The effects of noise on binocular rivalry waves: a stochastic neural field model

We analyse the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how multiplicative noise in the activity variables leads to a diffusive–like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. The multiplicative noise also renormalizes the mean speed of the wave. We use our analysis to calculate the first passage time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation leads to quenched disorder in the neural fields during propagation of a wave

A Heuristic Computational Model of Basic Cellular Processes and Oxygenation during Spheroid-Dependent Biofabrication

An emerging approach in biofabrication is the creation of 3D tissue constructs through scaffold-free, cell spheroid-only methods. The basic mechanism in this technology is spheroid fusion, which is driven by the minimization of energy, the same biophysical mechanism that governs spheroid formation. However, other factors such as oxygen and metabolite accessibility within spheroids impact on spheroid properties and their ability to form larger-scale structures. The goal of our work is to develop a simulation platform eventually capable of predicting the conditions that minimize metabolism-related cell loss within spheroids. To describe the behavior and dynamic properties of the cells in response to their neighbors and to transient nutrient concentration fields, we developed a hybrid discrete-continuous heuristic model, combining a cellular Potts-type approach with field equations applied to a randomly populated spheroid cross-section of prescribed cell-type constituency. This model allows for the description of: (i) cellular adhesiveness and motility; (ii) interactions with concentration fields, including diffusivity and oxygen consumption; and (iii) concentration-dependent, stochastic cell dynamics, driven by metabolite-dependent cell death. Our model readily captured the basic steps of spheroid-based biofabrication (as specifically dedicated to scaffold-free bioprinting), including intra-spheroid cell sorting (both in 2D and 3D implementations), spheroid defect closure, and inter-spheroid fusion. Moreover, we found that when hypoxia occurring at the core of the spheroid was set to trigger cell death, this was amplified upon spheroid fusion, but could be mitigated by external oxygen supplementation. In conclusion, optimization and further development of scaffold-free bioprinting techniques could benefit from our computational model which is able to simultaneously account for both cellular dynamics and metabolism in constructs obtained by scaffold-free biofabrication

Ciliary flocking and emergent instabilities enable collective agility in a non-neuromuscular animal

Effective organismal behavior responds appropriately to changes in the surrounding environment. Attaining this delicate balance of sensitivity and stability is a hallmark of the animal kingdom. By studying the locomotory behavior of a simple animal (\textit{Trichoplax adhaerens}) without muscles or neurons, here, we demonstrate how monociliated epithelial cells work collectively to give rise to an agile non-neuromuscular organism. Via direct visualization of large ciliary arrays, we report the discovery of sub-second ciliary reorientations under a rotational torque that is mediated by collective tissue mechanics and the adhesion of cilia to the underlying substrate. In a toy model, we show a mapping of this system onto an "active-elastic resonator". This framework explains how perturbations propagate information in this array as linear speed traveling waves in response to mechanical stimulus. Next, we explore the implications of parametric driving in this active-elastic resonator and show that such driving can excite mechanical 'spikes'. These spikes in collective mode amplitudes are consistent with a system driven by parametric amplification and a saturating nonlinearity. We conduct extensive numerical experiments to corroborate these findings within a polarized active-elastic sheet. These results indicate that periodic and stochastic forcing are valuable for increasing the sensitivity of collective ciliary flocking. We support these theoretical predictions via direct experimental observation of linear speed traveling waves which arise from the hybridization of spin and overdamped density waves. We map how these ciliary flocking dynamics result in agile motility via coupling between an amplified resonator and a tuning (Goldstone-like) mode of the system. This sets the stage for how activity and elasticity can self-organize into behavior which benefits the organism as a whole

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Quantitative MRI and machine learning for the diagnosis and prognosis of Multiple Sclerosis

Multiple sclerosis (MS) is an immune-mediated, inflammatory, neurological disease affecting myelin in the central nervous system, whose driving mechanisms are not yet fully understood. Conventional magnetic resonance imaging (MRI) is largely used in the MS diagnostic process, but because of its lack of specificity, it cannot reliably detect microscopic damage. Quantitative MRI provides instead feature maps that can be exploited to improve prognosis and treatment monitoring, at the cost of prolonged acquisition times and specialised MR-protocols. In this study, two converging approaches were followed to investigate how to best use the available MRI data for the diagnosis and prognosis of MS. On one hand, qualitative data commonly used in clinical research for lesion and anatomical purposes were shown to carry quantitative information that could be used to conduct myelin and relaxometry analyses on cohorts devoid of dedicated quantitative acquisitions. In this study arm, named bottom-up, qualitative information was up-converted to quantitative surrogate: traditional model-fitting and deep-learning frameworks were proposed and tested on MS patients to extract relaxometry and indirect-myelin quantitative data from qualitative scans. On the other hand, when using multi-modal MRI data to classify MS patients with different clinical status, different MR-features contribute to specific classification tasks. The top-down study arm consisted in using machine learning to reduce the multi-modal dataset dimensionality only to those MR-features that are more likely to be biophysically meaningful with respect to each MS phenotype pathophysiology. Results show that there is much more potential to qualitative data than lesion and tissue segmentation, and that specific MRI modalities might be better suited for investigating individual MS phenotypes. Efficient multi-modal acquisitions informed by biophysical findings, whilst being able to extract quantitative information from qualitative data, would provide huge statistical power through the use of large, historical datasets, as well as constitute a significant step forward in the direction of sustainable research

Lattice Element Method and its application to Multiphysics

In this thesis, a Lattice element modelling method is developed and is applied to model the loose and cemented, natural and artificial, granular matters subject to thermo-hydro-mechanical coupled loading conditions. In lattice element method, the lattice nodes which can be considered as the centres of the unit cells, are connected by cohesive links, such as spring beams that can carry normal and shear forces, bending and torsion moment. For the heat transfer due to conduction, the cohesive links are also used to carry heat as 1D pipes, and the physical properties of these rods are computed based on the Hertz contact model. The hydro part is included with the pore network modelling scheme. The voids are inscribed with the pore nodes and connected with throats, and then the meso level flow equation is solved. The Euler-Bernoulli and Timoshenko beams are chosen as the cohesive links or the lattice elements, while the latter should be used when beam elements are short and deep. This property becomes interesting in modelling auxetic materials. The model is applied to study benchmarks in geotechnical engineering. For heat transfer in the dry and full range of saturation, and fractures in the cemented granular media.How through porous media failure behaviours of rocks at high temperature and pressure and granular composites subjected to coupled Thermo hydro Mechanical loads. The model is further extended to capture the wave motion in the heterogeneous granular matter, and a few case studies for the wavefield modification with existing cracks are presented. The developed method is capable of capturing the complex interaction of crack wave interaction with relative ease and at a substantially less computational cost