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.

A standardized accelerometry method for characterizing tremor: Application and validation in an ageing population with postural and action tremor.

Background: Ordinal scales based on qualitative observation are the mainstay in the clinical assessment of tremor, but are limited by inter-rater reliability, measurement precision, range, and ceiling effects. Quantitative tremor evaluation is well-developed in research, but clinical application has lagged, in part due to cumbersome mathematical application and lack of established standards. Objectives: To develop a novel method for evaluating tremor that integrates a standardized clinical exam, wrist-watch accelerometers, and a software framework for data analysis that does not require advanced mathematical or computing skills. The utility of the method was tested in a sequential cohort of patients with predominant postural and action tremor presenting to a specialized surgical clinic with the presumptive diagnosis of Essential Tremor (ET). Methods: Wristwatch accelerometry was integrated with a standardized clinical exam. A MATLAB application was developed for automated data analysis and graphical representation of tremor. Measures from the power spectrum of acceleration of tremor in different upper limb postures were derived in 25 consecutive patients. The linear results from accelerometry were correlated with the commonly used non-linear Clinical Rating Scale for Tremor (CRST). Results: The acceleration power spectrum was reliably produced in all consecutive patients. Tremor frequency was stable in different postures and across patients. Both total and peak power of acceleration during postural conditions correlated well with the CRST. The standardized clinical examination with integrated accelerometry measures was therefore effective at characterizing tremor in a population with predominant postural and action tremor. The protocol is also illustrated on repeated measures in an ET patient who underwent Magnetic Resonance-Guided Focused Ultrasound thalamotomy. Conclusion: Quantitative assessment of tremor as a continuous variable using wristwatch accelerometry is readily applicable as a clinical tool when integrated with a standardized clinical exam and a user-friendly software framework for analysis. The method is validated for patients with predominant postural and action tremor, and can be adopted for characterizing tremor of different etiologies with dissemination in a wide variety of clinical and research contexts in ageing populations.

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.

Response to perturbation during quiet standing resembles delayed state feedback optimized for performance and robustness.

Postural sway is a result of a complex action-reaction feedback mechanism generated by the interplay between the environment, the sensory perception, the neural system and the musculation. Postural oscillations are complex, possibly even chaotic. Therefore fitting deterministic models on measured time signals is ambiguous. Here we analyse the response to large enough perturbations during quiet standing such that the resulting responses can clearly be distinguished from the local postural sway. Measurements show that typical responses very closely resemble those of a critically damped oscillator. The recovery dynamics are modelled by an inverted pendulum subject to delayed state feedback and is described in the space of the control parameters. We hypothesize that the control gains are tuned such that (H1) the response is at the border of oscillatory and nonoscillatory motion similarly to the critically damped oscillator; (H2) the response is the fastest possible; (H3) the response is a result of a combined optimization of fast response and robustness to sensory perturbations. Parameter fitting shows that H1 and H3 are accepted while H2 is rejected. Thus, the responses of human postural balance to "large" perturbations matches a delayed feedback mechanism that is optimized for a combination of performance and robustness.

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.

An integrate-and-fire model for pulsatility in the neuroendocrine system.

A model for pulsatility in neuroendocrine regulation is proposed which combines Goodwin-type feedback control with impulsive input from neurons located in the hypothalamus. The impulsive neural input is modeled using an integrate-and-fire mechanism; namely, inputs are generated only when the membrane potential crosses a threshold, after which it is reset to baseline. The resultant model takes the form of a functional-differential equation with continuous and impulsive components. Despite the impulsive nature of the inputs, realistic hormone profiles are generated, including ultradian and circadian rhythms, pulsatile secretory patterns, and even chaotic dynamics.

Human herpesvirus 6 meningitis in an adult.

Many cases of viral meningitis are idiopathic, but increased utilization of polymerase chain reaction testing has enabled physicians to better recognize rare causes of viral meningitis. This will likely continue to improve the rate of causative agent identification in seemingly idiopathic viral meningitis, including this case of human herpesvirus 6 (HHV-6) meningitis in an immunocompetent adult patient. More common viral etiologies need to be excluded before diagnosing HHV-6 meningitis, as this maximizes pretest probability and therefore increases validity of a positive result. By efficiently diagnosing HHV-6 meningitis, proper treatment protocols can be initiated earlier to reduce morbidity and mortality. Given the rarity of HHV-6 meningitis in immunocompetent adults, there are no established standard treatment guidelines; previous reported cases, as well as this case, suggest that either intravenous ganciclovir or intravenous foscarnet are the most reasonable first-line treatment options.

