Spatiotemporal Perturbations Research Articles

Real-time shimming with FID navigators.

To implement a method for real-time field control using rapid FID navigator (FIDnav) measurements and evaluate the efficacy of the proposed approach for mitigating dynamic field perturbations and improving -weighted image quality. FIDnavs were embedded in a gradient echo sequence and a subject-specific linear calibration model was generated on the scanner to facilitate rapid shim updates in response to measured FIDnav signals. To confirm the accuracy of FID-navigated field updates, phantom and volunteer scans were performed with online updates of the scanner B0 shim settings. To evaluate improvement in -weighted image quality with real-time shimming, 10 volunteers were scanned at 3T while performing deep-breathing and nose-touching tasks designed to modulate the B0 field. Quantitative image quality metrics were compared with and without FID-navigated field control. An additional volunteer was scanned at 7T to evaluate performance at ultra-high field. Applying measured FIDnav shim updates successfully compensated for applied global and linear field offsets in phantoms and across all volunteers. FID-navigated real-time shimming led to a substantial reduction in field fluctuations and a consequent improvement in -weighted image quality in volunteers performing deep-breathing and nose-touching tasks, with 7.57% ± 6.01% and 8.21% ± 10.90% improvement in peak SNR and structural similarity, respectively. FIDnavs facilitate rapid measurement and application of field coefficients for slice-wise B0 shimming. The proposed approach can successfully counteract spatiotemporal field perturbations and substantially improves -weighted image quality, which is important for a variety of clinical and research applications, particularly at ultra-high field.

Management of invasive cells in soft biological tissues through modulated nonlinear excitations: Long-range effects

In the present paper, we investigate the contribution of long-range diffusion and diffusive stresses on cellular waves generated during an invasion in soft biological tissues. To that end, we consider a set of three coupled nonlinear partial differential equations describing spatiotemporal evolutions of cell density, extracellular matrix (ECM), and spatial displacements of a material point taken in the ECM. In addition to long-range diffusion, diffusive stresses, and proliferation, the model also accounts for ECM production-degradation. The linear stability analysis reveals that in presence of temporal perturbations, there is no stability-instability transition in the system. In presence of spatiotemporal perturbations, instability dominates but the stability-instability transition is controlled by proliferation rate and long-range diffusion of cells. Analytical solutions are constructed as well as their existence conditions provided. Amongst the structures recovered, breathers are associated with the transport of a high number of cells. Long-range diffusive stresses, saturation, and ECM depletion rate significantly modify the wave structure as well as the number of cells carried. On the other hand, Proliferation, ECM production rate, long-range haptotaxis, diffusion, and traction affect both spatial rearrangement and the number of cells carried by the wave. Through our analysis, numerical solutions remain positive, do not diverge from their analytical counterpart, meaning that the solutions proposed are stable and may be used to probe the inherent biological realities of the model considered.

Spatiotemporal dynamics of a glioma immune interaction model

We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain.

Spatiotemporal perturbations in paced finger tapping suggest a common mechanism for the processing of time errors

Paced finger tapping is a sensorimotor synchronization task where a subject has to keep pace with a metronome while the time differences (asynchronies) between each stimulus and its response are recorded. A usual way to study the underlying error correction mechanism is to perform unexpected temporal perturbations to the stimuli sequence. An overlooked issue is that at the moment of a temporal perturbation two things change: the stimuli period (a parameter) and the asynchrony (a variable). In terms of experimental manipulation, it would be desirable to have separate, independent control of parameter and variable values. In this work we perform paced finger tapping experiments combining simple temporal perturbations (tempo step change) and spatial perturbations with temporal effect (raised or lowered point of contact). In this way we decouple the parameter-and-variable confounding, performing novel perturbations where either the parameter or the variable changes. Our results show nonlinear features like asymmetry and are compatible with a common error correction mechanism for all types of asynchronies. We suggest taking this confounding into account when analyzing perturbations of any kind in finger tapping tasks but also in other areas of sensorimotor synchronization, like music performance experiments and paced walking in gait coordination studies.

Front-induced transitions

Refractive index fronts propagating in waveguides are special spatiotemporal perturbations. The interaction of light with such fronts can be described in terms of an indirect transition where the frequency and wavenumber of a guided mode both are changed. In recent years, front-induced transitions have been used in dispersion-engineered waveguides for frequency conversion, optical delays, and bandwidth and pulse duration manipulation. These concepts have originated from different research areas of photonics, such as nonlinear fibre optics, slow-light waveguides, plasma physics, moving media and relativistic effects. Here, we discuss these concepts, providing a unifying theoretical description and highlight the potential of this exciting research field for light manipulation in guided optics. Front-induced transitions have been used in dispersion-engineered waveguides for frequency conversion, optical delays, and bandwidth and pulse duration manipulation. This Review provides a theoretical description of the subject and highlights the potential for light manipulation in guided optics.

