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Dupin I, Eyraud E, Maurat É, Sac-Épée JM, Vallois P. Probabilistic cellular automata modelling of intercellular interactions in airways: complex pattern formation in patients with chronic obstructive pulmonary disease. J Theor Biol 2023; 564:111448. [PMID: 36878400 DOI: 10.1016/j.jtbi.2023.111448] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Revised: 02/16/2023] [Accepted: 02/23/2023] [Indexed: 03/07/2023]
Abstract
Chronic obstructive pulmonary disease (COPD) is a highly prevalent lung disease characterized by chronic inflammation and tissue remodeling possibly induced by unusual interactions between fibrocytes and CD8+ T lymphocytes in the peribronchial area. To investigate this phenomenon, we developed a probabilistic cellular automata type model where the two types of cells follow simple local interaction rules taking into account cell death, proliferation, migration and infiltration. We conducted a rigorous mathematical analysis using multiscale experimental data obtained in control and disease conditions to estimate the model's parameters accurately. The simulation of the model is straightforward to implement, and two distinct patterns emerged that we can analyse quantitatively. In particular, we show that the change in fibrocyte density in the COPD condition is mainly the consequence of their infiltration into the lung during exacerbations, suggesting possible explanations for experimental observations in normal and COPD tissue. Our integrated approach that combines a probabilistic cellular automata model and experimental findings will provide further insights into COPD in future studies.
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Affiliation(s)
- Isabelle Dupin
- Univ-Bordeaux, Centre de Recherche Cardio-thoracique de Bordeaux, U1045, F-33000 Bordeaux, France; INSERM, Centre de Recherche Cardio-thoracique de Bordeaux, U1045, F-33000 Bordeaux, France.
| | - Edmée Eyraud
- Univ-Bordeaux, Centre de Recherche Cardio-thoracique de Bordeaux, U1045, F-33000 Bordeaux, France; INSERM, Centre de Recherche Cardio-thoracique de Bordeaux, U1045, F-33000 Bordeaux, France
| | - Élise Maurat
- Univ-Bordeaux, Centre de Recherche Cardio-thoracique de Bordeaux, U1045, F-33000 Bordeaux, France; INSERM, Centre de Recherche Cardio-thoracique de Bordeaux, U1045, F-33000 Bordeaux, France
| | | | - Pierre Vallois
- Université de Lorraine, CNRS, Inria, IECL., F-54000 Nancy, France
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Kozma R, Freeman WJ. Cinematic Operation of the Cerebral Cortex Interpreted via Critical Transitions in Self-Organized Dynamic Systems. Front Syst Neurosci 2017; 11:10. [PMID: 28352218 PMCID: PMC5348494 DOI: 10.3389/fnsys.2017.00010] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2016] [Accepted: 02/16/2017] [Indexed: 11/10/2022] Open
Abstract
Measurements of local field potentials over the cortical surface and the scalp of animals and human subjects reveal intermittent bursts of beta and gamma oscillations. During the bursts, narrow-band metastable amplitude modulation (AM) patters emerge for a fraction of a second and ultimately dissolve to the broad-band random background activity. The burst process depends on previously learnt conditioned stimuli (CS), thus different AM patterns may emerge in response to different CS. This observation leads to our cinematic theory of cognition when perception happens in discrete steps manifested in the sequence of AM patterns. Our article summarizes findings in the past decades on experimental evidence of cinematic theory of cognition and relevant mathematical models. We treat cortices as dissipative systems that self-organize themselves near a critical level of activity that is a non-equilibrium metastable state. Criticality is arguably a key aspect of brains in their rapid adaptation, reconfiguration, high storage capacity, and sensitive response to external stimuli. Self-organized criticality (SOC) became an important concept to describe neural systems. We argue that transitions from one AM pattern to the other require the concept of phase transitions, extending beyond the dynamics described by SOC. We employ random graph theory (RGT) and percolation dynamics as fundamental mathematical approaches to model fluctuations in the cortical tissue. Our results indicate that perceptions are formed through a phase transition from a disorganized (high entropy) to a well-organized (low entropy) state, which explains the swiftness of the emergence of the perceptual experience in response to learned stimuli.
