Risk factor-dependent dynamics of atopic dermatitis: modelling multi-scale regulation of epithelium homeostasis

Epithelial tissue provides the body with its first layer of protection against harmful environmental stimuli by enacting the regulatory interplay between a physical barrier preventing the influx of external stimuli and an inflammatory response to the infiltrating stimuli. Importantly, this interdependent regulation occurs on different time scales: the tissue-level barrier permeability is regulated over the course of hours, whereas the cellular-level enzymatic reactions leading to inflammation take place within minutes. This multi-scale regulation is key to the epithelium's function and its dysfunction leads to various diseases. This paper presents a mathematical model of regulatory mechanisms in the epidermal epithelium that includes processes on two different time scales at the cellular and tissue levels. We use this model to investigate the essential regulatory interactions between epidermal barrier integrity and skin inflammation and how their dysfunction leads to atopic dermatitis (AD). Our model exhibits a structure of dual (positive and negative) control at both cellular and tissue levels. We also determined how the variation induced by well-known risk factors for AD can break the balance of the dual control. Our model analysis based on time-scale separation suggests that each risk factor leads to qualitatively different dynamic behaviours of different severity for AD, and that the coincidence of multiple risk factors dramatically increases the fragility of the epithelium's function. The proposed mathematical framework should also be applicable to other inflammatory diseases that have similar time-scale separation and control architectures.

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Multi-scale event synchronization analysis for unravelling climate processes: A wavelet-based approach

10.5194/npg-2017-19 ◽

2017 ◽

Cited By ~ 1

Author(s):

Ankit Agarwal ◽

Norbert Marwan ◽

Maheswaran Rathinasamy ◽

Bruno Merz ◽

Jürgen Kurths

Keyword(s):

Time Series ◽

Time Scales ◽

Time Scale ◽

Temporal Dynamics ◽

Multiple Scales ◽

Nonlinear Interactions ◽

Reference Time ◽

Multi Scale ◽

Spatio Temporal ◽

Different Time Scales

Abstract. The temporal dynamics of climate processes are spread across different time scales and, as such, the study of these processes only at one selected time scale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. For capturing the nonlinear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analyse the time series at one reference time scale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, wavelet based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various time scales. The proposed method allows the study of spatio-temporal patterns across different time scales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different time scales.

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Accelerating the High-Fidelity Simulation of Turbulence: Ensemble Averaging

Volume 1B, Symposia: Fluid Mechanics (Fundamental Issues and Perspectives; Industrial and Environmental Applications); Multiphase Flow and Systems (Multiscale Methods; Noninvasive Measurements; Numerical Methods; Heat Transfer; Performance); Transport Phenomena (Clean Energy; Mixing; Manufacturing and Materials Processing); Turbulent Flows — Issues and Perspectives; Algorithms and Applications for High Performance CFD Computation; Fluid Power; Fluid Dynamics of Wind Energy; Marine Hydrodynamics ◽

10.1115/fedsm2016-7853 ◽

2016 ◽

Author(s):

Vakhtang Makarashvili ◽

Elia Merzari ◽

Aleksandr Obabko ◽

Paul Fischer ◽

Andrew Siegel

Keyword(s):

Time Scales ◽

Time Scale ◽

Computational Cost ◽

Turbulence Models ◽

Ensemble Averaging ◽

Time Step ◽

Scale Separation ◽

Industrial Systems ◽

Time Scale Separation ◽

Turbulent Statistics

Computational fluid dynamics (CFD) is increasingly used to simulate complex industrial systems. Most CFD analysis relies on the Reynolds-averaged Navier-Stokes (RANS) approach and traditional two-equation turbulence models. Higher-fidelity approaches to the simulation of turbulence such as wall-resolved large eddy simulation (LES) and direct numerical simulation (DNS) remain limited to smaller applications or to large supercomputing platforms. Nonetheless, continued advances in supercomputing are enabling the simulation of physical systems of increasing size and complexity. These simulations can be used to gain unprecedented insight into the physics of turbulence in complex flows and will become more widespread as petascale architectures become more accessible. As the scale and size of LES and DNS simulations increase, however, the limitations of current algorithms become apparent. For larger systems, more temporal and spatial scale must be resolved, thus increasing the time-scale separation. While the smaller time scales dictate the size and the computational cost associated with each time step, the larger time scales dictate the length of the transient. An increased time-scale separation leads to smaller time steps and longer transients, eventually leading to simulations that are impractical or infeasible. In practice the presence of multiple and strongly separated time scales limits the effectiveness of CFD algorithms for LES and DNS applied to large industrial systems. Moreover, the situation is likely to become worse as even larger systems are simulated, thus increasing the size and length of transients. At the same time transients currently simulated on petascale architectures are unlikely to become any faster on exascale architectures. This paper presents an ensemble-averaging technique for transient simulations, aimed at collecting averaged turbulent statistics faster. The focus is on ergodic flows and simulations. Ensemble averaging involves creating multiple models and combining them to produce a desired output. This technique is commonplace in machine learning and artificial neural networks, and it is at the basis of RANS/URANS turbulence modeling. In the proposed approach, multiple instances of the same ergodic flows are simulated in parallel for a short time and summed to create an ensemble. Provided each instance is sufficiently statistically decorrelated, this allows considerable reduction in the time to solution. This paper focuses on the theory and implementation of the methodology in Nek5000, a massively parallel open-source spectral-element code. Also presented is the application of the method to the DNS and LES simulation of channel flow and pipe flow.

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ASYMMETRIC TRANSITION AND TIME-SCALE SEPARATION IN INTERLINKED POSITIVE FEEDBACK LOOPS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127411029483 ◽

2011 ◽

Vol 21 (07) ◽

pp. 1895-1905 ◽

Cited By ~ 3

Author(s):

PENCHO YORDANOV ◽

STEFKA TYANOVA ◽

MARC-THORSTEN HÜTT ◽

ANNICK LESNE

Keyword(s):

Time Scales ◽

Positive Feedback ◽

Time Scale ◽

Feedback Loops ◽

Boolean Logic ◽

Scale Separation ◽

Time Scale Separation ◽

Stimulus Variation ◽

Frequent Motif ◽

Noise Buffering

In [Brandman et al., 2005] it was proposed that interlinked fast and slow positive feedback loops are a frequent motif in biological signaling, because such a device can allow for a rapid response to an external stimulus (sensitivity) along with a certain noise-buffering capacity (robustness), as soon as the two loops operate on different time scales. Here we explore the properties of the nonlinear system responsible for this behavior. We argue that (a) the noise buffering is not linked to the stochastic nature of the stimulus, but only to the time scale of the stimulus variation compared to the intrinsic time scales of the system, and (b) this buffering of stimulus variations follows from the stabilization of a region of the state space away from the equilibrium branches of the system. Our analysis is based on a slow-fast decomposition of the dynamics. We analyze the strength of this buffering as a function of the time scales involved and the Boolean logic of the coupling between dynamic variables, as well as of the amplitude of the stimulus variations. We underline that such a nonequilibrium regime is universal as soon as the stimulus time scale is smaller than the larger time scale of the system, preventing the prediction of the behavior from the features of the bifurcation diagram or using a linear analysis.

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