Evaluating the effects of virulence genotype, swarming motility, and multi-locus sequence types of Escherichia coli on layer chicken embryo.

AIMS: To determine the effects of swarming motility (SM), and Multi-locus sequence types (MLST) on the main effect of virulence genotype (VG) of E. coli through an embryos lethality assay between the 12th -18th days of incubation. METHODS AND RESULTS: We collected 58 E. coli isolates from asymptomatic commercial hens (n = 42) and lesions of colibacillosis cases (n = 16), then classified their VG as avirulent, moderately-virulent, virulent-healthy, and virulent-colibacillosis categories by the presence of 5 virulence-associated genes (iroN, ompT, hlyF, iutA, and iss). These isolates were further classified as non-motile, motile, or hyper-motile by SM assay. From the 58 isolates we selected 29 for embryo lethality assay (ELA) and determined their MLST. Each isolate was inoculated into 15 embryonated eggs through the allantoic cavity. We found the avirulent isolates reduced the relative embryo weight compared to virulent-colibacillosis and moderately-virulent isolates (37.49 vs. 41.51 and 40.34%, P = 0.03). Among the moderately-virulent and virulent-colibacillosis categories, embryo lethality was lower when isolates were non-motile. Yolk retention was unaffected by virulence categories, motility, or MLST. CONCLUSION: Interaction between VG and SM substantially influenced the ELA of E. coli isolates.

The influence of synaptic plasticity on critical coupling estimates for neural populations.

The presence or absence of synaptic plasticity can dramatically influence the collective behavior of populations of coupled neurons. In this work, we consider spike-timing dependent plasticity (STDP) and its resulting influence on phase cohesion in computational models of heterogeneous populations of conductance-based neurons. STDP allows for the influence of individual synapses to change over time, strengthening or weakening depending on the relative timing of the relevant action potentials. Using phase reduction techniques, we derive an upper bound on the critical coupling strength required to retain phase cohesion for a network of synaptically coupled, heterogeneous neurons with STDP. We find that including STDP can significantly alter phase cohesion as compared to a network with static synaptic connections. Analytical results are validated numerically. Our analysis highlights the importance of the relative ordering of action potentials emitted in a population of tonically firing neurons and demonstrates that order switching can degrade the synchronizing influence of coupling when STDP is considered.

Case management for integrated care of older people with frailty in community settings.