Action Generation Adapted to Low-Level and High-Level Robot-Object Interaction States.

Our daily environments are complex, composed of objects with different features. These features can be categorized into low-level features, e.g., an object position or temperature, and high-level features resulting from a pre-processing of low-level features for decision purposes, e.g., a binary value saying if it is too hot to be grasped. Besides, our environments are dynamic, i.e., object states can change at any moment. Therefore, robots performing tasks in these environments must have the capacity to (i) identify the next action to execute based on the available low-level and high-level object states, and (ii) dynamically adapt their actions to state changes. We introduce a method named Interaction State-based Skill Learning (IS2L), which builds skills to solve tasks in realistic environments. A skill is a Bayesian Network that infers actions composed of a sequence of movements of the robot's end-effector, which locally adapt to spatio-temporal perturbations using a dynamical system. In the current paper, an external agent performs one or more kinesthetic demonstrations of an action generating a dataset of high-level and low-level states of the robot and the environment objects. First, the method transforms each interaction to represent (i) the relationship between the robot and the object and (ii) the next robot end-effector movement to perform at consecutive instants of time. Then, the skill is built, i.e., the Bayesian network is learned. While generating an action this skill relies on the robot and object states to infer the next movement to execute. This movement selection gets inspired by a type of predictive models for action selection usually called affordances. The main contribution of this paper is combining the main features of dynamical systems and affordances in a unique method to build skills that solve tasks in realistic scenarios. More precisely, combining the low-level movement generation of the dynamical systems, to adapt to local perturbations, with the next movement selection simultaneously based on high-level and low-level states. This contribution was assessed in three experiments in realistic environments using both high-level and low-level states. The built skills solved the respective tasks relying on both types of states, and adapting to external perturbations.

Noise-reducing optogenetic negative-feedback gene circuits in human cells.

Gene autorepression is widely present in nature and is also employed in synthetic biology, partly to reduce gene expression noise in cells. Optogenetic systems have recently been developed for controlling gene expression levels in mammalian cells, but most have utilized activator-based proteins, neglecting negative feedback except for in silico control. Here, we engineer optogenetic gene circuits into mammalian cells to achieve noise-reduction for precise gene expression control by genetic, in vitro negative feedback. We build a toolset of these noise-reducing Light-Inducible Tuner (LITer) gene circuits using the TetR repressor fused with a Tet-inhibiting peptide (TIP) or a degradation tag through the light-sensitive LOV2 protein domain. These LITers provide a range of nearly 4-fold gene expression control and up to 5-fold noise reduction from existing optogenetic systems. Moreover, we use the LITer gene circuit architecture to control gene expression of the cancer oncogene KRAS(G12V) and study its downstream effects through phospho-ERK levels and cellular proliferation. Overall, these novel LITer optogenetic platforms should enable precise spatiotemporal perturbations for studying multicellular phenotypes in developmental biology, oncology and other biomedical fields of research.

Extrinsic and intrinsic dynamics in movement intermittency.

This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

3‐D Modeling of Induced Seismicity Along Multiple Faults: Magnitude, Rate, and Location in a Poroelasticity System

AbstractUnderstanding of the potential to injection‐induced seismicity along faults requires the response of fault zone system to spatiotemporal perturbations in pore pressure and stress. In this study, three‐dimensional (3‐D) model system consisting of the caprock, reservoir, and basement is intersected by vertical strike‐slip faults. We examine the full poroelastic behavior of the formation and perform the mechanical analysis along each fault zone using the Coulomb stress change. The magnitude, rate, and location of potential earthquakes are predicted using the spatial distribution of stresses and pore pressure over time. Rapid diffusion of pore pressure into conductive faults initiates failure, but the majority of induced seismicity occurs at deep fault zones due to poroelastic stabilization near the injection interval. Less permeable faults can be destabilized by either delayed pore pressure diffusion or poroelastic stressing. A two‐dimensional (2‐D) horizontal model, representing the interface between the reservoir and the basement, limits diffusion of pore pressure and deformation of the formation in the vertical direction that may overestimate or underestimate the potential of earthquakes along the fault. Our numerical results suggest that the 3‐D modeling of faulting system including poroelastic coupling can reduce the uncertainty in the seismic hazard prediction by considering the hydraulic and mechanical interaction between faults and bounding formations.

