An optimality principle for locomotor central pattern generators

Empowering human-like walking with a bio-inspired gait controller for an under-actuated torque-driven human model

Human gait simulation plays a crucial role in providing insights into various aspects of locomotion, such as diagnosing injuries and impairments, assessing abnormal gait patterns, and developing assistive and rehabilitation technologies. To achieve more realistic gait simulation results, it is essential to use a comprehensive model that accurately replicates the kinematics and kinetics of human movement. Human skeletal models in OpenSim software provide anatomically accurate and anthropomorphic structures, enabling users to create personalized models that accurately replicate individual human behavior. However, these torque-driven models encounter challenges in stabilizing unactuated degree of freedom of pelvis tilt in forward dynamic simulations Adopting a bio-inspired strategy that ensures human balance with a minimized energy expenditure during walking, this paper addresses a gait controller for a torque-driven human skeletal model to achieve stable walking. The proposed controller employs a nonlinear model-based approach to calculate a balance-equivalent control torque and utilizes the hip-ankle strategy to distribute this torque across the lower-limb joints during the stance phase. To optimize the parameters of the trajectory tracking controller and the balance distribution coefficients, we developed a forward dynamic simulation interface established between MATLAB and OpenSim. The simulation results indicated that the torque-driven model achieves a natural gait, with joint torques closely aligning with the experimental data. The robustness of the bio-inspired gait controller was further evaluated by applying a range of external forces on the skeletal model. The robustness analysis demonstrated efficient balance recovery mechanism of the proposed bio-inspired gait controller in response to external disturbances.

Adaptive locomotion of active solids

Active systems composed of energy-generating microscopic constituents are a promising platform to create autonomous functional materials1-16 that can, for example, locomote through complex and unpredictable environments. Yet coaxing these energy sources into useful mechanical work has proved challenging. Here we engineer active solids based on centimetre-scale building blocks that perform adaptive locomotion. These prototypes exhibit a non-variational form of elasticity characterized by odd moduli8,12,17, whose magnitude we predict from microscopics using coarse-grained theories and which we validate experimentally. When interacting with an external environment, these active solids spontaneously undergo limit cycles of shape changes, which naturally lead to locomotion such as rolling and crawling. The robustness of the locomotion is rooted in an emergent feedback loop between the active solid and the environment, which is mediated by elastic deformations and stresses. As a result, our active solids are able to accelerate, adjust their gaits and locomote through a variety of terrains with a similar performance to more complex control strategies implemented by neural networks. Our work establishes active solids as a bridge between materials and robots and suggests decentralized strategies to control the nonlinear dynamics of biological systems8,18-22, soft materials5,6,9,11,12,23-25 and driven nanomechanical devices7,26-30.

Dynamics of neural activity in early nervous system evolution

New techniques for largescale neural recordings from diverse animals are reshaping comparative systems neuroscience. This growth necessitates fresh conceptual paradigms for comparing neural circuits and activity patterns. Here, we take a systems neuroscience approach to early neural evolution, emphasizing the importance of considering nervous systems as multiply modulated, continuous dynamical systems. We argue that endogenous neural activity likely arose early in evolution to organize behaviors and internal states at the organismal level. This connects to a rich literature on the physiology of endogenous activity in small neural circuits: a field that has built links between data and dynamical systems models. Such models offer mechanistic insight and have robust predictive power. Using these tools, we suggest that the emergence of intrinsically active neurons and periodic dynamics played a critical role in the ascendancy of nervous systems, and that dynamical systems presents an appealing framework for comparing across species.