BACKGROUND: Ageing populations globally have contributed to increasing numbers of people living with frailty, which has significant implications for use of health and care services and costs. The British Geriatrics Society defines frailty as "a distinctive health state related to the ageing process in which multiple body systems gradually lose their inbuilt reserves". This leads to an increased susceptibility to adverse outcomes, such as reduced physical function, poorer quality of life, hospital admissions, and mortality. Case management interventions delivered in community settings are led by a health or social care professional, supported by a multidisciplinary team, and focus on the planning, provision, and co-ordination of care to meet the needs of the individual. Case management is one model of integrated care that has gained traction with policymakers to improve outcomes for populations at high risk of decline in health and well-being. These populations include older people living with frailty, who commonly have complex healthcare and social care needs but can experience poorly co-ordinated care due to fragmented care systems. OBJECTIVES: To assess the effects of case management for integrated care of older people living with frailty compared with usual care. SEARCH METHODS: We searched CENTRAL, MEDLINE, Embase, CINAHL, Health Systems Evidence, and PDQ Evidence and databases from inception to 23 September 2022. We also searched clinical registries and relevant grey literature databases, checked references of included trials and relevant systematic reviews, conducted citation searching of included trials, and contacted topic experts. SELECTION CRITERIA: We included randomised controlled trials (RCTs) that compared case management with standard care in community-dwelling people aged 65 years and older living with frailty. DATA COLLECTION AND ANALYSIS: We followed standard methodological procedures recommended by Cochrane and the Effective Practice and Organisation of Care Group. We used the GRADE approach to assess the certainty of the evidence. MAIN RESULTS: We included 20 trials (11,860 participants), all of which took place in high-income countries. Case management interventions in the included trials varied in terms of organisation, delivery, setting, and care providers involved. Most trials included a variety of healthcare and social care professionals, including nurse practitioners, allied healthcare professionals, social workers, geriatricians, physicians, psychologists, and clinical pharmacists. In nine trials, the case management intervention was delivered by nurses only. Follow-up ranged from three to 36 months. We judged most trials at unclear risk of selection and performance bias; this consideration, together with indirectness, justified downgrading the certainty of the evidence to low or moderate. Case management compared to standard care may result in little or no difference in the following outcomes. • Mortality at 12 months' follow-up (7.0% in the intervention group versus 7.5% in the control group; risk ratio (RR) 0.98, 95% confidence interval (CI) 0.84 to 1.15; I2 = 11%; 14 trials, 9924 participants; low-certainty evidence) • Change in place of residence to a nursing home at 12 months' follow-up (9.9% in the intervention group versus 13.4% in the control group; RR 0.73, 95% CI 0.53 to 1.01; I2 = 0%; 4 trials, 1108 participants; low-certainty evidence) • Quality of life at three to 24 months' follow-up (results not pooled; mean differences (MDs) ranged from -6.32 points (95% CI -11.04 to -1.59) to 6.1 points (95% CI -3.92 to 16.12) when reported; 11 trials, 9284 participants; low-certainty evidence) • Serious adverse effects at 12 to 24 months' follow-up (results not pooled; 2 trials, 592 participants; low-certainty evidence) • Change in physical function at three to 24 months' follow-up (results not pooled; MDs ranged from -0.12 points (95% CI -0.93 to 0.68) to 3.4 points (95% CI -2.35 to 9.15) when reported; 16 trials, 10,652 participants; low-certainty evidence) Case management compared to standard care probably results in little or no difference in the following outcomes. • Healthcare utilisation in terms of hospital admission at 12 months' follow-up (32.7% in the intervention group versus 36.0% in the control group; RR 0.91, 95% CI 0.79 to 1.05; I2 = 43%; 6 trials, 2424 participants; moderate-certainty evidence) • Change in costs at six to 36 months' follow-up (results not pooled; 14 trials, 8486 participants; moderate-certainty evidence), which usually included healthcare service costs, intervention costs, and other costs such as informal care. AUTHORS' CONCLUSIONS: We found uncertain evidence regarding whether case management for integrated care of older people with frailty in community settings, compared to standard care, improved patient and service outcomes or reduced costs. There is a need for further research to develop a clear taxonomy of intervention components, to determine the active ingredients that work in case management interventions, and identify how such interventions benefit some people and not others.

Data-driven identification of dynamical models using adaptive parameter sets.

This paper presents two data-driven model identification techniques for dynamical systems with fixed point attractors. Both strategies implement adaptive parameter update rules to limit truncation errors in the inferred dynamical models. The first strategy can be considered an extension of the dynamic mode decomposition with control (DMDc) algorithm. The second strategy uses a reduced order isostable coordinate basis that captures the behavior of the slowest decaying modes of the Koopman operator. The accuracy and robustness of both model identification algorithms is considered in a simple model with dynamics near a Hopf bifurcation. A more complicated model for nonlinear convective flow past an obstacle is also considered. In these examples, the proposed strategies outperform a collection of other commonly used data-driven model identification algorithms including Koopman model predictive control, Galerkin projection, and DMDc.

Control of coupled neural oscillations using near-periodic inputs.

Deep brain stimulation (DBS) is a commonly used treatment for medication resistant Parkinson's disease and is an emerging treatment for other neurological disorders. More recently, phase-specific adaptive DBS (aDBS), whereby the application of stimulation is locked to a particular phase of tremor, has been proposed as a strategy to improve therapeutic efficacy and decrease side effects. In this work, in the context of these phase-specific aDBS strategies, we investigate the dynamical behavior of large populations of coupled neurons in response to near-periodic stimulation, namely, stimulation that is periodic except for a slowly changing amplitude and phase offset that can be used to coordinate the timing of applied input with a specified phase of model oscillations. Using an adaptive phase-amplitude reduction strategy, we illustrate that for a large population of oscillatory neurons, the temporal evolution of the associated phase distribution in response to near-periodic forcing can be captured using a reduced order model with four state variables. Subsequently, we devise and validate a closed-loop control strategy to disrupt synchronization caused by coupling. Additionally, we identify strategies for implementing the proposed control strategy in situations where underlying model equations are unavailable by estimating the necessary terms of the reduced order equations in real-time from observables.

