical to the healthy development of an embryo but poorly understood. Several types of embryonic cells exhibit calcium-induced contractions and many experiments indicate that calcium signals and contractions are coupled via a two-way mechanochemical feedback mechanism. We present a new analysis of experimental data that supports the existence of this coupling during apical constriction. We then propose a simple mechanochemical model, building on early models that couple calcium dynamics to the cell mechanics and we replace the hypothetical bistable calcium release with modern, experimentally validated calcium dynamics. We assume that the cell is a linear, viscoelastic material and we model the calcium-induced contraction stress with a Hill function, i.e. saturating at high calcium levels. We also express, for the first time, the "stretch-activation" calcium flux in the early mechanochemical models as a bottom-up contribution from stretch-sensitive calcium channels on the cell membrane. We reduce the model to three ordinary differential equations and analyse its bifurcation structure semi-analytically as two bifurcation parameters vary-the [Formula: see text] concentration, and the "strength" of stretch activation, [Formula: see text]. The calcium system ([Formula: see text], no mechanics) exhibits relaxation oscillations for a certain range of [Formula: see text] values. As [Formula: see text] is increased the range of [Formula: see text] values decreases and oscillations eventually vanish at a sufficiently high value of [Formula: see text]. This result agrees with experimental evidence in embryonic cells which also links the loss of calcium oscillations to embryo abnormalities. Furthermore, as [Formula: see text] is increased the oscillation amplitude decreases but the frequency increases. Finally, we also identify the parameter range for oscillations as the mechanical responsiveness factor of the cytosol increases. This work addresses a very important and not well studied question regarding the coupling between chemical and mechanical signalling in embryogenesis.
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31
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Fornés J, Tomás Lázaro J, Alarcón T, Elena SF, Sardanyés J. Viral replication modes in single-peak fitness landscapes: A dynamical systems analysis. J Theor Biol 2018; 460:170-183. [PMID: 30300648 DOI: 10.1016/j.jtbi.2018.10.007] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2017] [Revised: 08/30/2018] [Accepted: 10/02/2018] [Indexed: 12/11/2022]
Abstract
Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation-induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation accumulation and demographic stochasticity). Here we analyze a dynamical system describing the intracellular amplification of viral RNA genomes evolving on a single-peak fitness landscape focusing on three cases considering neutral, deleterious, and lethal mutants. We analytically derive the critical mutation rates causing lethal mutagenesis and error threshold, governed by transcritical bifurcations that depend on parameters α (parameter introducing the mode of replication), replicative fitness of mutants (k1), and on the spontaneous degradation rates of the sequences (ϵ). Our results relate the error catastrophe with lethal mutagenesis in a model with continuous populations of viral genomes. The former case involves dominance of the mutant sequences, while the latter, a deterministic extinction of the viral RNAs during replication due to increased mutation. For the lethal case the critical mutation rate involving lethal mutagenesis is μc=1-ɛ/α. Here, the SMR involves lower critical mutation rates, being the system more robust to lethal mutagenesis replicating closer to the GR mode. This result is also found for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the error threshold once the replication mode surpasses a threshold given by α=ϵ/k1.
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Affiliation(s)
- Joan Fornés
- Departament de Matemàtiques, Universitat Politècnica de Catalunya, Av Diagonal, 647, Barcelona 08028, Spain
| | - J Tomás Lázaro
- Departament de Matemàtiques, Universitat Politècnica de Catalunya, Av Diagonal, 647, Barcelona 08028, Spain; Barcelona Graduate School of Mathematics (BGSMath) Campus de Bellaterra, Edifici C, Bellaterra, Barcelona 08193, Spain
| | - Tomás Alarcón
- Barcelona Graduate School of Mathematics (BGSMath) Campus de Bellaterra, Edifici C, Bellaterra, Barcelona 08193, Spain; Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, Bellaterra, Barcelona 08193, Spain; ICREA, Pg. Lluis Companys 23, Barcelona 08010, Spain; Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain
| | - Santiago F Elena
- Instituto de Biología Integrativa de Sistemas, CSIC-Universitat de València, Parc Cientific UV, Catedrático Agustín Escardino 9, Paterna, València 46980, Spain; The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
| | - Josep Sardanyés
- Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, Bellaterra, Barcelona 08193, Spain; Barcelona Graduate School of Mathematics (BGSMath) Campus de Bellaterra, Edifici C, Bellaterra, Barcelona 08193, Spain.
