A cascaded Nitinol Langevin transducer for resonance stability at elevated temperatures

Across power ultrasonics and sensing, piezoelectric ultrasonic transducers commonly experience degradation in mechanical, electrical, and dynamic performance due to the relatively high sensitivity of piezoelectric materials to changes in temperature. These changes, arising for example through high excitation voltages or environmental conditions, can lead to nonlinear dynamic behaviours which compromise device performance. To overcome this, the excitation signal to the piezoelectric material is often pulsed, mitigating the influence of temperature rises. However, there remain constraints on suitable candidate piezoelectric materials for power ultrasonic devices. As a novel approach to mitigating the influence of temperature on the properties of piezoelectric materials, the phase-transforming shape memory alloy Nitinol is incorporated into the piezoelectric stack of a Langevin power ultrasonic transducer, in a cascade formation. The underlying principle is that the nonlinear hardening response of Nitinol to rising temperature can be used to dynamically compensate for the nonlinear softening of the piezoelectric materials. Thus, the dynamic response of the transducer can be linearised at elevated excitation levels. In this study, two configurations of Langevin transducer are designed and characterised. One transducer incorporates a Nitinol middle mass, and in the second, titanium. A combination of electrical and thermomechanical characterisation is undertaken, where it is demonstrated that the nonlinear softening of the piezoelectric stack can be mitigated through control of the Nitinol microstructure. The vibration amplitudes of the Nitinol-middle cascaded transducer are higher and more stable when the Nitinol is austenite rather than a combination of martensite and austenite at room temperature. It has also been shown that the vibration amplitude and resonance frequency of Nitinol-middle cascaded transducer remain stable as temperature changes from 20 °C to 45 °C, dependent of the excitation voltage. Moreover, the self-heating experiment demonstrates the resonance stability of the Nitinol-middle cascaded transducer for continuous operation.

Linear thinking does not reflect the newer 21st-century anesthesia concepts. A narrative review

The brain constitutes a good example of a chaotic, nonlinear biological system where large neuronal networks operate chaotically with random connectivity. This critical state is significantly affected by the anesthetic loss of consciousness induced by drugs whose pharmacological behavior has been classically based on linear kinetics and dynamics. Recent developments in pharmacology and brain monitoring during anesthesia suggest a different view that we tried to explore in this article. The concepts of effect-site for hypnotic drugs modeling a maximum effect, electroencephalographic dynamics during induction, maintenance, and recovery from anesthesia are discussed, integrated into this alternative view, and how it may be applied in daily clinical practice.

Easy to build, modular and large scale pipe conveying fluid experimental setup

The pipe conveying fluid is a classic fluid structure interaction experiment. First studied for industrial applications such as liners and pipelines, it became a "paradigm" of non-linear dynamics in the same way as the vertical rotating shaft. Hundreds of papers studying different pipe instabilities and different phenomena with various numerical and analytical methods have been published in the last decades. However, many studies lack the comparison with experimental data to validate the analytical models and numerical simulations. Indeed, designing and building a pipe conveying fluid experimental setup can prove to be a long and a burdensome process. This paper presents an easy to build pipe conveying fluid experimental setup built in the LM2 laboratory at Polytechnique Montréal. Fig. 1 presents the global architecture of this experimental rig. This large scale setup uses relatively high speed cameras to track the pipe in three dimensions. It does not require heavy construction or major plumbing and electrical work. Moreover, it is removable and can be modified easily to observe different phenomena with various large scale pipes or boundary conditions. Lastly, it is relatively inexpensive as it costs less than 20 000 US dollars including all the sensors and acquisition systems.

Curved crease origami and topological singularities at a cellular scale enable hyper-extensibility of Lacrymaria olor

Eukaryotic cells undergo dramatic morphological changes during cell division, phagocytosis and motility. Fundamental limits of cellular morphodynamics such as how fast or how much cellular shapes can change without harm to a living cell remain poorly understood. Here we describe hyper-extensibility in the single-celled protist Lacrymaria olor, a 40 μm cell which is capable of reversible and repeatable extensions (neck-like protrusions) up to 1500 μm in 30 seconds. We discover that a unique and intricate organization of cortical cytoskeleton and membrane enables these hyper-extensions that can be described as the first cellular scale curved crease origami. Furthermore, we show how these topological singularities including d-cones and twisted domain walls provide a geometrical control mechanism for the deployment of membrane and microtubule sheets as they repeatably spool thousands of time from the cell body. We lastly build physical origami models to understand how these topological singularities provide a mechanism for the cell to control the hyper-extensile deployable structure. This new geometrical motif where a cell employs curved crease origami to perform a physiological function has wide ranging implications in understanding cellular morphodynamics and direct applications in deployable micro-robotics.

The dynamics behind diversity in suboscine songs

Vocal behavior plays a crucial evolutionary role. In the case of birds, song is critically important in courtship, male-male competition and other key behaviors linked to reproduction. However, under natural conditions, a variety of avian species live in close proximity and share an 'acoustic landscape'. Therefore, they need to be able to differentiate their calls or songs from those of other species and also from those of other individuals of the same species. To do this efficiently, birds display a remarkable diversity of sounds. For example, in the case of vocal learners, such as oscine passerines (i.e. songbirds), complex sequences and subtle acoustic effects are produced through the generation of complex neuromuscular instructions driving the vocal organ, which is remarkably conserved across approximately 4000 oscine species. By contrast, the majority of the sister clade of oscines, the suboscine passerines, are thought not to be vocal learners. Despite this, different suboscine species can generate a rich variety of songs and quite subtle acoustic effects. In the last few years, different suboscine species have been shown to possess morphological adaptations that allow them to produce a diversity of acoustic characteristics. Here, we briefly review the mechanisms of sound production in birds, before considering three suboscine species in more detail. The examples discussed in this Review, integrating biological experiments and biomechanical modeling using non-linear dynamical systems, illustrate how a morphological adaptation can produce complex acoustic properties without the need for complex neuromuscular control.

Exploring the performance of volatile mutations on evolutionary game dynamics in complex networks

The typical framework of replicator dynamics in evolutionary game theory assumes that all mutations are equally likely, meaning that the mutation of an evolving inhabitant only contributes constantly. However, in natural systems in biological and social sciences, mutations can arise due to their repetitive regeneration. The phenomenon of changing strategies (updating), typically prolonged sequences repeated many times, is defined as a volatile mutation that has been overlooked in evolutionary game theory. Implementing a repeated time framework introduces a dynamic mutation aspect incorporated with the pairwise Fermi rule. Network structure, ubiquitous in many natural and artificial systems, has significantly affected the dynamics and outcomes of evolutionary games. We examine the evolution of the pairwise game in terms of dilemma strength. It is revealed that mutation intensity can influence evolutionary dynamics. We also demonstrated that the obtained outcomes run by the deterministic and multi-agent simulation (MAS) process present similar stability regions for both linear and non-linear dynamics, even in various game classes. In particular, the most stimulating effect is detected for the relationship between the fraction of cooperation and the fraction of the mutated individuals, as inclination tends to provide an increasing tendency and supporting defection in the opposite case. In conclusion, we identified a form of volatile mutation as a form of noise that, under certain situations, could be used to enhance cooperation in social systems and design strategies for promoting cooperation in networked environments.

