Contribution of muscle short-range stiffness to initial changes in joint kinetics and kinematics during perturbations to standing balance: A simulation study

On the rate-limiting dynamics of force development in muscle

Skeletal muscles produce forces relatively slowly compared with the action potentials that excite them. The dynamics of force production are governed by multiple processes, such as calcium activation, cycling of cross-bridges between myofilaments, and contraction against elastic tissues and the body. These processes have been included piecemeal in some muscle models, but not integrated to reveal which are the most rate limiting. We therefore examined their integrative contributions to force development in two conventional types of muscle models: Hill-type and cross-bridge. We found that no combination of these processes can self-consistently reproduce classic data such as twitch and tetanus. Rather, additional dynamics are needed following calcium activation and facilitating cross-bridge cycling, such as for cooperative myofilament interaction and reconfiguration. We provisionally lump such processes into a simple first-order model of 'force facilitation dynamics' that integrate into a cross-bridge-type muscle model. The proposed model self-consistently reproduces force development for a range of excitations including twitch and tetanus and electromyography-to-force curves. The model's step response reveals relatively small timing contributions of calcium activation (3%), cross-bridge cycling (3%) and contraction (27%) to overall force development of human quadriceps, with the remainder (67%) explained by force facilitation. The same set of model parameters predicts the change in force magnitude (gain) and timing (phase delay) as a function of excitatory firing rate, or as a function of cyclic contraction frequency. Although experiments are necessary to reveal the dynamics of muscle, integrative models are useful for identifying the main rate-limiting processes.

A three filament mechanistic model of musculotendon force and impedance

The force developed by actively lengthened muscle depends on different structures across different scales of lengthening. For small perturbations, the active response of muscle is well captured by a linear-time-invariant (LTI) system: a stiff spring in parallel with a light damper. The force response of muscle to longer stretches is better represented by a compliant spring that can fix its end when activated. Experimental work has shown that the stiffness and damping (impedance) of muscle in response to small perturbations is of fundamental importance to motor learning and mechanical stability, while the huge forces developed during long active stretches are critical for simulating and predicting injury. Outside of motor learning and injury, muscle is actively lengthened as a part of nearly all terrestrial locomotion. Despite the functional importance of impedance and active lengthening, no single muscle model has all these mechanical properties. In this work, we present the viscoelastic-crossbridge active-titin (VEXAT) model that can replicate the response of muscle to length changes great and small. To evaluate the VEXAT model, we compare its response to biological muscle by simulating experiments that measure the impedance of muscle, and the forces developed during long active stretches. In addition, we have also compared the responses of the VEXAT model to a popular Hill-type muscle model. The VEXAT model more accurately captures the impedance of biological muscle and its responses to long active stretches than a Hill-type model and can still reproduce the force-velocity and force-length relations of muscle. While the comparison between the VEXAT model and biological muscle is favorable, there are some phenomena that can be improved: the low frequency phase response of the model, and a mechanism to support passive force enhancement.

Effect of prone trunk-extension on lumbar and lower limb muscle stiffness

This study investigated the effect of the prone trunk extension test (PTE) on lumbar and lower limb muscle stiffness to explore the optimal angle for lumbar muscle training, understand the peripheral muscle force transmission effect, and determine the modulation strategy and interaction mode of different muscles during PTE. Twenty healthy young females were recruited for this study, and the stiffness of the erector spinae (ES), semitendinosus (ST), biceps femoris (BF), medial head of the gastrocnemius (MG), and lateral head of the gastrocnemius (LG) was measured by MyotonPRO under four angular PTE conditions (0° horizontal position, 10°, 20°, and 30°). With the increasing angle, the stiffness of ES decreased gradually, while ST and BF increased first and then decreased. The stiffness of MG and LG increased first, then decreased, then increased. There was a moderate to strong negative correlation between ES stiffness variation and ST (r = -0.819 to -0.728, p < 0.001), BF (r = -0.620 to -0.527, p < 0.05), MG (r = -788 to -0.611, p < 0.01), and LG (r = -0.616 to -0.450, p < 0.05). Horizontal PTE maximizes the activation of ES. There is a tension transfer between the ES, hamstrings, and gastrocnemius, mainly between the ES, ST, and LG. The study provides data to explore the effect of peripheral muscle force transmission and the modulation strategies of different muscles during trunk extension.

Center of mass states render multi-joint torques throughout standing balance recovery

Successful reactive balance control requires coordinated modulation of hip, knee, and ankle torques. Stabilizing joint torques arise from feedforward neural signals that modulate the musculoskeletal system's intrinsic mechanical properties, namely muscle short-range stiffness, and neural feedback pathways that activate muscles in response to sensory input. Although feedforward and feedback pathways are known to modulate the torque at each joint, the role of each pathway to the balance-correcting response across joints is poorly understood. Since the feedforward and feedback torque responses act at different delays following perturbations to balance, we modified the sensorimotor response model (SRM), previously used to analyze the muscle activation response to perturbations, to consist of parallel feedback loops with different delays. Each loop within the model is driven by the same information, center of mass (CoM) kinematics, but each loop has an independent delay. We evaluated if a parallel loop SRM could decompose the reactive torques into the feedforward and feedback contributions during balance-correcting responses to backward support surface translations at four magnitudes. The SRM accurately reconstructed reactive joint torques at the hip, knee, and ankle, across all perturbation magnitudes (R 2 >0.84 & VAF>0.83). Moreover, the hip and knee exhibited feedforward and feedback components, while the ankle only exhibited feedback components. The lack of a feedforward component at the ankle may occur because the compliance of the Achilles tendon attenuates muscle short-range stiffness. Our model may provide a framework for evaluating changes in the feedforward and feedback contributions to balance that occur due to aging, injury, or disease.

NEWS AND NOTEWORTHY

Reactive balance control requires coordination of neurally-mediated feedforward and feedback pathways to generate stabilizing joint torques at the hip, knee, and ankle. Using a sensorimotor response model, we decomposed reactive joint torques into feedforward and feedback contributions based on delays relative to center of mass kinematics. Responses across joints were driven by the same signals, but contributions from feedforward versus feedback pathways differed, likely due to differences in musculotendon properties between proximal and distal muscles.

Muscle short-range stiffness behaves like a maxwell element, not a spring: Implications for joint stability

INTRODUCTION

Muscles play a critical role in supporting joints during activities of daily living, owing, in part, to the phenomenon of short-range stiffness. Briefly, when an active muscle is lengthened, bound cross-bridges are stretched, yielding forces greater than what is predicted from the force length relationship. For this reason, short-range stiffness has been proposed as an attractive mechanism for providing joint stability. However, there has yet to be a forward dynamic simulation employing a cross-bridge model, that demonstrates this stabilizing role. Therefore, the purpose of this investigation was to test whether Huxley-type muscle elements, which exhibit short-range stiffness, can stabilize a joint while at constant activation.

METHODS

We analyzed the stability of an inverted pendulum (moment of inertia: 2.7 kg m2) supported by Huxley-type muscle models that reproduce the short-range stiffness phenomenon. We calculated the muscle forces that would provide sufficient short-range stiffness to stabilize the system based in minimizing the potential energy. Simulations consisted of a 50 ms long, 5 Nm square-wave perturbation, with numerical simulations carried out in ArtiSynth.

