All animal studies were approved by the Institutional Animal Care and Use Committee at Northern Arizona University. Extensor digitorum longus (EDL) muscles from male and female wild-type mice (strain B6C3Fe a/a-Ttnmdm/J), aged 60-280 days, were used for the present study. The animals were obtained from a commercial source (see Table of Materials), and established in a colony at Northern Arizona University.
1. Selecting in vivo strain trajectory and preparing for use during ex vivo work loop experiments
NOTE: In this protocol, prior measurements from in vivo dynamic locomotion, provided directly to the authors (Nicolai Konow, UMass Lowell, personal communication), were used in ex vivo experiments. The original data was collected for Wakeling et al.15. Time, length or strain, EMG/activation, and force data are required to replicate the protocol.
Figure 1: Length over time of in vivo whole trial. Length (mm) plotted against time of rat MG. Strides are demarcated by circles, from shortest length to shortest length, considered single stride. Please click here to view a larger version of this figure.
2. Evaluating maximum isometric force of mouse muscle ex vivo
Experiment | Simulation Intensity (V) | Pulse Frequency (pps / Hz) | Stimulation Duration (ms) | Comments | ||||||||
1. "Warm-Up" | 80 | 1 | 1 | Increase or decrease length by 0.50 V to find passive tension of 1 V | ||||||||
2. Optimal muscle length twitch (L0) | 80 | 1 | 1 | Increase or decrease length by 0.50 V to find passive tension of ~1 V | ||||||||
3. Optimal muscle length tetanus (L0) | 80 | 180 | 500 | Rest 3 min between changing length by 0.50 V | ||||||||
4. Pre-experiment submaximal L0 | 45 | 110 | 500 | At length of L0 | ||||||||
6. Avatar experiments | 45 | 110 | Cyclically use representative length changes for mouse EDL | |||||||||
7. Post-experiment submaximal L0 | 45 | 110 | 500 | Return to L0 after experiment and measure L0 |
Table 1: Stimulation protocol. Stimulation protocol for finding supramaximal and submaximal twitch and tetanus optimal length. Protocol varies by stimulation intensity, timing, and pulses per second.
3. Completing "avatar" work loop technique using selected in vivo strain trajectories
Figure 2: Matching passive tension rise. Work loops showing the in vivo and ex vivo rise in passive tension (arrows). In vivo scaled work loop from rat MG (black) walking at 2.9 Hz (data from Wakeling et al.15). Ex vivo scaled work loops from mouse EDL (green) at 2.9 Hz. (A) Starting length of mouse EDL muscle is +5% L0. (B) Starting length of the mouse EDL muscle is L0. Note that the ex vivo passive tension rise matches the in vivo tension rise in A but not in B. Thicker lines indicate stimulation. Please click here to view a larger version of this figure.
Figure 3: Optimizing stimulation duration of mouse EDL to match in vivo force of rat MG (black line). The force generated by the mouse EDL using the EMG-based stimulation (green dashed line) decreases earlier than the in vivo force, likely due to faster deactivation of the mouse EDL compared to rat MG. To optimize the fit between the in vivo and ex vivo forces, the mouse EDL was stimulated for a longer duration (solid green line). EMG-based stimulation R2 = 0.55, Optimized stimulation R2 = 0.91. Please click here to view a larger version of this figure.
The goal of the "avatar" experiments is to replicate in vivo force production and work output as closely as possible during ex vivo work loop experiments. This study chose to use mouse EDL as an "avatar" for rat MG because mouse EDL and rat MG are both comprised of mostly of fast-twitch muscles20,21. Both muscles are primary movers of the ankle joint (EDL ankle dorsiflexor, MG ankle plantarflexor) with similar pennation angles (mouse EDL 12.4 + 2.12°22, rat MG 20° used in this study15). Scaled representative work loops of rat MG15 were compared to ex vivo "avatar" experiments (Figure 4) using two different stimulation protocols (one from measured EMG activity and one optimized as in step 3.3). R2 values presented here were calculated using the entire scaled stretch-shortening cycle (2 cycles/condition), with each cycle having more than 2000 points corresponding to the locomotor speed (walk = 5521 points, trot = 5002, gallop = 2502 points). Work loops were scaled to account for differences in muscle size, P0, and PCSA. Scaling was done by linearly mapping force and strain onto a similar scale (0-1) to compare rat MG and mouse EDL. Visually, it is apparent that optimizing the stimulation protocol (Figure 4B) to account for different activation dynamics of the mouse EDL and rat MG muscles improves the fit to the in vivo rat MG force compared to the EMG-based activation (see Discussion section). For the mouse EDL, approximately doubling the stimulation duration for slower strain trajectories (walk and trot) increased the R2 by 62% in walking and 109% in trot. For the faster strain trajectory (gallop), increasing stimulation time by half the observed time increased the R2 by 22%.