Data-driven inference of high-accuracy isostable-based dynamical models in response to external inputs.

Isostable reduction is a powerful technique that can be used to characterize behaviors of nonlinear dynamical systems using a basis of slowly decaying eigenfunctions of the Koopman operator. When the underlying dynamical equations are known, previously developed numerical techniques allow for high-order accuracy computation of isostable reduced models. However, in situations where the dynamical equations are unknown, few general techniques are available that provide reliable estimates of the isostable reduced equations, especially in applications where large magnitude inputs are considered. In this work, a purely data-driven inference strategy yielding high-accuracy isostable reduced models is developed for dynamical systems with a fixed point attractor. By analyzing steady-state outputs of nonlinear systems in response to sinusoidal forcing, both isostable response functions and isostable-to-output relationships can be estimated to arbitrary accuracy in an expansion performed in the isostable coordinates. Detailed examples are considered for a population of synaptically coupled neurons and for the one-dimensional Burgers' equation. While linear estimates of the isostable response functions are sufficient to characterize the dynamical behavior when small magnitude inputs are considered, the high-accuracy reduced order model inference strategy proposed here is essential when considering large magnitude inputs.

Analysis of input-induced oscillations using the isostable coordinate framework.

Many reduced order modeling techniques for oscillatory dynamical systems are only applicable when the underlying system admits a stable periodic orbit in the absence of input. By contrast, very few reduction frameworks can be applied when the oscillations themselves are induced by coupling or other exogenous inputs. In this work, the behavior of such input-induced oscillations is considered. By leveraging the isostable coordinate framework, a high-accuracy reduced set of equations can be identified and used to predict coupling-induced bifurcations that precipitate stable oscillations. Subsequent analysis is performed to predict the steady state phase-locking relationships. Input-induced oscillations are considered for two classes of coupled dynamical systems. For the first, stable fixed points of systems with parameters near Hopf bifurcations are considered so that the salient dynamical features can be captured using an asymptotic expansion of the isostable coordinate dynamics. For the second, an adaptive phase-amplitude reduction framework is used to analyze input-induced oscillations that emerge in excitable systems. Examples with relevance to circadian and neural physiology are provided that highlight the utility of the proposed techniques.

Exploiting circadian memory to hasten recovery from circadian misalignment.

Recent years have seen a sustained interest in the development of circadian reentrainment strategies to limit the deleterious effects of jet lag. Due to the dynamical complexity of many circadian models, phase-based model reduction techniques are often an imperative first step in the analysis. However, amplitude coordinates that capture lingering effects (i.e., memory) from past inputs are often neglected. In this work, we focus on these amplitude coordinates using an operational phase and an isostable coordinate framework in the context of the development of jet-lag amelioration strategies. By accounting for the influence of circadian memory, we identify a latent phase shift that can prime one's circadian cycle to reentrain more rapidly to an expected time-zone shift. A subsequent optimal control problem is proposed that balances the trade-off between control effort and the resulting latent phase shift. Data-driven model identification techniques for the inference of necessary reduced order, phase-amplitude-based models are considered in situations where the underlying model equations are unknown, and numerical results are illustrated in both a simple planar model and in a coupled population of circadian oscillators.

Using a multi-stakeholder experience-based design process to co-develop the Creating Active Schools Framework.

