Deep brain stimulation for movement disorder treatment: exploring frequency-dependent efficacy in a computational network model.

A large-scale computational model of the basal ganglia network and thalamus is proposed to describe movement disorders and treatment effects of deep brain stimulation (DBS). The model of this complex network considers three areas of the basal ganglia region: the subthalamic nucleus (STN) as target area of DBS, the globus pallidus, both pars externa and pars interna (GPe-GPi), and the thalamus. Parkinsonian conditions are simulated by assuming reduced dopaminergic input and corresponding pronounced inhibitory or disinhibited projections to GPe and GPi. Macroscopic quantities are derived which correlate closely to thalamic responses and hence motor programme fidelity. It can be demonstrated that depending on different levels of striatal projections to the GPe and GPi, the dynamics of these macroscopic quantities (synchronisation index, mean synaptic activity and response efficacy) switch from normal to Parkinsonian conditions. Simulating DBS of the STN affects the dynamics of the entire network, increasing the thalamic activity to levels close to normal, while differing from both normal and Parkinsonian dynamics. Using the mentioned macroscopic quantities, the model proposes optimal DBS frequency ranges above 130 Hz.

Coarse-scale PDEs from fine-scale observations via machine learning.

Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through, e.g., atomistic, agent-based, or lattice models) based on first principles. Some of these processes can also be successfully modeled at the macroscopic level using, e.g., partial differential equations (PDEs) describing the evolution of the right few macroscopic observables (e.g., concentration and momentum fields). Deriving good macroscopic descriptions (the so-called "closure problem") is often a time-consuming process requiring deep understanding/intuition about the system of interest. Recent developments in data science provide alternative ways to effectively extract/learn accurate macroscopic descriptions approximating the underlying microscopic observations. In this paper, we introduce a data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine-learning algorithms. Specifically, using Gaussian processes, artificial neural networks, and/or diffusion maps, the proposed framework uncovers the relation between the relevant macroscopic space fields and their time evolution (the right-hand side of the explicitly unavailable macroscopic PDE). Interestingly, several choices equally representative of the data can be discovered. The framework will be illustrated through the data-driven discovery of macroscopic, concentration-level PDEs resulting from a fine-scale, lattice Boltzmann level model of a reaction/transport process. Once the coarse evolution law is identified, it can be simulated to produce long-term macroscopic predictions. Different features (pros as well as cons) of alternative machine-learning algorithms for performing this task (Gaussian processes and artificial neural networks) are presented and discussed.

Towards an optimised deep brain stimulation using a large-scale computational network and realistic volume conductor model.

Objective. Constructing a theoretical framework to improve deep brain stimulation (DBS) based on the neuronal spatiotemporal patterns of the stimulation-affected areas constitutes a primary target.Approach. We develop a large-scale biophysical network, paired with a realistic volume conductor model, to estimate theoretically efficacious stimulation protocols. Based on previously published anatomically defined structural connectivity, a biophysical basal ganglia-thalamo-cortical neuronal network is constructed using Hodgkin-Huxley dynamics. We define a new biomarker describing the thalamic spatiotemporal activity as a ratio of spiking vs. burst firing. The per cent activation of the different pathways is adapted in the simulation to minimise the differences of the biomarker with respect to its value under healthy conditions.Main results.This neuronal network reproduces spatiotemporal patterns that emerge in Parkinson's disease. Simulations of the fibre per cent activation for the defined biomarker propose desensitisation of pallido-thalamic synaptic efficacy, induced by high-frequency signals, as one possible crucial mechanism for DBS action. Based on this activation, we define both an optimal electrode position and stimulation protocol using pathway activation modelling.Significance. A key advantage of this research is that it combines different approaches, i.e. the spatiotemporal pattern with the electric field and axonal response modelling, to compute the optimal DBS protocol. By correlating the inherent network dynamics with the activation of white matter fibres, we obtain new insights into the DBS therapeutic action.

Optimal vaccine roll-out strategies including social distancing for pandemics.

