John Milton

Assessing the fall risk of a patient in a busy clinical setting is challenging. Tests such as the timed-up-and-go test and narrow beam walking are difficult to perform due to space restrictions. Moreover, it is not easy to directly connect the results of these tests to fundamental biomechanical principles of gait stability, which emphasize the interplay between the movements of the body’s center of mass (CoM) and its base of support (BoS). Herein, we show how a 1.2 m-long treadmill and a single “time-of-flight” Azure Kinect camera can capture the CoM-BoS interplay within 5 min. The CoM was calculated by dividing the body into 14 segments determined from 20 joint positions measured by the Kinect camera’s body tracking SDK. By tracking the CoM and joint positions from stride to stride, we can evaluate different gait stability metrics using a markerless, contactless, space-efficient approach. A large digital database of CoM movements relative to foot placement will be useful for the future development of statistical and machine learning techniques for identifying subjects at higher risk of falling.

Aim: Hormone pulsatility is an important aspect of the hypothalamic-pituitary-adrenal (HPA) axis in health and disease. We use the properties of simple mathematical models to determine whether hormone pulsatility reflects the presence of a time delay in the production of hormones and/or is related to the impulsive nature of hormone secretion. Methods: The predictions of two models for HPA pulsatility are compared. The first model assumes pulsatility arises because of a time delay in the synthesis of glucocorticoids (GCs). The second model suggests that pulsatility reflects the impulsive nature of hormone secretion. The generation of oscillations by the second mechanism does not require a time delay. Results: The time delay for the synthesis of GC (0–10 minutes) may not be long enough to account for the oscillations in adrenocorticotrophin (ACTH) and GC observed with constant corticotrophin-releasing hormone (CRH) infusion in rats. A simple mechanism for hormone release, illustrated using an integrate-and-fire mechanism, reproduces the observed hormone pulsatility. Conclusions: The water solubility of CRH and ACTH draws attention to the role played by soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins in the calcium-dependent exocytosis of peptide hormones. Abnormalities in SNARE proteins are anticipated to cause changes in the amplitude modulation of ACTH and CRH hormone pulses. In mice, a mutation in a SNARE protein causes abnormalities in the HPA axis. Mutations in SNARE proteins occur in many neurodegenerative and neuropsychiatric diseases. Abnormalities in HPA function also occur in these disorders. The identification of SNARE protein mutations in exosomes in serum and cerebrospinal fluid in humans may make it possible to determine whether there exists a causal relationship between an SNARE protein mutation and abnormalities in the HPA axis in this patient group.

Confluent recent evidence indicates that the spectral slope of 1 /f neurophysiological recordings is correspondent to cortical excitation/inhibition (E/I) ratio. In this framework, a steeper power spectrum (i.e., one with a larger spectral exponent β ) is indicative of stronger inhibitory tone and thus lower E/I ratio, and vice versa. While the tools commonly utilized for estimating β are mostly consistent, there appears to be a lack of standardization among data processing protocols for slope analysis. In this work our goal is to draw attention to a fundamental consequence of this issue, namely that even in a confined, comparative research environment, applying different pre-processing steps to electroencephalography (EEG) data can lead to conflicting conclusions in terms of the E/I ratio. To this end, we analyzed resting-state EEG recordings in two independent datasets, containing data collected with eyes open (EO) and eyes closed (EC), with the latter considered as a physiological state with stronger inhibitory tone. Our analyses confirmed consistently in both cohorts that applying different spatial filtering schemes in an otherwise identical analytical pipeline indicated a decrease in E/I ratio over the prefrontal cortex in one case, but not the other when transitioning from EO to EC. In contrast, this same pattern was apparent over the occipital cortex regardless of the pre-processing scheme. This empirical evidence calls for the development of a standardized data processing protocol for EEG-based analyses of the E/I ratio. Highlights: Two EEG spatial filtering schemes - CAR and SL - are compared regarding E/I ratio CAR and SL are shown to substantially affect aperiodic spectral slope estimates CAR and SL yield opposite conclusions about frontal E/I ratio on the same data SL reverses the common β _lo < β _hi bimodal pattern over frontal cortex Spatial filtering effects are confirmed on two independent datasets

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 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.

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 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.

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.

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.