Walking on different inclines affects gait symmetry differently in the anterior-posterior and vertical directions: implication for future sensorimotor training

A symmetric gait pattern in humans reflects near-identical movement in bilateral limbs during walking. However, little is known about how gait symmetry changes on different inclines. This study aimed to address this knowledge gap using the central pattern generator and internal model hypotheses. Eighteen healthy young adults underwent five 2-minute walking trials (inclines of +15%, +8%, 0%, -8%, and -15%). Dependent variables included step time, step length, step width, maximum heel clearance, time to peaks of maximum heel clearance, their corresponding coefficients of variation (CV), and respective symmetry indices (SI). Significant differences were observed in SI of step length (p = .022), step length variability (p < .001), step width variability (p =.001), maximum heel clearance (p < .001), and maximum heel clearance variability (p = .049). Compared to level walking, walking at -8% and -15% inclines increased SI of step length (p = .011, p = .039 respectively) but decreased SI of maximum heel clearance (p = .025, p = .019 respectively). These observations suggested that incline walking affected gait symmetry differently, possibly due to varied internal models used in locomotion. Downhill walking improved vertical gait symmetry but reduced anterior-posterior symmetry compared to level walking. Downhill walking may be a preferable rehabilitation protocol for enhancing gait symmetry, as it activates internal model controls. Even slight downhill inclines could increase active control loading, beneficial for the elderly and those with impaired gait.

Sensorimotor control of robots mediated by electrophysiological measurements of fungal mycelia

Living tissues are still far from being used as practical components in biohybrid robots because of limitations in life span, sensitivity to environmental factors, and stringent culture procedures. Here, we introduce fungal mycelia as an easy-to-use and robust living component in biohybrid robots. We constructed two biohybrid robots that use the electrophysiological activity of living mycelia to control their artificial actuators. The mycelia sense their environment and issue action potential-like spiking voltages as control signals to the motors and valves of the robots that we designed and built. The paper highlights two key innovations: first, a vibration- and electromagnetic interference-shielded mycelium electrical interface that allows for stable, long-term electrophysiological bioelectric recordings during untethered, mobile operation; second, a control architecture for robots inspired by neural central pattern generators, incorporating rhythmic patterns of positive and negative spikes from the living mycelia. We used these signals to control a walking soft robot as well as a wheeled hard one. We also demonstrated the use of mycelia to respond to environmental cues by using ultraviolet light stimulation to augment the robots' gaits.

Sensory feedback and central neuronal interactions in mouse locomotion

Locomotion is a complex process involving specific interactions between the central neural controller and the mechanical components of the system. The basic rhythmic activity generated by locomotor circuits in the spinal cord defines rhythmic limb movements and their central coordination. The operation of these circuits is modulated by sensory feedback from the limbs providing information about the state of the limbs and the body. However, the specific role and contribution of central interactions and sensory feedback in the control of locomotor gait and posture remain poorly understood. We use biomechanical data on quadrupedal locomotion in mice and recent findings on the organization of neural interactions within the spinal locomotor circuitry to create and analyse a tractable mathematical model of mouse locomotion. The model includes a simplified mechanical model of the mouse body with four limbs and a central controller composed of four rhythm generators, each operating as a state machine controlling the state of one limb. Feedback signals characterize the load and extension of each limb as well as postural stability (balance). We systematically investigate and compare several model versions and compare their behaviour to existing experimental data on mouse locomotion. Our results highlight the specific roles of sensory feedback and some central propriospinal interactions between circuits controlling fore and hind limbs for speed-dependent gait expression. Our models suggest that postural imbalance feedback may be critically involved in the control of swing-to-stance transitions in each limb and the stabilization of walking direction.

Changes in intra- and interlimb reflexes from hindlimb cutaneous afferents after staggered thoracic lateral hemisections during locomotion in cats