Alternative stable states, nonlinear behavior, and predictability of microbiome dynamics

BACKGROUND

Microbiome dynamics are both crucial indicators and potential drivers of human health, agricultural output, and industrial bio-applications. However, predicting microbiome dynamics is notoriously difficult because communities often show abrupt structural changes, such as "dysbiosis" in human microbiomes.

METHODS

We integrated theoretical frameworks and empirical analyses with the aim of anticipating drastic shifts of microbial communities. We monitored 48 experimental microbiomes for 110 days and observed that various community-level events, including collapse and gradual compositional changes, occurred according to a defined set of environmental conditions. We analyzed the time-series data based on statistical physics and non-linear mechanics to describe the characteristics of the microbiome dynamics and to examine the predictability of major shifts in microbial community structure.

RESULTS

We confirmed that the abrupt community changes observed through the time-series could be described as shifts between "alternative stable states" or dynamics around complex attractors. Furthermore, collapses of microbiome structure were successfully anticipated by means of the diagnostic threshold defined with the "energy landscape" analysis of statistical physics or that of a stability index of nonlinear mechanics.

CONCLUSIONS

The results indicate that abrupt microbiome events in complex microbial communities can be forecasted by extending classic ecological concepts to the scale of species-rich microbial systems. Video Abstract.

Respiratory pattern complexity in newly-diagnosed asthmatic patients

BACKGROUND

The intensity of respiratory symptoms and expiratory airflow limitations in asthma fluctuate over time. Some studies have reported variable complexity of the respiratory patterns in asthmatic patients. Thus, we conducted a novel study to assess the correlation between asthma severity and breathing pattern dynamics in newly-diagnosed asthmatic patients.

METHODS

A total of 20 newly-diagnosed asthmatic patients (7 male, 13 female) and 20 healthy cases (11 male, 9 female) were included. The respiratory patterns of all participants and the asthma severity for asthmatic patients were measured using a spirometer (before and after a bronchodilator exposure) and airflow recorder, respectively. The peak-to-peak intervals and the amplitude of peaks were considered as the inter-breath interval (IBI) and lung volume (LV) series. The Detrended Fluctuation Analysis (DFA), Sample Entropy (SampEn), Multi-scale Entropy (MSE), short-term (SD1) and long-term (SD2) variability, and IBI and LV Cross-Sample Entropy of the respiratory pattern dynamics were calculated using MATLAB (Mathwork, USA).

RESULTS

Asthma patients showed notable increase in the average of sample entropy in both IBI and LV parameters (p = 0.025 and p = 0.018, respectively) and also decreased synchronization between IBI and LV (p = 0.042). The multi-scale sample entropy of both IBI and LV was significantly higher in asthmatic patients (p < 0.05). Furthermore, SD1 and SD2 were higher in the patients with asthma (p < 0.05). Significant correlations were detected between spirometric (forced expiratory flow (FEF) change, pre FEF, pre forced expiratory volume in one second (FEV1) / forced vital capacity (FVC), FVC change) and respiratory pattern (mean-IBI, mean-LV, mean-respiratory rate (RR), coefficient of variation (CV)-IBI, CV-LV, cross-sample entropy) parameters (p < 0.05). Furthermore, we identified a negative correlation between CV of IBI and asthma severity (r = -0.52, p = 0.021).

CONCLUSION

Here, we took a novel approach and observed increased irregularity (more complexity) in the breathing pattern of patients newly-diagnosed with asthma. Remarkable correlations were detected between breathing complexity markers and spirometric indices along with disease severity in asthmatic patients. Thus, our data suggests respiratory pattern indices could be utilized as an indicator of asthma and its severity. However, more clinical data are required to support this conclusion.

Linear and non-linear dynamics of the epidemics: System identification based parametric prediction models for the pandemic outbreaks

Coronavirus disease 2019 (COVID-19) has endured constituting formidable economic, social, educational, and phycological challenges for the societies. Moreover, during pandemic outbreaks, the hospitals are overwhelmed with patients requiring more intensive care units and intubation equipment. Therein, to cope with these urgent healthcare demands, the state authorities seek ways to develop policies based on the estimated future casualties. These policies are mainly non-pharmacological policies including the restrictions, curfews, closures, and lockdowns. In this paper, we construct three model structures of the S^pIⁿI^tI^bD-N (suspicious S^p, infected Iⁿ, intensive care I^t, intubated I^b, and dead D together with the non-pharmacological policies N) holding two key targets. The first one is to predict the future COVID-19 casualties including the intensive care and intubated ones, which directly determine the need for urgent healthcare facilities, and the second one is to analyse the linear and non-linear dynamics of the COVID-19 pandemic under the non-pharmacological policies. In this respect, we have modified the non-pharmacological policies and incorporated them within the models whose parameters are learned from the available data. The trained models with the data released by the Turkish Health Ministry confirmed that the linear S^pIⁿI^tI^bD-N model yields more accurate results under the imposed non-pharmacological policies. It is important to note that the non-pharmacological policies have a damping effect on the pandemic casualties and this can dominate the non-linear dynamics. Herein, a model without pharmacological or non-pharmacological policies might have more dominant non-linear dynamics. In addition, the paper considers two machine learning approaches to optimize the unknown parameters of the constructed models. The results show that the recursive neural network has superior performance for learning nonlinear dynamics. However, the batch least squares outperforms in the presence of linear dynamics and stochastic data. The estimated future pandemic casualties with the linear S^pIⁿI^tI^bD-N model confirm that the suspicious, infected, and dead casualties converge to zero from 200000, 1400, 200 casualties, respectively. The convergences occur in 120 days under the current conditions.

Changes in torque complexity and maximal torque after a fatiguing exercise protocol

Torque outputs exhibit non-random fluctuations in their temporal structure, i.e., complexity. Fatigue has been shown to alter this structure. The torque outputs typically become more regular, resulting in decreased adaptability. Importantly, torque complexity was shown a different recovery pattern after fatigue compared to maximal torque. However, it remains to be understood if these uncoupled patterns of recovery are muscle dependent. In addition, it also remains to be investigated if changes in maximal torque and complexity are correlated. This study investigated (i) the effects of a fatiguing protocol on the complexity and maximal torque from plantar flexors and (ii) the relationship between changes in these two outputs. Ten participants visited the laboratory, and measures were taken at baseline, immediately after, 1 h after and 24 h after the fatiguing protocol. Maximum voluntary contraction, isometric contractions at 30% of maximum and pain pressure threshold were collected. Both legs were assessed, but only one was given the fatiguing protocol. Two-way ANOVAs and correlations were conducted. The fatiguing protocol decreased torque complexity (~35%) and maximal torque (~20%), and they exhibited uncoupled patterns of recovery. Moreover, the correlation analysis showed no correlation between changes in these parameters. These findings support that these parameters are independent of each other.