BACKGROUND: UK and global policies recommend whole-school approaches to improve childrens' inadequate physical activity (PA) levels. Yet, recent meta-analyses establish current interventions as ineffective due to suboptimal implementation rates and poor sustainability. To create effective interventions, which recognise schools as complex adaptive sub-systems, multi-stakeholder input is necessary. Further, to ensure 'systems' change, a framework is required that identifies all components of a whole-school PA approach. The study's aim was to co-develop a whole-school PA framework using the double diamond design approach (DDDA). METHODOLOGY: Fifty stakeholders engaged in a six-phase DDDA workshop undertaking tasks within same stakeholder (n = 9; UK researchers, public health specialists, active schools coordinators, headteachers, teachers, active partner schools specialists, national organisations, Sport England local delivery pilot representatives and international researchers) and mixed (n = 6) stakeholder groupings. Six draft frameworks were created before stakeholders voted for one 'initial' framework. Next, stakeholders reviewed the 'initial' framework, proposing modifications. Following the workshop, stakeholders voted on eight modifications using an online questionnaire. RESULTS: Following voting, the Creating Active Schools Framework (CAS) was designed. At the centre, ethos and practice drive school policy and vision, creating the physical and social environments in which five key stakeholder groups operate to deliver PA through seven opportunities both within and beyond school. At the top of the model, initial and in-service teacher training foster teachers' capability, opportunity and motivation (COM-B) to deliver whole-school PA. National policy and organisations drive top-down initiatives that support or hinder whole-school PA. To the authors' knowledge, this is the first time practitioners, policymakers and researchers have co-designed a whole-school PA framework from initial conception. The novelty of CAS resides in identifying the multitude of interconnecting components of a whole-school adaptive sub-system; exposing the complexity required to create systems change. The framework can be used to shape future policy, research and practice to embed sustainable PA interventions within schools. To enact such change, CAS presents a potential paradigm shift, providing a map and method to guide future co-production by multiple experts of PA initiatives 'with' schools, while abandoning outdated traditional approaches of implementing interventions 'on' schools.

Optimal open-loop desynchronization of neural oscillator populations.

Deep brain stimulation (DBS) is an increasingly used medical treatment for various neurological disorders. While its mechanisms are not fully understood, experimental evidence suggests that through application of periodic electrical stimulation DBS may act to desynchronize pathologically synchronized populations of neurons resulting desirable changes to a larger brain circuit. However, the underlying mathematical mechanisms by which periodic stimulation can engender desynchronization in a coupled population of neurons is not well understood. In this work, a reduced phase-amplitude reduction framework is used to characterize the desynchronizing influence of periodic stimulation on a population of coupled oscillators. Subsequently, optimal control theory allows for the design of periodic, open-loop stimuli with the capacity to destabilize completely synchronized solutions while simultaneously stabilizing rotating block solutions. This framework exploits system nonlinearities in order to strategically modify unstable Floquet exponents. In the limit of weak neural coupling, it is shown that this method only requires information about the phase response curves of the individual neurons. The effects of noise and heterogeneity are also considered and numerical results are presented. This framework could ultimately be used to inform the design of more efficient deep brain stimulation waveforms for the treatment of neurological disease.

A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems.

Phase-amplitude reduction is of growing interest as a strategy for the reduction and analysis of oscillatory dynamical systems. Augmentation of the widely studied phase reduction with amplitude coordinates can be used to characterize transient behavior in directions transverse to a limit cycle to give a richer description of the dynamical behavior. Various definitions for amplitude coordinates have been suggested, but none are particularly well suited for implementation in experimental systems where output recordings are readily available but the underlying equations are typically unknown. In this work, a reduction framework is developed for inferring a phase-amplitude reduced model using only the observed model output from an arbitrarily high-dimensional system. This framework employs a proper orthogonal reduction strategy to identify important features of the transient decay of solutions to the limit cycle. These features are explicitly related to previously developed phase and isostable coordinates and used to define so-called data-driven phase and isostable coordinates that are valid in the entire basin of attraction of a limit cycle. The utility of this reduction strategy is illustrated in examples related to neural physiology and is used to implement an optimal control strategy that would otherwise be computationally intractable. The proposed data-driven phase and isostable coordinate system and associated reduced modeling framework represent a useful tool for the study of nonlinear dynamical systems in situations where the underlying dynamical equations are unknown and in particularly high-dimensional or complicated numerical systems for which standard phase-amplitude reduction techniques are not computationally feasible.