RESULTS

Despite the initial analysis predicting shared activity of antagonist and agonist muscles to maintain stable equilibrium, the inverted pendulum model was not stable, and did not maintain an upright posture even with fully activated muscles.

DISCUSSION & CONCLUSION

Our simulations suggested that short-range stiffness cannot be solely responsible for joint stability, even for modest perturbations. We argue that short-range stiffness cannot achieve stability because its dynamics do not behave like a typical spring. Instead, an alternative conceptual model for short-range stiffness is that of a Maxwell element (spring and damper in series), which can be obtained as a first-order approximation to the Huxley model. We postulate that the damping that results from short-range stiffness slows down the mechanical response and allows the central nervous system time to react and stabilize the joint. We speculate that other mechanisms, like reflexes or residual force enhancement/depression, may also play a role in joint stability. Joint stability is due to a combination of factors, and further research is needed to fully understand this complex system.

Identification of Neural and Non-Neural Origins of Joint Hyper-Resistance Based on a Novel Neuromechanical Model

Joint hyper-resistance is a common symptom in neurological disorders. It has both neural and non-neural origins, but it has been challenging to distinguish different origins based on clinical tests alone. Combining instrumented tests with parameter identification based on a neuromechanical model may allow us to dissociate the different origins of joint hyper-resistance in individual patients. However, this requires that the model captures the underlying mechanisms. Here, we propose a neuromechanical model that, in contrast to previously proposed models, accounts for muscle short-range stiffness (SRS) and its interaction with muscle tone and reflex activity. We collected knee angle trajectories during the pendulum test in 15 children with cerebral palsy (CP) and 5 typically developing children. We did the test in two conditions - hold and pre-movement - that have been shown to alter knee movement. We modeled the lower leg as an inverted pendulum actuated by two antagonistic Hill-type muscles extended with SRS. Reflex activity was modeled as delayed, linear feedback from muscle force. We estimated neural and non-neural parameters by optimizing the fit between simulated and measured knee angle trajectories during the hold condition. The model could fit a wide range of knee angle trajectories in the hold condition. The model with personalized parameters predicted the effect of pre-movement demonstrating that the model captured the underlying mechanism and subject-specific deficits. Our model may help with the identification of neural and non-neural origins of joint hyper-resistance and thereby opens perspectives for improved diagnosis and treatment selection in children with spastic CP, but such applications require further studies to establish the method's reliability.

The Simultaneous Model-Based Estimation of Joint, Muscle, and Tendon Stiffness is Highly Sensitive to the Tendon Force-Strain Relationship

OBJECTIVE

Accurate estimation of stiffness across anatomical levels (i.e., joint, muscle, and tendon) in vivo has long been a challenge in biomechanics. Recent advances in electromyography (EMG)-driven musculoskeletal modeling have allowed the non-invasive estimation of stiffness during dynamic joint rotations. Nevertheless, validation has been limited to the joint level due to a lack of simultaneous in vivo experimental measurements of muscle and tendon stiffness.

METHODS

With a focus on the triceps surae, we employed a novel perturbation-based experimental technique informed by dynamometry and ultrasonography to derive reference stiffness at the joint, muscle, and tendon levels simultaneously. Here, we propose a new EMG-driven model-based approach that does not require external joint perturbation, nor ultrasonography, to estimate multi-level stiffness. We present a novel set of closed-form equations that enables the person-specific tuning of musculoskeletal parameters dictating biological stiffness, including passive force-length relationships in modeled muscles and tendons.

RESULTS

Calibrated EMG-driven musculoskeletal models estimated the reference data with average normalized root-mean-square error ≈ 20%. Moreover, only when calibrated tendons were approximately four times more compliant than typically modeled, our approach could estimate multi-level reference stiffness.

CONCLUSION

EMG-driven musculoskeletal models can be calibrated on a larger set of reference data to provide more realistic values for the biomechanical variables across multiple anatomical levels. Moreover, the tendon models that are typically used in musculoskeletal modeling are too stiff.

SIGNIFICANCE

Calibrated musculoskeletal models informed by experimental measurements give access to an augmented range of biomechanical variables that might not be easily measured with sensors alone.

Increased velocity feedback gains in the presence of sensory noise can explain paradoxical changes in trunk motor control related to back pain

Literature reports paradoxical findings regarding effects of low-back pain (LBP) on trunk motor control. Compared to healthy individuals, patients with LBP, especially those with high pain-related anxiety, showed stronger trunk extensor reflexes and more resistance against perturbations. On the other hand, LBP patients and especially those with high pain-related anxiety showed decreased precision in unperturbed trunk movement and posture. These paradoxical effects might be explained by arousal potentially increasing average and variance of muscle spindle firing rates. Increased average firing rates could increase resistance against perturbations, but increased variance could decrease precision. We performed a simulation study to test this hypothesis. We modeled the trunk as a 2D inverted pendulum, stabilized by two antagonistic Hill-type muscles, based on their open-loop muscle activation dependent intrinsic stiffness and damping and through 25 ms-delayed, noisy contractile element length and velocity feedback. Reference feedback gains and sensory noise levels were tuned based on previously reported experimental data. We assessed the effect of increasing feedback gains on precision of trunk orientation at different perturbation magnitudes and assessed sensitivity of the effects to open-loop muscle stimulation and noise levels. At low perturbation magnitudes, increasing reflex gains consistently caused an increase in the variance of trunk orientation. At larger perturbation magnitudes, increasing reflex gains consistently caused a decrease in the variance of trunk orientation. Our results support the notion that LBP and related anxiety may increase reflex gains, resulting in an increase in the average and variance of spindle afference, which in turn increase resistance against perturbations and decrease movement precision.

History-dependent muscle resistance to stretch remains high after small, posturally relevant pre-movements

The contributions of intrinsic muscle fiber resistance during mechanical perturbations to standing and other postural behaviors are unclear. Muscle short-range stiffness is known to vary depending on the current level and history of the muscle's activation, as well as the muscle's recent movement history; this property has been referred to as history dependence or muscle thixotropy. However, we currently lack sufficient data about the degree to which muscle stiffness is modulated across posturally relevant characteristics of muscle stretch and activation. We characterized the history dependence of muscle's resistance to stretch in single, permeabilized, activated, muscle fibers in posturally relevant stretch conditions and activation levels. We used a classic paired muscle stretch paradigm, varying the amplitude of a 'conditioning' triangular stretch-shorten cycle followed by a 'test' ramp-and-hold imposed after a variable inter-stretch interval. We tested low (<15%), intermediate (15-50%) and high (>50%) muscle fiber activation levels, evaluating short-range stiffness and total impulse in the test stretch. Muscle fiber resistance to stretch remained high at conditioning amplitudes of <1% optimal fiber length, L0, and inter-stretch intervals of >1 s, characteristic of healthy standing postural sway. An ∼70% attenuation of muscle resistance to stretch was reached at conditioning amplitudes of >3% L0 and inter-stretch intervals of <0.1 s, characteristic of larger, faster postural sway in balance-impaired individuals. The thixotropic changes cannot be predicted solely on muscle force at the time of stretch. Consistent with the disruption of muscle cross-bridges, muscle resistance to stretch during behavior can be substantially attenuated if the prior motion is large enough and/or frequent enough.