Mineral profiling of muscle and hepatic tissues of Australian Merino, Damara and Dorper lambs: Effect of weight loss.

Seasonal weight loss (SWL) is a major constraint to extensive animal production systems. The Australian sheep production is based on merino sheep, a European breed not tolerant to SWL. Tolerant alternative breeds such as the fat-tailed Damara and the Dorper have been increasingly used in Australia and elsewhere, due to their robustness. The aim of this study was to understand the mineral profile of muscle and liver tissues of Australian Merino, Damara and Dorper, when subjected to SWL in order to understand SWL-tolerance physiology. Twenty-four lambs were divided randomly between growing (control) and nutritionally restricted groups for each breed. The trial lasted 42 days. Animals were weighed bi-weekly and at the end of the trial, lambs were slaughtered. Liver and muscle samples were taken immediately after slaughter. Mineral assessment was carried out using inductively coupled plasma-optical emission spectrometry. Analysis of variance showed mineral concentrations were generally increased in the muscle of restricted animals, mainly because of fat tissue mobilization. An increase in Zn and Fe concentrations indicates an increase of enzymatic activity in the liver of restricted sheep as well as differential abundance of Fe-containing proteins. High concentrations of Cu in the liver of Dorper indicate higher ability to accumulate this element, even under SWL.

Acquisition of Cholera Within the United States.

Cholera has been woven into human history through numerous pandemics, with the most recent ongoing since 1961. Global rates of cholera continue to decline, but outbreaks continue to pose diagnostic challenges for clinicians, which delays initiation of treatment and prolongs the disease course. Despite millions of infections and thousands of deaths worldwide each year, cholera remains rare in the United States, with the few cases each year usually being the result of pathogen acquisition while the patient traveled abroad. This article presents a unique case of cholera acquired in the United States, which emphasizes the necessary vigilance of symptom recognition, in the context of appropriate clinical investigation, in ensuring that the patient had a full recovery. Cholera in the United States is exceedingly rare, yet effective diagnosis with early initiation of treatment is known to reduce mortality and shorten disease course. While other more common diagnoses must definitely be excluded first, it is important for cholera to be kept on the differential for patients presenting with treatment refractory, watery diarrhea causing hypotension. This case of a patient with a recent travel history to Hawaii and infection with cholera underscores the importance of investigative medicine and clinical expertise in optimizing patient care, even when presented with rare illnesses.

Establishing metrics and control laws for the learning process: ball and beam balancing.

Understanding how dexterity improves with practice is a fundamental challenge of motor control and neurorehabilitation. Here we investigate a ball and beam implementation of a dexterity puzzle in which subjects stabilize a ball at the mid-point of a beam by manipulating the angular position of the beam. Stabilizability analysis of different biomechanical models for the ball and beam task with time-delayed proportional-derivative feedback identified the angular position of the beam as the manipulated variable. Consequently, we monitored the changes in the dynamics with learning by measuring changes in the control parameters. Two types of stable motion are possible: node type (nonoscillatory) and spiral type (oscillatory). Both types of motion are observed experimentally and correspond to well-defined regions in the parameter space of the control gains. With practice the control gains for each subject move close to or on the portion of the boundary which separates the node-type and spiral-type solutions and which is associated with the rightmost characteristic exponent of smallest real part. These observations suggest that with learning the control gains for ball and beam balancing change in such a way that minimizes overshoot and the settling time. This study provides an example of how mathematical analysis together with careful experimental observations can shed light onto the early stages of skill acquisition. Since the difficulty of this task depends on the length of the beam, ball and beam balancing tasks may be useful for the rehabilitation of children with dyspraxia and those recovering from a stroke.

Virtual stick balancing: sensorimotor uncertainties related to angular displacement and velocity.