Balance on different unstable supports: a complementary approach based on linear and non-linear analyses

Maintenance of postural control is a complex task that requires the integration of different sensory-motor processes. To improve postural control, balance training is often implemented using unstable surfaces. Little is known, however, about how different surfaces compare in terms of postural control strategy. Non-linear dynamical system analysis, like recurrent quantification analysis (RQA) applied to the center of pressure (CoP) trajectory, represents a useful tool in this respect. The aim of this study is to investigate the effects of different unstable supports on the CoP trajectory through a complementary approach based on linear and non-linear analyses. Seventeen healthy adults performed barefoot single-leg balance trials on a force plate and on three different balance training devices (soft disc, foam pad, and pillow). Sets of parameters were extracted from the CoP trajectories using classical stabilometric analysis (sway path, mean velocity, root mean square) and RQA (percent recurrence and determinism, maximum line length, entropy). Both classical and RQA analyses highlighted significant differences between stable (force plate) and unstable conditions (p < 0.001). Conversely, only classical stabilometric parameters showed significant differences among the considered balance training devices, indicating that the different characteristics of the devices do not influence the dynamic/temporal structure of the CoP trajectory. Analysis of the center of pressure trajectory during single-leg standing on three different balance training devices and on a rigid surface using both linear and non-linear techniques.

Phage strategies facilitate bacterial coexistence under environmental variability

Bacterial communities are often exposed to temporal variations in resource availability, which exceed bacterial generation times and thereby affect bacterial coexistence. Bacterial population dynamics are also shaped by bacteriophages, which are a main cause of bacterial mortality. Several strategies are proposed in the literature to describe infections by phages, such as "Killing the Winner", "Piggyback the loser" (PtL) or "Piggyback the Winner" (PtW). The two temperate phage strategies PtL and PtW are defined by a change from lytic to lysogenic infection when the host density changes, from high to low or from low to high, respectively. To date, the occurrence of different phage strategies and their response to environmental variability is poorly understood. In our study, we developed a microbial trophic network model using ordinary differential equations (ODEs) and performed 'in silico' experiments. To model the switch from the lysogenic to the lytic cycle, we modified the lysis rate of infected bacteria and their growth was turned on or off using a density-dependent switching point. We addressed whether and how the different phage strategies facilitate bacteria coexistence competing for limiting resources. We also studied the impact of a fluctuating resource inflow to evaluate the response of the different phage strategies to environmental variability. Our results show that the viral shunt (i.e. nutrient release after bacterial lysis) leads to an enrichment of the system. This enrichment enables bacterial coexistence at lower resource concentrations. We were able to show that an established, purely lytic model leads to stable bacterial coexistence despite fluctuating resources. Both temperate phage models differ in their coexistence patterns. The model of PtW yields stable bacterial coexistence at a limited range of resource supply and is most sensitive to resource fluctuations. Interestingly, the purely lytic phage strategy and PtW both result in stable bacteria coexistence at oligotrophic conditions. The PtL model facilitates stable bacterial coexistence over a large range of stable and fluctuating resource inflow. An increase in bacterial growth rate results in a higher resilience to resource variability for the PtL and the lytic infection model. We propose that both temperate phage strategies represent different mechanisms of phages coping with environmental variability. Our study demonstrates how phage strategies can maintain bacterial coexistence in constant and fluctuating environments.

Fatigue-induced changes in knee-extensor torque complexity and muscle metabolic rate are dependent on joint angle

Purpose

Joint angle is a significant determinant of neuromuscular and metabolic function. We tested the hypothesis that previously reported correlations between knee-extensor torque complexity and metabolic rate (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{m}\dot{\text{V}}\text{O}}_{{2}}$$\end{document}mV˙O2) would be conserved at reduced joint angles (i.e. shorter muscle lengths).

Methods

Eleven participants performed intermittent isometric knee-extensor contractions at 50% maximum voluntary torque for 30 min or until task failure (whichever occurred sooner) at joint angles of 30º, 60º and 90º of flexion (0º = extension). Torque and surface EMG were sampled continuously. Complexity and fractal scaling of torque were quantified using approximate entropy (ApEn) and detrended fluctuation analysis (DFA) α. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{m}\dot{\text{V}}\text{O}}_{{2}}$$\end{document}mV˙O2 was determined using near-infrared spectroscopy.

Results

Time to task failure/end increased as joint angle decreased (P < 0.001). Over time, complexity decreased at 90º and 60º (decreased ApEn, increased DFA α, both P < 0.001), but not 30º. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{m}\dot{\text{V}}\text{O}}_{{2}}$$\end{document}mV˙O2 increased at all joint angles (P < 0.001), though the magnitude of this increase was lower at 30º compared to 60º and 90º (both P < 0.01). There were significant correlations between torque complexity and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{m}\dot{\text{V}}\text{O}}_{{2}}$$\end{document}mV˙O2 at 90º (ApEn, r =  − 0.60, P = 0.049) and 60º (ApEn, r =  − 0.64, P = 0.035; DFA α, ρ = 0.68, P = 0.015).

Conclusion

The lack of correlation between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{m}\dot{\text{V}}\text{O}}_{{2}}$$\end{document}mV˙O2 and complexity at 30º was likely due to low relative task demands, given the similar kinetics of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{m}\dot{\text{V}}\text{O}}_{{2}}$$\end{document}mV˙O2 and torque complexity. An inverse correlation between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{m}\dot{\text{V}}\text{O}}_{{2}}$$\end{document}mV˙O2 and knee-extensor torque complexity occurs during high-intensity contractions at intermediate, but not short, muscle lengths.

Physiological linkage during interactions between doctors and cancer patients

INTRODUCTION

Doctors and patients influence each other when interacting and, as a result, can become similar to each other in affect and behavior. In the current work, we examine whether they also become similar to each other on a moment-to-moment basis in their physiological responses. Specifically, we examine physiological linkage-how much a doctor's (or patient's) physiological response predicts a patient's (or doctor's) response at a subsequent time interval-and whether this changes over the course of doctor-patient relationships (measured as the number of consultations held for each unique doctor-patient dyad).

METHODS

We collected interbeat interval responses (IBI) continuously during consultations between oncologists and patients undergoing cancer treatment (N = 102 unique doctor-patient interactions) at a hospital in Austria.