When the foot dorsum contacts an obstacle during locomotion, cutaneous afferents signal central circuits to coordinate muscle activity in the four limbs. Spinal cord injury disrupts these interactions, impairing balance and interlimb coordination. We evoked cutaneous reflexes by electrically stimulating left and right superficial peroneal nerves before and after two thoracic lateral hemisections placed on opposite sides of the cord at 9- to 13-week interval in seven adult cats (4 males and 3 females). We recorded reflex responses in ten hindlimb and five forelimb muscles bilaterally. After the first (right T5-T6) and second (left T10-T11) hemisections, coordination of the fore- and hindlimbs was altered and/or became less consistent. After the second hemisection, cats required balance assistance to perform quadrupedal locomotion. Short-latency reflex responses in homonymous and crossed hindlimb muscles largely remained unaffected after staggered hemisections. However, mid- and long-latency homonymous and crossed responses in both hindlimbs occurred less frequently after staggered hemisections. In forelimb muscles, homolateral and diagonal mid- and long-latency response occurrence significantly decreased after the first and second hemisections. In all four limbs, however, when present, short-, mid- and long-latency responses maintained their phase-dependent modulation. We also observed reduced durations of short-latency inhibitory homonymous responses in left hindlimb extensors early after the first hemisection and delayed short-latency responses in the right ipsilesional hindlimb after the first hemisection. Therefore, changes in cutaneous reflex responses correlated with impaired balance/stability and interlimb coordination during locomotion after spinal cord injury. Restoring reflex transmission could be used as a biomarker to facilitate locomotor recovery. KEY POINTS: Cutaneous afferent inputs coordinate muscle activity in the four limbs during locomotion when the foot dorsum contacts an obstacle. Thoracic spinal cord injury disrupts communication between spinal locomotor centres located at cervical and lumbar levels, impairing balance and limb coordination. We investigated cutaneous reflexes during quadrupedal locomotion by electrically stimulating the superficial peroneal nerve bilaterally, before and after staggered lateral thoracic hemisections of the spinal cord in cats. We showed a loss/reduction of mid- and long-latency responses in all four limbs after staggered hemisections, which correlated with altered coordination of the fore- and hindlimbs and impaired balance. Targeting cutaneous reflex pathways projecting to the four limbs could help develop therapeutic approaches aimed at restoring transmission in ascending and descending spinal pathways.

Biomechanical Assessment Methods Used in Chronic Stroke: A Scoping Review of Non-Linear Approaches

Non-linear and dynamic systems analysis of human movement has recently become increasingly widespread with the intention of better reflecting how complexity affects the adaptability of motor systems, especially after a stroke. The main objective of this scoping review was to summarize the non-linear measures used in the analysis of kinetic, kinematic, and EMG data of human movement after stroke. PRISMA-ScR guidelines were followed, establishing the eligibility criteria, the population, the concept, and the contextual framework. The examined studies were published between 1 January 2013 and 12 April 2023, in English or Portuguese, and were indexed in the databases selected for this research: PubMed®, Web of Science®, Institute of Electrical and Electronics Engineers®, Science Direct® and Google Scholar®. In total, 14 of the 763 articles met the inclusion criteria. The non-linear measures identified included entropy (n = 11), fractal analysis (n = 1), the short-term local divergence exponent (n = 1), the maximum Floquet multiplier (n = 1), and the Lyapunov exponent (n = 1). These studies focused on different motor tasks: reaching to grasp (n = 2), reaching to point (n = 1), arm tracking (n = 2), elbow flexion (n = 5), elbow extension (n = 1), wrist and finger extension upward (lifting) (n = 1), knee extension (n = 1), and walking (n = 4). When studying the complexity of human movement in chronic post-stroke adults, entropy measures, particularly sample entropy, were preferred. Kinematic assessment was mainly performed using motion capture systems, with a focus on joint angles of the upper limbs.

Action-rule-based cognitive control enables efficient execution of stimulus-response conflict tasks: a model validation of Simon task performance

Introduction

The human brain can flexibly modify behavioral rules to optimize task performance (speed and accuracy) by minimizing cognitive load. To show this flexibility, we propose an action-rule-based cognitive control (ARC) model. The ARC model was based on a stochastic framework consistent with an active inference of the free energy principle, combined with schematic brain network systems regulated by the dorsal anterior cingulate cortex (dACC), to develop several hypotheses for demonstrating the validity of the ARC model.

Methods

A step-motion Simon task was developed involving congruence or incongruence between important symbolic information (illustration of a foot labeled "L" or "R," where "L" requests left and "R" requests right foot movement) and irrelevant spatial information (whether the illustration is actually of a left or right foot). We made predictions for behavioral and brain responses to testify to the theoretical predictions.

Results

Task responses combined with event-related deep-brain activity (ER-DBA) measures demonstrated a key contribution of the dACC in this process and provided evidence for the main prediction that the dACC could reduce the Shannon surprise term in the free energy formula by internally reversing the irrelevant rapid anticipatory postural adaptation. We also found sequential effects with modulated dip depths of ER-DBA waveforms that support the prediction that repeated stimuli with the same congruency can promote remodeling of the internal model through the information gain term while counterbalancing the surprise term.

