An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics

The effect of uneven surfaces on inter-joint coordination during walking in children with cerebral palsy

Clinical gait analysis on uneven surfaces contributes to the ecological assessment of gait deviations of children with spastic cerebral palsy (CP). Walking on uneven surfaces requires specific motor strategies, which can be assessed by lower-limb kinematic and inter-joint coordination analyses. This study aimed to assess and compare kinematics and inter-joint coordination between children with CP and their typically developing (TD) peers when walking on even and two levels of uneven surfaces (medium and high). A total of 17 children with CP and 17 TD children (11.5 ± 3.5 and 10.4 ± 4.5 years old, respectively) were asked to complete 6-8 gait trials on a 4-m walkway of each surface (n = 3) in randomized blocks while fit with retro-reflective markers on their lower-limbs. Children with CP showed proximal gait adaptations (i.e., hip and knee) on uneven surfaces. Compared with the TD group, the CP group showed decreased hip extension during late stance (49-63%, d = 0.549, p < 0.001), and a more in-phase knee-hip coordination strategy during swing phase (75-84% of gait cycle, d = 1.035, p = 0.029 and 92-100%, d = 1.091, p = 0.030) when walking on an uneven (high), compared to even surface. This study provides a better understanding of kinematic strategies employed by children with spastic CP when facing typical daily life gait challenges. Further studies are needed to evaluate the benefits of integrating uneven surfaces in rehabilitation care.

Impact of balance on the energetic cost of walking and gait speed

BACKGROUND

Examine the relationship between balance test performance and the energetic cost of walking (ECW) and gait speed.

METHODS

Cross-sectional and longitudinal analyses of data from the Baltimore Longitudinal Study of Aging. Men (48%) and women aged 60-96 years enrolled in the BLSA between 2007 and 2020 (n = 1132). Balance was assessed using narrow walk (NW) and progressive standing balance tests (SB). ECW measured during 2.5-min usual paced walk while participants wore a portable indirect calorimeter. Gait speed assessed over 6-m. Each test parameterized using validated methods. Statistical analysis to compare balance measures to ECW, and gait speed used generalized logistic regression models and adjustments for age, sex, race, height, weight, and comorbidities.

RESULTS

Cross-sectionally, mean ECW was higher and gait speed slower in persons who failed the NW than those who passed (0.189 vs. 0.164 mL/kg/m, p < 0.0001 and 0.96 vs. 1.15 m/s, p < 0.0001, respectively). Mean ECW was increasingly higher and gait speed slower over three progressively challenging SB tests (0.207 vs. 0.171 vs. 0.164 mL/kg/m, p < 0.0001 and 0.95 vs. 1.05 vs. 1.15 m/s, p < 0.0001). Over an average 2.4 years, those who declined in SB and NW had a higher ECW and slower gait speed than persons who maintained performance (SB: 0.18 vs. 0.160 mL/kg/m, p = 0.0003, and 1.00 vs. 1.13 m/s, p = <0.001; NW: 0.175 vs. 0.160 mL/kg/m, p = 0.002, and 1.04 vs. 1.14 m/s, p = 0.001). Persons who improved had lower ECW and faster gait speed than those who failed at both visits (SB: 0.169 vs. 0.240 mL/kg/m, p = 0.0002, and 0.99 vs. 0.94 m/s, p = 0.67, NW: 0.163 vs. 0.195 mL/kg/m, p = 0.0005, and 1.10 vs. 0.92 m/s, p < 0.001).

CONCLUSION

Instability contributes to higher ECW and slower gait speed which suggests that rehabilitation efforts to improve balance may help maintain function further into older adulthood and delay mobility limitation.

Temporal organization of stride-to-stride variations contradicts predictive models for sensorimotor control of footfalls during walking

Walking exhibits stride-to-stride variations. Given ongoing perturbations, these variations critically support continuous adaptations between the goal-directed organism and its surroundings. Here, we report that stride-to-stride variations during self-paced overground walking show cascade-like intermittency-stride intervals become uneven because stride intervals of different sizes interact and do not simply balance each other. Moreover, even when synchronizing footfalls with visual cues with variable timing of presentation, asynchrony in the timings of the cue and footfall shows cascade-like intermittency. This evidence conflicts with theories about the sensorimotor control of walking, according to which internal predictive models correct asynchrony in the timings of the cue and footfall from one stride to the next on crossing thresholds leading to the risk of falling. Hence, models of the sensorimotor control of walking must account for stride-to-stride variations beyond the constraints of threshold-dependent predictive internal models.