Non-linear properties of the Achilles tendon determine ankle impedance over a broad range of activations in humans

Regulating ankle mechanics is essential for controlled interactions with the environment and rejecting unexpected disturbances. Ankle mechanics can be quantified by impedance, the dynamic relationship between an imposed displacement and the torque generated in response. Ankle impedance in the sagittal plane depends strongly on the triceps surae and Achilles tendon, but their relative contributions remain unknown. It is commonly assumed that ankle impedance is controlled by changing muscle activation and, thereby, muscle impedance, but this ignores that tendon impedance also changes with activation-induced loading. Thus, we sought to determine the relative contributions from the triceps surae and Achilles tendon during conditions relevant to postural control. We used a novel technique that combines B-mode ultrasound imaging with joint-level perturbations to quantify ankle, muscle and tendon impedance simultaneously across activation levels from 0% to 30% of maximum voluntary contraction. We found that muscle and tendon stiffness, the static component of impedance, increased with voluntary plantarflexion contractions, but that muscle stiffness exceeded tendon stiffness at very low loads (21±7 N). Above these loads, corresponding to 1.3% of maximal strength for an average participant in our study, ankle stiffness was determined predominately by Achilles tendon stiffness. At approximately 20% MVC for an average participant, ankle stiffness was 4 times more sensitive to changes in tendon stiffness than to changes in muscle stiffness. We provide the first empirical evidence demonstrating that the nervous system, through changes in muscle activations, leverages the non-linear properties of the Achilles tendon to increase ankle stiffness during postural conditions.

Voluntary muscle coactivation in quiet standing elicits reciprocal rather than coactive agonist-antagonist control of reactive balance

Muscle coactivation increases in challenging balance conditions as well as with advanced age and mobility impairments. Increased muscle coactivation can occur both in anticipation of (feedforward) and in reaction to (feedback) perturbations, however, the causal relationship between feedforward and feedback muscle coactivation remains elusive. Here, we hypothesized that feedforward muscle coactivation would increase both the body's initial mechanical resistance due to muscle intrinsic properties and the later feedback-mediated muscle coactivation in response to postural perturbations. Young adults voluntarily increased leg muscle coactivation using visual biofeedback before support-surface perturbations. In contrast to our hypothesis, feedforward muscle coactivation did not increase the body's initial intrinsic resistance to perturbations, nor did it increase feedback muscle coactivation. Rather, perturbations with feedforward muscle coactivation elicited a medium- to long-latency increase of feedback-mediated agonist activity but a decrease of feedback-mediated antagonist activity. This reciprocal rather than coactivation effect on ankle agonist and antagonist muscles enabled faster reactive ankle torque generation, reduced ankle dorsiflexion, and reduced center of mass (CoM) motion. We conclude that in young adults, voluntary feedforward muscle coactivation can be independently modulated with respect to feedback-mediated muscle coactivation. Furthermore, our findings suggest feedforward muscle coactivation may be useful for enabling quicker joint torque generation through reciprocal, rather than coactivated, agonist-antagonist feedback muscle activity. As such our results suggest that behavioral context is critical to whether muscle coactivation functions to increase agility versus stability.NEW & NOTEWORTHY Feedforward and feedback muscle coactivation are commonly observed in older and mobility impaired adults and are considered strategies to improve stability by increasing body stiffness prior to and in response to perturbations. In young adults, voluntary feedforward coactivation does not necessarily increase feedback coactivation in response to perturbations. Instead, feedforward coactivation enabled faster ankle torques through reciprocal agonist-antagonist muscle activity. As such, coactivation may promote either agility or stability depending on the behavioral context.

A review of the efforts to develop muscle and musculoskeletal models for biomechanics in the last 50 years

Both the Hill and the Huxley muscle models had already been described by the time the International Society of Biomechanics was founded 50 years ago, but had seen little use before the 1970s due to the lack of computing. As computers and computational methods became available in the 1970s, the field of musculoskeletal modeling developed and Hill type muscle models were adopted by biomechanists due to their relative computational simplicity as compared to Huxley type muscle models. Muscle forces computed by Hill type muscle models provide good agreement in conditions similar to the initial studies, i.e. for small muscles contracting under steady and controlled conditions. However, more recent validation studies have identified that Hill type muscle models are least accurate for natural in vivo locomotor behaviours at submaximal activations, fast speeds and for larger muscles, and thus need to be improved for their use in understanding human movements. Developments in muscle modelling have tackled these shortcomings. However, over the last 50 years musculoskeletal simulations have been largely based on traditional Hill type muscle models or even simplifications of this model that neglected the interaction of the muscle with a compliant tendon. The introduction of direct collocation in musculoskeletal simulations about 15 years ago along with further improvements in computational power and numerical methods enabled the use of more complex muscle models in simulations of whole-body movement. Whereas Hill type models are still the norm, we may finally be ready to adopt more complex muscle models into musculoskeletal simulations of human movement.

Muscle preflex response to perturbations in locomotion: In vitro experiments and simulations with realistic boundary conditions

Neuromuscular control loops feature substantial communication delays, but mammals run robustly even in the most adverse conditions. In vivo experiments and computer simulation results suggest that muscles' preflex-an immediate mechanical response to a perturbation-could be the critical contributor. Muscle preflexes act within a few milliseconds, an order of magnitude faster than neural reflexes. Their short-lasting action makes mechanical preflexes hard to quantify in vivo. Muscle models, on the other hand, require further improvement of their prediction accuracy during the non-standard conditions of perturbed locomotion. Our study aims to quantify the mechanical work done by muscles during the preflex phase (preflex work) and test their mechanical force modulation. We performed in vitro experiments with biological muscle fibers under physiological boundary conditions, which we determined in computer simulations of perturbed hopping. Our findings show that muscles initially resist impacts with a stereotypical stiffness response-identified as short-range stiffness-regardless of the exact perturbation condition. We then observe a velocity adaptation to the force related to the amount of perturbation similar to a damping response. The main contributor to the preflex work modulation is not the change in force due to a change in fiber stretch velocity (fiber damping characteristics) but the change in magnitude of the stretch due to the leg dynamics in the perturbed conditions. Our results confirm previous findings that muscle stiffness is activity-dependent and show that also damping characteristics are activity-dependent. These results indicate that neural control could tune the preflex properties of muscles in expectation of ground conditions leading to previously inexplicable neuromuscular adaptation speeds.

The impact of age-related increase in passive muscle stiffness on simulated upper limb reaching

Ageing changes the musculoskeletal and neural systems, potentially affecting a person's ability to perform daily living activities. One of these changes is increased passive stiffness of muscles, but its contribution to performance is difficult to separate experimentally from other ageing effects such as loss of muscle strength or cognitive function. A computational upper limb model was used to study the effects of increasing passive muscle stiffness on reaching performance across the model's workspace (all points reachable with a given model geometry). The simulations indicated that increased muscle stiffness alone caused deterioration of reaching accuracy, starting from the edges of the workspace. Re-tuning the model's control parameters to match the ageing muscle properties does not fully reverse ageing effects but can improve accuracy in selected regions of the workspace. The results suggest that age-related muscle stiffening, isolated from other ageing effects, impairs reaching performance. The model also exhibited oscillatory instability in a few simulations when the controller was tuned to the presence of passive muscle stiffness. This instability is not observed in humans, implying the presence of natural stabilizing strategies, thus pointing to the adaptive capacity of neural control systems as a potential area of future investigation in age-related muscle stiffening.

