The main purpose of this study is to compare two different feedback controllers for the stabilization of quiet standing in humans, taking into account that the intrinsic ankle stiffness is ...insufficient and that there is a large delay inducing instability in the feedback loop: 1) a standard linear, continuous-time PD controller and 2) an intermittent PD controller characterized by a switching function defined in the phase plane, with or without a dead zone around the nominal equilibrium state. The stability analysis of the first controller is carried out by using the standard tools of linear control systems, whereas the analysis of the intermittent controllers is based on the use of Poincaré maps defined in the phase plane. When the PD-control is off, the dynamics of the system is characterized by a saddle-like equilibrium, with a stable and an unstable manifold. The switching function of the intermittent controller is implemented in such a way that PD-control is 'off' when the state vector is near the stable manifold of the saddle and is 'on' otherwise. A theoretical analysis and a related simulation study show that the intermittent control model is much more robust than the standard model because the size of the region in the parameter space of the feedback control gains (P vs. D) that characterizes stable behavior is much larger in the latter case than in the former one. Moreover, the intermittent controller can use feedback parameters that are much smaller than the standard model. Typical sway patterns generated by the intermittent controller are the result of an alternation between slow motion along the stable manifold of the saddle, when the PD-control is off, and spiral motion away from the upright equilibrium determined by the activation of the PD-control with low feedback gains. Remarkably, overall dynamic stability can be achieved by combining in a smart way two unstable regimes: a saddle and an unstable spiral. The intermittent controller exploits the stabilizing effect of one part of the saddle, letting the system evolve by alone when it slides on or near the stable manifold; when the state vector enters the strongly unstable part of the saddle it switches on a mild feedback which is not supposed to impose a strict stable regime but rather to mitigate the impending fall. The presence of a dead zone in the intermittent controller does not alter the stability properties but improves the similarity with biological sway patterns. The two types of controllers are also compared in the frequency domain by considering the power spectral density (PSD) of the sway sequences generated by the models with additive noise. Different from the standard continuous model, whose PSD function is similar to an over-damped second order system without a resonance, the intermittent control model is capable to exhibit the two power law scaling regimes that are typical of physiological sway movements in humans.
The 1/
f
-like gait cycle variability, characterized by temporal changes in stride-time intervals during steady-state human walking, is a well-documented gait characteristic. Such gait fractality is ...apparent in healthy young adults, but tends to disappear in the elderly and patients with neurological diseases. However, mechanisms that give rise to gait fractality have yet to be fully clarified. We aimed to provide novel insights into neuro-mechanical mechanisms of gait fractality, based on a numerical simulation model of biped walking. A previously developed heel-toe footed, seven-rigid-link biped model with human-like body parameters in the sagittal plane was implemented and expanded. It has been shown that the gait model, stabilized rigidly by means of impedance control with large values of proportional (
P
) and derivative (
D
) gains for a linear feedback controller, is destabilized only in a low-dimensional eigenspace, as
P
and
D
decrease below and even far below critical values. Such low-dimensional linear instability can be compensated by impulsive, phase-dependent actions of nonlinear controllers (phase resetting and intermittent controllers), leading to the flexible walking with joint impedance in the model being as small as that in humans. Here, we added white noise to the model to examine
P
-value-dependent stochastic dynamics of the model for small
D
-values. The simulation results demonstrated that introduction of the nonlinear controllers in the model determined the fractal features of gait for a wide range of the
P
-values, provided that the model operates near the edge of stability. In other words, neither the model stabilized only by pure impedance control even at the edge of linear stability, nor the model stabilized by specific nonlinear controllers, but with
P
-values far inside the stability region, could induce gait fractality. Although only limited types of controllers were examined, we suggest that the impulsive nonlinear controllers and criticality could be major mechanisms for the genesis of gait fractality.
•Drop landing was modelled by a multibody system to assess a risk of sports injuries.•Measured and model-predicted impact ground reaction forces (GRFs) showed agreement.•Knee valgus torque was ...estimated for measured and hypothetical landing kinematics.•Landing kinematics generating high impact GRF and valgus torques were identified.