Phase Models Beyond Weak Coupling.

We use the theory of isostable reduction to incorporate higher order effects that are lost in the first order phase reduction of coupled oscillators. We apply this theory to weakly coupled complex Ginzburg-Landau equations, a pair of conductance-based neural models, and finally to a short derivation of the Kuramoto-Sivashinsky equations. Numerical and analytical examples illustrate bifurcations occurring in coupled oscillator networks that can cause standard phase-reduction methods to fail.

Recent advances in coupled oscillator theory.

We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems with applications to the Izhikevich neuron. We then introduce the idea of isostable reduction to explore behaviours that the weak coupling paradigm cannot explain. In an additional example, we show how bifurcations that change the stability of phase-locked solutions in a pair of identical coupled neurons can be understood using the notion of isostable reduction. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Phase reduction and phase-based optimal control for biological systems: a tutorial.

A powerful technique for the analysis of nonlinear oscillators is the rigorous reduction to phase models, with a single variable describing the phase of the oscillation with respect to some reference state. An analog to phase reduction has recently been proposed for systems with a stable fixed point, and phase reduction for periodic orbits has recently been extended to take into account transverse directions and higher-order terms. This tutorial gives a unified treatment of such phase reduction techniques and illustrates their use through mathematical and biological examples. It also covers the use of phase reduction for designing control algorithms which optimally change properties of the system, such as the phase of the oscillation. The control techniques are illustrated for example neural and cardiac systems.

Greater accuracy and broadened applicability of phase reduction using isostable coordinates.

The applicability of phase models is generally limited by the constraint that the dynamics of a perturbed oscillator must stay near its underlying periodic orbit. Consequently, external perturbations must be sufficiently weak so that these assumptions remain valid. Using the notion of isostables of periodic orbits to provide a simplified coordinate system from which to understand the dynamics transverse to a periodic orbit, we devise a strategy to correct for changing phase dynamics for locations away from the limit cycle. Consequently, these corrected phase dynamics allow for perturbations of larger magnitude without invalidating the underlying assumptions of the reduction. The proposed reduction strategy yields a closed set of equations and can be applied to periodic orbits embedded in arbitrarily high dimensional spaces. We illustrate the utility of this strategy in two models with biological relevance. In the first application, we find that an optimal control strategy for modifying the period of oscillation can be improved with the corrected phase reduction. In the second, the corrected phase reduced dynamics are used to understand adaptation and memory effects resulting from past perturbations.

Synchronization of heterogeneous oscillator populations in response to weak and strong coupling.

Synchronous behavior of a population of chemical oscillators is analyzed in the presence of both weak and strong coupling. In each case, we derive upper bounds on the critical coupling strength which are valid for arbitrary populations of nonlinear, heterogeneous oscillators. For weak perturbations, infinitesimal phase response curves are used to characterize the response to coupling, and graph theoretical techniques are used to predict synchronization. In the strongly perturbed case, we observe a phase dependent perturbation threshold required to elicit an immediate spike and use this behavior for our analytical predictions. Resulting upper bounds on the critical coupling strength agree well with our experimental observations and numerical simulations. Furthermore, important system parameters which determine synchronization are different in the weak and strong coupling regimes. Our results point to new strategies by which limit cycle oscillators can be studied when the applied perturbations become strong enough to immediately reset the phase.

Stochastic Pacing Inhibits Spatially Discordant Cardiac Alternans.