Neuromuscular mechanisms of motor adaptation to repeated gait-slip perturbations in older adults

Individuals can rapidly develop adaptive skills for fall prevention after their exposure to the repeated-slip paradigm. However, the changes in neuromuscular control contributing to such motor adaptation remain unclear. This study investigated changes in neuromuscular control across different stages of slip-adaptation by examining muscle synergies during slip training. Electromyography signals during 24 repeated slip trials in gait were collected for 30 healthy older adults. Muscle synergies in no-adaptation (novel slip), early-adaptation (slip 6 to 8), and late-adaptation trials (slip 22 to 24) were extracted. The similarity between the recruited muscle synergies in these different phases was subsequently analyzed. Results showed that participants made significant improvements in their balance outcomes from novel slips to adapted slips. Correspondingly, there was a significant increase in the muscle synergy numbers from no-adaptation slips to the adapted slips. The participants retained the majority of muscle synergies (5 out of 7) used in novel slips post adaptation. A few new patterns (n = 8) of muscle synergies presented in the early-adaptation stage to compensate for motor errors due to external perturbation. In the late-adaptation stage, only 2 out of these 8 new synergies were retained. Our findings indicated that the central nervous system could generate new muscle synergies through fractionating or modifying the pre-existing synergies in the early-adaptation phase, and these synergies produce motor strategies that could effectively assist in recovery from the slip perturbation. During the late-adaptation phase, the redundant synergies generated in the early-adaptation phase get eliminated as the adaptation process progresses with repeated exposure to the slips, which further consolidates the slip adaptation. Our findings improved the understanding of the key muscle synergies involved in preventing backward balance loss and how neuromuscular responses adapt through repeated slip training, which might be helpful to design synergy-based interventions for fall prevention.

An approximate stochastic optimal control framework to simulate nonlinear neuro-musculoskeletal models in the presence of noise

Optimal control simulations have shown that both musculoskeletal dynamics and physiological noise are important determinants of movement. However, due to the limited efficiency of available computational tools, deterministic simulations of movement focus on accurately modelling the musculoskeletal system while neglecting physiological noise, and stochastic simulations account for noise while simplifying the dynamics. We took advantage of recent approaches where stochastic optimal control problems are approximated using deterministic optimal control problems, which can be solved efficiently using direct collocation. We were thus able to extend predictions of stochastic optimal control as a theory of motor coordination to include muscle coordination and movement patterns emerging from non-linear musculoskeletal dynamics. In stochastic optimal control simulations of human standing balance, we demonstrated that the inclusion of muscle dynamics can predict muscle co-contraction as minimal effort strategy that complements sensorimotor feedback control in the presence of sensory noise. In simulations of reaching, we demonstrated that nonlinear multi-segment musculoskeletal dynamics enables complex perturbed and unperturbed reach trajectories under a variety of task conditions to be predicted. In both behaviors, we demonstrated how interactions between task constraint, sensory noise, and the intrinsic properties of muscle influence optimal muscle coordination patterns, including muscle co-contraction, and the resulting movement trajectories. Our approach enables a true minimum effort solution to be identified as task constraints, such as movement accuracy, can be explicitly imposed, rather than being approximated using penalty terms in the cost function. Our approximate stochastic optimal control framework predicts complex features, not captured by previous simulation approaches, providing a generalizable and valuable tool to study how musculoskeletal dynamics and physiological noise may alter neural control of movement in both healthy and pathological movements.

Standing horse posture: a longer stance is more stable

Horses stand for most of each day. Although they can use various leg configurations (postures), they usually stand with vertical legs. Why? We addressed this question with a 2D quasi-static model having three rigid parts: a trunk, massless fore-limbs and massless rear limbs, with hinges at the shoulders, hips, and hooves. The postural parameter we varied was ℓg, the distance between the hooves. For a given ℓg, statics finds an equilibrium configuration which, with no muscle stabilization (i.e. using minimal effort) is unstable. We assume a horse uses that configuration. To measure the neuromuscular effort needed to stabilize this equilibrium, we added springs at the shoulder and hip; the larger the springs needed to stabilize the model (kmin), the more neuromuscular effort needed to stabilize the posture. A canted-in posture (small ℓg), observed habitually in some domestic horses, needs about twice the spring stiffness (representing twice the effort) as is needed with vertical or slightly splayed-out (large ℓg) legs. This relationship of posture and stability might explain the prevalence of vertical or slightly splayed-out legs in wild and healthy domestic horses and leaves as a puzzle why some horses stand canted-in.

Finger stability in precision grips

Stable precision grips using the fingertips are a cornerstone of human hand dexterity. However, our fingers become unstable sometimes and snap into a hyperextended posture. This is because multilink mechanisms like our fingers can buckle under tip forces. Suppressing this instability is crucial for hand dexterity, but how the neuromuscular system does so is unknown. Here we show that people rely on the stiffness from muscle contraction for finger stability. We measured buckling time constants of 50 ms or less during maximal force application with the index finger—quicker than feedback latencies—which suggests that muscle-induced stiffness may underlie stability. However, a biomechanical model of the finger predicts that muscle-induced stiffness cannot stabilize at maximal force unless we add springs to stiffen the joints or people reduce their force to enable cocontraction. We tested this prediction in 38 volunteers. Upon adding stiffness, maximal force increased by 34 ± 3%, and muscle electromyography readings were 21 ± 3% higher for the finger flexors (mean ± SE). Muscle recordings and mathematical modeling show that adding stiffness offloads the demand for muscle cocontraction, thus freeing up muscle capacity for fingertip force. Hence, people refrain from applying truly maximal force unless an external stabilizing stiffness allows their muscles to apply higher force without losing stability. But more stiffness is not always better. Stiff fingers would affect the ability to adapt passively to complex object geometries and precisely regulate force. Thus, our results show how hand function arises from neurally tuned muscle stiffness that balances finger stability with compliance.

How Does Ankle Mechanical Stiffness Change as a Function of Muscle Activation in Standing and During the Late Stance of Walking?

OBJECTIVE

Ankle joint stiffness is known to be modulated by co-contraction of the ankle muscles; however, it is unclear to what extent changes in agonist muscle activation alone affect ankle joint stiffness. This study tested the effects of varying levels of ankle muscle activation on ankle joint mechanical stiffness in standing and during the late stance phase of walking.

METHODS

Dorsiflexion perturbations were applied at various levels of ankle muscle activation via a robotic platform in standing and walking conditions. In standing, muscle activation was modulated by having participants perform an EMG target matching task that required varying levels of plantarflexor activation. In walking, muscle activation was modulated by changing walking speeds through metronome-based auditory feedback. Ankle stiffness was evaluated by performing a Least-squares system identification using a parametric model consisting of stiffness, damping, and inertia. The association between ankle muscle activation and joint stiffness was evaluated using correlation analyses. Linear regression models were used to determine the extent to which muscle activation contributed to ankle stiffness. An inclusive statistical approach (both classical and Bayesian analyses) was adopted to measure the statistical significance (p-value) and Bayes Factor (BF₁₀).