This study aimed to validate a simple dynamic model of single-leg drop-landing to develop a methodological foundation for investigating mechanistic causes of anterior cruciate ligament (ACL) injury and to explore mechanical associations between knee valgus torque and landing kinematics that are considered clinically as a high-risk landing posture for the injury. A triple-inverted-pendulum model in three-dimensional space, composed of rigid-links of head-arms-trunk (HAT), thigh and shank, was employed. We derived causal relationships that can predict post-impact kinetics, including impact ground reaction forces (GRFs) and corresponding knee joint torques from a given body-kinematics immediately before impact, based on an assumption of a completely inelastic collision between a landing foot (the distal end-point of the shank in the model) and the ground. The concordance correlation coefficient (CCC) analysis revealed that our model can achieve an acceptable agreement between experimentally measured and model-predicted impact GRFs and corresponding knee joint torques. The 95% one-tailed lower confidence limit of CCC of vertical, mediolateral GRFs and the varus/valgus torque were 0.665>ρc,a=0.643,0.786>ρc,a=0.758 and 0.531>ρc,a=0.508, respectively, for the least acceptable values ρc,a. Using this model, effects of three types of hypothetical pre-impact kinematics with modulated (i) medial/lateral leaning HAT angle, (ii) forward/backward HAT tilt-angle, and (iii) knee flexion/extension angle on the impact GRF and corresponding knee joint torque were evaluated. We showed that the smaller knee flexion and the greater HAT leaning toward the landing-limb-side, the larger the knee valgus torque is generated, as a mechanical consequence between the specific pre-impact kinematics and the knee loading associated with the risk of ACL injury. Further exploration of hypothetical kinematics using the model in the future work might contribute to identifying the risky landing kinematics beyond experimental limitations.
Involuntary eye movement during gaze (GZ) fixation, referred to as fixational eye movement (FEM), consists of two types of components: a Brownian motion like component called drifts-tremor (DRT) and ...a ballistic component called microsaccade (MS) with a mean saccadic amplitude of about 0.3° and a mean inter-MS interval of about 0.5 s. During GZ fixation in healthy people in an eccentric position, typically with an eccentricity more than 30°, eyes exhibit oscillatory movements alternating between centripetal drift and centrifugal saccade with a mean saccadic amplitude of about 1° and a period in the range of 0.5-1.0 s, which has been known as the physiological gaze-evoked nystagmus (GEN). Here, we designed a simple experimental paradigm of GZ fixation on a target shifted horizontally from the front-facing position with fewer eccentricities. We found a clear tendency of centripetal DRT and centrifugal MS as in GEN, but with more stochasticity and with slower drift velocity compared to GEN, even during FEM at GZ positions with small eccentricities. Our results showed that the target shift-dependent balance between DRT and MS achieves the GZ bounded around each of the given targets. In other words, GZ relaxes slowly with the centripetal DRT toward the front-facing position during inter-MS intervals, as if there always exists a quasi-stable equilibrium posture in the front-facing position, and MS actions pull GZ intermittently back to the target position in the opposite direction to DRT.
Movement related beta band cortical oscillations, including beta rebound after execution and/or suppression of movement, have drawn attention in upper extremity motor control literature. However, ...fewer studies focused on beta band oscillations during postural control in upright stance. In this preliminary study, we examined beta rebound and other components of electroencephalogram (EEG) activity during perturbed upright stance to investigate supraspinal contributions to postural stabilization. Particularly, we aimed to clarify the timing and duration of beta rebound within a non-sustained, but long-lasting postural recovery process that occurs more slowly compared to upper extremities. To this end, EEG signals were acquired from nine healthy young adults in response to a brief support-surface perturbation, together with the center of pressure, the center of mass and electromyogram (EMG) activities of ankle muscles. Event-related potentials (ERPs) and event-related spectral perturbations were computed from EEG data using the perturbation-onset as a triggering event. After short-latency (<0.3 s) ERPs, our results showed a decrease in high-beta band oscillations (event-related desynchronization), which was followed by a significant increase (event-related synchronization) in the same band, as well as a decrease in theta band oscillations. Unlike during upper extremity motor tasks, the beta rebound in this case was initiated before the postural recovery was completed, and sustained for as long as 3 s with small EMG responses for the first half period, followed by no excessive EMG activities for the second half period. We speculate that those novel characteristics of beta rebound might be caused by slow postural dynamics along a stable manifold of the unstable saddle-type upright equilibrium of the postural control system without active feedback control, but with active monitoring of the postural state, in the framework of the intermittent control.
. Cervical transcutaneous spinal cord stimulation (tSCS) is a promising technology that can support motor function recovery of upper-limbs after spinal cord injury. Its efficacy may depend on the ...ability to recruit sensory afferents, conveying excitatory inputs onto motoneurons. Therefore, understanding its physiological mechanisms is critical to accelerate its development towards clinical applications. In this study, we used an anatomically realistic cervical tSCS computational model to compare α-motor, Aα-sensory, and Aβ-sensory fiber activation thresholds and activation sites.