RESULTS

Physiological linkage varied by an interaction between role (doctor vs. patient) and relationship length (in a non-linear, quadratic pattern). Patients showed significant positive linkage to their doctors (i.e., doctors' physiological responses positively, significantly predicted patients' responses) in relationships that spanned three to eight consultations together. Patients were not linked to their doctors in shorter or longer relationships. Doctors were never significantly linked to their patients, meaning that patients' physiological responses never predicted doctors' responses.

CONCLUSION

These results reveal that, by influencing patients' physiological responses on a moment-to-moment basis, doctors may have even more influence over patients' physiology than previously known.

Prescribed-time cluster lag consensus control for second-order non-linear leader-following multiagent systems

Prescribed-time Lag consensus, as a special case of prescribed-time cluster lag consensus, is first investigated. The task is to design a control protocol for each follower so that the multiagent system (MAS) achieves lag consensus in any specified time. To achieve this goal, we propose a new distributed controller, in which the control gains are designed as time-varying functions related to the pre-specified time. In addition, a state transformation is introduced to tackle the technical difficulty caused by time-varying functions of different powers in the theoretical proof process. Then, a solution for the cluster lag consensus problem of the MAS is provided, so that under the proposed control protocol, each subsystem composed of followers from the same group and the leader achieves lag consensus with a different lag time in the specified time. By using a state transformation, Graph theory and generalized Lyapunov stability theory, the validity of the designed schemes is verified theoretically and sufficient conditions for the two conclusions are given respectively. Finally, we give two simulation examples to show performances of the proposed solutions.

Rhythmic auditory stimuli modulate movement recovery in response to perturbation during locomotion

The capacity to recover after a perturbation is a well-known intrinsic property of physiological systems, including the locomotor system, and can be termed ‘resilience’. Despite an abundance of metrics proposed to measure the complex dynamics of bipedal locomotion, analytical tools for quantifying resilience are lacking. Here, we introduce a novel method to directly quantify resilience to perturbations during locomotion. We examined the extent to which synchronizing stepping with two different temporal structured auditory stimuli (periodic and 1/f structure) during walking modulates resilience to a large unexpected perturbation. Recovery time after perturbation was calculated from the horizontal velocity of the body's center of mass. Our results indicate that synchronizing stepping with a 1/f stimulus elicited greater resilience to mechanical perturbations during walking compared with the periodic stimulus (3.3 s faster). Our proposed method may help to gain a comprehensive understanding of movement recovery behavior of humans and other animals in their ecological contexts.

Summary: A new method for the evaluation of intrinsic resilience during unsteady locomotion in humans and animals, analysing the relationship between the structure of movement variability and resilience.

A non-linear analysis of running in the heavy and severe intensity domains

PURPOSE

Altered movement complexity, indicative of system dysfunction, has been demonstrated with increased running velocity and neuromuscular fatigue. The critical velocity (CV) denotes a metabolic and neuromuscular fatigue threshold. It remains unclear whether changes to complexity during running are coupled with the exercise intensity domain in which it is performed. The purpose of this study was to examine whether movement variability and complexity differ exclusively above the CV intensity during running.

METHODS

Ten endurance-trained participants ran at 95%, 100%, 105% and 115% CV for 20 min or to task failure, whichever occurred first. Movement at the hip, knee, and ankle were sampled throughout using 3D motion analysis. Complexity of kinematics in the first and last 30 s were quantified using sample entropy (SampEn) and detrended fluctuation analysis (DFA-α). Variability was determined using standard deviation (SD).

RESULTS

SampEn decreased during all trials in knee flexion/extension and it increased in hip internal/external rotation, whilst DFA-α increased in knee internal/external rotation. SD of ankle plantar/dorsiflexion and inversion/eversion, knee internal/external rotation, and hip flexion/extension and abduction/adduction increased during trials. Hip flexion/extension SampEn values were lowest below CV. DFA-α was lower at higher velocities compared to velocities below CV in ankle plantar/dorsiflexion, hip flexion/extension, hip adduction/abduction, hip internal/external rotation. In hip flexion/extension SD was highest at 115% CV.

CONCLUSIONS

Changes to kinematic complexity over time are consistent between heavy and severe intensity domains. The findings suggest running above CV results in increased movement complexity and variability, particularly at the hip, during treadmill running.

Effects of lumbosacral orthosis on dynamical structure of center of pressure fluctuations in patients with non-specific chronic low back pain: A randomized controlled trial

BACKGROUND

A few clinical trials have examined the effect of treatment interventions on postural control in patients with chronic low back pain, all of which have exclusively evaluated postural stability using traditional linear measures of postural sway. However, postural control improvement cannot be determined by exclusively relying on linear measurements, because these parameters provide no information on underlying motor control mechanisms.

OBJECTIVE

This study aimed to compare the effect of using lumbosacral orthoses (LSO) together with routine physical therapy, compared to routine physical therapy alone on postural control, using nonlinear analysis techniques.

METHODS

Forty-four patients with low back pain were randomly allocated to the intervention and control groups. Both groups underwent 8 sessions of physical therapy twice weekly for 4 weeks. The intervention group received LSO in addition to routine physical therapy. Before and after the intervention, non-linear dynamical features of center of pressure fluctuations were assessed during quiet standing at 3 difficulty levels of postural tasks, including eyes open while standing on a rigid surface, eyes closed while standing on a rigid surface, and eyes closed while standing on a foam surface.

RESULTS

The results of this study showed that a 4-week intervention consisting of LSO and routine physical therapy modalities did not affect the temporal structure of postural sways in patients with low back pain.

CONCLUSION

Treatment strategies, such as routine physical therapy modalities or LSO, which exclusively focus on the correction of peripheral mechanics, fail to affect the behavior of the postural control system.

Analysis and evaluation of handwriting in patients with Parkinson's disease using kinematic, geometrical, and non-linear features

BACKGROUND AND OBJECTIVES

Parkinson's disease is a neurological disorder that affects the motor system producing lack of coordination, resting tremor, and rigidity. Impairments in handwriting are among the main symptoms of the disease. Handwriting analysis can help in supporting the diagnosis and in monitoring the progress of the disease. This paper aims to evaluate the importance of different groups of features to model handwriting deficits that appear due to Parkinson's disease; and how those features are able to discriminate between Parkinson's disease patients and healthy subjects.

METHODS

Features based on kinematic, geometrical and non-linear dynamics analyses were evaluated to classify Parkinson's disease and healthy subjects. Classifiers based on K-nearest neighbors, support vector machines, and random forest were considered.

RESULTS

Accuracies of up to 93.1% were obtained in the classification of patients and healthy control subjects. A relevance analysis of the features indicated that those related to speed, acceleration, and pressure are the most discriminant. The automatic classification of patients in different stages of the disease shows κ indexes between 0.36 and 0.44. Accuracies of up to 83.3% were obtained in a different dataset used only for validation purposes.