Discussion

Overall, our results were consistent with experimental predictions, which may support the validity of the ARC model. The sequential effect accompanied by dip modulation of ER-DBA waveforms suggests that cognitive cost is saved while maintaining cognitive performance in accordance with the framework of the ARC based on 1-bit congruency-dependent selective control.

Sensory Feedback and Central Neuronal Interactions in Mouse Locomotion

Locomotion is a complex process involving specific interactions between the central neural controller and the mechanical components of the system. The basic rhythmic activity generated by locomotor circuits in the spinal cord defines rhythmic limb movements and their central coordination. The operation of these circuits is modulated by sensory feedback from the limbs providing information about the state of the limbs and the body. However, the specific role and contribution of central interactions and sensory feedback in the control of locomotor gait and posture remain poorly understood. We use biomechanical data on quadrupedal locomotion in mice and recent findings on the organization of neural interactions within the spinal locomotor circuitry to create and analyze a tractable mathematical model of mouse locomotion. The model includes a simplified mechanical model of the mouse body with four limbs and a central controller composed of four rhythm generators, each operating as a state machine controlling the state of one limb. Feedback signals characterize the load and extension of each limb as well as postural stability (balance). We systematically investigate and compare several model versions and compare their behavior to existing experimental data on mouse locomotion. Our results highlight the specific roles of sensory feedback and some central propriospinal interactions between circuits controlling fore and hind limbs for speed-dependent gait expression. Our models suggest that postural imbalance feedback may be critically involved in the control of swing-to-stance transitions in each limb and the stabilization of walking direction.

Variation in the rate of recovery in motor function between the upper and lower limbs in patients with stroke: some proposed hypotheses and their implications for research and practice

Background

Stroke results in impairment of motor function of both the upper and lower limbs. However, although it is debatable, motor function of the lower limb is believed to recover faster than that of the upper limb. The aim of this paper is to propose some hypotheses to explain the reasons for that, and discuss their implications for research and practice.

Method

We searched PubMED, Web of Science, Scopus, Embase and CENTRAL using the key words, stroke, cerebrovascular accident, upper extremity, lower extremity, and motor recovery for relevant literature.

Result

The search generated a total of 2,551 hits. However, out of this number, 51 duplicates were removed. Following review of the relevant literature, we proposed four hypotheses: natural instinct for walking hypothesis, bipedal locomotion hypothesis, central pattern generators (CPGs) hypothesis and role of spasticity hypothesis on the subject matter.

Conclusion

We opine that, what may eventually account for the difference, is the frequency of use of the affected limb or intensity of the rehabilitation intervention. This is because, from the above hypotheses, the lower limb seems to be used more frequently. When limbs are used frequently, this will result in use-dependent plasticity and eventual recovery. Thus, rehabilitation techniques that involve high repetitive tasks practice such as robotic rehabilitation, Wii gaming and constraint induced movement therapy should be used during upper limb rehabilitation.

Neuromechanical Strategies for Obstacle Negotiation during Overground Locomotion following Incomplete Spinal Cord Injury in Adult Cats

