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.

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.

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.

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.

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.

Human stick balancing: tuning Lèvy flights to improve balance control

State-dependent, or parametric, noise is an essential component of the neural control mechanism for stick balancing at the fingertip. High-speed motion analysis in three dimensions demonstrates that the controlling movements made by the fingertip during stick balancing can be described by a Lèvy flight. The Lèvy index, alpha, is approximately 0.9; a value close to optimal for a random search. With increased skill, the index alpha does not change. However, the tails of the Lèvy distribution become broader. These observations suggest a Lèvy flight that is truncated by the properties of the nervous and musculoskeletal system; the truncation decreasing as skill level increases. Measurements of the cross-correlation between the position of the tip of the stick and the fingertip demonstrate that the role of closed-loop feedback changes with increased skill. Moreover, estimation of the neural latencies for stick balancing show that for a given stick length, the latency increases with skill level. It is suggested that the neural control for stick balancing involves a mechanism in which brief intervals of consciously generated, corrective movements alternate with longer intervals of prediction-free control. With learning the truncation of the Lèvy flight becomes better optimized for balance control and hence the time between successive conscious corrections increases. These observations provide the first evidence that changes in a Lèvy flight may have functional significance for the nervous system. This work has implications for the control of balancing problems ranging from falling in the elderly to the design of two-legged robots and earthquake proof buildings.

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.

Amplitude and frequency dependence of spike timing: implications for dynamic regulation

The spike-time reliability of motoneurons in the Aplysia buccal motor ganglion was studied as a function of the frequency content and the relative amplitude of the fluctuations in the neuronal input, calculated as the coefficient of variation (CV). Measurements of spike-time reliability to sinusoidal and aperiodic inputs, as well as simulations of a noisy leaky integrate-and-fire neuron stimulated by spike trains drawn from a periodically modulated process, demonstrate that there are three qualitatively different CV-dependent mechanisms that determine reliability: noise-dominated (CV < 0.05 for Aplysia motoneurons) where spike timing is unreliable regardless of frequency content; resonance-dominated (CV approximately 0.05-0.25) where reliability is reduced by removal of input frequencies equal to motoneuron firing rate; and amplitude-dominated (CV >0.35) where reliability depends on input frequencies greater than motoneuron firing rate. In the resonance-dominated regime, changes in the activity of the presynaptic inhibitory interneuron B4/5 alter motoneuron spike-time reliability. The increases or decreases in reliability occur coincident with small changes in motoneuron spiking rate due to changes in interneuron activity. Injection of a hyperpolarizing current into the motoneuron reproduces the interneuron-induced changes in reliability. The rate-dependent changes in reliability can be understood from the phase-locking properties of regularly spiking motoneurons to periodic inputs. Our observations demonstrate that the ability of a neuron to support a spike-time code can be actively controlled by varying the properties of the neuron and its input.

Transient inability to distinguish between faces: electrophysiologic studies

It is not known with certainty at which level of face processing by the cortex the distinction between a familiar and an unfamiliar face is made. Subdural electrodes were implanted under the fusiform gyrus of the right temporal lobe in a patient who developed an unusual inability to distinguish differences between faces as part of the epileptic aura ("all faces looked the same"). A cortical region located posterior to the epileptic focus was identified that exhibited a maximum evoked response to the presentation of facial images (N165), but not to objects, scenes, or character strings. Evoked potentials elicited by a variety of visual images indicated that any perturbation away from novel whole-face stimuli produced submaximal responses from this region of the right temporal lobe. Electrical stimulation of this region resulted in an impairment of face discrimination. It was found that presentation of familiar faces (grandmother, treating physician) produced a different response from that observed for novel faces. These observations demonstrate that within 165 msec of face presentation, and before the conscious precept of face familiarity has formed, this cortical region has already begun to distinguish between a familiar and an unfamiliar face.

On-off intermittency in a human balancing task

Motion analysis in three dimensions demonstrate that the fluctuations in the vertical displacement angle of a stick balanced at the fingertip obey a scaling law characteristic of on-off intermittency and that >98% of the corrective movements occur fast compared to the measured time delay. These experimental observations are reproduced by a model for an inverted pendulum with time-delayed feedback in which parametric noise forces a control parameter across a particular stability boundary. Our observations suggest that parametric noise is an essential, but up until now underemphasized, component of the neural control of balance.

Synaptic heterogeneity and stimulus-induced modulation of depression in central synapses

Short-term plasticity is a pervasive feature of synapses. Synapses exhibit many forms of plasticity operating over a range of time scales. We develop an optimization method that allows rapid characterization of synapses with multiple time scales of facilitation and depression. Investigation of paired neurons that are postsynaptic to the same identified interneuron in the buccal ganglion of Aplysia reveals that the responses of the two neurons differ in the magnitude of synaptic depression. Also, for single neurons, prolonged stimulation of the presynaptic neuron causes stimulus-induced increases in the early phase of synaptic depression. These observations can be described by a model that incorporates two availability factors, e.g., depletable vesicle pools or desensitizing receptor populations, with different time courses of recovery, and a single facilitation component. This model accurately predicts the responses to novel stimuli. The source of synaptic heterogeneity is identified with variations in the relative sizes of the two availability factors, and the stimulus-induced decrement in the early synaptic response is explained by a slowing of the recovery rate of one of the availability factors. The synaptic heterogeneity and stimulus-induced modifications in synaptic depression observed here emphasize that synaptic efficacy depends on both the individual properties of synapses and their past history.