Non-pharmacological interventions (NPIs), principally social distancing, in combination with effective vaccines, aspire to develop a protective immunity shield against pandemics and particularly against the COVID-19 pandemic. In this study, an agent-based network model with small-world topology is employed to find optimal policies against pandemics, including social distancing and vaccination strategies. The agents' states are characterized by a variation of the SEIR model (susceptible, exposed, infected, recovered). To explore optimal policies, an equation-free method is proposed to solve the inverse problem of calibrating an agent's infection rate with respect to the vaccination efficacy. The results show that prioritizing the first vaccine dose in combination with mild social restrictions, is sufficient to control the pandemic, with respect to the number of deaths. Moreover, for the same mild number of social contacts, we find an optimal vaccination ratio of 0.85 between older people of ages > 65 compared to younger ones.

Bautin bifurcations in a forest-grassland ecosystem with human-environment interactions.

Ecosystems may be characterized by a complex dynamical behaviour where external disturbances and/or internal perturbations may trigger sudden/irreversible changes, called catastrophic shifts. Simple mathematical models in the form of ordinary and/or partial differential equations have been proposed to approximate in a qualitatively manner the observed complex phenomena, where catastrophic shifts are determined by bifurcation points. In this work, we show that in ecosystems, gradual/smooth changes may be transformed in sudden/catastrophic shifts as a consequence of codimension-2 bifurcations. We stress the importance of using the full arsenal of numerical bifurcation theory to systematically identify and characterize criticalities in ecological models in the 2D parameter space. For our demonstrations, we revisit the analysis of a simple model of a forest-grassland mosaic ecosystem constructing the 2D bifurcation diagram with respect to the impact of human influence and that of natural causes. Our numerical analysis reveals that this simple model is able to approximate both abrupt (catastrophic) and smooth transitions as the system undergoes Bautin bifurcations.

On the effect of the path length of small-world networks on epidemic dynamics.

We show how one can trace in a systematic way the coarse-grained solutions of individual-based stochastic epidemic models evolving on heterogeneous complex networks with respect to their topological characteristics. In particular, we illustrate the "distinct" impact of the average path length (with respect to the degree and clustering distributions) on the emergent behavior of detailed epidemic models; to achieve this we have developed an algorithm that allows its tuning at will. The framework could be used to shed more light on the influence of weak social links on epidemic spread within small-world network structures, and ultimately to provide novel systematic computational modeling and exploration of better contagion control strategies.

Dynamic analysis of EEG signals during spatial working memory used for either perception discrimination or planning of action.

We analysed multi-channel electroencephalographic (EEG) recordings during a spatial Working Memory (WM) task in order to test the hypothesis that segmentation of perception and action is present when the visual stimulus has been stored in spatial WM. To detect the interactions between different regions of the brain depending on the task we employed both Short Time Fourier Transformation (STFT) and the concept of Granger Causality (GC). Our computational analysis supports evidence that the Parietal Cortex (PC) is involved in WM processing.

Epidemionics: from the host-host interactions to the systematic analysis of the emergent macroscopic dynamics of epidemic networks.

One of the most critical issues in epidemiology revolves around the bridging of the diverse space and time scales stretching from the microscopic scale, where detailed knowledge on the immune mechanisms, host-microbe and host-host interactions is often available, to the macroscopic population-scale where the epidemic emerges, the questions arise and the answers are required. In this paper we show how the so called Equation-Free approach, a novel computational framework for multi-scale analysis, can be exploited to efficiently analyze the macroscopic emergent behavior of complex epidemic models on certain type of networks by acting directly on the multi-scale simulation. The methodology can be used to bypass the need of derivation of closures for the emergent population-level equations providing a systematic computational strict approach for macroscopic-level analysis. We illustrate the methodology through a stochastic individual-based model with agents acting on two different networks: a random regular and an Erdos-Rényi network. We construct the macroscopic bifurcation diagrams and locate the critical points that mark the onset of emergent hysteresis behavior which are associated with disease outbreaks. Finally, we perform a rare-events analysis that may in principle be used to estimate the mean time of possible outbreaks of phenomenologically latent infectious diseases.