Depressed heart rate variability is a well-established risk factor for sudden cardiac death in survivors of acute myocardial infarction and for those with congestive heart failure. Although measurements of heart rate variability provide a valuable prognostic tool, it is unclear whether reduced heart rate variability itself is proarrhythmic or if it simply correlates with the severity of autonomic nervous system dysfunction. In this work, we investigate a possible mechanism by which heart rate variability could protect against cardiac arrhythmia. Specifically, in numerical simulations, we observe an inverse relationship between the variance of stochastic pacing and the occurrence of spatially discordant alternans, an arrhythmia that is widely believed to facilitate the development of cardiac fibrillation. By analyzing the effects of conduction velocity restitution, cellular dynamics, electrotonic coupling, and stochastic pacing on the nodal dynamics of spatially discordant alternans, we provide intuition for this observed behavior and propose control strategies to inhibit discordant alternans.

Phasic Burst Stimulation: A Closed-Loop Approach to Tuning Deep Brain Stimulation Parameters for Parkinson's Disease.

We propose a novel, closed-loop approach to tuning deep brain stimulation (DBS) for Parkinson's disease (PD). The approach, termed Phasic Burst Stimulation (PhaBS), applies a burst of stimulus pulses over a range of phases predicted to disrupt pathological oscillations seen in PD. Stimulation parameters are optimized based on phase response curves (PRCs), which would be measured from each patient. This approach is tested in a computational model of PD with an emergent population oscillation. We show that the stimulus phase can be optimized using the PRC, and that PhaBS is more effective at suppressing the pathological oscillation than a single phasic stimulus pulse. PhaBS provides a closed-loop approach to DBS that can be optimized for each patient.

A model of cardiac ryanodine receptor gating predicts experimental Ca2+-dynamics and Ca2+-triggered arrhythmia in the long QT syndrome.

Abnormal Ca2+ handling is well-established as the trigger of cardiac arrhythmia in catecholaminergic polymorphic ventricular tachycardia and digoxin toxicity, but its role remains controversial in Torsade de Pointes (TdP), the arrhythmia associated with the long QT syndrome (LQTS). Recent experimental results show that early afterdepolarizations (EADs) that initiate TdP are caused by spontaneous (non-voltage-triggered) Ca2+ release from Ca2+-overloaded sarcoplasmic reticulum (SR) rather than the activation of the L-type Ca2+-channel window current. In bradycardia and long QT type 2 (LQT2), a second, non-voltage triggered cytosolic Ca2+ elevation increases gradually in amplitude, occurs before overt voltage instability, and then precedes the rise of EADs. Here, we used a modified Shannon-Puglisi-Bers model of rabbit ventricular myocytes to reproduce experimental Ca2+ dynamics in bradycardia and LQT2. Abnormal systolic Ca2+-oscillations and EADs caused by SR Ca2+-release are reproduced in a modified 0-dimensional model, where 3 gates in series control the ryanodine receptor (RyR2) conductance. Two gates control RyR2 activation and inactivation and sense cytosolic Ca2+ while a third gate senses luminal junctional SR Ca2+. The model predicts EADs in bradycardia and low extracellular [K+] and cessation of SR Ca2+-release terminate salvos of EADs. Ca2+-waves, systolic cell-synchronous Ca2+-release, and multifocal diastolic Ca2+ release seen in subcellular Ca2+-mapping experiments are observed in the 2-dimensional version of the model. These results support the role of SR Ca2+-overload, abnormal SR Ca2+-release, and the subsequent activation of the electrogenic Na+/Ca2+-exchanger as the mechanism of TdP. The model offers new insights into the genesis of cardiac arrhythmia and new therapeutic strategies.

Clustered Desynchronization from High-Frequency Deep Brain Stimulation.

While high-frequency deep brain stimulation is a well established treatment for Parkinson's disease, its underlying mechanisms remain elusive. Here, we show that two competing hypotheses, desynchronization and entrainment in a population of model neurons, may not be mutually exclusive. We find that in a noisy group of phase oscillators, high frequency perturbations can separate the population into multiple clusters, each with a nearly identical proportion of the overall population. This phenomenon can be understood by studying maps of the underlying deterministic system and is guaranteed to be observed for small noise strengths. When we apply this framework to populations of Type I and Type II neurons, we observe clustered desynchronization at many pulsing frequencies.