Neural ensemble coding and statistical periodicity: speculations on the operation of the mind's eye

Statistical periodicity is a statistical property of densities which arises in the description of retarded dynamical systems. This property is particularly attractive as a possible mechanism for the ensemble coding of information in the nervous system because it operates rapidly and has high storage capacity. For a population of neurons which exhibits statistical periodicity, information would not be encoded by the periodicity, but rather by the spatio-temporal distributions of neural activity. Statistical periodicity is discussed in relation to the temporal binding hypothesis and to the occurrence of multistability in neural systems.

Spontaneous fluctuations in pupil size are not triggered by lens accommodation

Fluctuations in pupil size and lens accommodation are measured concurrently under open loop conditions, constant illumination and far fixation. In 12/17 trials no correlation was measured between the fluctuations in pupil size and lens accommodation. For the remaining 5/17 trials no lag was observed between the changes in pupil size and lens accommodation indicating that this correlation does not arise as a consequence of a near response. These observations suggest that under conditions of constant illumination and far fixation, the supranuclear centers controlling the near response are not active.

Resonance effect for neural spike time reliability

The spike timing reliability of Aplysia motoneurons stimulated by repeated presentation of periodic or aperiodic input currents is investigated. Two properties of the input are varied, the frequency content and the relative amplitude of the fluctuations to the mean (expressed as the coefficient of variation: CV). It is shown that, for small relative amplitude fluctuations (CV approximately 0.05-0.15), the reliability of spike timing is enhanced if the input contains a resonant frequency equal to the firing rate of the neuron in response to the DC component of the input. This resonance-related enhancement in reliability decreases as the relative amplitude of the fluctuations increases (CV-->1). Similar results were obtained for a leaky integrate-and-fire neuronal model, suggesting that these effects are a general property of encoders that combine a threshold with a leaky integrator. These observations suggest that, when the magnitude of input fluctuations is small, changes in the power spectrum of the current fluctuations or in the spike discharge rate can have a pronounced effect on the ability of the neuron to encode a time-varying input with reliably timed spikes.

Myoclonic-like finger microdisplacements in patients with cerebellar deficits

BACKGROUND

Here we assess the ability of patients with cerebellar disease to execute a simple visually-guided movement task involving tracking of a target with the index finger.

METHODS

Spontaneous microdisplacements in index finger position are compared in patients with cerebellar deficits (ischemia [n = 3], multiple sclerosis [n = 3], degenerative cerebellar disease [n = 3]) and age-matched healthy subjects. Subjects were required to maintain a constant finger position relative to a stationary baseline displayed on an oscilloscope.

RESULTS

Unusual transient abrupt movements (saccadic or myoclonic-like) directed with or against gravity were seen in patients whose neurological deficits were the most severe (7/9 patients). These abrupt myoclonic-like movements occurred independently of visual input, were not associated with clinically observable myoclonus, and were not detected previously in patients with Parkinson's disease. These abrupt myoclonic-like movements were not associated with abnormalities in either physiological tremor, or oscillations in finger microdisplacements induced by insertion of a delay (300-1400 ms) into the visual feedback of this finger "holding" experiment. An unexpected finding is that the results obtained for patients with cerebellar deficits by insertion of an experimental delay are not significantly different from those obtained with their age-matched controls.

CONCLUSIONS

These observations suggest that abrupt myoclonic-like movements are a characteristic abnormality of patients with a variety of cerebellar deficits and emphasize the value of this simple motor tracking task for characterizing movement disorders.

Cortical asymmetry of REM sleep EEG following unilateral pontine hemorrhage

A 24-year-old woman with a left pontine hematoma showed marked asymmetry in the EEG of REM sleep, suggesting that a unilateral pontine lesion is sufficient to disrupt normal REM sleep EEG in the ipsilateral hemisphere. Other REM sleep characteristics (rapid eye movements, muscle atonia) were unaffected by this lesion.

Delayed visual feedback and movement control in Parkinson's disease

The dependence of movement on visual information was compared for healthy individuals and Stage II-III patients with Parkinson's disease (PD). A time delay (0-1400 ms) was introduced into a visually guided motor tracking task which required the subject to maintain constant index finger position relative to a stationary baseline on an oscilloscope. For healthy individuals, delayed visual feedback induced complex oscillations in finger displacement. Similar results were obtained for four of eight patients with PD. However, oscillations were not induced in four of eight patients with PD because of reduced gain and/or a higher tremor amplitude at zero delay which obscured the tracking error. These results suggest that some patients with PD are able to utilize visual information for controlling tracking in this motor task in the same manner as healthy individuals.