RESULTS

Results indicate that plantarflexor activity was positively correlated with ankle stiffness in both standing and walking (p<0.001, BF₁₀>900), whereas dorsiflexor activity was negatively correlated with ankle stiffness in walking (p = 0.014, BF₁₀ = 3.9) but not in standing (p = 0.725). Regression analyses indicated that ankle muscle activation predicted about 84% of the variation in ankle stiffness in standing and 45% in walking (p<0.001, BF₁₀>100).

CONCLUSION

Ankle muscle activation significantly contributes to ankle stiffness during standing and walking.

SIGNIFICANCE

The results highlight the role of muscle activation on maintaining joint stiffness and underscore the importance of accounting for muscle activation when measuring ankle stiffness in healthy as well as patient populations.

A Neural Controller Model Considering the Vestibulospinal Tract in Human Postural Control

Humans are able to control their posture in their daily lives. It is important to understand how this is achieved in order to understand the mechanisms that lead to impaired postural control in various diseases. The descending tracts play an important role in controlling posture, particularly the reticulospinal and the vestibulospinal tracts (VST), and there is evidence that the latter is impaired in various diseases. However, the contribution of the VST to human postural control remains unclear, despite extensive research using neuroscientific methods. One reason for this is that the neuroscientific approach limits our understanding of the relationship between an array of sensory information and the muscle outputs. This limitation can be addressed by carrying out studies using computational models, where it is possible to make and validate hypotheses about postural control. However, previous computational models have not considered the VST. In this study, we present a neural controller model that mimics the VST, which was constructed on the basis of physiological data. The computational model is composed of a musculoskeletal model and a neural controller model. The musculoskeletal model had 18 degrees of freedom and 94 muscles, including those of the neck related to the function of the VST. We used an optimization method to adjust the control parameters for different conditions of muscle tone and with/without the VST. We examined the postural sway for each condition. The validity of the neural controller model was evaluated by comparing the modeled postural control with (1) experimental results in human subjects, and (2) the results of a previous study that used a computational model. It was found that the pattern of results was similar for both. This therefore validated the neural controller model, and we could present the neural controller model that mimics the VST.

Simulating Human Upper and Lower Limb Balance Recovery Responses Using Nonlinear Model Predictive Control

The ability to generate predictive dynamic simulations of human movement using optimal control has been a growing point of interest in the design of medical/assistive devices, e.g. robotic exoskeletons. Despite this, many disseminated simulations of whole-body tasks, such as balance recovery, neglect the role of the upper body instead focusing on postural joints, e.g. ankle, knees, hips. Thus, the purpose of the current study was to use a novel nonlinear model predictive control (NMPC) approach to assess how actuated upper limbs, as well as different individual performance (optimality) criteria, can shape simulated reactive balance recovery responses. A sagittal biomechanical model of a young adult standing was designed and actuated via nonlinear muscle torque generators (rotational single-muscle equivalents). Forward dynamic simulations of balance recovery (NMPCdriven) following an unexpected support-surface perturbation were generated for each unique combination of selected performance criteria (6 total), perturbation direction (forward and backward), and arm joints free/locked. The observed joint trajectories provide insight into the emergence of human elements of postural control from individual optimality criteria, e.g. hip-ankle strategies emerge from single-joint regulation. Quantitative analysis of performance improvements with the arms free suggest that whether arm responses emerge in the simulations may be dependent on the problem's initial guess. Future work should focus on testing further performance criteria and improving NMPC as a model of the nervous system.

The deep hip muscles are unlikely to contribute to hip stability in the sagittal plane during walking: a stiffness approach

- Objective: This study determined whether the deep hip muscles could contribute to hip stability.

METHODS

Hip stability was defined as rotational hip stiffness in the sagittal plane, which was calculated for walking trials for 12 participants via electromyography (EMG)informed neuromusculoskeletal modelling that included all 22 hip spanning muscles. Three model configurations were compared that differed in the excitations of the deep hip muscles, but were identical in the excitations of all other muscles: (1) deep hip muscles informed by intramuscular EMG measurements (assisted activation); (2) deep hip muscles with simulated zero activation (no activation); (3) deep hip muscles with simulated maximal activation (maximal activation). Sagittal plane rotational hip stiffness over the gait cycle was compared between model configurations using a within-participant analysis of variance via statistical parametric mapping (p<0.05).

RESULTS

Compared to the assisted activation configuration, hip stiffness (mean (95% confidence interval)) was 0.8% (0.7 to 0.9) lower in the no activation configuration, and 3.2% (2.9 to 3.5) higher in the maximal activation configuration over the gait cycle.

CONCLUSION

Regardless of activation level, the deep hip muscles made little contribution to sagittal plane rotational hip stiffness, which casts uncertainty around their assumed function as hip stabilizers.

SIGNIFICANCE

The merit of targeted deep hip muscle strengthening to improve hip stability in rehabilitation programs for remains unclear.

Muscle synergy differences between voluntary and reactive backward stepping

Reactive stepping responses are essential to prevent falls after a loss of balance. It has previously been well described that both voluntary and reactive step training could improve the efficacy of reactive stepping in different populations. However, the effect of aging on neuromuscular control during voluntary and reactive stepping remains unclear. Electromyography (EMG) signals during both backward voluntary stepping in response to an auditory cue and backward reactive stepping elicited by a forward slip-like treadmill perturbation during stance were recorded in ten healthy young adults and ten healthy older adults. Using muscle synergy analysis, we extracted the muscle synergies for both voluntary and reactive stepping. Our results showed that fewer muscle synergies were used during reactive stepping than during voluntary stepping in both young and older adults. Minor differences in the synergy structure were observed for both voluntary and reactive stepping between age groups. Our results indicate that there is a low similarity of muscle synergies between voluntary stepping and reactive stepping and that aging had a limited effect on the structure of muscle synergies. This study enhances our understanding of the neuromuscular basis of both voluntary and reactive stepping as well as the potential effect of aging on neuromuscular control during balance tasks.

Similar sensorimotor transformations control balance during standing and walking

Standing and walking balance control in humans relies on the transformation of sensory information to motor commands that drive muscles. Here, we evaluated whether sensorimotor transformations underlying walking balance control can be described by task-level center of mass kinematics feedback similar to standing balance control. We found that delayed linear feedback of center of mass position and velocity, but not delayed linear feedback from ankle angles and angular velocities, can explain reactive ankle muscle activity and joint moments in response to perturbations of walking across protocols (discrete and continuous platform translations and discrete pelvis pushes). Feedback gains were modulated during the gait cycle and decreased with walking speed. Our results thus suggest that similar task-level variables, i.e. center of mass position and velocity, are controlled across standing and walking but that feedback gains are modulated during gait to accommodate changes in body configuration during the gait cycle and in stability with walking speed. These findings have important implications for modelling the neuromechanics of human balance control and for biomimetic control of wearable robotic devices. The feedback mechanisms we identified can be used to extend the current neuromechanical models that lack balance control mechanisms for the ankle joint. When using these models in the control of wearable robotic devices, we believe that this will facilitate shared control of balance between the user and the robotic device.

