Attenuation of muscle spindle firing with artificially increased series compliance during stretch of relaxed muscle

Muscle spindles relay vital mechanosensory information for movement and posture, but muscle spindle feedback is coupled to skeletal motion by a compliant tendon. Little is known about the effects of tendon compliance on muscle spindle feedback during movement, and the complex firing of muscle spindles makes these effects difficult to predict. Our goal was to investigate changes in muscle spindle firing using added series elastic elements (SEEs) to mimic a more compliant tendon, and to characterize the accompanying changes in firing with respect to muscle-tendon unit (MTU) and muscle fascicle displacements (recorded via sonomicrometry). Sinusoidal, ramp-and-hold and triangular stretches were analysed to examine potential changes in muscle spindle instantaneous firing rates (IFRs) in locomotor- and perturbation-like stretches as well as serial history dependence. Added SEEs effectively reduced overall MTU stiffness and generally reduced muscle spindle firing rates, but the effect differed across stretch types. During sinusoidal stretches, peak and mean firing rates were not reduced and IFR was best-correlated with fascicle velocity. During ramp stretches, SEEs reduced the initial burst, dynamic and static responses of the spindle. Notably, IFR was negatively related to fascicle displacement during the hold phase. During triangular stretches, SEEs reduced the mean IFR during the first and second stretches, affecting the serial history dependence of mean IFR. Overall, these results demonstrate that tendon compliance may attenuate muscle spindle feedback during movement, but these changes cannot be fully explained by reduced muscle fascicle length or velocity, or MTU force.

Intrafusal cross-bridge dynamics shape history-dependent muscle spindle responses to stretch

Computational models can be critical to linking complex properties of muscle spindle organs to the sensory information that they encode during behaviours such as postural sway and locomotion where few muscle spindle recordings exist. Here, we augment a biophysical muscle spindle model to predict the muscle spindle sensory signal. Muscle spindles comprise several intrafusal muscle fibres with varied myosin expression and are innervated by sensory neurons that fire during muscle stretch. We demonstrate how cross-bridge dynamics from thick and thin filament interactions affect the sensory receptor potential at the spike initiating region. Equivalent to the Ia afferent's instantaneous firing rate, the receptor potential is modelled as a linear sum of the force and rate change of force (yank) of a dynamic bag1 fibre and the force of a static bag2/chain fibre. We show the importance of inter-filament interactions in (i) generating large changes in force at stretch onset that drive initial bursts and (ii) faster recovery of bag fibre force and receptor potential following a shortening. We show how myosin attachment and detachment rates qualitatively alter the receptor potential. Finally, we show the effect of faster recovery of receptor potential on cyclic stretch-shorten cycles. Specifically, the model predicts history-dependence in muscle spindle receptor potentials as a function of inter-stretch interval (ISI), pre-stretch amplitude and the amplitude of sinusoidal stretches. This model provides a computational platform for predicting muscle spindle response in behaviourally relevant stretches and can link myosin expression seen in healthy and diseased intrafusal muscle fibres to muscle spindle function.

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.

Attenuation of muscle spindle firing with artificially increased series compliance during stretch of relaxed muscle

Muscle spindles relay vital mechanosensory information for movement and posture, but muscle spindle feedback is coupled to skeletal motion by a compliant tendon. Little is known about the effects of tendon compliance on muscle spindle feedback during movement, and the complex firing of muscle spindles make these effects difficult to predict. Our goal was to investigate changes in muscle spindle firing using added series elastic elements (SEEs) to mimic a more compliant tendon, and to characterize the accompanying changes in firing with respect to muscle-tendon unit (MTU) and muscle fascicle displacements (recorded via sonomicrometry). Sinusoidal, ramp-hold-release, and triangular stretches were analyzed to examine potential changes in muscle spindle instantaneous firing rates (IFRs) in locomotor- and perturbation-like stretches as well as history dependence. Added SEEs effectively reduced overall MTU stiffness and generally reduced muscle spindle firing rates, but the effect differed across stretch types. During sinusoidal stretches, peak firing rates were reduced and IFR was strongly correlated with fascicle velocity. During ramp stretches, SEEs reduced the dynamic and static responses of the spindle during lengthening but had no effect on initial bursts at the onset of stretch. Notably, IFR was negatively related to fascicle displacement during the hold phase. During triangular stretches, SEEs reduced the mean IFR during the first and second stretches, affecting the history dependence of mean IFR. Overall, these results demonstrate that tendon compliance may attenuate muscle spindle feedback during movement, but these changes cannot be fully explained by reduced muscle fascicle length and velocity.

