Antonio J. Pons

Helical crack-front instability in mixed-mode fracture

Planar crack propagation under pure tension loading (mode I) is generally stable. However, it becomes universally unstable with the superposition of a shear stress parallel to the crack front (mode III). Under this mixed-mode (I + III) loading configuration, an initially flat parent crack segments into an array of daughter cracks that rotate towards a direction of maximum tensile stress. This segmentation produces stepped fracture surfaces with characteristic ‘lance-shaped’ markings observed in a wide range of engineering and geological materials. The origin of this instability remains poorly understood and a theory with which to predict the surface roughness scale is lacking. Here we perform large-scale simulations of mixed-mode I + III brittle fracture using a continuum phase-field method that describes the complete three-dimensional crack-front evolution. The simulations reveal that planar crack propagation is linearly unstable against helical deformations of the crack front, which evolve nonlinearly into a segmented array of finger-shaped daughter cracks. Furthermore, during their evolution, facets gradually coarsen owing to the growth competition of daughter cracks in striking analogy with the coarsening of finger patterns observed in nonequilibrium growth phenomena. We show that the dynamically preferred unstable wavelength is governed by the balance of the destabilizing effect of far-field stresses and the stabilizing effect of cohesive forces on the process zone scale, and we derive a theoretical estimate for this scale using a new propagation law for curved cracks in three dimensions. The rotation angles of coarsened facets are also compared to theoretical predictions and available experimental data.

Relating structural and functional anomalous connectivity in the aging brain via neural mass modeling

The structural changes that arise as the brain ages influence its functionality. In many cases, the anatomical degradation simply leads to normal aging. In others, the neurodegeneration is large enough to cause neurological disorders (e.g. Alzheimers disease). Structure and function can be both currently measured using noninvasive techniques, such as magnetic resonance imaging (MRI) and electroencephalography (EEG) respectively. However, a full theoretical scheme linking structural and functional degradation is still lacking. Here we present a neural mass model that aims to bridge both levels of description and that reproduces experimentally observed multichannel EEG recordings of alpha rhythm in young subjects, healthy elderly subjects, and patients with mild cognitive impairment. We focus our attention in the dominant frequency of the signals at different electrodes and in the correlation between specific electrode pairs, measured via the phase-lag index. Our model allows us to study the influence of different structural connectivity pathways, independently of each other, on the normal and aberrantly aging brain. In particular, we study in detail the effect of the thalamic input on specific cortical regions, the long-range connectivity between cortical regions, and the short-range coupling within the same cortical area. Once the influence of each type of connectivity is determined, we characterize the regions of parameter space compatible with the EEG recordings of the populations under study. Our results show that the different types of connectivity must be fine-tuned to maintain the brain in a healthy functioning state independently of its age and brain condition.

Noise-induced up/down dynamics in scale-free neuronal networks

Cortical neuronal networks are known to exhibit regimes of dynamical activity characterized by periods of elevated firing (up states) separated by silent phases (down states). Here, we show that up/down dynamics may emerge spontaneously in scale-free neuronal networks, provided an optimal amount of noise acts upon all network nodes. Our conclusions are drawn from numerical simulations of networks of subthreshold integrate-and-fire neurons, connected to each other according to a scale-free topology. We study the structure of the up/down regime both in time and in terms of the node degree. We also examine whether localized random perturbations applied to specific network nodes are able to generate up/down dynamics, showing that this regime arises when noisy inputs are applied to low-degree (nonhub) network nodes, but not when they act upon network hubs.

Mesoscopic segregation of excitation and inhibition in a brain network model.

Neurons in the brain are known to operate under a careful balance of excitation and inhibition, which maintains neural microcircuits within the proper operational range. How this balance is played out at the mesoscopic level of neuronal populations is, however, less clear. In order to address this issue, here we use a coupled neural mass model to study computationally the dynamics of a network of cortical macrocolumns operating in a partially synchronized, irregular regime. The topology of the network is heterogeneous, with a few of the nodes acting as connector hubs while the rest are relatively poorly connected. Our results show that in this type of mesoscopic network excitation and inhibition spontaneously segregate, with some columns acting mainly in an excitatory manner while some others have predominantly an inhibitory effect on their neighbors. We characterize the conditions under which this segregation arises, and relate the character of the different columns with their topological role within the network. In particular, we show that the connector hubs are preferentially inhibitory, the more so the larger the nodes connectivity. These results suggest a potential mesoscale organization of the excitation-inhibition balance in brain networks.

Integration of cellular signals in chattering environments

Cells are constantly exposed to fluctuating environmental conditions. External signals are sensed, processed and integrated by cellular signal transduction networks, which translate input signals into specific cellular responses by means of biochemical reactions. These networks have a complex nature, and we are still far from having a complete characterization of the process through which they integrate information, specially given the noisy environment in which that information is embedded. Guided by the many instances of constructive influences of noise that have been reported in the physical sciences in the last decades, here we explore how multiple signals are integrated in an eukaryotic cell in the presence of background noise, or chatter. To that end, we use a Boolean model of a typical human signal transduction network. Despite its complexity, we find that the network is able to display simple patterns of signal integration. Furthermore, our computational analysis shows that these integration patterns depend on the levels of fluctuating background activity carried by other cell inputs. Taken together, our results indicate that signal integration is sensitive to environmental fluctuations, and that this background noise effectively determines the information integration capabilities of the cell.