Methods for integrating postural control into biomechanical human simulations: a systematic review

Understanding of the human body's internal processes to maintain balance is fundamental to simulate postural control behaviour. The body uses multiple sensory systems' information to obtain a reliable estimate about the current body state. This information is used to control the reactive behaviour to maintain balance. To predict a certain motion behaviour with knowledge of the muscle forces, forward dynamic simulations of biomechanical human models can be utilized. We aim to use predictive postural control simulations to give therapy recommendations to patients suffering from postural disorders in the future. It is important to know which types of modelling approaches already exist to apply such predictive forward dynamic simulations. Current literature provides different models that aim to simulate human postural control. We conducted a systematic literature research to identify the different approaches of postural control models. The different approaches are discussed regarding their applied biomechanical models, sensory representation, sensory integration, and control methods in standing and gait simulations. We searched on Scopus, Web of Science and PubMed using a search string, scanned 1253 records, and found 102 studies to be eligible for inclusion. The included studies use different ways for sensory representation and integration, although underlying neural processes still remain unclear. We found that for postural control optimal control methods like linear quadratic regulators and model predictive control methods are used less, when models' level of details is increasing, and nonlinearities become more important. Considering musculoskeletal models, reflex-based and PD controllers are mainly applied and show promising results, as they aim to create human-like motion behaviour considering physiological processes.

A Dynamical Systems Approach to Characterizing Brain-Body Interactions during Movement: Challenges, Interpretations, and Recommendations

Brain-body interactions (BBIs) have been the focus of intense scrutiny since the inception of the scientific method, playing a foundational role in the earliest debates over the philosophy of science. Contemporary investigations of BBIs to elucidate the neural principles of motor control have benefited from advances in neuroimaging, device engineering, and signal processing. However, these studies generally suffer from two major limitations. First, they rely on interpretations of 'brain' activity that are behavioral in nature, rather than neuroanatomical or biophysical. Second, they employ methodological approaches that are inconsistent with a dynamical systems approach to neuromotor control. These limitations represent a fundamental challenge to the use of BBIs for answering basic and applied research questions in neuroimaging and neurorehabilitation. Thus, this review is written as a tutorial to address both limitations for those interested in studying BBIs through a dynamical systems lens. First, we outline current best practices for acquiring, interpreting, and cleaning scalp-measured electroencephalography (EEG) acquired during whole-body movement. Second, we discuss historical and current theories for modeling EEG and kinematic data as dynamical systems. Third, we provide worked examples from both canonical model systems and from empirical EEG and kinematic data collected from two subjects during an overground walking task.

Human Gait Control Using Functional Electrical Stimulation Based on Controlling the Shank Dynamics

Introduction

Efficient gait control using Functional Electrical Stimulation (FES) is an open research problem. In this research, a new intermittent controller has been designed to control the human shank movement dynamics during gait.

Methods

In this approach, first, the three-dimensional phase space was constructed using the human shank movement data recorded from the healthy subjects. Then, three iterated sine-circle maps were extracted in the mentioned phase space. The three identified one-dimensional maps contained the essential information about the shank movement dynamics during a gait cycle. Next, an intermittent fuzzy controller was designed to control the shank angle. According to the adopted intermittent control strategy, the fuzzy controller is activated whenever the shank angle is far enough from the specific. The specific points are described using the identified iterated maps in the constructed phase space. In this manner, the designed controller is activated during a short-time fraction of the gait cycle time.

Results

The designed intermittent controller was evaluated through some simulation studies on a two-joint musculoskeletal model. The obtained results suggested that the pattern of the obtained hip and knee joint trajectories, the outputs of the musculoskeletal model, were acceptably similar to the joints' trajectories pattern of healthy subjects.

Conclusion

The intriguing similarity was observed between the dynamics of the recorded human data and those of the controlled musculoskeletal model. It supports the acceptable performance of the proposed control strategy.

Phase resetting and intermittent control at the edge of stability in a simple biped model generates 1/f-like gait cycle variability

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.