The split-belt rimless wheel

Split-belt treadmill walking, in which the two belts move at different speeds, reveals a mechanism through which energy can be extracted from the environment. When a person walks with positive step length asymmetry on a split-belt treadmill, the treadmill can perform net positive work on the person. Here we use a split-belt rimless wheel model to explore how people could take advantage of the treadmill. We show that a split-belt rimless wheel can passively walk steadily by capturing energy from the treadmill to overcome collision losses, whereas it loses energy on each step with no way to recover the losses when walking on tied belts. Our simulated split-belt rimless wheel can walk steadily for a variety of leg angle and belt speed combinations, tolerating both speed disturbances and ground height variability. The wheel can even capture enough energy to walk uphill. We also built a physical split-belt rimless wheel robot and demonstrated that it can walk continuously without additional energy input. In comparing the wheel solutions to human split-belt gait, we found that humans do not maximize positive work performed by the treadmill. Other aspects of walking, such as costs associated with swing, balance, and free vertical moments, likely limit people’s ability to benefit from the treadmill. This study uses a simple walking model to characterize the mechanics and energetics of split-belt walking, demonstrating that energy capture through intermittent contact with two belts is possible and providing a simple model framework for understanding human adaptation during split-belt walking.

General variability leads to specific adaptation toward optimal movement policies

Our nervous systems can learn optimal control policies in response to changes to our bodies, tasks, and movement contexts. For example, humans can learn to adapt their control policy in walking contexts where the energy-optimal policy is shifted along variables such as step frequency or step width. However, it is unclear how the nervous system determines which ways to adapt its control policy. Here, we asked how human participants explore through variations in their control policy to identify more optimal policies in new contexts. We created new contexts using exoskeletons that apply assistive torques to each ankle at each walking step. We analyzed four variables that spanned the levels of the whole movement, the joint, and the muscle: step frequency, ankle angle range, total soleus activity, and total medial gastrocnemius activity. We found that, across all of these analyzed variables, variability increased upon initial exposure to new contexts and then decreased with experience. This led to adaptive changes in the magnitude of specific variables, and these changes were correlated with reduced energetic cost. The timescales by which adaptive changes progressed and variability decreased were faster for some variables than others, suggesting a reduced search space within which the nervous system continues to optimize its policy. These collective findings support the principle that exploration through general variability leads to specific adaptation toward optimal movement policies.

Increasing the gradient of energetic cost does not initiate adaptation in human walking

When in a new situation, the nervous system may benefit from adapting its control policy. In determining whether or not to initiate this adaptation, the nervous system may rely on some features of the new situation. Here, we tested whether one such feature is salient cost savings. We changed cost saliency by manipulating the gradient of participants' energetic cost landscape during walking. We hypothesized that steeper gradients would cause participants to spontaneously adapt their step frequency to lower costs. To manipulate the gradient, a mechatronic system applied controlled fore-aft forces to the waist of participants as a function of their step frequency as they walked on a treadmill. These forces increased the energetic cost of walking at high step frequencies and reduced it at low step frequencies. We successfully created three cost landscapes of increasing gradients, where the natural variability in participants' step frequency provided cost changes of 3.6% (shallow), 7.2% (intermediate), and 10.2% (steep). Participants did not spontaneously initiate adaptation in response to any of the gradients. Using metronome-guided walking-a previously established protocol for eliciting initiation of adaptation-participants next experienced a step frequency with a lower cost. Participants then adapted by -1.41 ± 0.81 (P = 0.007) normalized units away from their originally preferred step frequency obtaining cost savings of 4.80% ± 3.12%. That participants would adapt under some conditions, but not in response to steeper cost gradients, suggests that the nervous system does not solely rely on the gradient of energetic cost to initiate adaptation in novel situations.NEW & NOTEWORTHY People can adapt to novel conditions but often require cues to initiate the adaptation. Using a mechatronic system to reshape energetic cost gradients during treadmill walking, we tested whether the nervous system can use information present in the cost gradient to spontaneously initiate adaptation. We found that our participants did not spontaneously initiate adaptation even in the steepest gradient. The nervous system does not rely solely on the cost gradient when initiating adaptation.

Using asymmetry to your advantage: learning to acquire and accept external assistance during prolonged split-belt walking

People can learn to exploit external assistance during walking to reduce energetic cost. For example, walking on a split-belt treadmill affords the opportunity for people to redistribute the mechanical work performed by the legs to gain assistance from the difference in belts' speed and reduce energetic cost. Though we know what people should do to acquire this assistance, this strategy is not observed during typical adaptation studies. We hypothesized that extending the time allotted for adaptation would result in participants adopting asymmetric step lengths to increase the assistance they can acquire from the treadmill. Here, participants walked on a split-belt treadmill for 45 min while we measured spatiotemporal gait variables, metabolic cost, and mechanical work. We show that when people are given sufficient time to adapt, they naturally learn to step further forward on the fast belt, acquire positive mechanical work from the treadmill, and reduce the positive work performed by the legs. We also show that spatiotemporal adaptation and energy optimization operate over different timescales: people continue to reduce energetic cost even after spatiotemporal changes have plateaued. Our findings support the idea that walking with symmetric step lengths, which is traditionally thought of as the endpoint of adaptation, is only a point in the process by which people learn to take advantage of the assistance provided by the treadmill. These results provide further evidence that reducing energetic cost is central in shaping adaptive locomotion, but this process occurs over more extended timescales than those used in typical studies.NEW & NOTEWORTHY Split-belt treadmill adaptation can be seen as a process where people learn to acquire positive work from the treadmill to reduce energetic cost. Though we know what people should do to reduce energetic cost, this strategy is not observed during adaptation studies. We extended the duration of adaptation and show that people continuously adapt their gait to acquire positive work from the treadmill to reduce energetic cost. This process requires longer exposure than traditionally allotted.

