Comparison of candidate models’ abilities to predict muscle spindle Ia afferent IFRs.

<p>(A) Testing dataset model results for 10 afferents with 6 candidate models. The candidate models include one containing only force-related variables (force and its first time-derivative, dF/dt: blue), length-related variables (length, velocity, and acceleration: red), length-related variables with velocity raised to a fractional power (light red), muscle fiber length-related variable estimates (fiber length, velocity, and acceleration estimated with low and high tendon compliance: orange and light orange, respectively), and a free regression with all predictor variables from the other candidate models (purple). Top row: model selection frequency (number of times model was selected as the best candidate) for each model for 100 randomized testing datasets. Middle row: mean normalized likelihood (or Akaike weights, w_i) that a given model is the best predictor of information in the IFRs, based on corrected Akaike Information Criterion (AICc) for regressions of the 100 randomized testing datasets. This is the relative weight of evidence in favor of a model being the best, given the set of candidate models. The sum of all 6 Akaike weights is equal to 1. Bottom row: mean R² (coefficient of determination) calculated between afferent instantaneous firing rate and model prediction for 100 randomized testing datasets. Error bars represent 1 standard deviation. (B) Similar statistics to (A), but calculated for all 1000 randomized datasets (100 randomizations for 10 afferents). Top row: total model selection frequency for each model out of 1000 randomized datasets. Middle row: relative likelihood that each model is the best model in the set. This was calculated from the mean AICc values of all 10 afferents in (A). Bottom row: mean R² across all 10 afferents in (A) for each model. Error bars represent 1 standard deviation.</p

Linear regression of perturbation acceleration and muscle dF/dt to muscle spindle initial burst amplitude in 6 afferents.

<p>(A-F) Black dots represent the initial burst amplitude (IBA) versus either dF/dt or acceleration. Blue traces indicate linear regression of IBA on corresponding peaks in dF/dt. Red traces indicate linear regression of IBA on corresponding peaks in acceleration for the same trials. For all 12 cases (6 afferents, 2 regressions each), p < 0.05.</p

Estimated muscle fascicle length.

<p>(A) The Achilles tendon was assumed to be arranged in series with the triceps surae muscle fascicles. The measured musculotendon force was used to estimate tendon elongation. Muscle fascicle length was found by subtracting estimated tendon length from measured musculotendon length. A rigid tendon assumes changes in muscle fascicle length are equal to measured changes in musculotendon length. (B) Recorded IFR and measured musculotendon force in response to ramp-and-hold (left) and ramp-and-release stretches. Musculotendon force was used to compute estimated tendon elongation. (C) Example of estimated muscle fascicle length-related variables for ramp-and-hold stretch (left) and repeated ramp-and-release stretch (right). Top row is measured change in musculotendon length (red dashed trace) and two estimates of change in muscle fiber length (high tendon compliance = 2 mm^-1: yellow; low tendon compliance = 6 mm^-1: orange). The second and third rows are velocity and acceleration estimates, respectively, using the same coloring convention as for length.</p

Similarity of muscle spindle IFRs and musculotendon force-related variables in during stretch.

<p>(A) An example ramp-hold-release length profile applied to the triceps surae at the calcaneus, and response of the musculotendon force and muscle spindle primary afferent spiking. The spike train from a single trial and corresponding instantaneous firing rate (IFR) are shown in black at the top as an example of a typical response. Perturbation kinematics (i.e. muscle length, velocity, and acceleration) are shown in red. The musculotendon response to this stretch (i.e. force and dF/dt) is shown in blue. (B) The similarities between muscle spindle IFR shown in black at the top (ensemble average of 20 trials with bin size of 20 ms) and the muscle force-related variables shown in A. Specifically, note the similarities between force (green box) and the plateau response of the muscle spindle (yellow box), and between rate change in force (light blue box) and the dynamic response of the muscle spindle afferent (magenta box). The examples shown are from afferent 2.</p

Muscle Spindle Afferent Stretch Recordings from Blum et al. 2017

Muscle Spindle Afferent Stretch Recordings from Blum et al. 201

Single muscle spindle afferent statistics and model parameter estimates.

<p>(A) Dynamic index measured for each ramp-and-hold stretch trial for every afferent, organized in descending order from left to right. For the 10 afferents analyzed, stretch trials were separated based on the velocity (indicated by colors) imposed on the muscle for that trial (divided into 5 10 mm/s velocity bins ranging from 0–50 mm/s). Bins with fewer than 4 trials were excluded from this figure. Horizontal red lines represent the mean, the colored bars represent the standard error of the mean (SEM), and the black dots represent individual trial values. (B) In contrast to DI, force-related model weights were relatively constant with increasing stretch velocity. The color scheme is the same as in A. The upper plot is model weight on dF/dt and the lower plot is the model weight on force. (C) Force-related model weights and distributions for 100 randomized testing datasets (fitting one set of parameters for the entire dataset) for each afferent. For each afferent, a range of stretch perturbations (e.g. varying length, velocity, acceleration and stretch type) were included in the testing dataset. Red lines represent the means, grey bars represent standard deviations, and the black dots represent values for each testing dataset. As in B, model weights on dF/dt are shown in in the upper plot and model weights on force are shown in the lower plot. (D) Responses to a ramp-and-hold stretch at 3mm hold length, and 20mm/s stretch velocity for each afferent. Bottom row indicates conduction velocity for each afferent included in this analysis.</p

Reconstruction of muscle spindle firing rates by two candidate models.

<p>(A) Two main candidate models for predicting IFRs are shown: the force-related model used a combination of the force developed in the musculotendon and its first time-derivative as input (linearly combined, inputs and model prediction in blue); the length-related model used a linear combination of the muscle length, velocity, and acceleration (inputs and model prediction in red). The instantaneous firing rate of the afferent (black dots) was used to compute the error to optimize model parameters. (B) Three examples of muscle stretch with different stretch speed are shown (10, 20, and 40 mm/s). The stretch was sustained for 1s before being released. From top to bottom, the force-related model output (blue line) is overlaid on the instantaneous firing rate during the stretch; the recorded force (light blue) and the response of the afferent (black dots and raster) are shown directly below the force-related model output; the length-related model output (red line) is overlaid on the instantaneous firing rate and shown with the controlled musculotendon length (light red) below the response of the afferent. (C) The muscle was stretched to the same final length and at the same velocity, but with different initial accelerations (700 and 1400 mm/s², respectively). (D) The muscle was stretched with sawtooth patterns, where stretches were not sustained but immediately released and repeated. In all cases, the force-related model fits were as good or better than the length-related model fits, as indicated by the R² value. The examples shown are for afferents 4 (A-B, D) and 5 (C).</p