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32
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Mair C, Rezgui D, Titurus B. Nonlinear stability analysis of whirl flutter in a rotor-nacelle system. Nonlinear Dyn 2018; 94:2013-2032. [PMID: 30956393 PMCID: PMC6413826 DOI: 10.1007/s11071-018-4472-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/19/2018] [Accepted: 07/09/2018] [Indexed: 06/09/2023]
Abstract
Whirl flutter is an aeroelastic instability that affects propellers/rotors and the surrounding airframe structure on which they are mounted. Whirl flutter analysis gets progressively more complicated with the addition of nonlinear effects. This paper investigates the impact of nonlinear pylon stiffness on the whirl flutter stability of a basic rotor-nacelle model, compared to a baseline linear stiffness version. The use of suitable nonlinear analysis techniques to address such a nonlinear model is also demonstrated. Three types of nonlinearity were investigated in this paper: cubic softening, cubic hardening and a combined cubic softening-quintic hardening case. The investigation was conducted through a combination of eigenvalue and bifurcation analyses, supplemented by time simulations, in order to fully capture the effects of nonlinear stiffness on the dynamic behaviour of the rotor-nacelle system. The results illustrate the coexistence of stable and unstable limit cycles and equilibria for a range of parameter values in the nonlinear cases, which are not found in the linear baseline model. These branches are connected by a number of different bifurcation types: fold, pitchfork, Hopf, homoclinic and heteroclinic. The results also demonstrate the importance of nonlinear whirl flutter models and analysis methods. Of particular interest are cases where the dynamics of the nacelle are unstable despite linear analysis predicting stable behaviour. A more complete stability envelope for the combined model was generated to take account of this phenomenon.
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Affiliation(s)
- Christopher Mair
- Department of Aerospace Engineering, University of Bristol, Queens Building, Bristol, UK
| | - Djamel Rezgui
- Department of Aerospace Engineering, University of Bristol, Queens Building, Bristol, UK
| | - Branislav Titurus
- Department of Aerospace Engineering, University of Bristol, Queens Building, Bristol, UK
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33
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Chumacero E, Yang J, Chagdes JR. Effect of sensory-motor latencies and active muscular stiffness on stability for an ankle-hip model of balance on a balance board. J Biomech 2018; 75:77-88. [PMID: 29861093 DOI: 10.1016/j.jbiomech.2018.04.045] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Revised: 03/29/2018] [Accepted: 04/26/2018] [Indexed: 11/22/2022]
Abstract
To achieve human upright posture (UP) and avoid falls, the central nervous system processes visual, vestibular, and proprioceptive information to activate the appropriate muscles to accelerate or decelerate the body's center of mass. In this process, sensory-motor (SM) latencies and muscular deficits, even in healthy older adults, may cause falls. This condition is worse for people with chronic neuromuscular deficits (stroke survivors, patients with multiple sclerosis or Parkinson's disease). One therapeutic approach is to recover or improve quiet UP by utilizing a balance board (BB) (a rotating surface with a tunable stiffness and time delay), where a patient attempts to maintain UP while task difficulty is manipulated. While BBs are commonly used, it is unclear how UP is maintained or how changes in system parameters such as SM latencies and BB time delay affect UP stability. To understand these questions, it is important that mathematical models be developed with enough degrees-of-freedom to capture the many responses evoked during the maintenance of UP on a BB. This paper presents an ankle-hip model of balance on a BB, which is used to study the combined effect of SM latencies and active muscular stiffness of the ankle and hip joints, and the BB stiffness and time delay on UP stability. The analysis predicts that people with proprioceptive, visual, vestibular loss, or increased SM latencies may show either leaning postures or larger body-sway. The results show that the BB time delay and the visual and vestibular feedback have the largest impact on UP stability.
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34
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O'Regan SM, Burton DL. How Stochasticity Influences Leading Indicators of Critical Transitions. Bull Math Biol 2018; 80:1630-1654. [PMID: 29713924 DOI: 10.1007/s11538-018-0429-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2017] [Accepted: 03/29/2018] [Indexed: 12/25/2022]
Abstract
Many complex systems exhibit critical transitions. Of considerable interest are bifurcations, small smooth changes in underlying drivers that produce abrupt shifts in system state. Before reaching the bifurcation point, the system gradually loses stability ('critical slowing down'). Signals of critical slowing down may be detected through measurement of summary statistics, but how extrinsic and intrinsic noises influence statistical patterns prior to a transition is unclear. Here, we consider a range of stochastic models that exhibit transcritical, saddle-node and pitchfork bifurcations. Noise was assumed to be either intrinsic or extrinsic. We derived expressions for the stationary variance, autocorrelation and power spectrum for all cases. Trends in summary statistics signaling the approach of each bifurcation depend on the form of noise. For example, models with intrinsic stochasticity may predict an increase in or a decline in variance as the bifurcation parameter changes, whereas models with extrinsic noise applied additively predict an increase in variance. The ability to classify trends of summary statistics for a broad class of models enhances our understanding of how critical slowing down manifests in complex systems approaching a transition.
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Affiliation(s)
- Suzanne M O'Regan
- Department of Mathematics, North Carolina A&T State University, Greensboro, NC, 27411, USA. .,National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, TN, USA.
| | - Danielle L Burton
- Department of Mathematics, University of Tennessee, Knoxville, TN, 37996, USA
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35
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Aldebert C, Kooi BW, Nerini D, Poggiale JC. Is structural sensitivity a problem of oversimplified biological models? Insights from nested Dynamic Energy Budget models. J Theor Biol 2018; 448:1-8. [PMID: 29550453 DOI: 10.1016/j.jtbi.2018.03.019] [Citation(s) in RCA: 6] [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] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Revised: 03/01/2018] [Accepted: 03/13/2018] [Indexed: 10/17/2022]
Abstract
Many current issues in ecology require predictions made by mathematical models, which are built on somewhat arbitrary choices. Their consequences are quantified by sensitivity analysis to quantify how changes in model parameters propagate into an uncertainty in model predictions. An extension called structural sensitivity analysis deals with changes in the mathematical description of complex processes like predation. Such processes are described at the population scale by a specific mathematical function taken among similar ones, a choice that can strongly drive model predictions. However, it has only been studied in simple theoretical models. Here, we ask whether structural sensitivity is a problem of oversimplified models. We found in predator-prey models describing chemostat experiments that these models are less structurally sensitive to the choice of a specific functional response if they include mass balance resource dynamics and individual maintenance. Neglecting these processes in an ecological model (for instance by using the well-known logistic growth equation) is not only an inappropriate description of the ecological system, but also a source of more uncertain predictions.