Cross-frequency transfer in a stochastically driven mesoscopic neuronal model.

The brain is known to operate in multiple coexisting frequency bands. Increasing experimental evidence suggests that interactions between those distinct bands play a crucial role in brain processes, but the dynamical mechanisms underlying this cross-frequency coupling are still under investigation. Two approaches have been proposed to address this issue. In the first one distinct nonlinear oscillators representing the brain rhythms involved are coupled actively (bidirectionally), whereas in the second one the oscillators are coupled unidirectionally and thus the driving between them is passive. Here we elaborate the latter approach by implementing a stochastically driven network of coupled neural mass models that operate in the alpha range. This model exhibits a broadband power spectrum with 1/fb form, similar to those observed experimentally. Our results show that such a model is able to reproduce recent experimental observations on the effect of slow rocking on the alpha activity associated with sleep. This suggests that passive driving can account for cross-frequency transfer in the brain, as a result of the complex nonlinear dynamics of its underlying oscillators.

Probing scale interaction in brain dynamics through synchronization

The mammalian brain operates in multiple spatial scales simultaneously, ranging from the microscopic scale of single neurons through the mesoscopic scale of cortical columns, to the macroscopic scale of brain areas. These levels of description are associated with distinct temporal scales, ranging from milliseconds in the case of neurons to tens of seconds in the case of brain areas. Here, we examine theoretically how these spatial and temporal scales interact in the functioning brain, by considering the coupled behaviour of two mesoscopic neural masses (NMs) that communicate with each other through a microscopic neuronal network (NN). We use the synchronization between the two NM models as a tool to probe the interaction between the mesoscopic scales of those neural populations and the microscopic scale of the mediating NN. The two NM oscillators are taken to operate in a low-frequency regime with different peak frequencies (and distinct dynamical behaviour). The microscopic neuronal population, in turn, is described by a network of several thousand excitatory and inhibitory spiking neurons operating in a synchronous irregular regime, in which the individual neurons fire very sparsely but collectively give rise to a well-defined rhythm in the gamma range. Our results show that this NN, which operates at a fast temporal scale, is indeed sufficient to mediate coupling between the two mesoscopic oscillators, which evolve dynamically at a slower scale. We also establish how this synchronization depends on the topological properties of the microscopic NN, on its size and on its oscillation frequency.

Information routing driven by background chatter in a signaling network.

Living systems are capable of processing multiple sources of information simultaneously. This is true even at the cellular level, where not only coexisting signals stimulate the cell, but also the presence of fluctuating conditions is significant. When information is received by a cell signaling network via one specific input, the existence of other stimuli can provide a background activity –or chatter– that may affect signal transmission through the network and, therefore, the response of the cell. Here we study the modulation of information processing by chatter in the signaling network of a human cell, specifically, in a Boolean model of the signal transduction network of a fibroblast. We observe that the level of external chatter shapes the response of the system to information carrying signals in a nontrivial manner, modulates the activity levels of the network outputs, and effectively determines the paths of information flow. Our results show that the interactions and node dynamics, far from being random, confer versatility to the signaling network and allow transitions between different information-processing scenarios.

Temporally correlated fluctuations drive epileptiform dynamics

Abstract Macroscopic models of brain networks typically incorporate assumptions regarding the characteristics of afferent noise, which is used to represent input from distal brain regions or ongoing fluctuations in non‐modelled parts of the brain. Such inputs are often modelled by Gaussian white noise which has a flat power spectrum. In contrast, macroscopic fluctuations in the brain typically follow a Symbol spectrum. It is therefore important to understand the effect on brain dynamics of deviations from the assumption of white noise. In particular, we wish to understand the role that noise might play in eliciting aberrant rhythms in the epileptic brain. Symbol. No caption available. To address this question we study the response of a neural mass model to driving by stochastic, temporally correlated input. We characterise the model in terms of whether it generates “healthy” or “epileptiform” dynamics and observe which of these dynamics predominate under different choices of temporal correlation and amplitude of an Ornstein‐Uhlenbeck process. We find that certain temporal correlations are prone to eliciting epileptiform dynamics, and that these correlations produce noise with maximal power in the &dgr; and &THgr; bands. Crucially, these are rhythms that are found to be enhanced prior to seizures in humans and animal models of epilepsy. In order to understand why these rhythms can generate epileptiform dynamics, we analyse the response of the model to sinusoidal driving and explain how the bifurcation structure of the model gives rise to these findings. Our results provide insight into how ongoing fluctuations in brain dynamics can facilitate the onset and propagation of epileptiform rhythms in brain networks. Furthermore, we highlight the need to combine large‐scale models with noise of a variety of different types in order to understand brain (dys‐)function. HighlightsWe use Jansen‐Rit model under stochastic and periodic driving to study ictogenesis.Correlation time of the driving noise modulates characteristic of the models output.Driving with delta/theta rhythms is most prone to initiate epileptic activity.

Synchronization-based computation through networks of coupled oscillators

The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates.