Pole balancing on the fingertip: model-motivated machine learning forecasting of falls.

Introduction: There is increasing interest in developing mathematical and computational models to forecast adverse events in physiological systems. Examples include falls, the onset of fatal cardiac arrhythmias, and adverse surgical outcomes. However, the dynamics of physiological systems are known to be exceedingly complex and perhaps even chaotic. Since no model can be perfect, it becomes important to understand how forecasting can be improved, especially when training data is limited. An adverse event that can be readily studied in the laboratory is the occurrence of stick falls when humans attempt to balance a stick on their fingertips. Over the last 20 years, this task has been extensively investigated experimentally, and presently detailed mathematical models are available. Methods: Here we use a long short-term memory (LTSM) deep learning network to forecast stick falls. We train this model to forecast stick falls in three ways: 1) using only data generated by the mathematical model (synthetic data), 2) using only stick balancing recordings of stick falls measured using high-speed motion capture measurements (human data), and 3) using transfer learning which combines a model trained using synthetic data plus a small amount of human balancing data. Results: We observe that the LTSM model is much more successful in forecasting a fall using synthetic data than it is in forecasting falls for models trained with limited available human data. However, with transfer learning, i.e., the LTSM model pre-trained with synthetic data and re-trained with a small amount of real human balancing data, the ability to forecast impending falls in human data is vastly improved. Indeed, it becomes possible to correctly forecast 60%-70% of real human stick falls up to 2.35 s in advance. Conclusion: These observations support the use of model-generated data and transfer learning techniques to improve the ability of computational models to forecast adverse physiological events.

Controlling stick balancing on a linear track: Delayed state feedback or delay-compensating predictor feedback?

A planar stick balancing task was investigated using stabilometry parameters (SP); a concept initially developed to assess the stability of human postural sway. Two subject groups were investigated: 6 subjects (MD) with many days of balancing a 90 cm stick on a linear track and 25 subjects (OD) with only one day of balancing experience. The underlying mechanical model is a pendulum-cart system. Two control force models were investigated by means of numerical simulations: (1) delayed state feedback (DSF); and (2) delay-compensating predictor feedback (PF). Both models require an internal model and are subject to certainty thresholds with delayed switching. Measured and simulated time histories were compared quantitatively using a cost function in terms of some essential SPs for all subjects. Minimization of the cost function showed that the control strategy of both OD and MD subjects can better be described by DSF. The control mechanism for the MD subjects was superior in two aspects: (1) they devoted less energy to controlling the cart's position; and (2) their perception threshold for the stick's angular velocity was found to be smaller. Findings support the concept that when sufficient sensory information is readily available, a delay-compensating PF strategy is not necessary.

Modeling pulsativity in the hypothalamic-pituitary-adrenal hormonal axis.

A new mathematical model for biological rhythms in the hypothalamic-pituitary-adrenal (HPA) axis is proposed. This model takes the form of a system of impulsive time-delay differential equations which include pulsatile release of adrenocorticotropin (ACTH) by the pituitary gland and a time delay for the release of glucocorticoid hormones by the adrenal gland. Numerical simulations demonstrate that the model's response to periodic and circadian inputs from the hypothalamus are consistent with those generated by recent models which do not include a pulsatile pituitary. In contrast the oscillatory phenomena generated by the impulsive delay equation mode occur even if the time delay is zero. The observation that the time delay merely introduces a small phase shift suggesting that the effects of the adrenal gland are "downstream" to the origin of pulsativity. In addition, the model accounts for the occurrence of ultradian oscillations in an isolated pituitary gland. These observations suggest that principles of pulse modulated control, familiar to control engineers, may have an increasing role to play in understanding the HPA axis.

Introduction to Focus Issue: Dynamical disease: A translational approach.

The concept of Dynamical Diseases provides a framework to understand physiological control systems in pathological states due to their operating in an abnormal range of control parameters: this allows for the possibility of a return to normal condition by a redress of the values of the governing parameters. The analogy with bifurcations in dynamical systems opens the possibility of mathematically modeling clinical conditions and investigating possible parameter changes that lead to avoidance of their pathological states. Since its introduction, this concept has been applied to a number of physiological systems, most notably cardiac, hematological, and neurological. A quarter century after the inaugural meeting on dynamical diseases held in Mont Tremblant, Québec [Bélair et al., Dynamical Diseases: Mathematical Analysis of Human Illness (American Institute of Physics, Woodbury, NY, 1995)], this Focus Issue offers an opportunity to reflect on the evolution of the field in traditional areas as well as contemporary data-based methods.

The effects of sensory quantization and control torque saturation on human balance control.

The effect of reaction delay, temporal sampling, sensory quantization, and control torque saturation is investigated numerically for a single-degree-of-freedom model of postural sway with respect to stability, stabilizability, and control effort. It is known that reaction delay has a destabilizing effect on the balancing process: the later one reacts to a perturbation, the larger the possibility of falling. If the delay is larger than a critical value, then stabilization is not even possible. In contrast, numerical analysis showed that quantization and control torque saturation have a stabilizing effect: the region of stabilizing control gains is greater than that of the linear model. Control torque saturation allows the application of larger control gains without overcontrol while sensory quantization plays a role of a kind of filter when sensory noise is present. These beneficial effects are reflected in the energy demand of the control process. On the other hand, neither control torque saturation nor sensory quantization improves stabilizability properties. In particular, the critical delay cannot be increased by adding saturation and/or sensory quantization.

Microchaos in human postural balance: Sensory dead zones and sampled time-delayed feedback.

Models for the stabilization of an inverted pendulum figure prominently in studies of human balance control. Surprisingly, fluctuations in measures related to the vertical displacement angle for quietly standing adults with eyes closed exhibit chaos. Here we show that small-amplitude chaotic fluctuations ("microchaos") can be generated by the interplay between three essential components of human neural balance control, namely time-delayed feedback, a sensory dead zone, and frequency-dependent encoding of force. When the sampling frequency of the force encoding is decreased, the sensitivity of the balance control to changes in the initial conditions increases. The sampled, time-delayed nature of the balance control may provide insights into why falls are more common in the very young and the elderly.

Quantization improves stabilization of dynamical systems with delayed feedback.

We show that an unstable scalar dynamical system with time-delayed feedback can be stabilized by quantizing the feedback. The discrete time model corresponds to a previously unrecognized case of the microchaotic map in which the fixed point is both locally and globally repelling. In the continuous-time model, stabilization by quantization is possible when the fixed point in the absence of feedback is an unstable node, and in the presence of feedback, it is an unstable focus (spiral). The results are illustrated with numerical simulation of the unstable Hayes equation. The solutions of the quantized Hayes equation take the form of oscillations in which the amplitude is a function of the size of the quantization step. If the quantization step is sufficiently small, the amplitude of the oscillations can be small enough to practically approximate the dynamics around a stable fixed point.

Phase resetting behavior in human gait is influenced by treadmill walking speed.

Gait is often modeled as a limit cycle oscillator. When perturbed, this type of system will reset its output in a stereotypical manner, which may be shifted in time with respect to its original trajectory. In contrast to other biological oscillators, relatively little is known regarding the phase resetting properties for human gait. Because humans must often reset their gait in response to perturbation, an improved understanding of this behavior may have implications for reducing the risk of fall. The purpose of this study was to further evaluate phase resetting behaviors in human gait with particular emphasis on (1) variance of the phase resetting response among healthy individuals and (2) the sensitivity of this response to walking speed. Seventeen healthy subjects walked on a treadmill at 2.0mph, 2.5mph, and 3.0mph while their right limb was perturbed randomly every 12-20 strides. Discrete, mechanical perturbations were applied by a rope that was attached to each subject's ankle and actuated by a motorized arm. Perturbations were applied once during a select stride, always at a different point in the swing phase, and the amount of phase shift that occurred on the subsequent stride was recorded. A subset of 8 subjects also walked at their preferred walking speed for 3 additional trials on a separate day in order to provide an estimate of within-subjects variability. The results suggested that phase resetting behavior is relatively consistent among subjects, but that minor variations in phase resetting behavior are attributable to walking at different treadmill speeds.

Whole-body vibration applied during upper body exercise improves performance.

Whole-body vibration (WBV) training has exercisers perform static and dynamic resistance training exercises on a ground-based platform. Exposure to WBV exposure has demonstrated benefits and no effect on lower body strength, power, and performance. The aim of this study was to determine if WBV exposure (50 Hz, 2.51 mm) has any potentiating effects postexercise by measuring the kinematic variables of a set of upper body elbow-extensor exercise (70% one-repetition maximum [1RM]) to volitional exhaustion. Sixteen recreationally active students (12 male and 4 female) performed 3 different experimental conditions on separate days. Each condition had the subjects perform 1 set of elbow-extension exercise to fatigue with 1 of 3 WBV treatments: WBV simultaneously during the set (AE); 60 seconds after application of WBV for 30 seconds (RE); and no WBV (CTRL). Kinematic parameters of each repetition were monitored by linking a rotary encoder to the highest load plate. The mean velocity and acceleration throughout the set and perceived exertion were analyzed. A significant increase (p < 0.05) was observed in the mean velocity for the whole set in the AE condition vs. the CTRL condition. The mean acceleration was significantly higher (p < 0.05) in the AE condition in comparison with RE (increased by 45.3%) and CTRL (increased by 50.4%) conditions. The positive effect induced by WBV on upper-limb performance is only achieved when the stimulus is applied during the exercise. However, WBV applied 60 seconds before upper body exercise results in no benefit.

Neuronal avalanches, epileptic quakes and other transient forms of neurodynamics.

Power-law behaviors in brain activity in healthy animals, in the form of neuronal avalanches, potentially benefit the computational activities of the brain, including information storage, transmission and processing. In contrast, power-law behaviors associated with seizures, in the form of epileptic quakes, potentially interfere with the brain's computational activities. This review draws attention to the potential roles played by homeostatic mechanisms and multistable time-delayed recurrent inhibitory loops in the generation of power-law phenomena. Moreover, it is suggested that distinctions between health and disease are scale-dependent. In other words, what is abnormal and defines disease it is not the propagation of neural activity but the propagation of activity in a neural population that is large enough to interfere with the normal activities of the brain. From this point of view, epilepsy is a disease that results from a failure of mechanisms, possibly located in part in the cortex itself or in the deep brain nuclei and brainstem, which truncate or otherwise confine the spatiotemporal scales of these power-law phenomena.

The delayed and noisy nervous system: implications for neural control.

Recent advances in the study of delay differential equations draw attention to the potential benefits of the interplay between random perturbations ('noise') and delay in neural control. The phenomena include transient stabilizations of unstable steady states by noise, control of fast movements using time-delayed feedback and the occurrence of long-lived delay-induced transients. In particular, this research suggests that the interplay between noise and delay necessitates the use of intermittent, discontinuous control strategies in which corrective movements are made only when controlled variables cross certain thresholds. A potential benefit of such strategies is that they may be optimal for minimizing energy expenditures associated with control. In this paper, the concepts are made accessible by introducing them through simple illustrative examples that can be readily reproduced using software packages, such as XPPAUT.

Spreading depression sends microglia on Lévy flights.

Spreading depression (SD) is thought to cause migraine aura, and perhaps migraine, and includes a transient loss of synaptic activity preceded and followed by increased neuronal excitability. Activated microglia influence neuronal activity and play an important role in homeostatic synaptic scaling via release of cytokines. Furthermore, enhanced neuronal function activates microglia to not only secrete cytokines but also to increase the motility of their branches, with somata remaining stationary. While SD also increases the release of cytokines from microglia, the effects on microglial movement from its synaptic activity fluctuations are unknown. Accordingly, we used time-lapse imaging of rat hippocampal slice cultures to probe for microglial movement associated with SD. We observed that in uninjured brain whole microglial cells moved. The movements were well described by the type of Lévy flight known to be associated with an optimal search pattern. Hours after SD, when synaptic activity rose, microglial cell movement was significantly increased. To test how synaptic activity influenced microglial movement, we enhanced neuronal activity with chemical long-term potentiation or LPS and abolished it with TTX. We found that microglial movement was significantly decreased by enhanced neuronal activity and significantly increased by activity blockade. Finally, application of glutamate and ATP to mimic restoration of synaptic activity in the presence of TTX stopped microglial movement that was otherwise seen with TTX. Thus, synaptic activity retains microglial cells in place and an absence of synaptic activity sends them off to influence wider expanses of brain. Perhaps increased microglial movements after SD are a long-lasting, and thus maladaptive, response in which these cells increase neuronal activity via contact or paracrine signaling, which results in increased susceptibility of larger brain areas to SD. If true, then targeting mechanisms that retard activity-dependent microglial Lévy flights may be a novel means to reduce susceptibility to migraine.

Projective clustering using neural networks with adaptive delay and signal transmission loss.

We develop a new neural network architecture for projective clustering of data sets that incorporates adaptive transmission delays and signal transmission information loss. The resultant selective output signaling mechanism does not require the addition of multiple hidden layers but instead is based on the assumption that the signal transmission velocity between input processing neurons and clustering neurons is proportional to the similarity between the input pattern and the feature vector (the top-down weights) of the clustering neuron. The mathematical model governing the evolution of the signal transmission delay, the short-term memory traces, and the long-term memory traces represents a new class of large-scale delay differential equations where the evolution of the delay is described by a nonlinear differential equation involving the similarity measure already noted. We give a complete description of the computational performance of the network for a wide range of parameter values.

Team research at the biology-mathematics interface: project management perspectives.

The success of interdisciplinary research teams depends largely upon skills related to team performance. We evaluated student and team performance for undergraduate biology and mathematics students who participated in summer research projects conducted in off-campus laboratories. The student teams were composed of a student with a mathematics background and an experimentally oriented biology student. The team mentors typically ranked the students' performance very good to excellent over a range of attributes that included creativity and ability to conduct independent research. However, the research teams experienced problems meeting prespecified deadlines due to poor time and project management skills. Because time and project management skills can be readily taught and moreover typically reflect good research practices, simple modifications should be made to undergraduate curricula so that the promise of initiatives, such as MATH-BIO 2010, can be implemented.

Epilepsy as a dynamic disease: a tutorial of the past with an eye to the future.

How can clinical epileptologists and computational neuroscientists learn to function together within the confines of interdisciplinary teams to develop new and more effective treatment strategies for epilepsy? Here we introduce epileptologists to the way modelers think about epilepsy as a dynamic disease. Not only is there terminology to be learned, but also it is necessary to identify those areas where clinical input might be expected to have the greatest impact. It is concluded that both groups have major roles to play in educating, evaluating, and shaping the direction of the efforts of each other.

Balancing with vibration: a prelude for "drift and act" balance control.

Stick balancing at the fingertip is a powerful paradigm for the study of the control of human balance. Here we show that the mean stick balancing time is increased by about two-fold when a subject stands on a vibrating platform that produces vertical vibrations at the fingertip (0.001 m, 15-50 Hz). High speed motion capture measurements in three dimensions demonstrate that vibration does not shorten the neural latency for stick balancing or change the distribution of the changes in speed made by the fingertip during stick balancing, but does decrease the amplitude of the fluctuations in the relative positions of the fingertip and the tip of the stick in the horizontal plane, A(x,y). The findings are interpreted in terms of a time-delayed "drift and act" control mechanism in which controlling movements are made only when controlled variables exceed a threshold, i.e. the stick survival time measures the time to cross a threshold. The amplitude of the oscillations produced by this mechanism can be decreased by parametric excitation. It is shown that a plot of the logarithm of the vibration-induced increase in stick balancing skill, a measure of the mean first passage time, versus the standard deviation of the A(x,y) fluctuations, a measure of the distance to the threshold, is linear as expected for the times to cross a threshold in a stochastic dynamical system. These observations suggest that the balanced state represents a complex time-dependent state which is situated in a basin of attraction that is of the same order of size. The fact that vibration amplitude can benefit balance control raises the possibility of minimizing risk of falling through appropriate changes in the design of footwear and roughness of the walking surfaces.

Introduction to focus issue: bipedal locomotion--from robots to humans.

Running and walking, collectively referred to as bipedal locomotion, represent self-organized behaviors generated by a spatially distributed dynamical system operating under the constraint that a person must be able to move without falling down. The organizing principles involve both forces actively regulated by the nervous system and those generated passively by the biomechanical properties of the musculoskeletal system and the environment in which the movements occur. With the development of modern motion capture and electrophysiological techniques it has become possible to explore the dynamical interplay between the passive and active controllers of locomotion in a manner that directly compares observation to predictions made by relevant mathematical and computer models. Consequently, many of the techniques initially developed to study nonlinear dynamical systems, including stability analyses, phase resetting and entrainment properties of limit cycles, and fractal and multifractal analysis, have come to play major roles in guiding progress. This Focus Issue discusses bipedal locomotion from the point of view of dynamical systems theory with the goal of stimulating discussion between the dynamical systems, physics, biomechanics, and neuroscience communities.

On the road to automatic: dynamic aspects in the development of expertise.

One of the important steps on the road to becoming expert in a motor skill occurs when the individual can perform the movements in a seemingly effortless and automatic fashion. The authors review two lines of investigations, namely, fMRI and mathematically guided studies of the dynamics of skill acquisition, that suggest that this road to automatic involves two steps: (1) an increasing reliance on the self-regulatory aspects of the motor task, and (2) a minimization of the role of mechanisms based on intentionally directed corrective movements. The interplay between these two mechanisms implies that, at a given skill level, performance decreases whenever intention intervenes. The observation that psychological factors may be as important as mechanical repetition for the development of expertise has important implications for the design of neurorehabilitative strategies.