Insight into the transfer function,gain, and oscillation onset for the pupil light reflex using nonlinear delay-differential equations

Analogies are drawn between a physiologically relevant nonlinear delay-differential equation (DDE) model for the pupil light reflex and servo control analytic approaches. This DDE is shown to be consistent with the measured open loop transfer function and hence physiological insight can be obtained into the gain of the reflex and its properties. A Hopf bifurcation analysis of the DDE shows that a limit cycle oscillation in pupil area occurs when the first mode of the characteristic equation becomes unstable. Its period agrees well with experimental measurements. Beyond the point of instability onset, more modes become unstable corresponding to multiple encirclings of (-1, 0) on the Nyquist plot. These modes primarily influence the shape of the oscillation. Techniques from dynamical systems theory, e.g. bifurcation analysis, can augment servo control analytic methods for the study of oscillations produced by nonlinear neural feedback mechanisms.     

Identification of Hammerstein model for bioreactors with input multiplicities

A closed loop identification method of Hammerstein model for continuous bioreactor with input multiplicity is proposed. Hammerstein model consists of nonlinear steady-state gain followed by a unity gain linear system. The method consists of first getting local first order plus time delay (FOPTD) models around the two input multiplicity values of the substrate feed concentration. The model parameters of the FOPTD is identified by a least square optimization method. The initial guess for the model parameters are obtained from the settling time, the initial delay in the closed loop servo response and using a simple proportional controller formula. From the local process gain values obtained for the several step changes around the two operating conditions, the nonlinear gain portion of the Hammerstein is then obtained. The actual nonlinear gain and the identified nonlinear gain is compared.     

Adaptation of reflexive feedback during arm posture to different environments

 In this study we have examined the ability of the central nervous system (CNS) to use spinal reflexes to minimize displacements during postural control while continuous force perturbations were applied at the hand. The subjects were instructed to minimize the displacements of the hand from a reference position that resulted from the force perturbations. The perturbations were imposed in one direction by means of a hydraulic manipulator of which the virtual mass and damping were varied. Resistance to the perturbations came from intrinsic and reflexive stiffness, and from the virtual environment. It is hypothesized that reflexive feedback during posture maintenance is optimally adjusted such that position deviations are minimal for a given virtual environment. Frequency response functions were estimated, capturing all mechanical properties of the arm at the end point (hand) level. Intrinsic and reflexive parameters were quantified by fitting a linear neuromuscular model to the frequency responses. The reflexive length feedback gain increased strongly with damping and little with the eigenfrequency of the total combined system (i.e. arm plus environment). The reflexive velocity feedback gain decreased slightly with relative damping at the largest eigenfrequency and more markedly at smaller eigenfrequencies. In the case of highest reflex gains, the total system remained stable and sufficiently damped while the responses of only the arm were severely underdamped and sometimes even unstable. To further analyse these results, a model optimization was performed. Intrinsic and reflexive parameters were optimized such that two criterion functions were minimized. The first concerns performance and penalized hand displacements from a reference point. The second one weights afferent control effort to avoid inefficient feedback. The simulations showed good similarities with the estimated values. Length feedback was adequately predicted by the model for all conditions. The predicted velocity feedback gains were larger in all cases, probably indicating a mutual gain limiting relation between length and velocity afferent signals. The results suggest that both reflex gains seem to be adjusted by the CNS, where in particular the length feedback gain was optimal so as to maximize performance at minimum control effort. Received: 23 July 2001 / Accepted in revised form: 15 January 2002     

Stability analysis of CO2 control of ventilation

A theoretical analysis of the CO2 control of the respiratory system is presented using both analytic and simulation techniques. A stability index (SI) is obtained by linearizing a dynamic first-order model with a time delay. Analytically, SI values greater than unity predict an unstable response to a disturbance. Because the first-order model is reduced from a higher-order physiological model, SI can be algebraically related to physiological parameters. This relationship shows that SI increases with a decrease in system tissue volume, metabolic rate, or inspired CO2 partial pressure; SI decreases with a decrease in time delay, cardiac output, controller gain, or controller intercept. Analytically, SI distinguishes stable from unstable domains. By simulations of the nonlinear first-order model, three domains are obtained: an unstable domain (sustained oscillations, SI greater than 1.1), an underdamped stable domain (transient oscillations, 0.3 less than SI less than 1.1), and an overdamped stable domain (no oscillations, 0 less than SI less than 0.3). With this classification, disturbances such as change of state (e.g., from awake to asleep) or sigh may produce transient oscillations if the system becomes underdamped even though stable. Potential applications of this work include quantitative distinction of the physiological factors in control disorders associated with short-term periodicities (e.g., Cheyne-Stokes breathing, sleep apnea, breathing at altitude).     

Effect of tongue position on postural stability during quiet standing in healthy young males

Abstract

Background and aims: Role of the neck and jaw sensory motor system in control of body balance has been established. Tongue is an integral part of jaw sensory motor system and helps in execution of purposeful and precise motor tasks like eating, drinking and speaking. The purpose of this study was to evaluate the possible effects of tongue position on the postural control system.

Materials and method: We compared the mean center of gravity (COG) velocity during quiet standing on an unstable surface with eyes closed during two test conditions: (i) with habitual jaw resting position and (ii) with instructed tongue positioned against the upper incisors. One hundred and sixteen normal healthy male subjects (average age 31.56?±?8.51 years and height 170.86?±?7.26?cm) participated in the study. Their COG velocity (deg/s) was measured using the NeuroCom® Balance Master version 8.5.0 (Clackamas, OR, USA).

Results and conclusions: The results show that COG velocity decreased significantly while tongue was positioned against upper incisors in comparison to the habitual jaw resting position. Our findings suggest that the tongue positioning can modulate postural control mechanisms. Tongue positioning against the upper incisors can enhance the postural stability during upright standing on an unstable surface and in the absence of vision in healthy young adults. Our findings can be of value for evaluation and rehabilitation protocols for postural control dysfunction.     

Dynamic stability of a human standing on a balance board

The neuromuscular system used to stabilize upright posture in humans is a nonlinear dynamical system with time delays. The analysis of this system is important for improving balance and for early diagnosis of neuromuscular disease. In this work, we study the dynamic coupling between the neuromuscular system and a balance board—an unstable platform often used to improve balance in young athletes, and older or neurologically impaired patients. Using a simple inverted pendulum model of human posture on a balance board, we describe a surprisingly broad range of divergent and oscillatory CoP/CoM responses associated with instabilities of the upright equilibrium. The analysis predicts that a variety of sudden changes in the stability of upright postural equilibrium occurs with slow continuous deterioration in balance board stiffness, neuromuscular gain, and time delay associated with the changes in proprioceptive/vestibular/visual-neuromuscular feedback. The analysis also provides deeper insight into changes in the control of posture that enable stable upright posture on otherwise unstable platforms.     

Associations between trunk postural control in walking and unstable sitting at various levels of task demand

Trunk postural control (TPC) has been investigated in several populations and tasks. Previous work observed targeted training of TPC via isolated trunk control tasks may improve performance in other activities (e.g., walking). However, the nature of this relationship remains unknown. We therefore investigated the relationship between TPC, at both the global (i.e., response to finite perturbations) and local (i.e., resistance to continuous perturbations) levels, during walking and unstable sitting, both at varying levels of task demand. Thirteen individuals (11 Male, 2 Female) with no recent history (past 12 months) of illness, injury, or musculoskeletal disorders walked on a dual-belt treadmill at four speeds (−20%, −10%, +10%, and + 20% of self-selected walking speed) and completed an unstable sitting task at four levels of chair instability (100, 75, 60, and 45% of an individual’s “neutral” stability as defined by the gravitational gradient). Three-dimensional trunk and pelvic kinematics were collected. Tri-planar Lyapunov exponents and sample entropy characterized local TPC. Global TPC was characterized by ranges of motion and, for seated trials, metrics derived from center-of-pressure time series (i.e., path length, 95% confidence ellipse area, mean velocity, and RMS position). No strong or significant correlations (−0.057 < ρ < 0.206) were observed between local TPC during walking and unstable sitting tasks. However, global TPC declined in both walking and unstable sitting as task demand increased, with a moderate inter-task relationship (0.336 < ρ < 0.544). While the mechanisms regulating local TPC are inherently different, global TPC may be similarly regulated across both tasks, supporting future translation of improvements in TPC between tasks.     

Predicted threshold against backward balance loss in gait

The purpose of this study was to determine the minimum forward center of mass (COM) velocity required to prevent backward loss of balance in gait as function of the initial COM position. We hypothesized that these threshold values would be different from those previously published for standing because of the postural differences between gait and standing. To investigate this issue, we constructed a seven-link, nine-degree-of-freedom biomechanical model and employed dynamic optimization to estimate these threshold values under two initial postural conditions: (1) the posture at the beginning of swing phase (i.e., at toe-off), and (2) symmetric bipedal standing. In particular, for a range of possible COM positions posterior to the base of support (BOS), simulated annealing was used to search for the minimum velocity that could carry the COM into the BOS and avoid backward loss of balance. We found that the stability boundary against backward balance loss in walking had a similar overall trend as that previously published for standing. In general, the minimal COM velocity necessary to prevent a backward loss of balance in walking was greater than that in symmetric bipedal standing, and the difference could approach 30% or more when the COM started 0.5 and 1.0 foot-lengths behind the BOS. These discrepancies suggest that simpler biomechanical models, while being more efficient and easier to employ, may not always be adequate for exploring stability limits of humans.     

Modeling human postural sway using an intermittent control and hemodynamic perturbations

Ground reaction force during human quiet stance is modulated synchronously with the cardiac cycle through hemodynamics [1]. This almost periodic hemodynamic force induces a small disturbance torque to the ankle joint, which is considered as a source of endogenous perturbation that induces postural sway. Here we consider postural sway dynamics of an inverted pendulum model with an intermittent control strategy, in comparison with the traditional continuous-time feedback controller. We examine whether each control model can exhibit human-like postural sway, characterized by its power law behavior at the low frequency band 0.1–0.7 Hz, when it is weakly perturbed by periodic and/or random forcing mimicking the hemodynamic perturbation. We show that the continuous control model with typical feedback gain parameters hardly exhibits the human-like sway pattern, in contrast with the intermittent control model. Further analyses suggest that deterministic, including chaotic, slow oscillations that characterize the intermittent control strategy, together with the small hemodynamic perturbation, could be a possible mechanism for generating the postural sway.     

A novel approach to evaluate the permeability of cake layer during cross-flow filtration in the flocculants added membrane bioreactors

In order to obtain a better understanding of the cake layer formation mechanism in the flocculants added MBRs, a model was developed on the basis of particle packing model considering cake collapse effect and a frictional force balance equation to predict the porosity and permeability of the cake layers. The important characteristic parameters of the flocs (e.g., floc size, fractal dimensions) and operating parameters of MBRs (e.g., transmembrane pressure, cross-flow velocity) are considered in this model. With this new model, the calculated results of porosities and specific cake resistances under different MBR operational conditions agree fairly well with the experimental data.     

Bifurcation and stability analysis in musculoskeletal systems: a study in human stance

Reflexes are important in the control of such daily activities as standing and walking. The goal of this study is to establish how reflexive feedback of muscle length, velocity, and force can lead to stable equilibria (i.e., posture) and limit cycles (e.g., ankle clonus and gait). The influence of stretch reflexes on the behavior and stability of musculoskeletal systems was examined using a model of human stance. We computed branches of fold and Hopf bifurcations by numerical bifurcation analysis of the model. These fold and Hopf branches divide the parameter space, constructed by the reflexive feedback gains, into regions of different behavior: unstable posture, stable posture, and stable limit cycles. These limit cycles correspond to a neural deficiency, termed ankle clonus. We also linked bifurcation analysis to known biomechanical concepts by linearizing the model: the fold branch corresponds to zero ankle stiffness and defines the minimal muscle length feedback necessary for stable posture; the Hopf branch is related to unstable reflex loops. Crossing the Hopf branch can lead to the above-mentioned stable limit cycles. The Hopf branch reduces with increasing time delays, making the subjects posture more susceptible to unstable reflex loops. This might be one of the reasons why elderly people, or those with injuries to the central nervous system, often have trouble with standing and other posture tasks. The influence of cocontraction and force feedback on the behavior of the posture model was also investigated. An increase in cocontraction leads to an increase in ankle stiffness (i.e., intrinsic muscle stiffness) and a decrease in the effective reflex loop gain. On the one hand, positive force feedback increases the ankle stiffness (i.e., intrinsic and reflexive muscle stiffness); on the other hand it makes the posture more susceptible to unstable reflex loops. For negative force feedback, the opposite is true. Finally, we calculated areas of reflex gains for perturbed stance and quiet stance in healthy subjects by fitting the model to data from the literature. The overlap of these areas of reflex gains could indicate that stretch reflexes are the major control mechanisms in both quiet and perturbed stance. In conclusion, this study has successfully combined bifurcation analysis with the more common biomechanical concepts and tools to determine the influence of reflexes on the stability and quality of stance. In the future, we will develop this line of research to look at rhythmic tasks, such as walking.     

Simulating mechanical consequences of voluntary movement upon whole-body equilibrium: the arm-raising paradigm revisited

Voluntary arm-raising movement performed during the upright human stance position imposes a perturbation to an already unstable bipedal posture characterised by a high body centre of mass (CoM). Inertial forces due to arm acceleration and displacement of the CoM of the arm which alters the CoM position of the whole body represent the two sources of disequilibrium. A current model of postural control explains equilibrium maintenance through the action of anticipatory postural adjustments (APAs) that would offset any destabilising effect of the voluntary movement. The purpose of this paper was to quantify, using computer simulation, the postural perturbation due to arm raising movement. The model incorporated four links, with shoulder, hip, knee and ankle joints constrained by linear viscoelastic elements. The input of the model was a torque applied at the shoulder joint. The simulation described mechanical consequences of the arm-raising movement for different initial conditions. The variables tested were arm inertia, the presence or not of gravity field, the initial standing position and arm movement direction. Simulations showed that the mechanical effect of arm-raising movement was mainly local, that is to say at the level of trunk and lower limbs and produced a slight forward displacement of the CoM (1.5 mm). Backward arm-raising movement had the same effect on the CoM displacement as the forward arm-raising movement. When the mass of the arm was increased, trunk rotation increased producing a CoM displacement in the opposite direction when compared to arm movement performed without load. Postural disturbance was minimised for an initial standing posture with the CoM vertical projection corresponding to the ankle joint axis of rotation. When the model was reduced to two degrees of freedom (ankle and shoulder joints only) the postural perturbation due to arm-raising movement increased compared to the four-joints model. On the basis of these results the classical assumption that APAs stabilise the CoM is challenged.     

A complex adaptive systems approach to the kinetic folding of RNA

The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base pairs engage in local stacking interactions that determine the probabilities (or fitnesses) of possible SRs. Meanwhile, selection operates at the level of SRs; an autonomous stochastic process periodically (i.e., from one time step to another) selects a subset of possible SRs for realization based on the fitnesses of the SRs. Using examples based on selected natural and synthetic RNAs, the model is shown to reproduce characteristic (nonlinear) RNA folding dynamics such as the attainment by RNAs of alternative stable states. Possible applications of the model to the analysis of properties of fitness landscapes, and of the RNA sequence-to-structure mapping are discussed.     

Comparing internal models of the dynamics of the visual environment

It is well known that the human postural control system responds to motion of the visual scene, but the implicit assumptions it makes about the visual environment and what quantities, if any, it estimates about the visual environment are unknown. This study compares the behavior of four models of the human postural control system to experimental data. Three include internal models that estimate the state of the visual environment, implicitly assuming its dynamics to be that of a linear stochastic process (respectively, a random walk, a general first-order process, and a general second-order process). In each case, all of the coefficients that describe the process are estimated by an adaptive scheme based on maximum likelihood. The fourth model does not estimate the state of the visual environment. It adjusts sensory weights to minimize the mean square of the control signal without making any specific assumptions about the dynamic properties of the environmental motion.We find that both having an internal model of the visual environment and its type make a significant difference in how the postural system responds to motion of the visual scene. Notably, the second-order process model outperforms the human postural system in its response to sinusoidal stimulation. Specifically, the second-order process model can correctly identify the frequency of the stimulus and completely compensate so that the motion of the visual scene has no effect on sway. In this case the postural control system extracts the same information from the visual modality as it does when the visual scene is stationary. The fourth model that does not simulate the motion of the visual environment is the only one that reproduces the experimentally observed result that, across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases but the phase remains roughly constant. Our results suggest that the human postural control system does not estimate the state of the visual environment to respond to sinusoidal stimuli.     

