scholarly journals Dynamical informational structures characterize the different human brain states of wakefulness and deep sleep

2019 ◽  
Author(s):  
J. A. Galadí ◽  
S. Silva Pereira ◽  
Y. S. Perl ◽  
M.L. Kringelbach ◽  
I. Gayte ◽  
...  
Keyword(s):  
Dynamical System ◽  
Human Brain ◽  
Directed Graphs ◽  
Global Attractors ◽  
Mathematical Formalism ◽  
Invariant Sets ◽  
Time Variability ◽  
Brain State ◽  
Deep Sleep ◽  
Brain States

ABSTRACTThe dynamical activity of the human brain describes an extremely complex energy landscape changing over time and its characterisation is central unsolved problem in neuroscience. We propose a novel mathematical formalism for characterizing how the landscape of attractors sustained by a dynamical system evolves in time. This mathematical formalism is used to distinguish quantitatively and rigorously between the different human brain states of wakefulness and deep sleep. In particular, by using a whole-brain dynamical ansatz integrating the underlying anatomical structure with the local node dynamics based on a Lotka-Volterra description, we compute analytically the global attractors of this cooperative system and their associated directed graphs, here called the informational structures. The informational structure of the global attractor of a dynamical system describes precisely the past and future behaviour in terms of a directed graph composed of invariant sets (nodes) and their corresponding connections (links). We characterize a brain state by the time variability of these informational structures. This theoretical framework is potentially highly relevant for developing reliable biomarkers of patients with e.g. neuropsychiatric disorders or different levels of coma.

scholarly journals Non-autonomous invariant sets and attractors: Random dynamical system

2020 ◽  
Vol 25 (4) ◽  
pp. 17-23
Author(s):  
Mohamedsh Imran ◽  
Ihsan Jabbar Kadhim
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Global Attractors ◽  
Random Dynamical Systems ◽  
Invariant Sets ◽  
Random Dynamical System ◽  
Pullback Attractor ◽  
Pullback Attractors ◽  
Deterministic Dynamical System

 In this paper the concepts of pullback attractor ,pullback absorbing family in (deterministic) dynamical system are defined in (random) dynamical systems. Also some main result such as (existence) of pullback attractors ,upper semi-continuous of pullback attractors and uniform and global attractors are proved in random dynamical system .

scholarly journals The expression of established cognitive brain states stabilizes with working memory development

eLife ◽  
2017 ◽  
Vol 6 ◽  
Author(s):  
David Florentino Montez ◽  
Finnegan J Calabro ◽  
Beatriz Luna
Keyword(s):  
Working Memory ◽  
Reaction Time ◽  
Developmental Trajectories ◽  
Time Variability ◽  
Brain State ◽  
Reaction Time Variability ◽  
Memory Processing ◽  
Saccade Task ◽  
Brain States ◽  
Sensorimotor Processes

We present results from a longitudinal study conducted over 10 years in a sample of 126 8–33 year olds demonstrating that adolescent development of working memory is supported by decreased variability in the amplitude of expression of whole brain states of task-related activity. fMRI analyses reveal that putative gain signals affecting maintenance and retrieval aspects of working memory processing stabilize during adolescence, while those affecting sensorimotor processes do not. We show that trial-to-trial variability in the reaction time and accuracy of eye-movements during a memory guided saccade task are related to fluctuations in the amplitude of expression of task-related brain states, or brain state variability, and also provide evidence that individual developmental trajectories of reaction time variability are related to individual trajectories of brain state variability. These observations demonstrate that the stabilization of widespread gain signals affecting already available cognitive processes underlies the maturation of cognition during adolescence.

scholarly journals Personalized Immunotherapy Treatment Strategies for a Dynamical System of Chronic Myelogenous Leukemia

Cancers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 2030
Author(s):  
Paul A. Valle ◽  
Luis N. Coria ◽  
Corina Plata
Keyword(s):  
Dynamical System ◽  
Cancer Cells ◽  
Chronic Myelogenous Leukemia ◽  
Sufficient Conditions ◽  
Treatment Strategies ◽  
Myelogenous Leukemia ◽  
Invariant Sets ◽  
Cellular Immunotherapy ◽  
Complete Eradication ◽  
Treatment Parameter

This paper is devoted to exploring personalized applications of cellular immunotherapy as a control strategy for the treatment of chronic myelogenous leukemia described by a dynamical system of three first-order ordinary differential equations. The latter was achieved by applying both the Localization of Compact Invariant Sets and Lyapunov’s stability theory. Combination of these two approaches allows us to establish sufficient conditions on the immunotherapy treatment parameter to ensure the complete eradication of the leukemia cancer cells. These conditions are given in terms of the system parameters and by performing several in silico experimentations, we formulated a protocol for the therapy application that completely eradicates the leukemia cancer cells population for different initial tumour concentrations. The formulated protocol does not dangerously increase the effector T cells population. Further, complete eradication is considered when solutions go below a finite critical value below which cancer cells cannot longer persist; i.e., one cancer cell. Numerical simulations are consistent with our analytical results.

scholarly journals Capturing the non-stationarity of whole-brain dynamics underlying human brain states