Combined effect of matrix quality and spatial heterogeneity on biodiversity decline

The land-sparing/land-sharing debate remains an oversimplified framework to evaluate landscape management strategies that aim to reconcile food production and biodiversity conservation. Still, biodiversity-yield curves, on which the framework has relied, provide valuable qualitative information on biodiversity's sensitivity to agricultural practices, and much research has studied this relationship. But the potential effect of landscape configuration on biodiversity's response to intensification has rarely been considered; besides, studies have often taken yield as an indicator of agricultural management and have generalized conclusions from studying particular taxonomic groups. In this work we adapt a metacommunity model to analyze factors that shape biodiversity's response to agricultural intensification while addressing some of the simplifications of the sparing/sharing dichotomy. In particular, we study species richness decline in landscapes encompassing a combined gradient in matrix quality and configurational heterogeneity of habitat patches, and considering community dynamics. We found that species richness along an intensification gradient shifts from following a robust response to presenting an abrupt decline, as landscape heterogeneity increases, as minimum viable population increases or as habitat area decreases. Our work highlights the interdependent effects of heterogeneity, habitat availability and matrix quality on biodiversity and contributes to a nuanced understanding of ecological and landscape factors that enable a robust response of biodiversity in the face of spatiotemporal perturbations.

Nocturnal Near-Surface Temperature, but not Flow Dynamics, can be Predicted by Microtopography in a Mid-Range Mountain Valley

We investigate nocturnal flow dynamics and temperature behaviour near the surface of a 170-m long gentle slope in a mid-range mountain valley. In contrast to many existing studies focusing on locations with significant topographic variations, gentle slopes cover a greater spatial extent of the Earth’s surface. Air temperatures were measured using the high-resolution distributed-temperature-sensing method within a two-dimensional fibre-optic array in the lowest metre above the surface. The main objectives are to characterize the spatio-temporal patterns in the near-surface temperature and flow dynamics, and quantify their responses to the microtopography and land cover. For the duration of the experiment, including even clear-sky nights with weak winds and strong radiative forcing, the classical cold-air drainage predicted by theory could not be detected. In contrast, we show that the airflow for the two dominant flow modes originates non-locally. The most abundant flow mode is characterized by vertically-decoupled layers featuring a near-surface flow perpendicular to the slope and strong stable stratification, which contradicts the expectation of a gravity-driven downslope flow of locally produced cold air. Differences in microtopography and land cover clearly affect spatio-temporal temperature perturbations. The second most abundant flow mode is characterized by strong mixing, leading to vertical coupling with airflow directed down the local slope. Here variations of microtopography and land cover lead to negligible near-surface temperature perturbations. We conclude that spatio-temporal temperature perturbations, but not flow dynamics, can be predicted by microtopography, which complicates the prediction of advective-heat components and the existence and dynamics of cold-air pools in gently sloped terrain in the absence of observations.

Coupled-mode theory for electromagnetic pulse propagation in dispersive media undergoing a spatiotemporal perturbation: Exact derivation, numerical validation, and peculiar wave mixing

We present an extension of the canonical coupled-mode theory of electromagnetic waves to the case of pulses and spatiotemporal perturbations in complex media. Unlike previous attempts to derive such a model, our approach involves no approximation, and it does not impose any restriction on the spatiotemporal profile. Moreover, the effect of modal dispersion on mode evolution and on the coupling to other modes is fully taken into account. Thus, our approach can yield any required accuracy by retaining as many terms in the expansion as needed. It also avoids various artifacts of previous derivations by introducing the correct form of the solution. We then validate the coupled-mode equations with exact numerical simulations, and we demonstrate the wide range of possibilities enabled by spatiotemporal perturbations of pulses, including pulse shortening or broadening or more complex shaping. Our formulation is valid across the electromagnetic spectrum, and it can be applied directly also to other wave systems.

Prenatal ethanol exposure in mice phenocopies Cdon mutation by impeding Shh function in the etiology of optic nerve hypoplasia.

ABSTRACTSepto-optic dysplasia (SOD) is a congenital disorder characterized by optic nerve, pituitary and midline brain malformations. The clinical presentation of SOD is highly variable with a poorly understood etiology. The majority of SOD cases are sporadic, but in rare instances inherited mutations have been identified in a small number of transcription factors, some of which regulate the expression of Sonic hedgehog (Shh) during mouse forebrain development. SOD is also associated with young maternal age, suggesting that environmental factors, including alcohol consumption at early stages of pregnancy, might increase the risk of developing this condition. Here, we address the hypothesis that SOD is a multifactorial disorder stemming from interactions between mutations in Shh pathway genes and prenatal ethanol exposure. Mouse embryos with mutations in the Shh co-receptor, Cdon, were treated in utero with ethanol or saline at embryonic day 8 (E8.0) and evaluated for optic nerve hypoplasia (ONH), a prominent feature of SOD. We show that both Cdon−/− mutation and prenatal ethanol exposure independently cause ONH through a similar pathogenic mechanism that involves selective inhibition of Shh signaling in retinal progenitor cells, resulting in their premature cell-cycle arrest, precocious differentiation and failure to properly extend axons to the optic nerve. The ONH phenotype was not exacerbated in Cdon−/− embryos treated with ethanol, suggesting that an intact Shh signaling pathway is required for ethanol to exert its teratogenic effects. These results support a model whereby mutations in Cdon and prenatal ethanol exposure increase SOD risk through spatiotemporal perturbations in Shh signaling activity.