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Affiliation(s)
- Robert Kozma
- College of Information and Computer Sciences, University of MassachusettsAmherst, MA, USA; Department of Mathematical Sciences, University of MemphisMemphis, TN, USA
| | - Walter J Freeman
- Department of Molecular and Cell Biology, University of California at Berkeley Berkeley, CA, USA
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Heck DH, McAfee SS, Liu Y, Babajani-Feremi A, Rezaie R, Freeman WJ, Wheless JW, Papanicolaou AC, Ruszinkó M, Sokolov Y, Kozma R. Breathing as a Fundamental Rhythm of Brain Function. Front Neural Circuits 2017; 10:115. [PMID: 28127277 PMCID: PMC5226946 DOI: 10.3389/fncir.2016.00115] [Citation(s) in RCA: 99] [Impact Index Per Article: 14.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2016] [Accepted: 12/26/2016] [Indexed: 11/17/2022] Open
Abstract
Ongoing fluctuations of neuronal activity have long been considered intrinsic noise that introduces unavoidable and unwanted variability into neuronal processing, which the brain eliminates by averaging across population activity (Georgopoulos et al., 1986; Lee et al., 1988; Shadlen and Newsome, 1994; Maynard et al., 1999). It is now understood, that the seemingly random fluctuations of cortical activity form highly structured patterns, including oscillations at various frequencies, that modulate evoked neuronal responses (Arieli et al., 1996; Poulet and Petersen, 2008; He, 2013) and affect sensory perception (Linkenkaer-Hansen et al., 2004; Boly et al., 2007; Sadaghiani et al., 2009; Vinnik et al., 2012; Palva et al., 2013). Ongoing cortical activity is driven by proprioceptive and interoceptive inputs. In addition, it is partially intrinsically generated in which case it may be related to mental processes (Fox and Raichle, 2007; Deco et al., 2011). Here we argue that respiration, via multiple sensory pathways, contributes a rhythmic component to the ongoing cortical activity. We suggest that this rhythmic activity modulates the temporal organization of cortical neurodynamics, thereby linking higher cortical functions to the process of breathing.
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Affiliation(s)
- Detlef H Heck
- Department of Anatomy and Neurobiology, University of Tennessee Health Science Center Memphis, TN, USA
| | - Samuel S McAfee
- Department of Anatomy and Neurobiology, University of Tennessee Health Science Center Memphis, TN, USA
| | - Yu Liu
- Department of Anatomy and Neurobiology, University of Tennessee Health Science Center Memphis, TN, USA
| | - Abbas Babajani-Feremi
- Department of Anatomy and Neurobiology, University of Tennessee Health Science CenterMemphis, TN, USA; Department of Pediatrics, Division of Pediatric Neurology, University of Tennessee Health Science Center and Le Bonheur Children's Hospital Neuroscience InstituteMemphis, TN, USA
| | - Roozbeh Rezaie
- Department of Pediatrics, Division of Pediatric Neurology, University of Tennessee Health Science Center and Le Bonheur Children's Hospital Neuroscience Institute Memphis, TN, USA
| | - Walter J Freeman
- Department of Molecular and Cell Biology, Division of Neurobiology, University of California at Berkeley Berkeley, CA, USA
| | - James W Wheless
- Department of Pediatrics, Division of Pediatric Neurology, University of Tennessee Health Science Center and Le Bonheur Children's Hospital Neuroscience Institute Memphis, TN, USA
| | - Andrew C Papanicolaou
- Department of Anatomy and Neurobiology, University of Tennessee Health Science CenterMemphis, TN, USA; Department of Pediatrics, Division of Pediatric Neurology, University of Tennessee Health Science Center and Le Bonheur Children's Hospital Neuroscience InstituteMemphis, TN, USA
| | - Miklós Ruszinkó
- Rényi Institute of Mathematics, Hungarian Academy of Sciences Budapest, Hungary
| | - Yury Sokolov
- Department of Mathematical Sciences, University of Memphis Memphis, TN, USA
| | - Robert Kozma
- Department of Mathematical Sciences, University of MemphisMemphis, TN, USA; Department Computer Sciences, University of Massachusetts AmherstAmherst, MA, USA
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Kozma R. Reflections on a giant of brain science: How lucky we are having Walter J. Freeman as our beacon in cognitive neurodynamics research. Cogn Neurodyn 2016; 10:457-469. [PMID: 27891195 PMCID: PMC5106457 DOI: 10.1007/s11571-016-9403-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2016] [Revised: 08/19/2016] [Accepted: 08/19/2016] [Indexed: 10/21/2022] Open
Abstract
Walter J. Freeman was a giant of the field of neuroscience whose visionary work contributed various experimental and theoretical breakthroughs to brain research in the past 60 years. He has pioneered a number of Electroencephalogram and Electrocorticogram tools and approaches that shaped the field, while "Freeman Neurodynamics" is a theoretical concept that is widely known, used, and respected among neuroscientists all over the world. His recent death is a profound loss to neuroscience and biomedical engineering. Many of his revolutionary ideas on brain dynamics have been ahead of their time by decades. We summarize his following groundbreaking achievements: (1) Mass Action in the Nervous System, from microscopic (single cell) recordings, through mesoscopic populations, to large-scale collective brain patterns underlying cognition; (2) Freeman-Kachalsky model of multi-scale, modular brain dynamics; (3) cinematic theory of cognitive dynamics; (4) phase transitions in cortical dynamics modeled with random graphs and quantum field theory; (5) philosophical aspects of intentionality, consciousness, and the unity of brain-mind-body. His work has been admired by many of his neuroscientist colleagues and followers. At the same time, his multidisciplinary approach combining advanced concepts of control theory and the mathematics of nonlinear systems and chaos, poses significant challenges to those who wish to thoroughly understand his message. The goal of this commemorative paper is to review key aspects of Freeman's neurodynamics and to provide some handles to gain better understanding about Freeman's extraordinary intellectual achievement.
