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.

Diverse and complex muscle spindle afferent firing properties emerge from multiscale muscle mechanics.

Despite decades of research, we lack a mechanistic framework capable of predicting how movement-related signals are transformed into the diversity of muscle spindle afferent firing patterns observed experimentally, particularly in naturalistic behaviors. Here, a biophysical model demonstrates that well-known firing characteristics of mammalian muscle spindle Ia afferents - including movement history dependence, and nonlinear scaling with muscle stretch velocity - emerge from first principles of muscle contractile mechanics. Further, mechanical interactions of the muscle spindle with muscle-tendon dynamics reveal how motor commands to the muscle (alpha drive) versus muscle spindle (gamma drive) can cause highly variable and complex activity during active muscle contraction and muscle stretch that defy simple explanation. Depending on the neuromechanical conditions, the muscle spindle model output appears to 'encode' aspects of muscle force, yank, length, stiffness, velocity, and/or acceleration, providing an extendable, multiscale, biophysical framework for understanding and predicting proprioceptive sensory signals in health and disease.

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.

Elastic tissue forces mask muscle fiber forces underlying muscle spindle Ia afferent firing rates in stretch of relaxed rat muscle.

Stretches of relaxed cat and rat muscle elicit similar history-dependent muscle spindle Ia firing rates that resemble history-dependent forces seen in single activated muscle fibers ( Nichols and Cope, 2004). Owing to thixotropy, whole musculotendon forces and muscle spindle firing rates are history dependent during stretch of relaxed cat muscle, where both muscle force and muscle spindle firing rates are elevated in the first stretch in a series of stretch-shorten cycles ( Blum et al., 2017). By contrast, rat musculotendon exhibits only mild thixotropy, such that the measured forces when stretched cannot explain history-dependent muscle spindle firing rates in the same way ( Haftel et al., 2004). We hypothesized that history-dependent muscle spindle firing rates elicited in stretch of relaxed rat muscle mirror history-dependent muscle fiber forces, which are masked at the level of whole musculotendon force by extracellular tissue force. We removed estimated extracellular tissue force contributions from recorded musculotendon force using an exponentially elastic tissue model. We then showed that the remaining estimated muscle fiber force resembles history-dependent muscle spindle firing rates recorded simultaneously. These forces also resemble history-dependent forces recorded in stretch of single activated fibers that are attributed to muscle cross-bridge mechanisms ( Campbell and Moss, 2000). Our results suggest that history-dependent muscle spindle firing in both rats and cats arise from history-dependent forces owing to thixotropy in muscle fibers.

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.

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.