CONCLUSIONS

The results confirmed the negative impact of aging in the classification process when we considered different groups of healthy subjects. In addition, the results reported with the separate validation set comprise a step towards the development of automated tools to support the diagnosis process in clinical practice.

Stimulation history affects vasomotor responses in rat mesenteric arterioles

Resistance vessels regulate blood flow by continuously adjusting activity of the wall smooth muscle cells. These cells integrate a variety of stimuli from blood, endothelium, autonomic nerves, and surrounding tissues. Each stimulus elicits an intracellular signaling cascade that eventually influences activation of the contractile machinery. The characteristic time scale of each cascade and the sharing of specific reactions between cascades provide for complex behavior when a vessel receives multiple stimuli. Here, we apply sequential stimulation with invariant concentrations of vasoconstrictor (norepinephrine/methoxamine) and vasodilator (SNAP/carbacol) to rat mesenteric vessels in the wire myograph to show that (1) time elapsed between addition of two vasoactive drugs and (2) the sequence of addition may significantly affect final force development. Furthermore, force oscillations (vasomotion) often appear upon norepinephrine administration. Using computational modeling in combination with nitric oxide (NO) inhibition/NO addition experiments, we show that (3) amplitude and number of oscillating vessels increase over time, (4) the ability of NO to induce vasomotion depends on whether it is applied before or after norepinephrine, and (5) emergence of vasomotion depends on the prior dynamical state of the system; in simulations, this phenomenon appears as "hysteresis." These findings underscore the time-dependent nature of vascular tone generation which must be considered when evaluating the vasomotor effects of multiple, simultaneous stimuli in vitro or in vivo.

Actigraphy as an objective intra-individual marker of activity patterns in acute-phase bipolar disorder: a case series

Background

Actigraphy could be an objective alternative to clinical ratings of motor activity in bipolar disorder (BD), which is of importance now that increased activity and energy are added as cardinal symptoms of (hypo)mania in the DSM-5 and commonly used rating scales give inadequate information about motor symptoms. To date, most actigraphy studies have been conducted in groups and/or used mean activity levels as the variable of interest. The novelty of this case series is therefore to indicate the potential of actigraphy and non-parametric analysis as an objective and personalized marker of intra-individual activity patterns in different phases of BD. To our knowledge, this is the first case series that provides an objective assessment of non-linear dynamics in within-person activity patterns during acute BD episodes.

Results

We report on three cases of bipolar I disorder with 24-h actigraphy recordings undertaken during the first few days of two or more separate admissions for an acute illness episode, including admissions for individuals in different phases of BD, or with different levels of severity in the same phase of illness. For each recording, we calculated mean activity levels over 24 h, but especially focused on key measures of variability and complexity in activity. Intra-individual activity patterns were found to be different according to phase of illness, but showed consistency within the same phase. With increasing psychotic symptoms, there was evidence of a lower overall level and greater irregularity in activity. As such, sample entropy (a measure of irregularity) may have particular utility in characterizing mania and psychotic symptoms, while assessment of the distribution of rest versus activity over 24 h may distinguish between phases of BD within an individual.

Conclusions

This case series indicates that objective, intra-individual, real-time recordings of patterns of activity may have clinical impact as a valuable adjunct to clinical observation and symptom ratings. We suggest that actigraphy combined with detailed mathematical analysis provides a biological variable that could become an important tool for developing a personalized approach to diagnostics and treatment monitoring in BD.

Electronic supplementary material

The online version of this article (10.1186/s40345-017-0115-3) contains supplementary material, which is available to authorized users.

Dynamic complexity measures and entropy paths for modelling and comparison of evolution of patients with drug resistant epileptic encephalopathy syndromes (DREES)

Epileptic encephalopathies (EE) is a term coined by the International League Against Epilepsy (ILAE) to refer to a group of epilepsies in which the ictal and interictal abnormalities may contribute to progressive cerebral dysfunction. Among them, two affect mainly children and are very difficult to deal with, Doose and Lennox-Gastaut syndromes, (DS and LGS, respectively). So far (Zavala-Yoe et al., J Integr Neurosci 15(2):205-223, 2015a and works of ours there), quantitative analysis of single case studies of EE have been performed. All of them are manifestations of drug resistant epileptic encephalopathies (DREES) and as known, such disorders require a lot of EEG studies through all patient's life. As a consequence, dozens of EEG records are stored by parents and neurologists as time goes by. However, taking into account all this massive information, our research questions (keeping colloquial wording by parents) arise: a) Which zone of the brain has been the most affected so far? b) On which year was the child better? c) How bad is our child with respect to others? We must reflect that despite clinical assessment of the EEG has undergone standardization by establishment of guidelines such as the recently published guidelines of the American Clinical Neurophysiology Society (Tsuchida et al., J Clin Neurophysiol 4(33):301-302, 2016), qualitative EEG will never be as objective as quantitative EEG, since it depends largely on the education and experience of the conducting neurophysiologist (Grant et al., Epilepsy Behav 2014(32):102-107, 2014, Rating, Z Epileptologie, Springer Med 27(2):139-142, 2014). We already answered quantitatively the above mentioned questions in the references of ours given above where we provided entropy curves and an entropy index which encompasses the complexity of bunches of EEG making possible to deal with massive data and to make objective comparisons among some patients simultaneously. However, we have refined that index here and we also offer another two measures which are spatial and dynamic. Moreover, from those indices we also provide what we call a temporal dynamic complexity path which shows in a standard 10-20 system head diagram the evolution of the lowest complexity per brain zone with respect to the EEG period. These results make it possible to compare quantitatively/graphically the progress of several patients at the same time, answering the questions posed above. The results obtained showed that we can associate low spatio-temporal entropy indices to multiple seizures events in several patients at the same time as well as tracking seizure progress in space and time with our entropy path, coinciding with neurophysiologists observations.

Gait alterations in the UAE population with and without diabetic complications using both traditional and entropy measures

Diabetic foot, one of the most common and debilitating manifestations of type 2 diabetes mellitus (T2DM), is the leading cause of worldwide non-traumatic lower extremity amputations. Diabetics who are at risk of ulceration are currently mainly identified by a thorough clinical examination of the feet, which typically does not show clear symptoms during the early stages of disease progression. In this study, we used a non-linear dynamics tool, gait entropy (GaitEN), in addition to traditional linear gait analysis methods, to investigate gait alterations amongst diabetic patients with combinations of three types of T2DM related complications: retinopathy, diabetic peripheral neuropathy (DPN) and nephropathy. Peak plantar pressure (PPP) was not significantly different in the group with DPN as compared to the control group (diabetics with no complications, CONT) in the forefoot region (DPN: mean±SD: 396±69.4kPa, CONT: 409±68.9kPa), although it was significantly lower in the heel region (DPN: mean±SD: 285±43.1.4kPa, CONT: 295±61.8kPa). On the other hand, gait entropy was significantly lower for the DPN compared to CONT group (DPN: 0.95±0.34, CONT: 1.03±0.28, p<0.05). The significant low entropy was maintained when neuropathy was combined with either retinopathy or nephropathy. For the group with all three complications (ALL-C), the entropy was higher than CONT (ALL-C: 1.07±0.26). This may indicate an intrinsic sensorimotor feedback mechanism for the DPN patients to regulate their gait. However, this feedback gets weaker as patients develop multiple complications. Further analysis with longer walking time and different speeds is needed to verify the entropy results.