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Affiliation(s)
- Robert Kozma
- Department of Mathematics, University of Memphis, Memphis, TN 38152 USA
- Department of Computer Science, University of Massachusetts, Amherst, MA 01003 USA
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Abstract
We consider a network of coupled excitatory and inhibitory theta neurons which is capable of supporting stable spatially-localized “bump” solutions. We randomly add long-range and simultaneously remove short-range connections within the network to form a small-world network and investigate the effects of this rewiring on the existence and stability of the bump solution. We consider two limits in which continuum equations can be derived; bump solutions are fixed points of these equations. We can thus use standard numerical bifurcation analysis to determine the stability of these bumps and to follow them as parameters (such as rewiring probabilities) are varied. We find that under some rewiring schemes bumps are quite robust, whereas in other schemes they can become unstable via Hopf bifurcation or even be destroyed in saddle-node bifurcations.
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Affiliation(s)
- Carlo R Laing
- Institute of Natural and Mathematical Sciences, Massey University Auckland, New Zealand
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Kozma R, Puljic M. Random graph theory and neuropercolation for modeling brain oscillations at criticality. Curr Opin Neurobiol 2014; 31:181-8. [PMID: 25460075 DOI: 10.1016/j.conb.2014.11.005] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2014] [Revised: 11/13/2014] [Accepted: 11/17/2014] [Indexed: 01/24/2023]
Abstract
Mathematical approaches are reviewed to interpret intermittent singular space-time dynamics observed in brain imaging experiments. The following aspects of brain dynamics are considered: nonlinear dynamics (chaos), phase transitions, and criticality. Probabilistic cellular automata and random graph models are described, which develop equations for the probability distributions of macroscopic state variables as an alternative to differential equations. The introduced modular neuropercolation model is motivated by the multilayer structure and dynamical properties of the cortex, and it describes critical brain oscillations, including background activity, narrow-band oscillations in excitatory-inhibitory populations, and broadband oscillations in the cortex. Input-induced and spontaneous transitions between states with large-scale synchrony and without synchrony exhibit brief episodes with long-range spatial correlations as observed in experiments.
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Affiliation(s)
- Robert Kozma
- Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA.
| | - Marko Puljic
- Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA
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Kozma R, Puljic M. Hierarchical random cellular neural networks for system-level brain-like signal processing. Neural Netw 2013; 45:101-10. [PMID: 23548329 DOI: 10.1016/j.neunet.2013.02.010] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2012] [Revised: 01/08/2013] [Accepted: 02/23/2013] [Indexed: 11/28/2022]
Abstract
Sensory information processing and cognition in brains are modeled using dynamic systems theory. The brain's dynamic state is described by a trajectory evolving in a high-dimensional state space. We introduce a hierarchy of random cellular automata as the mathematical tools to describe the spatio-temporal dynamics of the cortex. The corresponding brain model is called neuropercolation which has distinct advantages compared to traditional models using differential equations, especially in describing spatio-temporal discontinuities in the form of phase transitions. Phase transitions demarcate singularities in brain operations at critical conditions, which are viewed as hallmarks of higher cognition and awareness experience. The introduced Monte-Carlo simulations obtained by parallel computing point to the importance of computer implementations using very large-scale integration (VLSI) and analog platforms.
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Affiliation(s)
- Robert Kozma
- Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA.
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Mathematical theories of physical intelligence. Phys Life Rev 2013; 10:110-1; discussion 112-6. [DOI: 10.1016/j.plrev.2013.03.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Goodfellow M, Taylor PN, Wang Y, Garry DJ, Baier G. Modelling the role of tissue heterogeneity in epileptic rhythms. Eur J Neurosci 2012; 36:2178-87. [DOI: 10.1111/j.1460-9568.2012.08093.x] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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The KIV model of intentional dynamics and decision making. Neural Netw 2009; 22:277-85. [DOI: 10.1016/j.neunet.2009.03.019] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2009] [Revised: 03/16/2009] [Accepted: 03/19/2009] [Indexed: 11/18/2022]
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