Following incomplete spinal cord injury in animals, including humans, substantial locomotor recovery can occur. However, functional aspects of locomotion, such as negotiating obstacles, remains challenging. We collected kinematic and electromyography data in 10 adult cats (5 males, 5 females) before and at weeks 1-2 and 7-8 after a lateral mid-thoracic hemisection on the right side of the cord while they negotiated obstacles of three different heights. Intact cats always cleared obstacles without contact. At weeks 1-2 after hemisection, the ipsilesional right hindlimb contacted obstacles in ∼50% of trials, triggering a stumbling corrective reaction or absent responses, which we termed Other. When complete clearance occurred, we observed exaggerated ipsilesional hindlimb flexion when crossing the obstacle with contralesional Left limbs leading. At weeks 7-8 after hemisection, the proportion of complete clearance increased, Other responses decreased, and stumbling corrective reactions remained relatively unchanged. We found redistribution of weight support after hemisection, with reduced diagonal supports and increased homolateral supports, particularly on the left contralesional side. The main neural strategy for complete clearance in intact cats consisted of increased knee flexor activation. After hemisection, ipsilesional knee flexor activation remained, but it was insufficient or more variable as the limb approached the obstacle. Intact cats also increased their speed when stepping over an obstacle, an increase that disappeared after hemisection. The increase in complete clearance over time after hemisection paralleled the recovery of muscle activation patterns or new strategies. Our results suggest partial recovery of anticipatory control through neuroplastic changes in the locomotor control system.SIGNIFICANCE STATEMENT Most spinal cord injuries (SCIs) are incomplete and people can recover some walking functions. However, the main challenge for people with SCIs that do recover a high level of function is to produce a gait that can adjust to everyday occurrences, such as turning, stepping over an obstacle, etc. Here, we use the cat model to answer two basic questions: How does an animal negotiate an obstacle after an incomplete SCI and why does it fail to safely clear it? We show that the inability to clear an obstacle is because of improper activation of muscles that flex the knee. Animals recover a certain amount of function thanks to new strategies and changes within the nervous system.

Integration of feedforward and feedback control in the neuromechanics of vertebrate locomotion: a review of experimental, simulation and robotic studies

Animal locomotion is the result of complex and multi-layered interactions between the nervous system, the musculo-skeletal system and the environment. Decoding the underlying mechanisms requires an integrative approach. Comparative experimental biology has allowed researchers to study the underlying components and some of their interactions across diverse animals. These studies have shown that locomotor neural circuits are distributed in the spinal cord, the midbrain and higher brain regions in vertebrates. The spinal cord plays a key role in locomotor control because it contains central pattern generators (CPGs) - systems of coupled neuronal oscillators that provide coordinated rhythmic control of muscle activation that can be viewed as feedforward controllers - and multiple reflex loops that provide feedback mechanisms. These circuits are activated and modulated by descending pathways from the brain. The relative contributions of CPGs, feedback loops and descending modulation, and how these vary between species and locomotor conditions, remain poorly understood. Robots and neuromechanical simulations can complement experimental approaches by testing specific hypotheses and performing what-if scenarios. This Review will give an overview of key knowledge gained from comparative vertebrate experiments, and insights obtained from neuromechanical simulations and robotic approaches. We suggest that the roles of CPGs, feedback loops and descending modulation vary among animals depending on body size, intrinsic mechanical stability, time required to reach locomotor maturity and speed effects. We also hypothesize that distal joints rely more on feedback control compared with proximal joints. Finally, we highlight important opportunities to address fundamental biological questions through continued collaboration between experimentalists and engineers.

The nervous system tunes sensorimotor gains when reaching in variable mechanical environments

Humans often move in the presence of mechanical disturbances that can vary in direction and amplitude throughout movement. These disturbances can jeopardize the outcomes of our actions, such as when drinking from a glass of water on a turbulent flight or carrying a cup of coffee while walking on a busy sidewalk. Here, we examine control strategies that allow the nervous system to maintain performance when reaching in the presence of mechanical disturbances that vary randomly throughout movement. Healthy participants altered their control strategies to make movements more robust against disturbances. The change in control was associated with faster reaching movements and increased responses to proprioceptive and visual feedback that were tuned to the variability of the disturbances. Our findings highlight that the nervous system exploits a continuum of control strategies to increase its responsiveness to sensory feedback when reaching in the presence of increasingly variable physical disturbances.

Does ankle push-off correct for errors in anterior-posterior foot placement relative to center-of-mass states?