A pilot study to determine whether combinations of objectively measured activity parameters can be used to differentiate between mixed states, mania, and bipolar depression

BACKGROUND

Until recently, actigraphy studies in bipolar disorders focused on sleep rather than daytime activity in mania or depression, and have failed to analyse mixed episodes separately. Furthermore, even those studies that assessed activity parameters reported only mean levels rather than complexity or predictability of activity. We identified cases presenting in one of three acute phases of bipolar disorder and examined whether the application of non-linear dynamic models to the description of objectively measured activity can be used to predict case classification.

METHODS

The sample comprised 34 adults who were hospitalized with an acute episode of mania (n = 16), bipolar depression (n = 12), or a mixed state (n = 6), who agreed to wear an actiwatch for a continuous period of 24 h. Mean level, variability, regularity, entropy, and predictability of activity were recorded for a defined 64-min active morning and active evening period. Discriminant function analysis was used to determine the combination of variables that best classified cases based on phase of illness.

RESULTS

The model identified two discriminant functions: the first was statistically significant and correlated with intra-individual fluctuation in activity and regularity of activity (sample entropy) in the active morning period; the second correlated with several measures of activity from the evening period (e.g. Fourier analysis, autocorrelation, sample entropy). A classification table generated from both functions correctly classified 79% of all cases based on phase of illness (χ ² = 36.21; df 4; p = 0.001). However, 42% of bipolar depression cases were misclassified as being in manic phase.

CONCLUSIONS

The findings should be treated with caution as this was a small-scale pilot study and we did not control for prescribed treatments, medication adherence, etc. However, the insights gained should encourage more widespread adoption of statistical approaches to the classification of cases alongside the application of more sophisticated modelling of activity patterns. The difficulty of accurately classifying cases of bipolar depression requires further research, as it is unclear whether the lower prediction rate reflects weaknesses in a model based only on actigraphy data, or if it reflects clinical reality i.e. the possibility that there may be more than one subtype of bipolar depression.

Mathematical modelling of cytokines, MMPs and fibronectin fragments in osteoarthritic cartilage

Osteoarthritis (OA) is a degenerative disease which causes pain and stiffness in joints. OA progresses through excessive degradation of joint cartilage, eventually leading to significant joint degeneration and loss of function. Cytokines, a group of cell signalling proteins, present in raised concentrations in OA joints, can be classified into pro-inflammatory and anti-inflammatory groups. They mediate cartilage degradation through several mechanisms, primarily the up-regulation of matrix metalloproteinases (MMPs), a group of collagen-degrading enzymes. In this paper we show that the interactions of cytokines within cartilage have a crucial role to play in OA progression and treatment. We develop a four-variable ordinary differential equation model for the interactions between pro- and anti-inflammatory cytokines, MMPs and fibronectin fragments (Fn-fs), a by-product of cartilage degradation and up-regulator of cytokines. We show that the model has four classes of dynamic behaviour: homoeostasis, bistable inflammation, tristable inflammation and persistent inflammation. We show that positive and negative feedbacks controlling cytokine production rates can determine either a pre-disposition to OA or initiation of OA. Further, we show that manipulation of cytokine, MMP and Fn-fs levels can be used to treat OA, but we suggest that multiple treatment targets may be essential to halt or slow disease progression.

Investigations on dynamics of interacting cavitation bubbles in strong acoustic fields

Given its importance to the dynamics of cavitation bubbles, the mutual interaction between bubbles was carefully investigated in this work. The cavitation noises emitted in different sonication conditions were recorded to study the dynamical behavior of the bubbles. The frequency spectra of the noises suggest that the dispersing state of the bubbles severely influence the oscillations of bubbles, and that the nonlinear feature of the dynamics of cavitation bubbles, imposed by the mutual bubble-bubble interaction, gradually develops with the decrease of the dispersing height. Theoretical analysis shows that the size difference between the interacting bubbles should be responsible for the increase of nonlinearity of the oscillation, and that the decrease of the distance between them could effectively enhance the nonlinear feature of the oscillation of the bubble, both of which agree well with the experimental observation.

Complex intervention modelling should capture the dynamics of adaptation

Background

Complexity has been linked to health interventions in two ways: first as a property of the intervention, and secondly as a property of the system into which the intervention is implemented. The former recognizes that interventions may consist of multiple components that act both independently and interdependently, making it difficult to identify the components or combinations of components (and their contexts) that are important mechanisms of change. The latter recognizes that interventions are implemented in complex adaptive systems comprised of intelligent agents who modify their behaviour (including any actions required to implement the intervention) in an effort to improve outcomes relative to their own perspective and objectives. Although an intervention may be intended to take a particular form, its implementation and impact within the system may deviate from its original intentions as a result of adaptation. Complexity highlights the challenge in developing interventions as effective health solutions. The UK Medical Research Council provides guidelines on the development and evaluation of complex interventions. While mathematical modelling is included in the guidelines, there is potential for mathematical modeling to play a greater role.

Discussion

The dynamic non-linear nature of complex adaptive systems makes mathematical modelling crucial. However, the tendency is for models of interventions to limit focus on the ecology of the system - the ‘real-time’ operation of the system and impacts of the intervention. These models are deficient by not modelling the way the system reacts to the intervention via agent adaptation. Complex intervention modelling needs to capture the consequences of adaptation through the inclusion of an evolutionary dynamic to describe the long-term emergent outcomes that result as agents respond to the ecological changes introduced by intervention in an effort to produce better outcomes for themselves. Mathematical approaches such as those found in economics in evolutionary game theory and mechanism design can inform the design and evaluation of health interventions. As an illustration, the introduction of a central screening clinic is modeled as an example of a health services delivery intervention.

Summary

Complexity necessitates a greater role for mathematical models, especially those that capture the dynamics of human actions and interactions.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-016-0149-8) contains supplementary material, which is available to authorized users.