Syncope, cerebral perfusion, and oxygenation.

During standing, both the position of the cerebral circulation and the reductions in mean arterial pressure (MAP) and cardiac output challenge cerebral autoregulatory (CA) mechanisms. Syncope is most often associated with the upright position and can be provoked by any condition that jeopardizes cerebral blood flow (CBF) and regional cerebral tissue oxygenation (cO(2)Hb). Reflex (vasovagal) responses, cardiac arrhythmias, and autonomic failure are common causes. An important defense against a critical reduction in the central blood volume is that of muscle activity ("the muscle pump"), and if it is not applied even normal humans faint. Continuous tracking of CBF by transcranial Doppler-determined cerebral blood velocity (V(mean)) and near-infrared spectroscopy-determined cO(2)Hb contribute to understanding the cerebrovascular adjustments to postural stress; e.g., MAP does not necessarily reflect the cerebrovascular phenomena associated with (pre)syncope. CA may be interpreted as a frequency-dependent phenomenon with attenuated transfer of oscillations in MAP to V(mean) at low frequencies. The clinical implication is that CA does not respond to rapid changes in MAP; e.g., there is a transient fall in V(mean) on standing up and therefore a feeling of lightheadedness that even healthy humans sometimes experience. In subjects with recurrent vasovagal syncope, dynamic CA seems not different from that of healthy controls even during the last minutes before the syncope. Redistribution of cardiac output may affect cerebral perfusion by increased cerebral vascular resistance, supporting the view that cerebral perfusion depends on arterial inflow pressure provided that there is a sufficient cardiac output.     

People Bouncing on Trampolines: Dramatic Energy Transfer,a Table-Top Demonstration,Complex Dynamics and a Zero Sum Game

Jumping on trampolines is a popular backyard recreation. In some trampoline games (e.g., “seat drop war”), when two people land on the trampoline with only a small time-lag, one person bounces much higher than the other, as if energy has been transferred from one to the other. First, we illustrate this energy-transfer in a table-top demonstration, consisting of two balls dropped onto a mini-trampoline, landing almost simultaneously, sometimes resulting in one ball bouncing much higher than the other. Next, using a simple mathematical model of two masses bouncing passively on a massless trampoline with no dissipation, we show that with specific landing conditions, it is possible to transfer all the kinetic energy of one mass to the other through the trampoline – in a single bounce. For human-like parameters, starting with equal energy, the energy transfer is maximal when one person lands approximately when the other is at the bottom of her bounce. The energy transfer persists even for very stiff surfaces. The energy-conservative mathematical model exhibits complex non-periodic long-term motions. To complement this passive bouncing model, we also performed a game-theoretic analysis, appropriate when both players are acting strategically to steal the other player''s energy. We consider a zero-sum game in which each player''s goal is to gain the other player''s kinetic energy during a single bounce, by extending her leg during flight. For high initial energy and a symmetric situation, the best strategy for both subjects (minimax strategy and Nash equilibrium) is to use the shortest available leg length and not extend their legs. On the other hand, an asymmetry in initial heights allows the player with more energy to gain even more energy in the next bounce. Thus synchronous bouncing unstable is unstable both for passive bouncing and when leg lengths are controlled as in game-theoretic equilibria.     