Understanding the mechanisms humans use to stabilize walking is vital for predicting falls in elderly. Modeling studies identified two potential mechanisms to stabilize gait in the anterior-posterior direction: foot placement control and ankle push-off control: foot placement depends on position and velocity of the center-of-mass (CoM) and push-off covaries with deviations between actual and predicted CoM trajectories. While both control mechanisms have been reported in humans, it is unknown whether especially the latter one is employed in unperturbed steady-state walking. Based on the finding of Wang and Srinivasan that foot placement deviates in the same direction as the CoM states in the preceding swing phase, and assuming that this covariance serves the role of stabilizing gait, the covariance between the CoM states and foot placement can be seen as a measure of foot placement accuracy. We subsequently interpreted the residual variance in foot placement from a linear regression model as "errors" that must be compensated, and investigated whether these foot placement errors were correlated to push-off kinetic time series of the subsequent double stance phase. We found ankle push-off torque to be correlated to the foot placement errors in 30 participants when walking at normal and slow speeds, with peak correlations over the double stance phase up to 0.39. Our study suggests that humans use a push-off strategy for correcting foot placement errors in steady-state walking.

Investigation of neural and biomechanical impairments leading to pathological toe and heel gaits using neuromusculoskeletal modelling

KEY POINTS

Pathological toe and heel gaits are commonly present in various conditions such as spinal cord injury, stroke or cerebral palsy. These conditions present various neural and biomechanical impairments and the cause-effect relationships between these impairments and pathological gaits are hard to establish clinically. Based on neuromechanical simulation, this study focuses on the plantarflexor muscles and builds a new reflex circuit controller to model and evaluate the potential effect of both neural and biomechanical impairments on gait. Our results suggest an important contribution of active reflex mechanisms in pathological toe gait. This "what if" based on neuromechanical modelling is thus deemed of great interest to target potential pathological gait causes.

ABSTRACT

This study investigates the pathological toe and heel gaits in human locomotion using neuromusculoskeletal modelling and simulation. In particular, it aims at investigating potential cause-effect relationships between biomechanical or neural impairments and pathological gaits. Toe and heel gaits are commonly present in spinal cord injury, stroke or cerebral palsy. Toe walking is mainly attributed to spasticity and contracture at plantarflexor muscles, whereas heel walking can be attributed to muscle weakness from biomechanical or neural origin. To investigate the effect of these impairments on gait, this study focuses on the soleus and gastrocnemius muscles as they contribute to ankle plantarflexion. We built a reflex circuit model on top of Geyer and Herr's work (2010) with additional pathways affecting the plantarflexor muscles. The SCONE software, which provides optimisation tools for 2D neuromechanical simulation of human locomotion, is used to optimise the corresponding reflex parameters and simulate healthy gait. We then modelled various bilateral plantarflexors biomechanical and neural impairments, and individually introduced them in the healthy model. We characterised the resulting simulated gaits as pathological or not by comparing ankle kinematics and ankle moment with the healthy optimised gait based on metrics used in clinical studies. Our simulations suggest that toe walking can be generated by hyperreflexia, whereas muscle and neural weaknesses induce partially heel gait. Thus, this "what if" approach is deemed of great interest as it allows the investigation of the effect of various impairments on gait and suggests an important contribution of active reflex mechanisms in pathological toe gait. Abstract figure legend Various biomechanical and neural impairments are individually modelled at the level of the plantarflexor muscles in a musculoskeletal model and a complex reflex circuit-based gait controller. For instance, as shown on the left, the plantarflexors spindle reflex gain (KS) is increased to mimic hyperreflexia. The gait controller is then optimised for each of the impaired condition and the resulting gaits are characterised as pathological gait based on ankle kinematics and ankle moment metrics used in clinical studies. Thus, this "what if" approach allows the investigation of the effect of various impairments on gait presented in the table on the right. This article is protected by copyright. All rights reserved.

A leg to stand on: computational models of proprioception

Dexterous motor control requires feedback from proprioceptors, internal mechanosensory neurons that sense the body's position and movement. An outstanding question in neuroscience is how diverse proprioceptive feedback signals contribute to flexible motor control. Genetic tools now enable targeted recording and perturbation of proprioceptive neurons in behaving animals; however, these experiments can be challenging to interpret, due to the tight coupling of proprioception and motor control. Here, we argue that understanding the role of proprioceptive feedback in controlling behavior will be aided by the development of multiscale models of sensorimotor loops. We review current phenomenological and structural models for proprioceptor encoding and discuss how they may be integrated with existing models of posture, movement, and body state estimation.