Sensory uncertainties and imperfections in motor control play important roles in neural control and Bayesian approaches to neural encoding. However, it is difficult to estimate these uncertainties experimentally. Here, we show that magnitude of the uncertainties during the generation of motor control force can be measured for a virtual stick balancing task by varying the feedback delay, τ. It is shown that the shortest stick length that human subjects are able to balance is proportional to τ  2. The proportionality constant can be related to a combined effect of the sensory uncertainties and the error in the realization of the control force, based on a delayed proportional-derivative (PD) feedback model of the balancing task. The neural reaction delay of the human subjects was measured by standard reaction time tests and by visual blank-out tests. Experimental observations provide an estimate for the upper boundary of the average sensorimotor uncertainty associated either with angular position or with angular velocity. Comparison of balancing trials with 27 human subjects to the delayed PD model suggests that the average uncertainty in the control force associated purely with the angular position is at most 14% while that associated purely with the angular velocity is at most 40%. In the general case when both uncertainties are present, the calculations suggest that the allowed uncertainty in angular velocity will always be greater than that in angular position.

Acting together, destabilizing influences can stabilize human balance.

The causes of falling in the elderly are multi-factorial. Three factors that influence balance stability are the time delay, a sensory dead zone and the maximum ankle torque that can be generated by muscular contraction. Here, the effects of these contributions are evaluated in the context of a model of an inverted pendulum stabilized by time-delayed proportional-derivative (PD) feedback. The effect of the sensory dead zone is to produce a hybrid type of control in which the PD feedback is switched ON or OFF depending on whether or not the controlled variable is larger or smaller than the detection threshold, Π. It is shown that, as Π increases, the region in the plane of control parameters where the balance time (BT) is greater than 60 s is increased slightly. However, when maximum ankle torque is also limited, there is a dramatic increase in the parameter region associated with BTs greater than 60 s. This increase is due to the effects of a torque limitation on over-control associated with bang-bang type switching controllers. These observations show that acting together influences, which are typically thought to destabilize balance, can actually stabilize balance. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

The ovine hepatic mitochondrial proteome: Understanding seasonal weight loss tolerance in two distinct breeds.

Seasonal weight loss (SWL) is a primary constraint for farmers in the Mediterranean and tropics. One cost-effective solution to SWL is utilizing breeds like the Damara sheep that have adapted to deal with nutritional stress. Previous studies concluded that one of the adaptation mechanisms of SWL is a specialized fatty acid metabolism. Accordingly, hepatic-mitochondrial proteomes were compared across two different breeds (24 sheep total, Merino, n = 12 and Damara, n = 12) and two different diets (restricted vs unrestricted diet, 6 per breed, per diet, 24 total). Mitochondrial-proteins were isolated and relatively quantified using Blue native PAGE / 2D-electrophoresis and then analyzed via mass spectrometry. The tool ReviGO summarized the proteomes' gene-ontology terms. A total of 50 proteins were identified with 7 changing significantly in abundance (ANOVA p-value<0.05). Specific abundance patterns of corticosteroid and inflammatory response-associated proteins such as annexin and glutamate dehydrogenase suggests that the Damara has an unusual inflammation response when subjected to SWL in addition to its unique metabolism. All significant proteins warrant further study; Annexin in particular shows promise as a potentially useful biomarker.

Outgrowing seizures in Childhood Absence Epilepsy: time delays and bistability.

We formulate a conductance-based model for a 3-neuron motif associated with Childhood Absence Epilepsy (CAE). The motif consists of neurons from the thalamic relay (TC) and reticular nuclei (RT) and the cortex (CT). We focus on a genetic defect common to the mouse homolog of CAE which is associated with loss of GABAA receptors on the TC neuron, and the fact that myelination of axons as children age can increase the conduction velocity between neurons. We show the combination of low GABAA mediated inhibition of TC neurons and the long corticothalamic loop delay gives rise to a variety of complex dynamics in the motif, including bistability. This bistability disappears as the corticothalamic conduction delay shortens even though GABAA activity remains impaired. Thus the combination of deficient GABAA activity and changing axonal myelination in the corticothalamic loop may be sufficient to account for the clinical course of CAE.

Ovine liver proteome: Assessing mechanisms of seasonal weight loss tolerance between Merino and Damara sheep.