Figure 4: Comparison of in vivo and ex vivo work loops. Work loops of in vivo rat MG (black) and ex vivo mouse EDL (green) during walking (2.9Hz) using in vivo strain trajectories. The thicker line indicates stimulation in both in vivo and ex vivo work loops. (A) Work loop of in vivo rat MG (black) and ex vivo mouse EDL (dashed green) during walking using EMG-based stimulation protocol. (B) Work loop of in vivo rat MG (black) and ex vivo mouse EDL (solid green) during walking (2.9Hz) using optimized stimulation. Please click here to view a larger version of this figure.
High R2 between mouse EDL ex vivo force production and in vivo force production of rat medial gastrocnemius (MG)15 indicates good replication (Figure 5). In EMG-based stimulation experiments, average R2 values were 0.535, 0.428, and 0.77 for walk, trot, and gallop, respectively. In optimized stimulation experiments, average R2 values were 0.872, 0.895, and 0.936 in walk, trot, and gallop, respectively. As previously discussed (step 3.3, Figure 5), depending on the activation dynamics of the muscles used, the stimulation protocol may also need to be optimized. Prediction of in vivo MG force using ex vivo mouse EDL was improved across all locomotor speeds by optimizing stimulation, increasing R2 (Figure 5A,B), and decreasing root mean square error (RMSE). RMSE decreased after optimization for all speeds (Figure 6). Averaged RMSE for EMG-based stimulation was 0.31, 0.43, and 0.158 for walk, trot, and gallop. Averaged RMSE for optimized stimulation was 0.181, 0.116, 0.101 for walk, trot, and gallop.
Figure 5: R2 Values for in vivo and ex vivo force production: Box and whisker plot of R2 values for in vivo and ex vivo force comparisons. Individual observations plotted, median, 25th, and 75th percentile indicated. (A) R2 values for in vivo and ex vivo force production using stimulation protocol based on measured in vivo EMG signal during walking at 2.9 Hz (green), trotting at 3.2 Hz (magenta), and galloping at 6.2 Hz (cyan). (B) R2 values for in vivo and ex vivo force production using optimized stimulation (see Figure 2). Optimizing the stimulation onset and duration increased R2 for all gaits. EMG-based stimulation: walk R2 = 0.50-0.55, trot R2 = 0.37-0.47, gallop R2= 0.62-0.90; optimized stimulation: walk R2 = 0.74-0.93, trot R2 = 0.85-0.92, gallop R2 = 0.87-0.97. Please click here to view a larger version of this figure.
Figure 6: Root-mean square error (RMSE) for in vivo and ex vivo force production. Box and whisker plot of RMSE values for in vivo and ex vivo force comparisons. Individual observations plotted, median, 25th, and 75th percentile indicated. (A) RMSE values for in vivo and ex vivo force production using EMG-based stimulation protocol. (B) RMSE values for in vivo and ex vivo using optimized stimulation protocol. Optimizing the stimulation onset and duration reduced RMSE for all gaits. Walking at 2.9 Hz (green), trot at 3.2 Hz (magenta), and gallop at 6.4 Hz (cyan). Please click here to view a larger version of this figure.
To test the performance of traditional work loop methods at predicting in vivo muscle forces, sinusoidal work loops were also performed for the mouse EDL at the same frequency, length excursion, starting length, stimulation onset, and duration as for the "avatar" experiments using in vivo rat MG strain trajectories. R2 values were significantly lower than for the in vivo strain trajectories for both EMG-based and optimized stimulation protocols (Figure 7). Averaged R2 values for EMG-based stimulation using sinusoidal length trajectories were 0.062, 0.067, and 0.141 at walk, trot, and gallop frequencies. Averaged R2 values for optimized stimulation using sinusoidal length trajectories were 0.09, 0.067, and 0.141 at walk, trot, and gallop frequencies.
Figure 7: R2 Values for in vivo and ex vivo force production using sinusoidal length changes. Box and whisker plot of RMSE values for in vivo and ex vivo force comparisons. Individual observations plotted, median, 25th, and 75th percentile indicated. R2 values for walk (green, 2.9 Hz), trot (magenta, 3.2 Hz), and gallop (cyan, 6.2 Hz) using sinusoidal length changes with EMG-based (translucent) and optimized (opaque) stimulation protocols. For both EMG-based and optimized stimulation, the R2 values were lower for the sinusoidal length changes than for in vivo length changes. EMG-based stimulation: walk R2 = 0.00 – 0.30, trot R2 = 0.00 – 0.02, gallop R2= 0.03 – 0.07; optimized stimulation: walk R2 = 0.02 – 0.21, trot R2 = 0.02 – 0.12, gallop R2 = 0.12 – 0.17. Please click here to view a larger version of this figure.