How humans initiate energy optimization and converge on their optimal gaits

A central principle in motor control is that the coordination strategies learned by our nervous system are often optimal. Here, we combined human experiments with computational reinforcement learning models to study how the nervous system navigates possible movements to arrive at an optimal coordination. Our experiments used robotic exoskeletons to reshape the relationship between how participants walk and how much energy they consume. We found that while some participants used their relatively high natural gait variability to explore the new energetic landscape and spontaneously initiate energy optimization, most participants preferred to exploit their originally preferred, but now suboptimal, gait. We could nevertheless reliably initiate optimization in these exploiters by providing them with the experience of lower cost gaits, suggesting that the nervous system benefits from cues about the relevant dimensions along which to re-optimize its coordination. Once optimization was initiated, we found that the nervous system employed a local search process to converge on the new optimum gait over tens of seconds. Once optimization was completed, the nervous system learned to predict this new optimal gait and rapidly returned to it within a few steps if perturbed away. We then used our data to develop reinforcement learning models that can predict experimental behaviours, and applied these models to inductively reason about how the nervous system optimizes coordination. We conclude that the nervous system optimizes for energy using a prediction of the optimal gait, and then refines this prediction with the cost of each new walking step.

Taking advantage of external mechanical work to reduce metabolic cost: the mechanics and energetics of split-belt treadmill walking

KEY POINTS

The neuromotor system generates flexible motor patterns that can adapt to changes in our bodies or environment and also take advantage of assistance provided by the environment. We ask how energy minimization influences adaptive learning during human locomotion to improve economy when walking on a split-belt treadmill. We use a model-based approach to predict how people should adjust their walking pattern to take advantage of the assistance provided by the treadmill, and we validate these predictions empirically. We show that adaptation to a split-belt treadmill can be explained as a process by which people reduce step length asymmetry to take advantage of the work performed by the treadmill to reduce metabolic cost. Our results also have implications for the evaluation of devices designed to reduce effort during walking, as locomotor adaptation may serve as a model approach to understand how people learn to take advantage of external assistance.

ABSTRACT

In everyday tasks such as walking and running, we often exploit the work performed by external sources to reduce effort. Recent research has focused on designing assistive devices capable of performing mechanical work to reduce the work performed by muscles and improve walking function. The success of these devices relies on the user learning to take advantage of this external assistance. Although adaptation is central to this process, the study of adaptation is often done using approaches that seem to have little in common with the use of external assistance. We show in 16 young, healthy participants that a common approach for studying adaptation, split-belt treadmill walking, can be understood from a perspective in which people learn to take advantage of mechanical work performed by the treadmill. Initially, during split-belt walking, people step further forward on the slow belt than the fast belt which we measure as a negative step length asymmetry, but this asymmetry is reduced with practice. We demonstrate that reductions in asymmetry allow people to extract positive work from the treadmill, reduce the positive work performed by the legs, and reduce metabolic cost. We also show that walking with positive step length asymmetries, defined by longer steps on the fast belt, minimizes metabolic cost, and people choose this pattern after guided experience of a wide range of asymmetries. Our results suggest that split-belt adaptation can be interpreted as a process by which people learn to take advantage of mechanical work performed by an external device to improve economy.

An Overview on Principles for Energy Efficient Robot Locomotion

Despite enhancements in the development of robotic systems, the energy economy of today's robots lags far behind that of biological systems. This is in particular critical for untethered legged robot locomotion. To elucidate the current stage of energy efficiency in legged robotic systems, this paper provides an overview on recent advancements in development of such platforms. The covered different perspectives include actuation, leg structure, control and locomotion principles. We review various robotic actuators exploiting compliance in series and in parallel with the drive-train to permit energy recycling during locomotion. We discuss the importance of limb segmentation under efficiency aspects and with respect to design, dynamics analysis and control of legged robots. This paper also reviews a number of control approaches allowing for energy efficient locomotion of robots by exploiting the natural dynamics of the system, and by utilizing optimal control approaches targeting locomotion expenditure. To this end, a set of locomotion principles elaborating on models for energetics, dynamics, and of the systems is studied.