The effect of feed restriction on the liver protein profiles of two different breeds of sheep was studied. We compared Merino with the Damara, breeds with respectively low and high tolerance to nutritional stress. Each breed was grouped into two nutritional treatments: restricted (12-14% loss of live weight) and control (maintenance). The trial lasted 42 days. Animals were sacrificed and liver samples subjected to label free shotgun proteomics. The resultant proteins had both their fold change and statistical significance in an unpaired t-test calculated to identify differential protein abundance. The tool WebGestalt was utilized to perform an Overrepresentation Enrichment Analysis (ORA) for gene ontology terms associated with the significant proteins. We further validated shotgun proteomics findings using a selected reaction monitoring (SRM)-based targeted proteomics approach, where similar trends in regulation were obtained for a subset of relevant proteins across an independent cohort of animals. Results confirm that Damara has adapted to nutritional stress by mobilizing stored fatty acids within adipose tissue and converting them to energy more efficiently than Merino. Finally, Merino had an overabundance pattern primarily directed to protein synthesis pathways. Regulated proteins identified may be used as a basis for marker selection towards tolerance to nutritional stress. BIOLOGICAL SIGNIFICANCE: Sheep are one of the most important livestock animals. They remain however poorly understudied and described. Seasonal weight loss (SWL) due to pasture scarcity during the dry season is one of the most limiting conditions to ruminant production in the tropics. To counter SWL, farmers may use supplementation, expensive or difficult to implement. A more suitable long-term solution would be to use breeds that are naturally adapted to nutritional stress. This work contrasts two breeds with different levels of tolerance to SWL, the Damara and the Merino, respectively well and poorly adapted. Comparison is conducted at the level of the hepatic tissue and using label free proteomics. This work identifies a series of pathways in the liver of the Damara via label free proteomics that suggest a unique fatty acid metabolic process within this breed. Proteins that have increased abundance in the Damara in association with fatty acid metabolism may be used as potential markers of tolerance to nutritional stress. This research will pave the way for more viable, long-term solutions for farmers facing annual production problems due to drought in the tropics and the Mediterranean region.

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.

The sheep (Ovis aries) muscle proteome: Decoding the mechanisms of tolerance to Seasonal Weight Loss using label-free proteomics.

Seasonal Weight Loss (SWL) is one of the most pressing issues in animal production in the tropics and Mediterranean. This work aims to characterize muscle proteome changes as a consequence of SWL in meat producing sheep, using a label-free proteomics approach. We compare three breeds: the Australian Merino (SWL susceptible), the Damara (SWL tolerant) and the Dorper (SWL intermediate tolerance). We identified 668 proteins of the sheep proteome, 95 with differential regulation. Also we observe that the more vulnerable to SWL a breed is, the more differential abundance proteins we find. Protein binding was the most frequently altered molecular function identified. We suggest 6 putative markers for restricted nutritional conditions independently of breed: ferritin heavy-chain; immunoglobulin V lambda chain; transgelin; fatty acid synthase; glutathione S-transferase A2; dihydrodiol dehydrogenase 3-like. Moreover, we suggest as related to SWL tolerance: S100-A10 Serpin A3-5-like and Catalase, subject however to necessary validation assays. The identification of SWL-tolerance related proteins using proteomics will lead to increased stock productivity of relevant interest to animal production, particularly if identified at the muscle level, the tissue of economic importance in meat production. BIOLOGICAL SIGNIFICANCE: Seasonal Weight Loss (SWL) is the most pressing issue in animal production in the tropics and the Mediterranean. To counter SWL, farmers often use animal breeds that have a natural ability to withstand pasture scarcity. Here we study the sheep muscle proteome at the muscle level, the tissue of economic importance in meat production. Furthermore, the identification of proteins that change their abundance in response to SWL using proteomics can contribute to increased stock productivity of relevant interest to animal production. We identified 668 proteins of the sheep proteome. We demonstrate that the following proteins are affected by restricted nutritional conditions: ferritin heavy chain; immunoglobulin V lambda chain; transgelin; fatty acid synthase; glutathione S-transferase A2; dihydrodiol dehydrogenase 3-like. Furthermore, S100-A10, Serpin A3-5-like and Catalase are proteins that changed their abundance in response to SWL. Nevertheless, it is important to highlight that Catalase values for the merino breed were close to significance and therefore catalase validation is of utmost importance.