Control of human gait stability through foot placement

During human walking, the centre of mass (CoM) is outside the base of support for most of the time, which poses a challenge to stabilizing the gait pattern. Nevertheless, most of us are able to walk without substantial problems. In this review, we aim to provide an integrative overview of how humans cope with an underactuated gait pattern. A central idea that emerges from the literature is that foot placement is crucial in maintaining a stable gait pattern. In this review, we explore this idea; we first describe mechanical models and concepts that have been used to predict how foot placement can be used to control gait stability. These concepts, such as for instance the extrapolated CoM concept, the foot placement estimator concept and the capture point concept, provide explicit predictions on where to place the foot relative to the body at each step, such that gait is stabilized. Next, we describe empirical findings on foot placement during human gait in unperturbed and perturbed conditions. We conclude that humans show behaviour that is largely in accordance with the aforementioned concepts, with foot placement being actively coordinated to body CoM kinematics during the preceding step. In this section, we also address the requirements for such control in terms of the sensory information and the motor strategies that can implement such control, as well as the parts of the central nervous system that may be involved. We show that visual, vestibular and proprioceptive information contribute to estimation of the state of the CoM. Foot placement is adjusted to variations in CoM state mainly by modulation of hip abductor muscle activity during the swing phase of gait, and this process appears to be under spinal and supraspinal, including cortical, control. We conclude with a description of how control of foot placement can be impaired in humans, using ageing as a primary example and with some reference to pathology, and we address alternative strategies available to stabilize gait, which include modulation of ankle moments in the stance leg and changes in body angular momentum, such as rapid trunk tilts. Finally, for future research, we believe that especially the integration of consideration of environmental constraints on foot placement with balance control deserves attention.

A Simple Algorithm for Assimilating Marker-Based Motion Capture Data During Periodic Human Movement Into Models of Multi-Rigid-Body Systems

Human movement analysis is often performed with a model of multi-rigid-body system, whereby reflective-marker-based motion capture data are assimilated into the model for characterizing kinematics and kinetics of the movements quantitatively. Accuracy of such analysis is limited, due to motions of the markers on the skin relative to the underlying skeletal system, referred to as the soft tissue artifact (STA). Here we propose a simple algorithm for assimilating motion capture data during periodic human movements, such as bipedal walking, into models of multi-rigid-body systems in a way that the assimilated motions are not affected by STA. The proposed algorithm assumes that STA time-profiles during periodic movements are also periodic. We then express unknown STA profiles using Fourier series, and show that the Fourier coefficients can be determined optimally based solely on the periodicity assumption for the STA and kinematic constraints requiring that any two adjacent rigid-links are connected by a rotary joint, leading to the STA-free assimilated motion that is consistent with the multi-rigid-link model. To assess the efficiency of the algorithm, we performed a numerical experiment using a dynamic model of human gait composed of seven rigid links, on which we placed STA-affected markers, and showed that the algorithm can estimate the STA accurately and retrieve the non-STA-affected true motion of the model. We also confirmed that our STA-removal processing improves accuracy of the inverse dynamics analysis, suggesting the usability of the proposed algorithm for gait analysis.

Dynamic Determinants of the Uncontrolled Manifold during Human Quiet Stance

Human postural sway during stance arises from coordinated multi-joint movements. Thus, a sway trajectory represented by a time-varying postural vector in the multiple-joint-angle-space tends to be constrained to a low-dimensional subspace. It has been proposed that the subspace corresponds to a manifold defined by a kinematic constraint, such that the position of the center of mass (CoM) of the whole body is constant in time, referred to as the kinematic uncontrolled manifold (kinematic-UCM). A control strategy related to this hypothesis (CoM-control-strategy) claims that the central nervous system (CNS) aims to keep the posture close to the kinematic-UCM using a continuous feedback controller, leading to sway patterns that mostly occur within the kinematic-UCM, where no corrective control is exerted. An alternative strategy proposed by the authors (intermittent control-strategy) claims that the CNS stabilizes posture by intermittently suspending the active feedback controller, in such a way to allow the CNS to exploit a stable manifold of the saddle-type upright equilibrium in the state-space of the system, referred to as the dynamic-UCM, when the state point is on or near the manifold. Although the mathematical definitions of the kinematic- and dynamic-UCM are completely different, both UCMs play similar roles in the stabilization of multi-joint upright posture. The purpose of this study was to compare the dynamic performance of the two control strategies. In particular, we considered a double-inverted-pendulum-model of postural control, and analyzed the two UCMs defined above. We first showed that the geometric configurations of the two UCMs are almost identical. We then investigated whether the UCM-component of experimental sway could be considered as passive dynamics with no active control, and showed that such UCM-component mainly consists of high frequency oscillations above 1 Hz, corresponding to anti-phase coordination between the ankle and hip. We also showed that this result can be better characterized by an eigenfrequency associated with the dynamic-UCM. In summary, our analysis highlights the close relationship between the two control strategies, namely their ability to simultaneously establish small CoM variations and postural stability, but also make it clear that the intermittent control hypothesis better explains the spectral characteristics of sway.