The stability of human standing and walking is remarkable, given that from a mechanical point of view standing and walking are highly unstable and therefore require well-coordinated control actions from the central nervous system. The nervous system continuously receives information on the state of the body through sensory inputs, which is processed to generate descending motor commands to the muscles. It remains, however, unclear how the central nervous system uses information from multiple sensors to control walking balance. In standing balance, such sensorimotor transformations have been studied. When standing balance is perturbed, previous studies suggest that the central nervous system estimates the movement of the whole body center of mass to activate muscles and control balance. Here, we investigated whether the same sensorimotor transformations underlie control of walking balance. We found that changes in muscle activity and ankle moments in response to perturbations of walking balance were indeed proportional to center of mass movement. These findings suggest that common processes underlie control of standing and walking balance. Our work is significant because it captures the result of complex underlying neural processes in a simple relation between the body’s center of mass movement and corrective joint moments that can be implemented in the control of prostheses and exoskeletons to support balance control in a human-like manner.

Perspective on musculoskeletal modelling and predictive simulations of human movement to assess the neuromechanics of gait

Locomotion results from complex interactions between the central nervous system and the musculoskeletal system with its many degrees of freedom and muscles. Gaining insight into how the properties of each subsystem shape human gait is challenging as experimental methods to manipulate and assess isolated subsystems are limited. Simulations that predict movement patterns based on a mathematical model of the neuro-musculoskeletal system without relying on experimental data can reveal principles of locomotion by elucidating cause-effect relationships. New computational approaches have enabled the use of such predictive simulations with complex neuro-musculoskeletal models. Here, we review recent advances in predictive simulations of human movement and how those simulations have been used to deepen our knowledge about the neuromechanics of gait. In addition, we give a perspective on challenges towards using predictive simulations to gain new fundamental insight into motor control of gait, and to help design personalized treatments in patients with neurological disorders and assistive devices that improve gait performance. Such applications will require more detailed neuro-musculoskeletal models and simulation approaches that take uncertainty into account, tools to efficiently personalize those models, and validation studies to demonstrate the ability of simulations to predict gait in novel circumstances.

Interactions between initial posture and task-level goal explain experimental variability in postural responses to perturbations of standing balance

Postural responses to similar perturbations of standing balance vary widely within and across subjects. Here, we identified two sources of variability and their interactions by combining experimental observations with computational modeling: differences in posture at perturbation onset across trials and differences in task-level goals across subjects. We first collected postural responses to unpredictable backward support-surface translations during standing in 10 young adults. We found that maximal trunk lean in postural responses to backward translations were highly variable both within subjects (mean of ranges = 28.3°) and across subjects (range of means = 39.9°). Initial center of mass (COM) position was correlated with maximal trunk lean during the response, but this relation was subject specific (R² = 0.29-0.82). We then used predictive simulations to assess causal relations and interactions with task-level goal. Our simulations showed that initial posture explains the experimentally observed intrasubject variability with a more anterior initial COM position increasing the use of the hip strategy. Differences in task-level goal explain observed intersubject variability with prioritizing effort minimization leading to ankle strategies and prioritizing stability leading to hip strategies. Interactions between initial posture and task-level goal explain observed differences in intrasubject variability across subjects. Our findings suggest that variability in initial posture due to increased sway as observed in older adults might increase the occurrence of less stable postural responses to perturbations. Insight in factors causing movement variability will advance our ability to study the origin of differences between groups and conditions.NEW & NOTEWORTHY Responses to perturbations of standing balance vary both within and between individuals. By combining experimental observations with computational modeling, we identified causes of observed kinematic variability in healthy young adults. First, we found that trial-by-trial differences in posture at perturbation onset explain most of the kinematic variability observed within subjects. Second, we found that differences in prioritizing effort versus stability explained differences in the postural response as well as differences in trial-by-trial variability across subjects.

Exploring the Contribution of Proprioceptive Reflexes to Balance Control in Perturbed Standing

Humans control balance using different feedback loops involving the vestibular system, the visual system, and proprioception. In this article, we focus on proprioception and explore the contribution of reflexes based on force and length feedback to standing balance. In particular, we address the questions of how much proprioception alone could explain balance control, and whether one modality, force or length feedback, is more important than the other. A sagittal plane neuro-musculoskeletal model was developed with six degrees of freedom and nine muscles in each leg. A controller was designed using proprioceptive reflexes and a dead zone. No feedback control was applied inside the dead zone. Reflexes were active once the center of mass moved outside the dead zone. Controller parameters were found by solving an optimization problem, where effort was minimized while the neuro-musculoskeletal model should remain standing upright on a perturbed platform. The ground was perturbed with random square pulses in the sagittal plane with different amplitudes and durations. The optimization was solved for three controllers: using force and length feedback (base model), using only force feedback, and using only length feedback. Simulations were compared to human data from previous work, where an experiment with the same perturbation signal was performed. The optimized controller yielded a similar posture, since average joint angles were within 5 degrees of the experimental average joint angles. The joint angles of the base model, the length only model, and the force only model correlated weakly (ankle) to moderately with the experimental joint angles. The ankle moment correlated weakly to moderately with the experimental ankle moment, while the hip and knee moment were only weakly correlated, or not at all. The time series of the joint angles showed that the length feedback model was better able to explain the experimental joint angles than the force feedback model. Changes in time delay affected the correlation of the joint angles and joint moments. The objective of effort minimization yielded lower joint moments than in the experiment, suggesting that other objectives are also important in balance control, which cause an increase in effort and thus larger joint moments.

Predicting Perturbed Human Arm Movements in a Neuro-Musculoskeletal Model to Investigate the Muscular Force Response

Human movement is generated by a dynamic interplay between the nervous system, the biomechanical structures, and the environment. To investigate this interaction, we propose a neuro-musculoskeletal model of human goal-directed arm movements. Using this model, we simulated static perturbations of the inertia and damping properties of the arm, as well as dynamic torque perturbations for one-degree-of freedom movements around the elbow joint. The controller consists of a feed-forward motor command and feedback based on muscle fiber length and contraction velocity representing short-latency (25 ms) or long-latency (50 ms) stretch reflexes as the first neuronal responses elicited by an external perturbation. To determine the open-loop control signal, we parameterized the control signal resulting in a piecewise constant stimulation over time for each muscle. Interestingly, such an intermittent open-loop signal results in a smooth movement that is close to experimental observations. So, our model can generate the unperturbed point-to-point movement solely by the feed-forward command. The feedback only contributed to the stimulation in perturbed movements. We found that the relative contribution of this feedback is small compared to the feed-forward control and that the characteristics of the musculoskeletal system create an immediate and beneficial reaction to the investigated perturbations. The novelty of these findings is (1) the reproduction of static as well as dynamic perturbation experiments in one neuro-musculoskeletal model with only one set of basic parameters. This allows to investigate the model's neuro-muscular response to the perturbations that-at least to some degree-represent stereotypical interactions with the environment; (2) the demonstration that in feed-forward driven movements the muscle characteristics generate a mechanical response with zero-time delay which helps to compensate for the perturbations; (3) that this model provides enough biomechanical detail to allow for the prediction of internal forces, including joint loads and muscle-bone contact forces which are relevant in ergonomics and for the development of assistive devices but cannot be observed in experiments.

