Escalas do tempo

Viral epidemics are processes in which temporality obviously constitutes an essential variable. But different time scales must be distinguished. To see the current pandemic as a singular event is but an illusion due to the “mesoscopic” timescale we are embracing. There is a microscopic scale — that of physiological processes —, a mesoscopic scale, which only allows to see the closest evidence, and a macroscopic scale, that of the ecological determinisms which explain the emergence of the disease in the history of the relationships between species. The article focuses on the mesoscopic level and highlights some semiotic specificities of today’s experience : a temporal suspension, the threat of pure, dramatic and final discontinuity, the behavior of a virus that appears to have “intentionality”, a strong intensity coupled with a long duration, a time of exception, drawn to a final end, and a victory which will only be achieved with great effort.

Stability and dynamics of a spectral graph model of brain oscillations

We explore the stability and dynamic properties of a hierarchical, linearized, and analytic spectral graph model for neural oscillations that integrates the structuring wiring of the brain. Previously we have shown that this model can accurately capture the frequency spectra and the spatial patterns of the alpha and beta frequency bands obtained from magnetoencephalography recordings without regionally varying parameters. Here, we show that this macroscopic model based on long-range excitatory connections exhibits dynamic oscillations with a frequency in the alpha band even without any oscillations implemented at the mesoscopic level. We show that depending on the parameters, the model can exhibit combinations of damped oscillations, limit cycles, or unstable oscillations. We determined bounds on model parameters that ensure stability of the oscillations simulated by the model. Finally, we estimated time-varying model parameters to capture the temporal fluctuations in magnetoencephalography activity. We show that a dynamic spectral graph modeling framework with a parsimonious set of biophysically interpretable model parameters can thereby be employed to capture oscillatory fluctuations observed in electrophysiological data in various brain states and diseases.

Geometrical model of lobular structure and its importance for the liver perfusion analysis

A convenient geometrical description of the microvascular network is necessary for computationally efficient mathematical modelling of liver perfusion, metabolic and other physiological processes. The tissue models currently used are based on the generally accepted schematic structure of the parenchyma at the lobular level, assuming its perfect regular structure and geometrical symmetries. Hepatic lobule, portal lobule, or liver acinus are considered usually as autonomous functional units on which particular physiological problems are studied. We propose a new periodic unit—the liver representative periodic cell (LRPC) and establish its geometrical parametrization. The LRPC is constituted by two portal lobulae, such that it contains the liver acinus as a substructure. As a remarkable advantage over the classical phenomenological modelling approaches, the LRPC enables for multiscale modelling based on the periodic homogenization method. Derived macroscopic equations involve so called effective medium parameters, such as the tissue permeability, which reflect the LRPC geometry. In this way, mutual influences between the macroscopic phenomena, such as inhomogeneous perfusion, and the local processes relevant to the lobular (mesoscopic) level are respected. The LRPC based model is intended for its use within a complete hierarchical model of the whole liver. Using the Double-permeability Darcy model obtained by the homogenization, we illustrate the usefulness of the LRPC based modelling to describe the blood perfusion in the parenchyma.

Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting

Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller–Segel equation and a chemotaxis kinetic equation. These two equations describe the organism’s movement at the macro- and mesoscopic level, respectively, and are asymptotically equivalent in the parabolic regime. The way in which the organism responds to a chemical stimulus is embedded in the diffusion/advection coefficients of the Keller–Segel equation or the turning kernel of the chemotaxis kinetic equation. Experiments are conducted to measure the time dynamics of the organisms’ population level movement when reacting to certain stimulation. From this, one infers the chemotaxis response, which constitutes an inverse problem. In this paper, we discuss the relation between both the macro- and mesoscopic inverse problems, each of which is associated with two different forward models. The discussion is presented in the Bayesian framework, where the posterior distribution of the turning kernel of the organism population is sought. We prove the asymptotic equivalence of the two posterior distributions.

Modeling and Simulation of Non-Uniform Electrolytic Machining Based on Cellular Automata

Porous microstructure is a common surface morphology that is widely used in antifouling, drag reduction, adsorption, and other applications. In this paper, the lattice gas automata (LGA) method was used to simulate the non-uniform electrochemical machining of porous structure at the mesoscopic level. In a cellular space, the metal and the electrolyte were separated into orderly grids, the migration of corrosive particles was determined by an electric field, and the influences of the concentration gradient and corrosion products were considered. It was found that different pore morphologies were formed due to the competition between dissolution and diffusion. When the voltage was low, diffusion was sufficient, and no deposit was formed at the bottom of the pore. The pore grew faster along the depth and attained a cylindrical shape with a large depth-to-diameter ratio. As the voltage increased, the dissolution rates in all directions were the same; therefore, the pore became approximately spherical. When the voltage continued to increase, corrosion products were not discharged in time due to the rapid dissolution rate. Consequently, a sedimentary layer was formed at the bottom of the pore and hindered further dissolution. In turn, a disc-shaped pore with secondary pores was formed. The obtained simulation results were verified by experimental findings. This study revealed the causes of different morphologies of pores, which has certain guiding significance for non-uniform electrochemical machining.