Adaptation mechanism of interlimb coordination in human split-belt treadmill walking through learning of foot contact timing: a robotics study

Human walking behaviour adaptation strategies have previously been examined using split-belt treadmills, which have two parallel independently controlled belts. In such human split-belt treadmill walking, two types of adaptations have been identified: early and late. Early-type adaptations appear as rapid changes in interlimb and intralimb coordination activities when the belt speeds of the treadmill change between tied (same speed for both belts) and split-belt (different speeds for each belt) configurations. By contrast, late-type adaptations occur after the early-type adaptations as a gradual change and only involve interlimb coordination. Furthermore, interlimb coordination shows after-effects that are related to these adaptations. It has been suggested that these adaptations are governed primarily by the spinal cord and cerebellum, but the underlying mechanism remains unclear. Because various physiological findings suggest that foot contact timing is crucial to adaptive locomotion, this paper reports on the development of a two-layered control model for walking composed of spinal and cerebellar models, and on its use as the focus of our control model. The spinal model generates rhythmic motor commands using an oscillator network based on a central pattern generator and modulates the commands formulated in immediate response to foot contact, while the cerebellar model modifies motor commands through learning based on error information related to differences between the predicted and actual foot contact timings of each leg. We investigated adaptive behaviour and its mechanism by split-belt treadmill walking experiments using both computer simulations and an experimental bipedal robot. Our results showed that the robot exhibited rapid changes in interlimb and intralimb coordination that were similar to the early-type adaptations observed in humans. In addition, despite the lack of direct interlimb coordination control, gradual changes and after-effects in the interlimb coordination appeared in a manner that was similar to the late-type adaptations and after-effects observed in humans. The adaptation results of the robot were then evaluated in comparison with human split-belt treadmill walking, and the adaptation mechanism was clarified from a dynamic viewpoint.

Phase-dependent changes in local dynamic stability during walking in elderly with and without knee osteoarthritis

Previously, we reported reduced time-averaged knee local stability, in the unaffected, but not the affected leg of elderly with knee osteoarthritis OA compared to controls. Since stability may show phase-related changes, we reanalyzed the dataset reported previously using time-dependent local stability, λ(t), and also calculated time-averaged local stability, λs, for comparison. We studied treadmill walking at increasing speeds, focusing on sagittal plane knee movements. 16 patients, 12 healthy peers and 15 young subjects were measured. We found a clear maximum in λ(t) (i.e. minimum in stability) at around 60% of the stride cycle (StanceMax λ(t)), a second clear maximum (SwingMax λ(t)) at around 95% followed by a minimum between 70% and 100% (SwingMin λ(t)). StanceMax λ(t) of both legs was significantly higher in the OA than the young control group. Values for healthy elderly fell between those of the other groups, were significantly higher than in young adults, but there was only a trend towards a significant difference with the StanceMax λ(t) of the OA group׳s affected side. Time-averaged and time-dependent stability measures within one leg were uncorrelated, while time-dependent stability measures at the affected side were inversely correlated with λs at the unaffected side. The results indicate that time-dependent local dynamic stability might provide a more detailed insight into the problems of gait stability in OA than conventional averaged local dynamic stability measures and support the notion that the paradoxical decline in unaffected side time-averaged local stability may be caused by a trade-off between affected and unaffected side stability.