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Affiliation(s)
- Clement Aldebert
- Mediterranean Institute of Oceanography, Aix-Marseille University, Toulon University, CNRS/INSU,IRD, MIO, UM 110, Marseille, Cedex 09 13288, France; University of Zurich, Institute of Evolutionary Biology and Environmental Studies, Winterthurerstrasse 190, Zurich 8057, Switzerland.
| | - Bob W Kooi
- Faculty of Science, VU University, de Boelelaan 1085,HV Amsterdam 1081, The Netherlands
| | - David Nerini
- Mediterranean Institute of Oceanography, Aix-Marseille University, Toulon University, CNRS/INSU,IRD, MIO, UM 110, Marseille, Cedex 09 13288, France.
| | - Jean-Christophe Poggiale
- Mediterranean Institute of Oceanography, Aix-Marseille University, Toulon University, CNRS/INSU,IRD, MIO, UM 110, Marseille, Cedex 09 13288, France.
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36
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Duits R, Meesters SPL, Mirebeau JM, Portegies JM. Optimal Paths for Variants of the 2D and 3D Reeds-Shepp Car with Applications in Image Analysis. J Math Imaging Vis 2018; 60:816-848. [PMID: 31007388 PMCID: PMC6445415 DOI: 10.1007/s10851-018-0795-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2017] [Accepted: 01/27/2018] [Indexed: 06/08/2023]
Abstract
We present a PDE-based approach for finding optimal paths for the Reeds-Shepp car. In our model we minimize a (data-driven) functional involving both curvature and length penalization, with several generalizations. Our approach encompasses the two- and three-dimensional variants of this model, state-dependent costs, and moreover, the possibility of removing the reverse gear of the vehicle. We prove both global and local controllability results of the models. Via eikonal equations on the manifoldR d × S d - 1 we compute distance maps w.r.t. highly anisotropic Finsler metrics, which approximate the singular (quasi)-distances underlying the model. This is achieved using a fast-marching (FM) method, building on Mirebeau (Numer Math 126(3):515-557, 2013; SIAM J Numer Anal 52(4):1573-1599, 2014). The FM method is based on specific discretization stencils which are adapted to the preferred directions of the Finsler metric and obey a generalized acuteness property. The shortest paths can be found with a gradient descent method on the distance map, which we formalize in a theorem. We justify the use of our approximating metrics by proving convergence results. Our curve optimization model inR d × S d - 1 with data-driven cost allows to extract complex tubular structures from medical images, e.g., crossings, and incomplete data due to occlusions or low contrast. Our work extends the results of Sanguinetti et al. (Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications LNCS 9423, 2015) on numerical sub-Riemannian eikonal equations and the Reeds-Shepp car to 3D, with comparisons to exact solutions by Duits et al. (J Dyn Control Syst 22(4):771-805, 2016). Numerical experiments show the high potential of our method in two applications: vessel tracking in retinal images for the case d = 2 and brain connectivity measures from diffusion-weighted MRI data for the case d = 3 , extending the work of Bekkers et al. (SIAM J Imaging Sci 8(4):2740-2770, 2015). We demonstrate how the new model without reverse gear better handles bifurcations.
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Affiliation(s)
- R. Duits
- CASA, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - S. P. L. Meesters
- CASA, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - J.-M. Mirebeau
- University Paris-Sud, CNRS, University Paris-Saclay, 91405 Orsay, France
| | - J. M. Portegies
- CASA, Eindhoven University of Technology, Eindhoven, The Netherlands
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37
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Cushing JM, Henson SM. Periodic matrix models for seasonal dynamics of structured populations with application to a seabird population. J Math Biol 2018; 77:1689-1720. [PMID: 29397422 DOI: 10.1007/s00285-018-1211-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2017] [Revised: 01/06/2018] [Indexed: 11/29/2022]
Abstract
For structured populations with an annual breeding season, life-stage interactions and behavioral tactics may occur on a faster time scale than that of population dynamics. Motivated by recent field studies of the effect of rising sea surface temperature (SST) on within-breeding-season behaviors in colonial seabirds, we formulate and analyze a general class of discrete-time matrix models designed to account for changes in behavioral tactics within the breeding season and their dynamic consequences at the population level across breeding seasons. As a specific example, we focus on egg cannibalism and the daily reproductive synchrony observed in seabirds. Using the model, we investigate circumstances under which these life history tactics can be beneficial or non-beneficial at the population level in light of the expected continued rise in SST. Using bifurcation theoretic techniques, we study the nature of non-extinction, seasonal cycles as a function of environmental resource availability as they are created upon destabilization of the extinction state. Of particular interest are backward bifurcations in that they typically create strong Allee effects in population models which, in turn, lead to the benefit of possible (initial condition dependent) survival in adverse environments. We find that positive density effects (component Allee effects) due to increased adult survival from cannibalism and the propensity of females to synchronize daily egg laying can produce a strong Allee effect due to a backward bifurcation.