Control of Turing patterns and their usage as sensors, memory arrays, and logic gates

We study a model system of three diffusively coupled reaction cells arranged in a linear array that display Turing patterns with special focus on the case of equal coupling strength for all components. As a suitable model reaction we consider a two-variable core model of glycolysis. Using numerical continuation and bifurcation techniques we analyze the dependence of the system's steady states on varying rate coefficient of the recycling step while the coupling coefficients of the inhibitor and activator are fixed and set at the ratios 100:1, 1:1, and 4:5. We show that stable Turing patterns occur at all three ratios but, as expected, spontaneous transition from the spatially uniform steady state to the spatially nonuniform Turing patterns occurs only in the first case. The other two cases possess multiple Turing patterns, which are stabilized by secondary bifurcations and coexist with stable uniform periodic oscillations. For the 1:1 ratio we examine modular spatiotemporal perturbations, which allow for controllable switching between the uniform oscillations and various Turing patterns. Such modular perturbations are then used to construct chemical computing devices utilizing the multiple Turing patterns. By classifying various responses we propose: (a) a single-input resettable sensor capable of reading certain value of concentration, (b) two-input and three-input memory arrays capable of storing logic information, (c) three-input, three-output logic gates performing combinations of logical functions OR, XOR, AND, and NAND.

Influence of ZNMF jet flow control on the spatio-temporal flow structure over a NACA-0015 airfoil

The spatio-temporal flow structure associated with zero-net-mass-flux (ZNMF) jet forcing at the leading edge of a NACA-0015 airfoil (Re = 3 × 104) is investigated using high-repetition rate particle image velocimetry. Measurements are performed at an angle of attack of 18°, where in the absence of forcing, flow separation occurs at the leading edge. Forcing is applied at a frequency of f+ = 1.3 and a momentum coefficient cμ = 0.0014 for which previous force measurements indicated a 45 % increase in lift over the unforced case. The structure and dynamics associated with both the forced and unforced case are considered. The dominant frequencies associated with separation in the unforced case are identified with the first harmonic of the bluff body shedding fwake closely corresponding to the forcing frequency of f+ = 1.3. A triple-decomposition of the velocity field is performed to identify the spatio-temporal perturbations produced by the ZNMF jet forcing. This forcing results in a reattachment of the flow, which is caused by the generation of large-scale vortices that entrain high-momentum fluid from the freestream. Forcing at 2fwake produces a series of vortices that advect parallel to the airfoil surface at a speed lower than the freestream velocity. Potential mechanisms by which these vortices affect flow reattachment are discussed.

Flash Photolysis of Caged Compounds during Simultaneous Imaging of Calcium and Voltage in the Whole Heart using Light-Emitting-Diodes

Flash photolysis of caged-compounds (i.e. photoactivatable compounds) allows one to interact with tissue by controlling the release of bioactive components, both spatially and temporally. The use of ultraviolet light-emitting-diodes (UV LEDs) for uncaging such compounds in cells has recently generated excitement, since LEDs offer high-speed control and are low cost.Traditional methods for simultaneous imaging of intracellular calcium transients (CaT) and membrane voltage (Vm) are technically challenging and require the use of two cameras. We developed a single-camera (Cascade 128+; Photometrics) approach that images rhod-2 (CaT) and the new near-infrared di-4-ANBDQPQ (Vm), without cross-talk. The technique relies on the isosbestic-point of di-4-ANBDQPQ, a custom-built multi-band optical filter (Chroma Technology) and visible LEDs (Luminus Devices). As the excitation wavelengths of these dyes are significantly longer than those needed to photoactivate caged-compounds, we combined them with a UV-sensitive calcium buffer (NP-EGTA; Invitrogen) to locally modulate free calcium in Langendorff-perfused rat hearts (N=3, Wistar-rat female).We demonstrate local uncaging of calcium by photo-inhibition of NP-EGTA with a powerful 365nm UV LED (Nichia), while simultaneously imaging CaT and Vm (128x128 pixels; 511 frames-per-second). CaT (shape and kinetics) were dramatically altered, in keeping with reported effects of EGTA-AM in whole-heart studies. The kinetics of CaT recovery changed from biphasic (in the presence of functional EGTA) to monophasic (after photo-inhibition of the buffer), and CaT duration increased.In summary: Caged-compounds can be used in multi-cellular preparations like the whole-heart to investigate the effects of spatiotemporal perturbations of bioactive compound concentrations, such as calcium buffers, and this approach can be combined with simultaneous measurement of CaT and Vm.Supported by NIH grant EB001963; Human Frontier Science Program grant RGP0027/09; The Clarendon Fund Scholarship; and The British Heart Foundation.