NeuroImage ◽  
2021 ◽  
pp. 118551
Author(s):  
J.A. Galadí ◽  
S. Silva Pereira ◽  
Y. Sanz Perl ◽  
M.L. Kringelbach ◽  
I. Gayte ◽  
...  
Keyword(s):  
Human Brain ◽  
Brain Dynamics ◽  
Whole Brain ◽  
Brain States

scholarly journals Theta activity paradoxically boosts gamma and ripple frequency sensitivity in prefrontal interneurons

2021 ◽  
Vol 118 (51) ◽  
pp. e2114549118
Author(s):  
Ricardo Martins Merino ◽  
Carolina Leon-Pinzon ◽  
Walter Stühmer ◽  
Martin Möck ◽  
Jochen F. Staiger ◽  
...  
Keyword(s):  
Low Frequency ◽  
Gamma Oscillations ◽  
Brain State ◽  
Gabaergic Interneurons ◽  
Time Resolved ◽  
Cortical Rhythms ◽  
Brain States ◽  
Fast Spiking ◽  
Fast Oscillations ◽  
Cross Frequency Coupling

Fast oscillations in cortical circuits critically depend on GABAergic interneurons. Which interneuron types and populations can drive different cortical rhythms, however, remains unresolved and may depend on brain state. Here, we measured the sensitivity of different GABAergic interneurons in prefrontal cortex under conditions mimicking distinct brain states. While fast-spiking neurons always exhibited a wide bandwidth of around 400 Hz, the response properties of spike-frequency adapting interneurons switched with the background input’s statistics. Slowly fluctuating background activity, as typical for sleep or quiet wakefulness, dramatically boosted the neurons’ sensitivity to gamma and ripple frequencies. We developed a time-resolved dynamic gain analysis and revealed rapid sensitivity modulations that enable neurons to periodically boost gamma oscillations and ripples during specific phases of ongoing low-frequency oscillations. This mechanism predicts these prefrontal interneurons to be exquisitely sensitive to high-frequency ripples, especially during brain states characterized by slow rhythms, and to contribute substantially to theta-gamma cross-frequency coupling.

scholarly journals Segregated brain state during hypnosis

2019 ◽  
Author(s):  
Jarno Tuominen ◽  
Sakari Kallio ◽  
Valtteri Kaasinen ◽  
Henry Railo
Keyword(s):  
Transcranial Magnetic Stimulation ◽  
Magnetic Stimulation ◽  
Brain Activation ◽  
Brain State ◽  
Neural Connectivity ◽  
Single Word ◽  
Electrophysiological Response ◽  
Hypnotic Induction ◽  
Brain States ◽  
The Brain

Can the brain be shifted into a different state using a simple social cue, as tests on highly hypnotisable subjects would suggest? Demonstrating an altered brain state is difficult. Brain activation varies greatly during wakefulness and can be voluntarily influenced. We measured the complexity of electrophysiological response to transcranial magnetic stimulation (TMS) in one “hypnotic virtuoso”. Such a measure produces a response outside the subject’s voluntary control and has been proven adequate for discriminating conscious from unconscious brain states. We show that a single-word hypnotic induction robustly shifted global neural connectivity into a state where activity remained sustained but failed to ignite strong, coherent activity in frontoparietal cortices. Changes in perturbational complexity indicate a similar move toward a more segregated state. We interpret these findings to suggest a shift in the underlying state of the brain, likely moderating subsequent hypnotic responding. [preprint updated 20/02/2020]

Changes During Weeks in Effects of Tricyclic Drugs on the Human Sleeping Brain

1972 ◽  
Vol 120 (559) ◽  
pp. 663-672 ◽  
Author(s):  
D. L. F. Dunleavy ◽  
Vlasta Brezinova ◽  
Ian Oswald ◽  
A. W. Maclean ◽  
M. Tinker
Keyword(s):  
Human Brain ◽  
Time Scale ◽  
Mode Of Action ◽  
Tricyclic Antidepressants ◽  
Brain State ◽  
Clinical Use ◽  
Brain Physiology ◽  
Brain Functions ◽  
Drug Actions ◽  
Brain Changes

The tricyclic antidepressants are established in therapy but not in mode of action. Effects on mouse or rat brain of single and relatively enormous doses provide the basis for theories. Yet it may be inferred that the clinical use of tricyclic antidepressants relies upon an induction of brain changes on a time-scale of weeks. Studies of tricyclic drug actions upon human brain physiology are as scanty as are easily-measurable human brain functions. Electrophysiological techniques, however, can conveniently be applied during one principal brain-state, namely sleep, when there is a relative freedom from uncontrollable extraneous variables.

Exponential global attractors for semigroups in metric spaces with applications to differential equations

2011 ◽  
Vol 31 (6) ◽  
pp. 1641-1667 ◽  
Author(s):  
ALEXANDRE N. CARVALHO ◽  
JAN W. CHOLEWA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Attractor ◽  
Metric Space ◽  
Metric Spaces ◽  
Global Attractors ◽  
Invariant Sets ◽  
Bounded Subset ◽  
Partial Differential ◽  
Unstable Manifolds

AbstractIn this article semigroups in a general metric space V, which have pointwise exponentially attracting local unstable manifolds of compact invariant sets, are considered. We show that under a suitable set of assumptions these semigroups possess strong exponential dissipative properties. In particular, there exists a compact global attractor which exponentially attracts each bounded subset of V. Applications of abstract results to ordinary and partial differential equations are given.

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