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Affiliation(s)
- J M Cushing
- Department of Mathematics and Interdisciplinary Program in Applied Mathematics, University of Arizona, 617 N Santa Rita, Tucson, AZ, 84721, USA.
| | - Shandelle M Henson
- Department of Mathematics, Andrews University, 4260 Administration Drive, Berrien Springs, MI, 49104, USA.,Department of Biology, Andrews University, 4280 Administration Drive, Berrien Springs, MI, 49104, USA
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Fan G, Huff R, Muir J, Nektalova Z, Kruchowsky J, Kepler JL, Wang H, Marshall PA, Solis FJ. Bifurcations and limit cycles in cytosolic yeast calcium. Math Biosci 2018; 298:58-70. [PMID: 29104134 DOI: 10.1016/j.mbs.2017.11.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2017] [Revised: 05/30/2017] [Accepted: 11/01/2017] [Indexed: 11/20/2022]
Abstract
Calcium homeostasis is a fundamental cellular process in yeast. The regulation of the cytosolic calcium concentration is required for volume preservation and to regulate many vital calcium dependent processes such as mating and response to stress. The homeostatic mechanism is often studied by applying calcium pulses: sharply changing the calcium concentration in the yeast environment and observing the cellular response. To address these experimental investigations, several mathematical models have been proposed to describe this response. In this article we demonstrate that a previously studied model for this response predicts the presence of limit point instabilities and limit cycles in the dynamics of the calcium homeostasis system. We discuss the ways in which such dynamic characteristics can be observed with luminometric techniques. We contrast these predictions with experimentally observed responses and find that the experiments reveal a number of features that are consistent with modeling predictions. In particular, we find that equilibrium cytosolic concentrations have a sharp change in behavior as pulse size changes in the micromolar range. We show that such change is consistent with the presence of limit point instabilities. Additionally, we find that the response of synchronized yeast cells to millimolar range pulses is non-monotonic in its late stages. This response has characteristics similar to those associated with limit cycles.
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Barreiro AK, Kutz JN, Shlizerman E. Symmetries Constrain Dynamics in a Family of Balanced Neural Networks. J Math Neurosci 2017; 7:10. [PMID: 29019105 PMCID: PMC5635020 DOI: 10.1186/s13408-017-0052-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/12/2017] [Accepted: 09/19/2017] [Indexed: 06/07/2023]
Abstract
We examine a family of random firing-rate neural networks in which we enforce the neurobiological constraint of Dale's Law-each neuron makes either excitatory or inhibitory connections onto its post-synaptic targets. We find that this constrained system may be described as a perturbation from a system with nontrivial symmetries. We analyze the symmetric system using the tools of equivariant bifurcation theory and demonstrate that the symmetry-implied structures remain evident in the perturbed system. In comparison, spectral characteristics of the network coupling matrix are relatively uninformative about the behavior of the constrained system.
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Affiliation(s)
- Andrea K. Barreiro
- Department of Mathematics, Southern Methodist University, POB 750156, Dallas, TX 75275 USA
| | - J. Nathan Kutz
- Department of Applied Mathematics, University of Washington, Box 353925, Seattle, WA 98195-3925 USA
| | - Eli Shlizerman
- Department of Applied Mathematics, University of Washington, Box 353925, Seattle, WA 98195-3925 USA
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40
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Barré J, Carrillo JA, Degond P, Peurichard D, Zatorska E. Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions. J Nonlinear Sci 2017; 28:235-268. [PMID: 29367810 PMCID: PMC5756578 DOI: 10.1007/s00332-017-9408-z] [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] [Subscribe] [Scholar Register] [Received: 01/30/2017] [Accepted: 08/01/2017] [Indexed: 06/07/2023]
Abstract
We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation-diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.
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Affiliation(s)
- J. Barré
- Laboratoire MAPMO, CNRS, UMR 7349, Fédération Denis Poisson, FR 2964, Université d’Orléans, B.P. 6759, 45067 Orléans Cedex 2, France
- Institut Universitaire de France, Paris, France
| | - J. A. Carrillo
- Department of Mathematics, Imperial College London, London, SW7 2AZ UK
| | - P. Degond
- Department of Mathematics, Imperial College London, London, SW7 2AZ UK
| | - D. Peurichard
- Faculty of Mathematics, University of Vienna, Oskar-Morgenstern Platz 1, 1090 Vienna, Austria
| | - E. Zatorska
- Department of Mathematics, Imperial College London, London, SW7 2AZ UK
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41
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Cocchi L, Gollo LL, Zalesky A, Breakspear M. Criticality in the brain: A synthesis of neurobiology, models and cognition. Prog Neurobiol 2017; 158:132-152. [PMID: 28734836 DOI: 10.1016/j.pneurobio.2017.07.002] [Citation(s) in RCA: 223] [Impact Index Per Article: 31.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Revised: 06/15/2017] [Accepted: 07/13/2017] [Indexed: 11/26/2022]
Abstract
Cognitive function requires the coordination of neural activity across many scales, from neurons and circuits to large-scale networks. As such, it is unlikely that an explanatory framework focused upon any single scale will yield a comprehensive theory of brain activity and cognitive function. Modelling and analysis methods for neuroscience should aim to accommodate multiscale phenomena. Emerging research now suggests that multi-scale processes in the brain arise from so-called critical phenomena that occur very broadly in the natural world. Criticality arises in complex systems perched between order and disorder, and is marked by fluctuations that do not have any privileged spatial or temporal scale. We review the core nature of criticality, the evidence supporting its role in neural systems and its explanatory potential in brain health and disease.