Model-Based Estimation of Ankle Joint Stiffness During Dynamic Tasks: a Validation-Based Approach

Joint stiffness estimation under dynamic conditions still remains a challenge. Current stiffness estimation methods often rely on the external perturbation of the joint. In this study, a novel 'perturbation-free' stiffness estimation method via electromyography (EMG)-driven musculoskeletal modeling was validated for the first time against system identification techniques. EMG signals, motion capture, and dynamic data of the ankle joint were collected in an experimental setup to study the ankle joint stiffness in a controlled way, i.e. at a movement frequency of 0.6 Hz as well as in the presence and absence of external perturbations. The model-based joint stiffness estimates were comparable to system identification techniques. The ability to estimate joint stiffness at any instant of time, with no need to apply joint perturbations, might help to fill the gap of knowledge between the neural and the muscular systems and enable the subsequent development of tailored neurorehabilitation therapies and biomimetic prostheses and orthoses.

History-dependent perturbation response in limb muscle

Muscle mediates movement but movement is typically unsteady and perturbed. Muscle is known to behave non-linearly and with history-dependent properties during steady locomotion, but the importance of history dependence in mediating muscle function during perturbations remains less clear. To explore the capacity of muscles to mitigate perturbations during locomotion, we constructed a series of perturbations that varied only in kinematic history, keeping instantaneous position, velocity and time from stimulation constant. We found that the response of muscle to a perturbation is profoundly history dependent, varying 4-fold as baseline frequency changes, and dissipating energy equivalent to ∼6 times the kinetic energy of all the limbs in 5 ms (nearly 2400 W kg^-1). Muscle energy dissipation during a perturbation is predicted primarily by the force at the onset of the perturbation. This relationship holds across different frequencies and timings of stimulation. This history dependence behaves like a viscoelastic memory producing perturbation responses that vary with the frequency of the underlying movement.

Anticipatory coadaptation of ankle stiffness and sensorimotor gain for standing balance

External perturbation forces may compromise standing balance. The nervous system can intervene only after a delay greater than 100 ms, during which the body falls freely. With ageing, sensorimotor delays are prolonged, posing a critical threat to balance. We study a generic model of stabilisation with neural delays to understand how the organism should adapt to challenging balance conditions. The model suggests that ankle stiffness should be increased in anticipation of perturbations, for example by muscle co-contraction, so as to slow down body fall during the neural response delay. Increased ankle muscle co-contraction is indeed observed in young adults when standing in challenging balance conditions, and in older relative to young adults during normal stance. In parallel, the analysis of the model shows that increases in either stiffness or neural delay must be coordinated with decreases in spinal sensorimotor gains, otherwise the feedback itself becomes destabilizing. Accordingly, a decrease in spinal feedback is observed in challenging conditions, and with age-related increases in neural delay. These observations have been previously interpreted as indicating an increased reliance on cortical rather than spinal control of balance, despite the fact that cortical responses have a longer latency. Our analysis challenges this interpretation by showing that these observations are consistent with a functional coadaptation of spinal feedback gains to functional changes in stiffness and neural delay.

Being able to stand still can be difficult when faced with an unexpected push. It takes the nervous system more than a tenth of a second to respond to such a perturbation, and during this delay the body falls under the influence of its own weight. By co-contracting their ankle muscles in anticipation of a perturbation, subjects can increase their ankle stiffness, which slows down their fall during the neural delay. Young subjects indeed adopt this strategy when they need to remain particularly still (for example when they stand in front of a cliff). Older subjects adopt this strategy even during normal standing. We present a model of standing balance that shows that this postural strategy provides partial compensation for the increase in neural delays with ageing. According to our model, increasing ankle stiffness only improves balance if it is accompanied by a decrease in sensorimotor gain. This provides a novel and functional interpretation for the decrease in spinal feedback observed during ageing, and observed in young subjects when they stand in challenging balance conditions.

Yank: the time derivative of force is an important biomechanical variable in sensorimotor systems

The derivative of force with respect to time does not have a standard term in physics. As a consequence, the quantity has been given a variety of names, the most closely related being 'rate of force development'. The lack of a proper name has made it difficult to understand how different structures and processes within the sensorimotor system respond to and shape the dynamics of force generation, which is critical for survival in many species. We advocate that ∂[Formula: see text]/∂t be termed 'yank', a term that has previously been informally used and never formally defined. Our aim in this Commentary is to establish the significance of yank in how biological motor systems are organized, evolve and adapt. Further, by defining the quantity in mathematical terms, several measurement variables that are commonly reported can be clarified and unified. In this Commentary, we first detail the many types of motor function that are affected by the magnitude of yank generation, especially those related to time-constrained activities. These activities include escape, prey capture and postural responses to perturbations. Next, we describe the multi-scale structures and processes of the musculoskeletal system that influence yank and can be modified to increase yank generation. Lastly, we highlight recent studies showing that yank is represented in the sensory feedback system, and discuss how this information is used to enhance postural stability and facilitate recovery from postural perturbations. Overall, we promote an increased consideration of yank in studying biological motor and sensory systems.

Postural control of a musculoskeletal model against multidirectional support surface translations

The human body is a complex system driven by hundreds of muscles, and its control mechanisms are not sufficiently understood. To understand the mechanisms of human postural control, neural controller models have been proposed by different research groups, including our feed-forward and feedback control model. However, these models have been evaluated under forward and backward perturbations, at most. Because a human body experiences perturbations from many different directions in daily life, neural controller models should be evaluated in response to multidirectional perturbations, including in the forward/backward, lateral, and diagonal directions. The objective of this study was to investigate the validity of an NC model with FF and FB control under multidirectional perturbations. We developed a musculoskeletal model with 70 muscles and 15 degrees of freedom of joints, positioned it in a standing posture by using the neural controller model, and translated its support surface in multiple directions as perturbations. We successfully determined the parameters of the neural controller model required to maintain the stance of the musculoskeletal model for each perturbation direction. The trends in muscle response magnitudes and the magnitude of passive ankle stiffness were consistent with the results of experimental studies. We conclude that the neural controller model can adapt to multidirectional perturbations by generating suitable muscle activations. We anticipate that the neural controller model could be applied to the study of the control mechanisms of patients with torso tilt and diagnosis of the change in control mechanisms from patients' behaviors.

Musculoskeletal Simulation for Determining Influences of the Magnitude of Sensory Noise and Stiffness on the Selection of Hip or Ankle Movement Strategies

While standing, the elderly exhibit different move- ment behaviors compared to young people. However, the causes of these differences remain clear. The purpose of this study was to verify a hypothesis that only the magnitude of sensory noise and stiffness can reproducibly determine trends in the hip or ankle movement strategies. Simulations of postural control of a musculoskeletal model for three noise conditions and three stiffness conditions were performed. Variations in the angles of the hip and ankle suggested that the sensory noise amplitude had no influence on the selection. However, the ankle strategy tended to be selected with the increase of stiffness. Strategy shifts of elderly may be derived from other components; muscle weakness, increase of neurological time delay, or learning based on other evaluation index.