Evaluation of pupil constriction and dilation from cycling measurements

Pupil cycling was produced using an electronic circuit so that the retina was illuminated in Maxwellian view only when pupil area exceeded an adjustable area threshold, Aref. The maximum (Amax) and minimum (Amin) amplitude of the oscillations varied linearly with Aref. These observations are described by a delay-differential equation. The Aref-dependent changes in Amax, Amin were used, respectively, to quantitate dilation and constriction. A comparison of the predicted and observed period of pupil cycling suggests that the latency times for light onset and offset are the same. Measurements of Amax, Amin provide a method for determining the average pupil light response.

A deterministic approach to survival statistics

Survival functions of the form p(t) = exp[-(lambda t) gamma], gamma greater than 0 can be generated by deterministic nonlinear, asymptotically stable (chaotic) dynamical systems. These systems thus provide an alternative to stochastic interpretations of failure time data. We use this approach to analyze cancer patient survival statistics. In this manner we are able to obtain fresh insights into the implications of negative and positive clinical trials.

Modelling autonomous oscillations in the human pupil light reflex using non-linear delay-differential equations

Neurophysiological and anatomical observations are used to derive a non-linear delay-differential equation for the pupil light reflex with negative feedback. As the gain or the time delay in the reflex is increased, a supercritical Hopf bifurcation occurs from a stable fixed point to a stable limit cycle oscillation in pupil area. A Hopf bifurcation analysis is used to determine the conditions for instability and the period and amplitude of these oscillations. The more complex waveforms typical of the occurrence of higher order bifurcations were not seen in numerical simulations of the model. This model provides a general framework to study the different types of dynamical behaviors which can be produced by the pupil light reflex, e.g. edge-light pupil cycling.

Irregular pupil cycling as a characteristic abnormality in patients with demyelinative optic neuropathy

We used an infrared videopupillometer combined with an electronic circuit that regulated the retinal light level as a function of pupil area to assess the regularity of pupil cycling in normal subjects and in patients with known abnormalities in the pupil light reflex pathways. The light stimulus was turned on whenever pupil area exceeded a preset value. Two types of abnormalities were observed for patients with demyelinative optic neuropathy: a failure of the pupil to cycle despite a preserved pupillary response to a single light pulse; and, for those patients in whom cycling was possible, a characteristic intermittent irregularity in the amplitude of pupil cycling. These abnormalities were not seen in normal subjects or in patients with ischemic optic neuropathy, surgical lesions involving the optic chiasm, Adie's syndrome, or Horner's syndrome.

Timing of seizure recurrence in adult epileptic patients: a statistical analysis

Seizure diaries were maintained prospectively in 24 epileptic patients (19 with partial complex, three with partial simple, and three with primary generalized seizures) who were selected consecutively, had stable seizure patterns, were reliable historians, and were known to be compliant with medications. Diaries were maintained for an average of 237 days (range, 61-365), and an average of 18 seizures were recorded per patient (range, 5-76). Seizure patterns were analyzed by using the methods appropriate for a time series of events (point process). Two patients had a decreasing trend in seizure frequency. For 12 patients, seizure occurrence was indistinguishable from that of a Poisson process. The remaining 10 patients had an exponential distribution of seizure intervals, but did not fit other criteria for a Poisson process; 3 of these showed evidence for seizure clustering; none showed evidence for a seizure cycle. It is concluded that the pattern of seizure occurrence in most epileptic people is random, but in approximately 50%, it is not occurring according to a Poisson process. These observations indicate that seizure cycling and/or clustering are not common in epileptic patients, but do not exclude the possibility that seizures have been precipitated by some randomly occurring event, such as sleep deprivation or increased stress.

Unusual properties of platelet shape in coronary and cerebral artery disease

Platelet shape was examined in freshly fixed whole blood, using phase contrast microscopy, from 7 patients post-myocardial infarction, 9 patients undergoing elective angiography for the investigation of angina, and 17 patients with stroke. Platelet shape was abnormal in 29/33 patients and in 20 of them the distribution of platelet shape did not resemble that produced by known platelet activators, by venipuncture techniques known to produce platelet activation, nor by shearing platelet-rich plasma. In particular, the proportion of spherical platelets is too high relative to the proportion of smooth discoid shaped platelets. Addition of platelet-poor plasma from a patient post-myocardial infarction to normal platelet-rich plasma did not reproduce the abnormality in platelet shape. In contrast, for patients post-myocardial infarction platelet shape was normal in platelet-rich plasma, but the platelets were hypersensitive to ADP-induced aggregation. Incubation of citrated whole blood at 37 degrees C resulted in an incomplete disappearance of the spherical platelets suggesting that the abnormal distribution of platelet shape consists of both a reversible and a more persistent abnormality. The reversible portion of the platelet shape abnormality seen in patients with stroke and coronary artery disease may be related to venipuncture-induced platelet activation; however, the nature of the persistent abnormality in platelet shape is presently unknown.