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Affiliation(s)
- Luca Cocchi
- QIMR Berghofer Medical Research Institute, Brisbane, Australia.
| | | | - Andrew Zalesky
- Melbourne Neuropsychiatry Centre, The University of Melbourne, Melbourne, Australia
| | - Michael Breakspear
- QIMR Berghofer Medical Research Institute, Brisbane, Australia; Metro North Mental Health Service, Brisbane, Australia
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42
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Hellenkamp K, Becker A, Gabriel YD, Hasenfuß G, Hünlich M, Jacobshagen C, Schillinger W, Schroeter MR. Mid- to long-term outcome of patients treated with everolimus-eluting bioresorbable vascular scaffolds: Data of the BVS registry Göttingen predominantly from ACS patients. Int J Cardiol 2017; 234:58-63. [PMID: 28258843 DOI: 10.1016/j.ijcard.2017.02.069] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/03/2016] [Revised: 12/27/2016] [Accepted: 02/20/2017] [Indexed: 11/30/2022]
Abstract
BACKGROUND Bioresorbable vascular scaffolds (BVS) are widely used in routine clinical practice. While previous studies reported acceptable short- to midterm outcome after BVS implantation, data on longer-term outcome are rare. METHODS Patients treated with at least one Absorb®-BVS were consecutively enrolled. Follow-up data were assessed after 834.0 [769.0-1026.0] days. The primary device-oriented composite endpoint (DOCE) was defined as cardiovascular death, myocardial infarction (MI) and/or target lesion revascularization (TLR). RESULTS Between 2012 and 2014, 195 patients were included into study analysis. Overall, 244 BVS were implanted. Mean patient age was 64.0[54.3-74.0] years. Three-quarter of patients had an ACS; of those 42.9% had ST-elevation-MI and 40.8% had non-ST-elevation-MI. DOCE occurred in 3.1%, 6.7%, 11.8% and 15.4% of patients during hospital stay, within 6-months, 18-months or during the complete follow-up period, respectively. In those patients, median time until DOCE was 211.5[43.25-567.25] days. In 11 (36.7%) patients DOCE occurred after >12months. Using univariable analysis, bifurcation stenting was associated with a hazard ratio (HR) of 11.8[2.38-58.57] for TLR (p=0.002) and 2.1[1.02-4.49] for DOCE (p=0.045). Similarly, in ACS patients, bifurcation stenting was associated with an increased risk for TLR (HR=10.4[2.01-53.56]; p=0.005) and for DOCE (HR=2.4[1.09-5.32]; p=0.029) and in multivariable analysis, it remained an independent predictor of DOCE (HR=3.0; p=0.018). CONCLUSIONS Although, the rates of (potentially) device-related complications following BVS implantation are acceptable, they are nonetheless not negligible. Interestingly, they did not decline over time. Bifurcation stenting could be found as relevant procedure-related predictor of DOCE, especially in ACS patients. Randomized trials are warranted to confirm these findings.
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Affiliation(s)
- Kristian Hellenkamp
- Clinic for Cardiology & Pneumology/Heart Center, University Medical Center Göttingen, DZHK - German Center for Cardiovascular Research, Germany
| | - Alexander Becker
- Clinic for Cardiology & Pneumology/Heart Center, University Medical Center Göttingen, DZHK - German Center for Cardiovascular Research, Germany; Clinic for Cardiology, Robert-Bosch Hospital, Stuttgart, Germany
| | - Yannick D Gabriel
- Clinic for Cardiology & Pneumology/Heart Center, University Medical Center Göttingen, DZHK - German Center for Cardiovascular Research, Germany
| | - Gerd Hasenfuß
- Clinic for Cardiology & Pneumology/Heart Center, University Medical Center Göttingen, DZHK - German Center for Cardiovascular Research, Germany
| | - Mark Hünlich
- Clinic for Cardiology & Pneumology/Heart Center, University Medical Center Göttingen, DZHK - German Center for Cardiovascular Research, Germany
| | - Claudius Jacobshagen
- Clinic for Cardiology & Pneumology/Heart Center, University Medical Center Göttingen, DZHK - German Center for Cardiovascular Research, Germany
| | - Wolfgang Schillinger
- Clinic for Cardiology & Pneumology/Heart Center, University Medical Center Göttingen, DZHK - German Center for Cardiovascular Research, Germany; Medical Clinic I, Helios Albert-Schweitzer Clinic Northeim, Northeim, Germany
| | - Marco R Schroeter
- Clinic for Cardiology & Pneumology/Heart Center, University Medical Center Göttingen, DZHK - German Center for Cardiovascular Research, Germany.