. We developed a 3D geometry of the cervical body and tSCS electrodes with a cathode centred at the C7 spinous process and an anode placed over the anterior neck. The geometrical model was used to estimate the electric potential distributions along motor and sensory fiber trajectories at the C7 spinal level using a finite element method. We implemented dedicated motor and sensory fiber models to simulate the α-motor and Aα-sensory fibers using 12, 16, and 20 µm diameter fibers, and Aβ-sensory fibers using 6, 9, and 12 µm diameter fibers. We estimated nerve fiber activation thresholds and sites for a 2 ms monophasic stimulating pulse and compared them across the fiber groups.
. Our results showed lower activation thresholds of Aα- and Aβ-sensory fibers compared with α-motor fibers, suggesting preferential sensory fiber activation. We also found no differences between activation thresholds of Aα-sensory and large Aβ-sensory fibers, implying their co-activation. The activation sites were located at the dorsal and ventral root levels.
. Using a realistic computational model, we demonstrated preferential activation of dorsal root Aα- and Aβ-sensory fibers compared with ventral root α-motor fibers during cervical tSCS. These findings suggest high proprioceptive and cutaneous contributions to neural activations during cervical tSCS, which inform the underlying mechanisms of upper-limb functional motor recovery.
Delivering short trains of electric pulses to the muscles and nerves can elicit action potentials resulting in muscle contractions. When the stimulations are sequenced to generate functional ...movements, such as grasping or walking, the application is referred to as functional electrical stimulation (FES). Implications of the motor and sensory recruitment of muscles using FES go beyond simple contraction of muscles. Evidence suggests that FES can induce short- and long-term neurophysiological changes in the central nervous system by varying the stimulation parameters and delivery methods. By taking advantage of this, FES has been used to restore voluntary movement in individuals with neurological injuries with a technique called FES therapy (FEST). However, long-lasting cortical re-organization (neuroplasticity) depends on the ability to synchronize the descending (voluntary) commands and the successful execution of the intended task using a FES. Brain-computer interface (BCI) technologies offer a way to synchronize cortical commands and movements generated by FES, which can be advantageous for inducing neuroplasticity. Therefore, the aim of this review paper is to discuss the neurophysiological mechanisms of electrical stimulation of muscles and nerves and how BCI-controlled FES can be used in rehabilitation to improve motor function.
It has been considered that the brain stabilizes unstable body dynamics by regulating co-activation levels of antagonist muscles. Here we critically reexamined this established theory of impedance ...control in a postural balancing task using a novel EMG-based human-computer interface, in which subjects were asked to balance a virtual inverted pendulum using visual feedback information on the pendulum's position. The pendulum was actuated by a pair of antagonist joint torques determined in real-time by activations of the corresponding pair of antagonist ankle muscles of subjects standing upright. This motor-task raises a frustrated environment; a large feedback time delay in the sensorimotor loop, as a source of instability, might favor adopting the non-reactive, preprogrammed impedance control, but the ankle muscles are relatively hard to co-activate, which hinders subjects from adopting the impedance control. This study aimed at discovering how experimental subjects resolved this frustrated environment through motor learning. One third of subjects adapted to the balancing task in a way of the impedance-like control. It was remarkable, however, that the majority of subjects did not adopt the impedance control. Instead, they acquired a smart and energetically efficient strategy, in which two muscles were inactivated simultaneously at a sequence of optimal timings, leading to intermittent appearance of periods of time during which the pendulum was not actively actuated. Characterizations of muscle inactivations and the pendulum¡Çs sway showed that the strategy adopted by those subjects was a type of intermittent control that utilizes a stable manifold of saddle-type unstable upright equilibrium that appeared in the state space of the pendulum when the active actuation was turned off.
As an important component of ascending activating systems, brainstem cholinergic neurons in the pedunculopontine tegmental nucleus (PPTg) are involved in the regulation of motor control (locomotion, ...posture and gaze) and cognitive processes (attention, learning and memory). The PPTg is highly interconnected with several regions of the basal ganglia, and one of its key functions is to regulate and relay activity from the basal ganglia. Together, they have been implicated in the motor control system (such as voluntary movement initiation or inhibition), and modulate aspects of executive function (such as motivation). In addition to its intimate connection with the basal ganglia, projections from the PPTg to the cerebellum have been recently reported to synaptically activate the deep cerebellar nuclei. Classically, the cerebellum and basal ganglia were regarded as forming separated anatomical loops that play a distinct functional role in motor and cognitive behavioral control. Here, we suggest that the PPTg may also act as an interface device between the basal ganglia and cerebellum. As such, part of the therapeutic effect of PPTg deep brain stimulation (DBS) to relieve gait freezing and postural instability in advanced Parkinson's disease (PD) patients might also involve modulation of the cerebellum. We review the anatomical position and role of the PPTg in the pathway of basal ganglia and cerebellum in relation to motor control, cognitive function and PD.
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