Entropy of cardiac repolarization predicts ventricular arrhythmias and mortality in patients receiving an implantable cardioverter-defibrillator for primary prevention of sudden death

AIMS

The need for a readily available, inexpensive, non-invasive method for improved risk stratification of heart failure (HF) patients is paramount. Prior studies have proposed that distinct fluctuation patterns underlying the variability of physiological signals have unique prognostic value. We tested this hypothesis in an extensively phenotyped cohort of HF patients using EntropyX_QT, a novel non-linear measure of cardiac repolarization dynamics.

METHODS AND RESULTS

In a prospective, multicentre, observational study of 852 patients in sinus rhythm undergoing clinically indicated primary prevention implantable cardioverter-defibrillator (ICD) implantation (2003-10), exposures included demographics, history, physical examination, medications, laboratory results, serum biomarkers, ejection fraction, conventional electrocardiographic (ECG) analyses of heart rate and QT variability, and EntropyX_QT. The primary outcome was first 'appropriate' ICD shock for ventricular arrhythmias. The secondary outcome was composite events (appropriate ICD shock and all-cause mortality). After exclusions, the cohort (n = 816) had a mean age of 60 ± 13 years, 28% women, 36% African Americans, 56% ischaemic cardiomyopathy, and 29 ± 16% Seattle HF risk score (SHFS) 5-year predicted mortality. Over 45 ± 24 months, there were 134 appropriate shocks and 166 deaths. After adjusting for 30 exposures, the hazard ratios (comparing the 5th to 1st quintile of EntropyX_QT) for primary and secondary outcomes were 3.29 (95% CI 1.74-6.21) and 2.28 (1.53-3.41), respectively. Addition of EntropyX_QT to a model comprised of the exposures or SHFS significantly increased net reclassification and the ROC curve area.

CONCLUSIONS

EntropyX_QT measured during ICD implantation strongly and independently predicts appropriate shock and all-cause mortality over follow-up. EntropyX_QT complements conventional risk predictors and has the potential for broad clinical application.

Complexity and variability of the center of pressure time series during quiet standing in patients with knee osteoarthritis

BACKGROUND

While several studies have investigated the traditional linear measures in patients with knee osteoarthritis, no study has yet reported the non-linear structure of postural sway in these patients.

METHODS

We used two non-linear methods, recurrence quantification analysis (percent of determinism-%DET) and central tendency measure, to respectively investigate differences in the complexity and variability of sway dynamics between two groups of knee osteoarthritis patients (n=27) and healthy controls (n=27) under different conditions of postural and cognitive tasks. The experimental conditions included standing on (1) rigid surface with open eyes; (2) rigid surface with closed eyes; (3) foam surface with open eyes; and (4) foam surface with closed eyes. All these conditions were performed isolated (single-task) and while performing concurrent cognitive task (dual-task).

FINDINGS

The results showed greater %DET and lesser central tendency measure (both in mediolateral direction) in patients compared with healthy subjects. Moreover, in both groups, the %DET increased and central tendency measure decreased with increasing postural difficulty while %DET decreased and central tendency measure increased when moving from single- to dual-task conditions.

INTERPRETATIONS

The complexity loss was observed in patients compared with healthy controls. The observed increase in the variability coupled with a decrease in the complexity could be explained by the exploratory behavior of postural control system to gather information during difficult postural conditions relative to the easy ones. Moreover, the observed increase in the complexity coupled with the decrease in the amount of variability may enhance the flow of information to facilitate the perceptual control of standing balance during dual-task conditions.

Cardiac autonomic modulation in non-frail, pre-frail and frail elderly women: a pilot study

Frailty has been defined as a geriatric syndrome that results in high vulnerability to health adverse outcomes. This increased vulnerability state results from dysregulation of multiple physiological systems and its complex interactions. Thus, assessment of physiological systems integrity and of its dynamic interactions seems to be useful in the context of frailty management. Heart rate variability (HRV) analysis provides information about autonomic nervous system (ANS) function, which is responsible to control several physiologic functions. This study investigated the cardiac autonomic modulation by HRV analysis in community-dwelling elderly women classified as non-frail, pre-frail and frail. Twenty-three elderly women were assigned to the following groups: non-frail (n = 8), pre-frail (n = 8) and frail (n = 7). HRV assessment was performed through linear and non-linear analysis of cardiac interval variability. It was observed a higher sympathetic and lower parasympathetic modulation in frail when compared with non-frail and pre-frail groups (p < 0.05) as indicated by frequency domain indices. Additionally, frail group had a decreased 2LV % pattern (that reflects parasympathetic modulation) in the symbolic analysis in comparison with non-frail group. These findings suggest that frail elderly women present an autonomic imbalance characterized by a shift towards sympathetic predominance. Thus, monitoring ANS function in the context of frailty management may be an important strategy to prevention, diagnosis and treatment of this syndrome and its consequences.

Sensor positioning and experimental constraints influence estimates of local dynamic stability during repetitive spine movements

Application of non-linear dynamics analyses to study human movement has increased recently, which necessitates an understanding of how dependent measures may be influenced by experimental design and setup. Quantifying local dynamic stability for a multi-articulated structure such as the spine presents the possibility for estimates to be influenced by positioning of kinematic sensors used to measure spine angular kinematics. Oftentimes researchers will also choose to constrain the spine's movement by physically restraining the pelvis and/or using targets to control movement endpoints. Ten healthy participants were recruited, and asked to perform separate trials of 35 consecutive cycles of spine flexion under both constrained and unconstrained conditions. Electromagnetic sensors that measure three-dimensional angular orientations were positioned over the pelvis and the spinous processes of L3, L1, and T11. Using the pelvic sensor as a reference, each sensor location on the spine was used to obtain a different representation of the three-dimensional spine angular kinematics. Local dynamic stability of each kinematic time-series was determined by calculating the maximum finite-time Lyapunov exponent (λmax). Estimates for λmax were significantly lower (i.e. dynamically more stable) for spine kinematic data obtained from the L3 sensor than those obtained from kinematic data using either the L1 or T11 sensors. Likewise, λmax was lower when the movement was constrained. These results emphasize the importance of proper placement of instrumentation for quantifying local dynamic stability of spine kinematics and are especially relevant for repeated measures designs where data are obtained from the same individual on multiple days.

Time series prediction of lung cancer patients' breathing pattern based on nonlinear dynamics

This study focuses on predicting breathing pattern, which is crucial to deal with system latency in the treatments of moving lung tumors. Predicting respiratory motion in real-time is challenging, due to the inherent chaotic nature of breathing patterns, i.e. sensitive dependence on initial conditions. In this work, nonlinear prediction methods are used to predict the short-term evolution of the respiratory system for 62 patients, whose breathing time series was acquired using respiratory position management (RPM) system. Single step and N-point multi step prediction are performed for sampling rates of 5 Hz and 10 Hz. We compare the employed non-linear prediction methods with respect to prediction accuracy to Adaptive Infinite Impulse Response (IIR) prediction filters. A Local Average Model (LAM) and local linear models (LLMs) combined with a set of linear regularization techniques to solve ill-posed regression problems are implemented. For all sampling frequencies both single step and N-point multi step prediction results obtained using LAM and LLM with regularization methods perform better than IIR prediction filters for the selected sample patients. Moreover, since the simple LAM model performs as well as the more complicated LLM models in our patient sample, its use for non-linear prediction is recommended.