Work loops produced by the ex vivo mouse EDL muscle using sinusoidal length trajectories do not as accurately emulate in vivo rat MG force compared to in vivo strain trajectories (Figure 8). The change in work produced by sinusoidal vs. in vivo strain trajectories can be explained by the absence of strain and velocity transients in the sinusoidal trajectory (Figure 9). While the muscles were stimulated at similar lengths during the active shortening phase of the contractions in both sinusoidal trajectories and in vivo-based strain trajectories, the onset of stimulation occurred at different phases of the cycle (e.g., stimulation onset occurred at a phase of 74% for trot EMG-based stimulation, but at a phase of 43% for walking EMG-based stimulation; see Discussion section).
Figure 8: Comparing in vivo and ex vivo sinusoidal work loops. (A) In vivo work loop (black) from rat MG and ex vivo work loop (dashed magenta) from mouse EDL using sinusoidal strain trajectory and EMG-based stimulation. (B) In vivo work loop (black) from rat MG and ex vivo work loop (solid magenta) from mouse EDL using sinusoidal strain trajectory and optimized stimulation. Note that the sinusoidal work loops overestimate the in vivo work due to the absence of strain and velocity transients in the sinusoidal trajectory. EMG-based stimulation R2 = 0.0003, optimized stimulation R2 = 0.084. Please click here to view a larger version of this figure.
Figure 9: Comparison of in vivo strain and ex vivo sinusoidal length trajectories. Comparison of in vivo strain and ex vivo sinusoidal length trajectories at walk (green), trot (magenta), and gallop (blue). The solid line is in vivo strain trajectory. Dashed line ex vivo sinusoidal length trajectory. The highlighted portion is stimulation. Stimulation started at the same length during the shortening phase of the stride. Arrows indicating strain and velocity transients. Deviations from sinusoidal are impedance from outside forces on muscle. Please click here to view a larger version of this figure.
Supplementary Figure 1: Program used to collect isometric maximal force at optimal length. The program used to determine optimal length during supramaximal and submaximal twitch and tetanic stimulation. Please click here to download this File.
Supplementary Figure 2: Viable twitch response. Twitch response of mouse EDL. Twitch force rises and falls quickly and should reach active tension of ~1 V. "Noise" should be minimal after the peak active tension has been reached. Please click here to download this File.
Supplementary Figure 3: Program used to collect work loop data. The program used to control muscle length of and timing of stimulation in ex vivo work loops. Please click here to download this File.
Supplementary Coding File 1: MATLab code used to segment and create an experimental protocol for the work loop. MATLab code that was used to segment target step information (length, EMG activation, and force) into individual strides. Code includes scaling and interpolating target animal steps into lengths that ex vivo mouse EDL can stretch. Additionally, includes code to smooth EMG signal and compare activation to select onset and duration of stimulation in ex vivo work loop experiments. Please click here to download this File.
Braided Non-Absorbable Silk Suture 4-0 | Mersilk | 734H | |
Calcium Chloride Dihydrate (CaCl2) | Sigma-Aldrich | 1086436 | Krebs-Henseleit solution |
Dextrose | Sigma-Aldrich | D9434 | Krebs-Henseleit solution |
HEPES | Sigma-Aldrich | PHR1428 | Krebs-Henseleit solution |
Hydorchloric Acid (HCl) | Sigma-Aldrich | 1.37055 | Krebs-Henseleit solution |
LabView Data Collection | Lab-View | ||
Magnesium Sulfate (MgSO4) | Sigma-Aldrich | M7506 | Krebs-Henseleit solution |
Potassium Chloride (KCl) | Sigma-Aldrich | P3911 | Krebs-Henseleit solution |
Potassium Phosphate Monobasic (KH2PO4) | Sigma-Aldrich | 5.43841 | Krebs-Henseleit solution |
S88 Stimulator | Grass | M643H05 | Available for purchase on Ebay |
Series 300B Lever System | Aurora | 1200A | includes water-jacket tissue bath |
Sodium Bicarbonate (NaHCO3) | Sigma-Aldrich | S5761 | Krebs-Henseleit solution |
Sodium Chloride (NaCl) | Sigma-Aldrich | S9888 | Krebs-Henseleit solution |
Sodium Hydroxide (NaOH) | Sigma-Aldrich | S5881 | Krebs-Henseleit solution |
Wild Type Mice | Jackson Laboratory | B6C3Fe a/a Ttn mdm/J |