Interaction between muscle tone, short-range stiffness and increased sensory feedback gains explains key kinematic features of the pendulum test in spastic cerebral palsy: A simulation study

The pendulum test is a sensitive clinical assessment of spasticity where the lower leg is dropped from the horizontal position and features of limb motion are recorded. Three key kinematic features are associated with the degree of severity of spasticity in children with cerebral palsy: decreased initial limb excursion, reduced number of limb oscillations, and a non-vertical resting limb angle. While spasticity is attributed to increased velocity-dependent resistance to motion, prior models simulating increased sensorimotor feedback of muscle velocity fail to explain the key pendulum test kinematic outcomes in spastic individuals. Here we hypothesized that increased muscle tone, causing a transient increase in muscle force, i.e. short-range stiffness, could account for reduced first swing excursion and non-vertical resting limb angle. We further hypothesized that hyperreflexia modeled based on muscle fiber force, and not velocity, feedback would be necessary to reduce the number of oscillations because of its interaction with transiently increased muscle force due to short-range stiffness. We simulated the lower leg as a torque-driven single-link pendulum. Muscle tone was modeled as a constant baseline joint torque, short-range stiffness torque was dependent on the level of muscle tone, and delayed sensory feedback torque to simulate reflex activity was based on either muscle velocity or force. Muscle tone and transient short-range stiffness were necessary to simulate decreased initial swing excursion and non-vertical resting leg angle. Moreover, the reduction in the number of oscillations was best reproduced by simulating stretch reflex activity in terms of force, and not velocity, feedback. Varying only baseline muscle torque and reflex gain, we simulated a range of pendulum test kinematics observed across different levels of spasticity. Our model lends insight into physiological mechanisms of spasticity whose contributions can vary on an individual-specific basis, and potentially across different neurological disorders that manifest spasticity as a symptom.

Synthesis of Subject-Specific Human Balance Responses Using a Task-Level Neuromuscular Control Platform

Many activities of daily living require a high level of neuromuscular coordination and balance control to avoid falls. Complex musculoskeletal models paired with detailed neuromuscular simulations complement experimental studies and uncover principles of coordinated and uncoordinated movements. Here, we created a closed-loop forward dynamic simulation framework that utilizes a detailed musculoskeletal model (19 degrees of freedom, and 92 muscles) to synthesize human balance responses after support-surface perturbation. In addition, surrogate response models of task-level experimental kinematics from two healthy subjects were provided as inputs to our closed-loop simulations to inform the design of the task-level controller. The predicted muscle activations and the resulting synthesized subject joint angles showed good conformity with the average of experimental trials. The simulated whole-body center of mass displacements, generated from a single kinematics trial per perturbation direction, were on average, within 7 mm (anterior perturbations) and 13 mm (posterior perturbations) of experimental displacements. Our results confirmed how a complex subject-specific movement can be reconstructed by sequencing and prioritizing multiple task-level commands to achieve desired movements. By combining the multidisciplinary approaches of robotics and biomechanics, the platform demonstrated here offers great potential for studying human movement control and subject-specific outcome prediction.

The Relationship Between Medial Gastrocnemius Lengthening Properties and Stretch Reflexes in Cerebral Palsy

Stretch reflex hyperactivity in the gastrocnemius of children with spastic cerebral palsy (CP) is commonly evaluated by passively rotating the ankle joint into dorsiflexion at different velocities, such as applied in conventional clinical spasticity assessments. However, surface electromyography (sEMG) collected from the medial gastrocnemius (MG) during such examination reveals unexplained heterogeneity in muscle activation between patients. Recent literature also highlights altered muscle tensile behavior in children with spastic CP. We aimed to document MG muscle and tendon lengthening during passive ankle motion at slow and fast velocity and explore its interdependence with the elicited hyperactive stretch reflex. The ankle of 15 children with CP (11 ± 3 years, GMFCS 9I 6II, 8 bilateral, 7 unilateral) and 16 typically developing children (TDC) was passively rotated over its full range of motion at slow and fast velocity. Ultrasound, synchronized with motion-analysis, was used to track the movement of the MG muscle-tendon junction and extract the relative lengthening of muscle and tendon during joint rotation. Simultaneously, MG sEMG was measured. Outcome parameters included the angular and muscle lengthening velocities 30 ms before EMG onset and the gain in root mean square EMG during stretch, as a measure of stretch reflex activity. Compared to slow rotation, the muscle lengthened less and stretch reflex activity was higher during fast rotation. These velocity-induced changes were more marked in CP compared to TDC. In the CP group, muscle-lengthening velocity had higher correlation coefficients with stretch reflex hyperactivity than joint angular velocity. Muscles with greater relative muscle lengthening during slow rotation had earlier and stronger stretch reflexes during fast rotation. These initial results suggest that ankle angular velocity is not representative of MG muscle lengthening velocity and is less related to stretch reflex hyperactivity than MG muscle lengthening. In addition, muscles that lengthened more during slow joint rotation were more likely to show a velocity-dependent stretch reflex. This interdependence of muscle lengthening and stretch reflexes may be important to consider when administering treatment. However, muscle and tendon lengthening properties alone could not fully explain the variability in stretch reflexes, indicating that other factors should also be investigated.

Force encoding in muscle spindles during stretch of passive muscle

Muscle spindle proprioceptive receptors play a primary role in encoding the effects of external mechanical perturbations to the body. During externally-imposed stretches of passive, i.e. electrically-quiescent, muscles, the instantaneous firing rates (IFRs) of muscle spindles are associated with characteristics of stretch such as length and velocity. However, even in passive muscle, there are history-dependent transients of muscle spindle firing that are not uniquely related to muscle length and velocity, nor reproduced by current muscle spindle models. These include acceleration-dependent initial bursts, increased dynamic response to stretch velocity if a muscle has been isometric, and rate relaxation, i.e., a decrease in tonic IFR when a muscle is held at a constant length after being stretched. We collected muscle spindle spike trains across a variety of muscle stretch kinematic conditions, including systematic changes in peak length, velocity, and acceleration. We demonstrate that muscle spindle primary afferents in passive muscle fire in direct relationship to muscle force-related variables, rather than length-related variables. Linear combinations of whole muscle-tendon force and the first time derivative of force (dF/dt) predict the entire time course of transient IFRs in muscle spindle Ia afferents during stretch (i.e., lengthening) of passive muscle, including the initial burst, the dynamic response to lengthening, and rate relaxation following lengthening. Similar to acceleration scaling found previously in postural responses to perturbations, initial burst amplitude scaled equally well to initial stretch acceleration or dF/dt, though later transients were only described by dF/dt. The transient increase in dF/dt at the onset of lengthening reflects muscle short-range stiffness due to cross-bridge dynamics. Our work demonstrates a critical role of muscle cross-bridge dynamics in history-dependent muscle spindle IFRs in passive muscle lengthening conditions relevant to the detection and sensorimotor response to mechanical perturbations to the body, and to previously-described history-dependence in perception of limb position.