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López Garza G, Castellanos NP, Godínez R. Cell-to-cell modeling of the interface between atrial and sinoatrial anisotropic heterogeneous nets. Comput Biol Chem 2017; 68:245-259. [PMID: 28460307 DOI: 10.1016/j.compbiolchem.2017.04.008] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2016] [Accepted: 04/17/2017] [Indexed: 10/19/2022]
Abstract
The transition between sinoatrial cells and atrial cells in the heart is not fully understood. Here we focus on cell-to-cell mathematical models involving typical sinoatrial cells and atrial cells connected with experimentally observed conductance values. We are interested mainly in the geometry of the microstructure of the conduction paths in the sinoatrial node. We show with some models that appropriate source-sink relationships between atrial and sinoatrial cells may occur according to certain geometric arrangements.
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Affiliation(s)
- Gabriel López Garza
- Mathematics Department, Universidad Autónoma Metropolitana, M. City, Mexico.
| | - Norma P Castellanos
- Electric Engineering Department, Universidad Autónoma Metropolitana, M. City, Mexico
| | - Rafael Godínez
- Electric Engineering Department, Universidad Autónoma Metropolitana, M. City, Mexico
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Ma QX, Arneodo A, Ding GH, Argoul F. Dynamical study of Νaν channel excitability under mechanical stress. Biol Cybern 2017; 111:129-148. [PMID: 28233067 DOI: 10.1007/s00422-017-0712-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2016] [Accepted: 02/06/2017] [Indexed: 06/06/2023]
Abstract
Alteration of [Formula: see text] channel functions (channelopathies) has been encountered in various hereditary muscle diseases. [Formula: see text] channel mutations lead to aberrant excitability in skeletal muscle myotonia and paralysis. In general, these mutations disable inactivation of the [Formula: see text] channel, producing either repetitive action potential firing (myotonia) or electrical dormancy (flaccid paralysis) in skeletal muscles. These "sick-excitable" cell conditions were shown to correlate with a mechanical stretch-driven left shift of the conductance factors of the two gating mechanisms of a fraction of [Formula: see text] channels, which make them firing at inappropriate hyperpolarised (left-shifted) voltages. Here we elaborate on a variant of the Hodgkin-Huxley model that includes a stretch elasticity energy component in the activation and inactivation gate kinetic rates. We show that this model reproduces fairly well sick-excitable cell behaviour and can be used to predict the parameter domains where aberrant excitability or paralysis may occur. By allowing us to separate the incidences of activation and inactivation gate impairments in [Formula: see text] channel excitability, this model could be a strong asset for diagnosing the origin of excitable cell disorders.
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Affiliation(s)
- Q X Ma
- Shanghai Key Laboratory for Acupuncture Mechanism and Acupoint Function, Department of Aeronautics and Astronautics, Fudan University, Shanghai, 200433, China
| | - A Arneodo
- LOMA, CNRS, UMR 5798, Université de Bordeaux, 51 Cours de la Libération, 33405, Talence, France
- Laboratoire de Physique, ENS Lyon, CNRS UMR5672, Université de Lyon, 46 Allée d'Italie, 69364, Lyon, France
| | - G H Ding
- Shanghai Key Laboratory for Acupuncture Mechanism and Acupoint Function, Department of Aeronautics and Astronautics, Fudan University, Shanghai, 200433, China
| | - F Argoul
- LOMA, CNRS, UMR 5798, Université de Bordeaux, 51 Cours de la Libération, 33405, Talence, France.
- Laboratoire de Physique, ENS Lyon, CNRS UMR5672, Université de Lyon, 46 Allée d'Italie, 69364, Lyon, France.
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45
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Abstract
In this paper we construct and analyze a model of cell receptor aggregation. Experiments have shown that receptors in an aggregated state have greatly reduced mobility. We model the effects of this reduced mobility with a density dependent diffusion and study the impact of density dependent diffusion on aggregate formation in a one-dimensional domain. Critical values of receptor diffusivity and receptor activation are found and compared with numerical simulations. We find that the role of density dependant diffusion is quite limited in the formation of aggregate structures. In the case of receptor activation, the analytical results agree very well with the numerical calculations. Finally, we consider our model in higher dimensional domains. In this case our analysis is primarily numerical.