A microbial model of economic trading and comparative advantage

The economic theory of comparative advantage postulates that beneficial trading relationships can be arrived at by two self-interested entities producing the same goods as long as they have opposing relative efficiencies in producing those goods. The theory predicts that upon entering trade, in order to maximize consumption both entities will specialize in producing the good they can produce at higher efficiency, that the weaker entity will specialize more completely than the stronger entity, and that both will be able to consume more goods as a result of trade than either would be able to alone. We extend this theory to the realm of unicellular organisms by developing mathematical models of genetic circuits that allow trading of a common good (specifically, signaling molecules) required for growth in bacteria in order to demonstrate comparative advantage interactions. In Conception 1, the experimenter controls production rates via exogenous inducers, allowing exploration of the parameter space of specialization. In Conception 2, the circuits self-regulate via feedback mechanisms. Our models indicate that these genetic circuits can demonstrate comparative advantage, and that cooperation in such a manner is particularly favored under stringent external conditions and when the cost of production is not overly high. Further work could involve implementing the models in living bacteria and searching for naturally occurring cooperative relationships between bacteria that conform to the principles of comparative advantage.

Dynamic instability during post-stroke hemiparetic walking

Falls and fall-related injuries cause extremely costly and potentially fatal health problems in people post-stroke. However, there is no global indicator of walking instability for detecting which individuals will have increased risk of falls. The purposes of this study were to directly quantify walking stability in stroke survivors and neurologically intact controls and to determine which stability measures would reveal the changes in walking stability following stroke. This study thus provided an initial step to establish objective measures for identifying potential fallers. Nine post-stroke individuals and nine controls walked on a treadmill at four different speeds. We computed short-term local divergence exponent (LDE) and maximum Floquet multiplier (maxFM) of the trunk motion, average and variability of dynamic margins of stability (MOS) and step spatiotemporal measures. Post-stroke individuals demonstrated larger short-term LDE (p = 0.002) and maxFM (p = 0.041) in the mediolateral (ML) direction compared to the controls but remained orbitally stable (maxFM < 1). In addition, post-stroke individuals walked with greater average step width (p = 0.003) but similar average ML MOS (p = 0.154) compared to the controls. Post-stroke individuals also exhibited greater variability in all MOS and step measures (all p < 0.005). Our findings indicate that post-stroke individuals walked with greater local and orbital instability and gait variability than neurologically intact controls. The results suggest that short-term LDE of ML trunk motion and the variability of MOS and step spatiotemporal measures detect the changes in walking stability associated with stroke. These stability measures may have the potential for identifying those post-stroke individuals at increased risk of falls.

Auditory and Nociceptive Stimuli Responses in the Electroencephalogram. A Non-linear Measures and Time-frequency Representation Based Analysis

INTRODUCTION

This article is part of the Focus Theme of Methods of Information in Medicine on "Biosignal Interpretation: Advanced Methods for Neural Signals and Images".

OBJECTIVES

An efficient way to investigate the neural basis of nociceptive responses is the analysis of the event-related brain potentials (ERPs). The main objective of this work was to study how adaptation and fatigue affect the ERPs to stimuli of different modalities, by characterizing the responses to infrequent and frequent stimulation in different recording periods.

METHODS

In this work, series of averaged EEG epochs recorded after thermal, electrical and auditory stimulation were analyzed with time-frequency representation and non-linear measures as spectral entropy and auto-mutual information function. The study was performed by considering the traditional EEG frequency bands.

RESULTS

The defined measures presented a statistical significance p-value < 0.01 and accuracy higher than 60% by differentiating windows of response to infrequent (I) and frequent (F) stimuli between the start and end of the EEG recording.

CONCLUSIONS

These measures permitted to observe some aspects of the subject's adaptation and the nociceptive response.

Mathematical modeling of the hypothalamic-pituitary-adrenal gland (HPA) axis, including hippocampal mechanisms

This paper presents a mathematical model of the HPA axis. The HPA axis consists of the hypothalamus, the pituitary and the adrenal glands in which the three hormones CRH, ACTH and cortisol interact through receptor dynamics. Furthermore, it has been suggested that receptors in the hippocampus have an influence on the axis. A model is presented with three coupled, non-linear differential equations, with the hormones CRH, ACTH and cortisol as variables. The model includes the known features of the HPA axis, and includes the effects from the hippocampus through its impact on CRH in the hypothalamus. The model is investigated both analytically and numerically for oscillating solutions, related to the ultradian rhythm seen in data, and for multiple fixed points related to hypercortisolemic and hypocortisolemic depression. The existence of an attracting trapping region guarantees that solution curves stay non-negative and bounded, which can be interpreted as a mathematical formulation of homeostasis. No oscillating solutions are present when using physiologically reasonable parameter values. This indicates that the ultradian rhythm originate from different mechanisms. Using physiologically reasonable parameters, the system has a unique fixed point, and the system is globally stable. Therefore, solutions converge to the fixed point for all initial conditions. This is in agreement with cortisol levels returning to normal, after periods of mild stress, in healthy individuals. Perturbing parameters lead to a bifurcation, where two additional fixed points emerge. Thus, the system changes from having a unique stable fixed point into having three fixed points. Of the three fixed points, two are stable and one is unstable. Further investigations show that solutions converge to one of the two stable fixed points depending on the initial conditions. This could explain why healthy people becoming depressed usually fall into one of two groups: a hypercortisolemic depressive group or a hypocortisolemic depressive group.

Effects of mutual influence of photoinduced electron transitions and slow structural rearrangements in bacterial photosynthetic reaction centers

We describe the phenomenon of light-induced structural transformations in the reaction centers (RC) of photosynthetic bacteria which makes self-regulation of the RC charge separation efficiency possible. The nature of the effect is that the light-driven electron transfer (ET) between the RC redox-cofactors causes structural changes in the protein-cofactors system and this in turn affects the ET kinetics. If the electron-conformation interaction is strong enough, then such self-regulation gives birth to a new RC conformational state of enhanced charge separation efficiency. We show experimental results of stationary and kinetic absorbance change characteristics under different photoexcitation conditions, indicating structural rearrangements on a rather long (minutes) time scale, mainly within the secondary acceptor binding pocket. To simplify the description, in constructing a theory of structure-function reorganization in the RC we employ the adiabatic approach. Final expressions enable us to make qualitative comparison with experimentally observed kinetics of the fast and slow stages of 'free' and 'structurally controlled' electron relaxation, respectively.