Canard solutions in neural mass models: consequences on critical regimes

Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neuronal subpopulations without explicitly representing the underlying cellular activity. The mesoscopic level offered by the neural mass formulation has been used to model electroencephalographic (EEG) recordings and to investigate various cerebral mechanisms, such as the generation of physiological and pathological brain activities. In this work, we consider a NMM widely accepted in the context of epilepsy, which includes four interacting neuronal subpopulations with different synaptic kinetics. Due to the resulting three-time-scale structure, the model yields complex oscillations of relaxation and bursting types. By applying the principles of geometric singular perturbation theory, we unveil the existence of the canard solutions and detail how they organize the complex oscillations and excitability properties of the model. In particular, we show that boundaries between pathological epileptic discharges and physiological background activity are determined by the canard solutions. Finally we report the existence of canard-mediated small-amplitude frequency-specific oscillations in simulated local field potentials for decreased inhibition conditions. Interestingly, such oscillations are actually observed in intracerebral EEG signals recorded in epileptic patients during pre-ictal periods, close to seizure onsets.

Multi-Scopic Neuro-Cognitive Adaptation for Legged Locomotion Robots

Dynamic locomotion is realized through a simultaneous integration of adaptability and optimality. This article proposes a neuro-cognitive model for multi-legged locomotion robot that can seamlessly integrate multi-modal sensing, ecological perception, and cognition through the coordination of interoceptive and exteroceptive sensory information. Importantly, cognitive models can be discussed as micro-, meso-, and macro-scopic; these concepts correspond to sensing, perception, and cognition; and short-, medium-, and long-term adaptation (in terms of ecological psychology). The proposed neuro-cognitive model integrates these intelligent functions from a multi-scopic point of view. Macroscopic-level presents an attention mechanism with short-term adaptive locomotion control conducted by lower-level sensorimotor coordination-based model. Macrosopic-level serves environmental cognitive map featuring higher-level behavior planning. Mesoscopic level shows integration between the microscopic and macroscopic approaches, enabling the model to reconstruct a map and conduct localization using bottom-up facial environmental information and top-down map information, generating intention towards the ultimate goal at the macroscopic level. The experiments demonstrated that adaptability and optimality of multi-legged locomotion could be achieved using the proposed multi-scale neuro-cognitive model, from short to long-term adaptation, with efficient computational usage. Future research directions can be implemented not only in robotics contexts but also in the context of interdisciplinary studies incorporating cognitive science and ecological psychology.

Direction-dependent turning leads to anisotropic diffusion and persistence

Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet their formulations usually assume a constant turning rate. Here we relax this simplification, extending to include a turning rate that varies according to the anisotropy of a heterogeneous environment. We extend known methods of parabolic and hyperbolic scaling and apply the results to cell movement on micropatterned domains. We show that inclusion of orientation dependence in the turning rate can lead to persistence of motion in an otherwise fully symmetric environment and generate enhanced diffusion in structured domains.

A coarse-grained approach to model the dynamics of the actomyosin cortex

The dynamics of the actomyosin machinery is at the core of many important biological processes. Several relevant cellular responses such as the rhythmic compression of the cell cortex are governed, at a mesoscopic level, by the nonlinear interaction between actin monomers, actin crosslinkers and myosin motors. Coarse grained models are an optimal tool to study actomyosin systems, since they can include processes that occur at long time and space scales, while maintaining the most relevant features of the molecular interactions. Here, we present a coarse grained model of a two-dimensional actomyosin cortex, adjacent to a three-dimensional cytoplasm. Our simplified model incorporates only well characterized interactions between actin monomers, actin cross- linkers and myosin, and it is able to reproduce many of the most important aspects of actin filament and actomyosin network formation, such as dynamics of polymerization and depolymerization, treadmilling, network formation and the autonomous oscilla- tory dynamics of actomyosin. Furthermore, the model can be used to predict the in vivo response of actomyosin networks to changes in key parameters of the system, such as alterations in the anchor of actin filaments to the cell cortex.

Network Structured Kinetic Models of Social Interactions

The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of interactions, which we treat by an appropriate mesoscopic description, and a different role of interacting agents. The latter differs from interactions treated in classical statistical mechanics in the sense that the agents do not have symmetric roles, but there is rather an active and a passive agent. We will demonstrate how a certain form of kinetic equations can be obtained to describe such interactions at a mesoscopic level and moreover obtain macroscopic models from monokinetics solutions of those. The derivation naturally leads to systems of nonlocal reaction-diffusion equations (or in a suitable limit local versions thereof), which can explain spatial phase separation phenomena found to emerge from the microscopic interactions. We will highlight the approach in three examples, namely the evolution and coarsening of dialects in human language, the construction of social norms, and the spread of an epidemic.