Electroosmotic flows with simultaneous spatio-temporal modulations in zeta potential: cases of thick electrical double layers beyond the Debye Hückel limit

We devise a mathematical model for analyzing the effects of spatio-temporal perturbations in zeta potential on electroosmotic transport in narrow fluidic confinements, considering thick electrical double layer limits. The spatial perturbations in zeta potential may be attributed to surface charge patterning, either designed or manifested as a natural artifact of the surface inhomogeneities. The time-dependent variations in zeta potential, as considered in this work, may stem from the temporal perturbations in the bulk ionic concentrations in the end-channel reservoirs or ‘wells’. Overcoming the simplifications routinely employed in the literature, we develop here an improved analytical formalism, without imposing any constraints on the magnitude of the zeta potential. Using these solutions, we highlight the possibilities of obtaining designed rotationalities in the flow structure with simultaneous spatial variations in the zeta potential and temporal variations in the well concentrations. We show that such combinations of spatial and temporal variations, in effect, render the flow system to be capable of shedding vortex structures that are not otherwise obtainable with spatial variations in zeta potential alone.

Higher order reconstruction for MRI in the presence of spatiotemporal field perturbations

Despite continuous hardware advances, MRI is frequently subject to field perturbations that are of higher than first order in space and thus violate the traditional k-space picture of spatial encoding. Sources of higher order perturbations include eddy currents, concomitant fields, thermal drifts, and imperfections of higher order shim systems. In conventional MRI with Fourier reconstruction, they give rise to geometric distortions, blurring, artifacts, and error in quantitative data. This work describes an alternative approach in which the entire field evolution, including higher order effects, is accounted for by viewing image reconstruction as a generic inverse problem. The relevant field evolutions are measured with a third-order NMR field camera. Algebraic reconstruction is then formulated such as to jointly minimize artifacts and noise in the resulting image. It is solved by an iterative conjugate-gradient algorithm that uses explicit matrix-vector multiplication to accommodate arbitrary net encoding. The feasibility and benefits of this approach are demonstrated by examples of diffusion imaging. In a phantom study, it is shown that higher order reconstruction largely overcomes variable image distortions that diffusion gradients induce in EPI data. In vivo experiments then demonstrate that the resulting geometric consistency permits straightforward tensor analysis without coregistration.

Kink propagation in inhomogeneous systems driven by spatiotemporal perturbations

We investigate the propagation of kinks in inhomogeneous media. We show that the extended character of the kink, the internal mode instabilities and the phenomenon of disappearance of the translational mode can affect the kink motion in the presence of space-dependent external perturbations. We apply the results to the analysis of kink ratchets and the propagation of kinks driven by wave fields.

Learning Non-linear Multivariate Dynamics of Motion in Robotic Manipulators

Motion imitation requires reproduction of a dynamical signature of a movement, i.e. a robot should be able to encode and reproduce a particular path together with a specific velocity and/or an acceleration profile. Furthermore, a human provides only few demonstrations, which cannot cover all possible contexts in which the robot will need to reproduce the motion autonomously. Therefore, the encoding should be able to efficiently generalize knowledge by generating similar motions in unseen contexts. This work follows a recent trend in programming by demonstration in which the dynamics of the motion is learned. We present an algorithm to estimate multivariate robot motions through a mixture of Gaussians. The strengths of the proposed encoding are three-fold: (i) it allows a generalization of motion to unseen context; (ii) it provides fast on-line replanning of the motion in case of of spatio-temporal perturbations; (iii) it may embed different types of dynamics, governed by different attractors. The generality of the method to estimate arbitrary non-linear motion dynamics is demonstrated by accurately estimating a set of known non-linear dynamical systems. The platform-independency and real-time performance of the method are further validated to learn the non-linear motion dynamics of manipulation tasks with different robotic platforms. We provide an experimental comparison of our approach with a related state-of-the-art method.