Mutual and asynchronous anticipation and action in sports as globally competitive and locally coordinative dynamics

Humans interact by changing their actions, perceiving other’s actions and executing solutions in conflicting situations. Using oscillator models, nonlinear dynamics have been considered for describing these complex human movements as an emergence of self-organisation. However, these frameworks cannot explain the hierarchical structures of complex behaviours between conflicting inter-agent and adapting intra-agent systems, especially in sport competitions wherein mutually quick decision making and execution are required. Here we adopt a hybrid multiscale approach to model an attack-and-defend game during which both players predict the opponent’s movement and move with a delay. From both simulated and measured data, one synchronous outcome between two-agent (i.e. successful defence) can be described as one attractor. In contrast, the other coordination-breaking outcome (i.e. successful attack) cannot be explained using gradient dynamics because the asymmetric interaction cannot always assume a conserved physical quantity. Instead, we provide the asymmetric and asynchronous hierarchical dynamical models to discuss two-agent competition. Our framework suggests that possessing information about an opponent and oneself in local-coordinative and global-competitive scale enables us to gain a deeper understanding of sports competitions. We anticipate developments in the scientific fields of complex movement adapting to such uncontrolled environments.

Beta activity in the premotor cortex is increased during stabilized as compared to normal walking

Walking on two legs is inherently unstable. Still, we humans perform remarkable well at it, mostly without falling. To gain more understanding of the role of the brain in controlling gait stability we measured brain activity using electro-encephalography (EEG) during stabilized and normal walking. Subjects walked on a treadmill in two conditions, each lasting 10 min; normal, and while being laterally stabilized by elastic cords. Kinematics of trunk and feet, electro-myography (EMG) of neck muscles, as well as 64-channel EEG were recorded. To assess gait stability the local divergence exponent, step width, and trunk range of motion were calculated from the kinematic data. We used independent component (IC) analysis to remove movement, EMG, and eyeblink artifacts from the EEG, after which dynamic imaging of coherent sources beamformers were determined to identify cortical sources that showed a significant difference between conditions. Stabilized walking led to a significant increase in gait stability, i.e., lower local divergence exponents. Beamforming analysis of the beta band activity revealed significant sources in bilateral pre-motor cortices. Projection of sensor data on these sources showed a significant difference only in the left premotor area, with higher beta power during stabilized walking, specifically around push-off, although only significant around contralateral push-off. It appears that even during steady gait the cortex is involved in the control of stability.

Preparatory Body State before Reacting to an Opponent: Short-Term Joint Torque Fluctuation in Real-Time Competitive Sports

In a competitive sport, the outcome of a game is determined by an athlete’s relationship with an unpredictable and uncontrolled opponent. We have previously analyzed the preparatory state of ground reaction forces (GRFs) dividing non-weighted and weighted states (i.e., vertical GRFs below and above 120% of body weight, respectively) in a competitive ballgame task and demonstrated that the non-weighted state prevented delay of the defensive step and promoted successful guarding. However, the associated kinetics of lower extremity joints during a competitive sports task remains unknown. The present study aims to investigate the kinetic characteristics of a real-time competitive sport before movement initiation. As a first kinetic study on a competitive sport, we initially compared the successful defensive kinetics with a relatively stable preparatory state and the choice-reaction sidestep as a control movement. Then, we investigated the kinetic cause of the outcome in a 1-on-1 dribble in terms of the preparatory states according to our previous study. The results demonstrated that in successful defensive motions in the non-weighted state guarding trial, the times required for the generation of hip abduction and three extension torques for the hip, knee, and ankle joints were significantly shortened compared with the choice-reaction sidestep, and hip abduction and hip extension torques were produced almost simultaneously. The sport-specific movement kinetics emerges only in a more-realistic interactive experimental setting. A comparison of the outcomes in the 1-on-1 dribble and preparatory GRF states showed that, in the non-weighted state, the defenders guarded successfully in 68.0% of the trials, and the defender’s initiation time was earlier than that in the weighted state (39.1%). In terms of kinetics, the root mean squares of the derivative of hip abduction and three extension torques in the non-weighted state were smaller than those in the weighted state, irrespective of the outcome. These results indicate that the preparatory body state as explained by short-term joint torque fluctuations before the defensive step would help explain the performance in competitive sports, and will give insights into understanding human adaptive behavior in unpredicted and uncontrolled environments.