Narrow-band oscillations in probabilistic cellular automata

Probabilistic cellular automata modelling of intercellular interactions in airways: complex pattern formation in patients with chronic obstructive pulmonary disease

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.

Cinematic Operation of the Cerebral Cortex Interpreted via Critical Transitions in Self-Organized Dynamic Systems

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.

Breathing as a Fundamental Rhythm of Brain Function

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.

Reflections on a giant of brain science: How lucky we are having Walter J. Freeman as our beacon in cognitive neurodynamics research

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.

Bumps in Small-World Networks

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.

Random graph theory and neuropercolation for modeling brain oscillations at criticality

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.

Hierarchical random cellular neural networks for system-level brain-like signal processing

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.