Movement behaviors are emergent features of dynamic systems that result from muscle force production and work output. The interplay between neural and mechanical systems occurs at all levels of biological organization concurrently, from the tuning of leg muscle properties while running to the dynamics of the limbs interacting with the ground. Understanding the conditions under which animals shift their neural control strategies toward intrinsic muscle mechanics ('preflexes') in the control hierarchy would allow muscle models to predict in vivo muscle force and work more accurately. To understand in vivo muscle mechanics, ex vivo investigation of muscle force and work under dynamically varying strain and loading conditions similar to in vivo locomotion is required. In vivo strain trajectories typically exhibit abrupt changes (i.e., strain and velocity transients) that arise from interactions among neural activation, musculoskeletal kinematics, and loads applied by the environment. The principal goal of our "avatar" technique is to investigate how muscles function during abrupt changes in strain rate and loading when the contribution of intrinsic mechanical properties to muscle force production may be highest. In the "avatar" technique, the traditional work-loop approach is modified using measured in vivo strain trajectories and electromyographic (EMG) signals from animals during dynamic movements to drive ex vivo muscles through multiple stretch-shortening cycles. This approach is similar to the work-loop technique, except that in vivo strain trajectories are scaled appropriately and imposed on ex vivo mouse muscles attached to a servo motor. This technique allows one to: (1) emulate in vivo strain, activation, stride frequency, and work-loop patterns; (2) vary these patterns to match in vivo force responses most accurately; and (3) vary specific features of strain and/or activation in controlled combinations to test mechanistic hypotheses.
Movement behaviors are emergent features of dynamic systems that result from muscle force production and work output. The interplay between neural and mechanical systems occurs at all levels of biological organization concurrently, from the tuning of leg muscle properties while running to the dynamics of the limbs interacting with the ground. Understanding the conditions under which animals shift their neural control strategies toward intrinsic muscle mechanics ('preflexes') in the control hierarchy would allow muscle models to predict in vivo muscle force and work more accurately. To understand in vivo muscle mechanics, ex vivo investigation of muscle force and work under dynamically varying strain and loading conditions similar to in vivo locomotion is required. In vivo strain trajectories typically exhibit abrupt changes (i.e., strain and velocity transients) that arise from interactions among neural activation, musculoskeletal kinematics, and loads applied by the environment. The principal goal of our "avatar" technique is to investigate how muscles function during abrupt changes in strain rate and loading when the contribution of intrinsic mechanical properties to muscle force production may be highest. In the "avatar" technique, the traditional work-loop approach is modified using measured in vivo strain trajectories and electromyographic (EMG) signals from animals during dynamic movements to drive ex vivo muscles through multiple stretch-shortening cycles. This approach is similar to the work-loop technique, except that in vivo strain trajectories are scaled appropriately and imposed on ex vivo mouse muscles attached to a servo motor. This technique allows one to: (1) emulate in vivo strain, activation, stride frequency, and work-loop patterns; (2) vary these patterns to match in vivo force responses most accurately; and (3) vary specific features of strain and/or activation in controlled combinations to test mechanistic hypotheses.
Movement behaviors are emergent features of dynamic systems that result from muscle force production and work output. The interplay between neural and mechanical systems occurs at all levels of biological organization concurrently, from the tuning of leg muscle properties while running to the dynamics of the limbs interacting with the ground. Understanding the conditions under which animals shift their neural control strategies toward intrinsic muscle mechanics ('preflexes') in the control hierarchy would allow muscle models to predict in vivo muscle force and work more accurately. To understand in vivo muscle mechanics, ex vivo investigation of muscle force and work under dynamically varying strain and loading conditions similar to in vivo locomotion is required. In vivo strain trajectories typically exhibit abrupt changes (i.e., strain and velocity transients) that arise from interactions among neural activation, musculoskeletal kinematics, and loads applied by the environment. The principal goal of our "avatar" technique is to investigate how muscles function during abrupt changes in strain rate and loading when the contribution of intrinsic mechanical properties to muscle force production may be highest. In the "avatar" technique, the traditional work-loop approach is modified using measured in vivo strain trajectories and electromyographic (EMG) signals from animals during dynamic movements to drive ex vivo muscles through multiple stretch-shortening cycles. This approach is similar to the work-loop technique, except that in vivo strain trajectories are scaled appropriately and imposed on ex vivo mouse muscles attached to a servo motor. This technique allows one to: (1) emulate in vivo strain, activation, stride frequency, and work-loop patterns; (2) vary these patterns to match in vivo force responses most accurately; and (3) vary specific features of strain and/or activation in controlled combinations to test mechanistic hypotheses.