Multisensory fusion and the stochastic structure of postural sway

 We analyze the stochastic structure of postural sway and demonstrate that this structure imposes important constraints on models of postural control. Linear stochastic models of various orders were fit to the center-of-mass trajectories of subjects during quiet stance in four sensory conditions: (i) light touch and vision, (ii) light touch, (iii) vision, and (iv) neither touch nor vision. For each subject and condition, the model of appropriate order was determined, and this model was characterized by the eigenvalues and coefficients of its autocovariance function. In most cases, postural-sway trajectories were similar to those produced by a third-order model with eigenvalues corresponding to a slow first-order decay plus a faster-decaying damped oscillation. The slow-decay fraction, which we define as the slow-decay autocovariance coefficient divided by the total variance, was usually near 1. We compare the stochastic structure of our data to two linear control-theory models: (i) a proportional–integral–derivative control model in which the postural system's state is assumed to be known, and (ii) an optimal-control model in which the system's state is estimated based on noisy multisensory information using a Kalman filter. Under certain assumptions, both models have eigenvalues consistent with our results. However, the slow-decay fraction predicted by both models is less than we observe. We show that our results are more consistent with a modification of the optimal-control model in which noise is added to the computations performed by the state estimator. This modified model has a slow-decay fraction near 1 in a parameter regime in which sensory information related to the body's velocity is more accurate than sensory information related to position and acceleration. These findings suggest that: (i) computation noise is responsible for much of the variance observed in postural sway, and (ii) the postural control system under the conditions tested resides in the regime of accurate velocity information. Received: 20 March 2001 / Accepted: 17 April 2002 Acknowledgements. We thank Tjeerd Dijkstra for bringing the slow-decay component of postural sway to our attention. Funding for this research was provided by National Institutes of Health grant R29 N35070–01A2, John J. Jeka, PI. Correspondence to: T. Kiemel (Tel.: +1-301-4056176, Fax: +1-301-3149358 e-mail: kiemel@glue.umd.edu)     

Tissue Damage Disrupts Developmental Progression and Ecdysteroid Biosynthesis in Drosophila

In humans, chronic inflammation, severe injury, infection and disease can result in changes in steroid hormone titers and delayed onset of puberty; however the pathway by which this occurs remains largely unknown. Similarly, in insects injury to specific tissues can result in a global developmental delay (e.g. prolonged larval/pupal stages) often associated with decreased levels of ecdysone – a steroid hormone that regulates developmental transitions in insects. We use Drosophila melanogaster as a model to examine the pathway by which tissue injury disrupts developmental progression. Imaginal disc damage inflicted early in larval development triggers developmental delays while the effects are minimized in older larvae. We find that the switch in injury response (e.g. delay/no delay) is coincident with the mid-3rd instar transition – a developmental time-point that is characterized by widespread changes in gene expression and marks the initial steps of metamorphosis. Finally, we show that developmental delays induced by tissue damage are associated with decreased expression of genes involved in ecdysteroid synthesis and signaling.     

Financial Conflicts of Interest and Reporting Bias Regarding the Association between Sugar-Sweetened Beverages and Weight Gain: A Systematic Review of Systematic Reviews

Background

Industry sponsors'' financial interests might bias the conclusions of scientific research. We examined whether financial industry funding or the disclosure of potential conflicts of interest influenced the results of published systematic reviews (SRs) conducted in the field of sugar-sweetened beverages (SSBs) and weight gain or obesity.

Methods and Findings

We conducted a search of the PubMed, Cochrane Library, and Scopus databases to identify published SRs from the inception of the databases to August 31, 2013, on the association between SSB consumption and weight gain or obesity. SR conclusions were independently classified by two researchers into two groups: those that found a positive association and those that did not. These two reviewers were blinded with respect to the stated source of funding and the disclosure of conflicts of interest.We identified 17 SRs (with 18 conclusions). In six of the SRs a financial conflict of interest with some food industry was disclosed. Among those reviews without any reported conflict of interest, 83.3% of the conclusions (10/12) were that SSB consumption could be a potential risk factor for weight gain. In contrast, the same percentage of conclusions, 83.3% (5/6), of those SRs disclosing some financial conflict of interest with the food industry were that the scientific evidence was insufficient to support a positive association between SSB consumption and weight gain or obesity. Those reviews with conflicts of interest were five times more likely to present a conclusion of no positive association than those without them (relative risk: 5.0, 95% CI: 1.3–19.3).An important limitation of this study is the impossibility of ruling out the existence of publication bias among those studies not declaring any conflict of interest. However, the best large randomized trials also support a direct association between SSB consumption and weight gain or obesity.

Conclusions

Financial conflicts of interest may bias conclusions from SRs on SSB consumption and weight gain or obesity. Please see later in the article for the Editors'' Summary