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46
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Garnier A, Vidal A, Benali H. A Theoretical Study on the Role of Astrocytic Activity in Neuronal Hyperexcitability by a Novel Neuron-Glia Mass Model. J Math Neurosci 2016; 6:10. [PMID: 28004309 PMCID: PMC5177605 DOI: 10.1186/s13408-016-0042-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2016] [Accepted: 11/26/2016] [Indexed: 05/07/2023]
Abstract
Recent experimental evidence on the clustering of glutamate and GABA transporters on astrocytic processes surrounding synaptic terminals pose the question of the functional relevance of the astrocytes in the regulation of neural activity. In this perspective, we introduce a new computational model that embeds recent findings on neuron-astrocyte coupling at the mesoscopic scale intra- and inter-layer local neural circuits. The model consists of a mass model for the neural compartment and an astrocyte compartment which controls dynamics of extracellular glutamate and GABA concentrations. By arguments based on bifurcation theory, we use the model to study the impact of deficiency of astrocytic glutamate and GABA uptakes on neural activity. While deficient astrocytic GABA uptake naturally results in increased neuronal inhibition, which in turn results in a decreased neuronal firing, deficient glutamate uptake by astrocytes may either decrease or increase neuronal firing either transiently or permanently. Given the relevance of neuronal hyperexcitability (or lack thereof) in the brain pathophysiology, we provide biophysical conditions for the onset identifying different physiologically relevant regimes of operation for astrocytic uptake transporters.
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Affiliation(s)
- Aurélie Garnier
- Laboratoire d’Imagerie Biomédicale (LIB), Sorbonne Universités, UPMC Univ Paris 06, CNRS, INSERM, Paris, 75013 France
| | - Alexandre Vidal
- Laboratoire de Mathématiques et Modélisation d’Évry (LaMME), CNRS UMR 8071, Université d’Évry-Val-d’Essonne, Évry, 91000 France
| | - Habib Benali
- Laboratoire d’Imagerie Biomédicale (LIB), Sorbonne Universités, UPMC Univ Paris 06, CNRS, INSERM, Paris, 75013 France
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Sardanyés J, Martínez R, Simó C, Solé R. Abrupt transitions to tumor extinction: a phenotypic quasispecies model. J Math Biol 2016; 74:1589-1609. [PMID: 27714432 DOI: 10.1007/s00285-016-1062-9] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2016] [Revised: 09/09/2016] [Indexed: 12/20/2022]
Abstract
The dynamics of heterogeneous tumor cell populations competing with healthy cells is an important topic in cancer research with deep implications in biomedicine. Multitude of theoretical and computational models have addressed this issue, especially focusing on the nature of the transitions governing tumor clearance as some relevant model parameters are tuned. In this contribution, we analyze a mathematical model of unstable tumor progression using the quasispecies framework. Our aim is to define a minimal model incorporating the dynamics of competition between healthy cells and a heterogeneous population of cancer cell phenotypes involving changes in replication-related genes (i.e., proto-oncogenes and tumor suppressor genes), in genes responsible for genomic stability, and in house-keeping genes. Such mutations or loss of genes result into different phenotypes with increased proliferation rates and/or increased genomic instabilities. Despite bifurcations in the classical deterministic quasispecies model are typically given by smooth, continuous shifts (i.e., transcritical bifurcations), we here identify a novel type of bifurcation causing an abrupt transition to tumor extinction. Such a bifurcation, named as trans-heteroclinic, is characterized by the exchange of stability between two distant fixed points (that do not collide) involving tumor persistence and tumor clearance. The increase of mutation and/or the decrease of the replication rate of tumor cells involves this catastrophic shift of tumor cell populations. The transient times near bifurcation thresholds are also characterized, showing a power law dependence of exponent [Formula: see text] of the transients as mutation is changed near the bifurcation value. These results are discussed in the context of targeted cancer therapy as a possible therapeutic strategy to force a catastrophic shift by simultaneously delivering mutagenic and cytotoxic drugs inside tumor cells.
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Affiliation(s)
- Josep Sardanyés
- ICREA-Complex Systems Lab, Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona, Spain. .,Institut de Biologia Evolutiva, CSIC-Universitat Pompeu Fabra, Barcelona, Spain.
| | - Regina Martínez
- Departament de Matemàtiques, Edifici C. Facultat de Ciències, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain
| | - Carles Simó
- Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Spain
| | - Ricard Solé
- ICREA-Complex Systems Lab, Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona, Spain.,Institut de Biologia Evolutiva, CSIC-Universitat Pompeu Fabra, Barcelona, Spain.,The Santa Fe Institute, Santa Fe, New Mexico, USA
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De Paolis M, Felix C, van Ditzhuijzen N, Fam JM, Karanasos A, de Boer S, van Mieghem NM, Daemen J, Costa F, Bergoli LC, Ligthart JMR, Regar E, de Jaegere PP, Zijlstra F, van Geuns RJ, Diletti R. Everolimus-eluting bioresorbable vascular scaffolds implanted in coronary bifurcation lesions: Impact of polymeric wide struts on side-branch impairment. Int J Cardiol 2016; 221:656-64. [PMID: 27423087 DOI: 10.1016/j.ijcard.2016.06.153] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/06/2016] [Accepted: 06/24/2016] [Indexed: 10/21/2022]
Abstract
BACKGROUND Limited data are available on bioresorbable vascular scaffolds (BVS) performance in bifurcations lesions and on the impact of BVS wider struts on side-branch impairment. METHODS Patients with at least one coronary bifurcation lesion involving a side-branch ≥2mm in diameter and treated with at least one BVS were examined. Procedural and angiographic data were collected and a dedicated methodology for off-line quantitative coronary angiography (QCA) in bifurcation was applied (eleven-segment model), to assess side-branch impairment occurring any time during the procedure. Two- and three-dimensional QCA were used. Optical coherence tomography (OCT) analysis was performed in a subgroup of patients and long-term clinical outcomes reported. RESULTS A total of 102 patients with 107 lesions, were evaluated. Device- and procedural-successes were 99.1% and 94.3%, respectively. Side-branch impairment occurring any time during the procedure was reported in 13 bifurcations (12.1%) and at the end of the procedure in 6.5%. Side-branch minimal lumen diameter (Pre: 1.45±0.41mm vs Final: 1.48±0.42mm, p=0.587) %diameter-stenosis (Pre: 26.93±16.89% vs Final: 27.80±15.57%, p=0.904) and minimal lumen area (Pre: 1.97±0.89mm(2) vs Final: 2.17±1.09mm(2), p=0.334), were not significantly affected by BVS implantation. Mean malapposed struts at the bifurcation polygon-of-confluence were 0.63±1.11. CONCLUSIONS The results of the present investigation suggest feasibility and relative safety of BVS implantation in coronary bifurcations. BVS wide struts have a low impact on side-branch impairment when considering bifurcations with side-branch diameter≥2mm.
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Affiliation(s)
- Marcella De Paolis
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Cordula Felix
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Nienke van Ditzhuijzen
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Jiang Ming Fam
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Antonis Karanasos
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Sanneke de Boer
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Nicolas M van Mieghem
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Joost Daemen
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Francesco Costa
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Luis Carlos Bergoli
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Jurgen M R Ligthart
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Evelyn Regar
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Peter P de Jaegere
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Felix Zijlstra
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Robert Jan van Geuns
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands
| | - Roberto Diletti
- Department of Interventional Cardiology, Thoraxcenter, Erasmus MC, Rotterdam, The Netherlands.
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Gramlich P, Plitzko SJ, Rudolf L, Drossel B, Gross T. The influence of dispersal on a predator-prey system with two habitats. J Theor Biol 2016; 398:150-61. [PMID: 27038668 DOI: 10.1016/j.jtbi.2016.03.015] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [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: 07/22/2015] [Revised: 02/12/2016] [Accepted: 03/11/2016] [Indexed: 11/19/2022]
Abstract
Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and comprehensive study of the simplest possible system that includes dispersal and local interactions, namely a 2-patch 2-species system. We evaluate the impact of dispersal on stability and on the occurrence of bifurcations, including pattern forming bifurcations that lead to spatial heterogeneity, in 19 different classes of models with the help of the generalized modelling approach. We find that dispersal often destabilizes equilibria, but it can stabilize them if it increases population losses. If dispersal is nonrandom, i.e. if emigration or immigration rates depend on population densities, the correlation of stability with dispersal rates is positive in part of the models. We also find that many systems show all four types of bifurcations and that antisynchronous oscillations occur mostly with nonrandom dispersal.
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Affiliation(s)
- P Gramlich
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstraße, 6 D-64289 Darmstadt, Germany.
| | - S J Plitzko
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstraße, 6 D-64289 Darmstadt, Germany.
| | - L Rudolf
- Department of Engineering Mathematics, University of Bristol, Bristol, UK.
| | - B Drossel
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstraße, 6 D-64289 Darmstadt, Germany.
| | - T Gross
- Department of Engineering Mathematics, University of Bristol, Bristol, UK.
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50
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Abstract
We investigate the dynamics and transitions to extinction of hypercycles governed by periodic orbits. For a large enough number of hypercycle species (n>4) the existence of a stable periodic orbit has been previously described, showing an apparent coincidence of the vanishing of the periodic orbit with the value of the replication quality factor Q where two unstable (non-zero) equilibrium points collide (named QSS). It has also been reported that, for values below QSS, the system goes to extinction. In this paper, we use a suitable Poincaré map associated to the hypercycle system to analyze the dynamics in the bistability regime, where both oscillatory dynamics and extinction are possible. The stable periodic orbit is identified, together with an unstable periodic orbit. In particular, we are able to unveil the vanishing mechanism of the oscillatory dynamics: a saddle-node bifurcation of periodic orbits as the replication quality factor, Q, undergoes a critical fidelity threshold, QPO. The identified bifurcation involves the asymptotic extinction of all hypercycle members, since the attractor placed at the origin becomes globally stable for values Q<QPO. Near the bifurcation, these extinction dynamics display a periodic remnant that provides the system with an oscillating delayed transition. Surprisingly, we found that the value of QPO is slightly higher than QSS, thus identifying a gap in the parameter space where the oscillatory dynamics has vanished while the unstable equilibrium points are still present. We also identified a degenerate bifurcation of the unstable periodic orbits for Q=1.
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Affiliation(s)
- Antoni Guillamon
- Departament de Matemàtica Aplicada I, EPSEB, Universitat Politècnica de Catalunya, Av. Doctor Marañón, 44-50, 08028 Barcelona, Spain
| | - Ernest Fontich
- Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain.
| | - Josep Sardanyés
- ICREA-Complex Systems Lab, Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Dr. Aiguader 88, 08003 Barcelona, Spain; Institut de Biologia Evolutiva (CSIC-Universitat Pompeu Fabra), Passeig Maritim de la Barceloneta 37, 08003 Barcelona, Spain.
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