“Avatar”, a Modified Ex vivo Work Loop Experiments Using In vivo Strain and Activation

Özet

This article details the methodology for emulating in vivo muscle force production during ex vivo work loop experiments using an “avatar” muscle from a laboratory rodent to assess the contributions of strain transients and activation to the muscle force response.

Abstract

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.

Introduction

Moving animals achieve impressive athletic feats of endurance, speed, and agility in complex environments. Animal locomotion is particularly impressive in contrast to human-engineered machines-the stability and agility of current-legged robots, prostheses, and exoskeletons remain poor compared to animals. Legged locomotion in natural terrain requires precise control and rapid adjustments to alter the speed and maneuver environmental features that act as unexpected perturbations^1,2,3,4. Yet, understanding non-steady locomotion is inherently challenging because the dynamics depend on complex interactions between the physical environment, musculoskeletal mechanics, and sensorimotor control^1,2. Legged locomotion requires responding to unexpected perturbations with rapid multi-modal processing of sensory information and coordinated actuation of limbs and joints^1,5. Ultimately, movement is made possible by muscles producing force via intrinsic mechanical properties of the musculoskeletal system as well as from neural control^1,5,6,7. An outstanding question of neuromechanics is how these factors interact to produce coordinated movement in response to unexpected perturbations. The following technique utilizes muscle's intrinsic mechanical response to deformation using in vivo strain trajectories during controllable ex vivo experiments with an "avatar" muscle.

The muscle work loop technique has provided an important framework for understanding intrinsic muscle mechanics during cyclical movements^8,9,10. The traditional work loop technique drives muscles through predefined, typically sinusoidal, strain trajectories using frequencies and activation patterns measured during in vivo experiments^2,8,9,11. Using sinusoidal length trajectories can realistically estimate work and power output during flight¹² and swimming² under conditions where animals do not undergo rapid changes in strain trajectories due to interaction with the environment and musculoskeletal kinematics. However, in vivo muscle strain trajectories during legged locomotion arise dynamically from interactions among neural activation, musculoskeletal kinematics, and loads applied by the environment^5,7,13,14. A more realistic work loop technique is needed to emulate loads, strain trajectories, and force production that corresponds to in vivo muscle-tendon dynamics and provides insight into how intrinsic muscle mechanics and neural control interact to produce coordinated movement in the face of perturbations.

Here, we present a novel way to emulate in vivo muscle forces during treadmill locomotion by using an "avatar" muscle from a laboratory rodent during controlled ex vivo experiments with in vivo strain trajectories that represent time-varying in vivo loads. Using the measured in vivo strain trajectories from a target muscle on muscles from a laboratory animal during controlled ex vivo experiments will emulate loads experienced during locomotion. In the experiments described here, the ex vivo mouse extensor digitorum longus (EDL) muscle is used as an "avatar" for the in vivo rat medial gastrocnemius (MG) muscle during walking, trotting, and galloping on a treadmill¹³. 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. While mouse EDL muscles differ in size, fiber type, and architecture compared to the rat MG, it is possible to control for these differences. The "avatar" 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.

Protocol

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-Ttn^mdm/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.

1. Segment the entire in vivo trial into individual strides using any programming platform (MATLab code provided in Suplementary Coding File 1).
   1. Plot the length changes vs. time for the entire in vivo trial. This is used to visualize individual strides (stance to stance) and to assess among-stride variability (Figure 1).
   2. Calculate strain for the entire trial (Length (L) /Maximum Isometric Force at Optimal Length L₀).
   3. Select a stride from the entire trial that is representative of all strides, and that begins and ends at similar lengths. This can be done visually by graphing the lengths on top of each other to compare each stride.
   4. After a representative stride is selected, segment out strain, EMG/activation, and force data from the entire trial using any programming platform (see Supplementary Coding File 1 for the codes used in MATLab¹⁶).
   5. If sampling frequency differs for strain, EMG/activation or force, interpolate the data points so that all are sampled at the same frequency.
      NOTE: Researchers can determine the frequency of capture based on the time intervals between each point sampled in the entire trial. If variables are captured at the same frequency, the sampling times will be the same.
2. Calculate the frequency of segmented strides.
   1. Calculate the frequency by determining the duration of a segmented stride in seconds and dividing 1 (second) by the duration (1/duration = # strides per second).
   2. Manually determine how many data points must be acquired in ex vivo experiments to match the frequency.
   3. Calculate the time required for two strides. Repeat the strides at least once for estimating within muscle measurement error, which will be required for subsequent statistical analysis.
3. Determine the phase of stimulation relative to strain input using the measured EMG activity to determine the onset and duration of the stimulation for the ex vivo work loops. Any programming platform can be used (see Supplementary Coding File 1 for the code used in this study).
   1. View EMG signal over the same x-axis range (time) as strain change (Figure 1). Enlarge the EMG signal to be visible; this can be done by multiplying the EMG signal by an arbitrary number, rescaling the strain and EMG to be on the same scale, and/or adding the EMG signal to the strain.
      NOTE: Authors rescaled the strain and EMG to be on the same scale using "rescale" function in MATLab (see Supplementary Figure 1).
   2. Find where EMG activity starts and stops, as indicated by a change in intensity of two standard deviations^17,18.
      NOTE: Depending on the animal and muscle, EMG onset might or might not correspond with foot contact (Monica Daley, UC Irvine, personal communication) (see Discussion section).
   3. Calculate the percentage of the strain cycle (e.g., 40%) at which the EMG activation onset occurs and for how long the stimulation will occur (e.g., 222 ms).
      NOTE: Researchers will need to account for an excitation-contraction coupling (ECC) delay that differs between in vivo movement and ex vivo work loops and may be different for each animal and muscle (e.g., in vivo ECC is 24.5 ms for rat MG, ex vivo ECC is ~5 ms for mouse EDL).
4. Prepare representative strain inputs for the work loop controller program. Any program that can capture force output with input for strain and stimulation can be used for the work loop controller program (see Discussion section).
   1. Take the selected stride and interpolate to the appropriate number of points necessary to have the step captured at in vivo frequency for two cycles (see step 1.2).
   2. Rescale the stride to start and stop at "zero strain" (e.g., L₀ or 95% L₀) after stretching by a pre-determined length excursion (see step 3.3).
   3. "Scale" selected stride, if necessary, to use as an input for strain changes in mouse EDL (see Discussion section). To scale, select a length excursion to which the mouse EDL can be stretched without damage (e.g., we typically stretch the mouse EDL by 10% L₀ regardless of the in vivo species). This may need to change based on preliminary results (see step 3.3).

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

1. Set up equipment and surgery.
   NOTE: See the Discussion section for an explanation of the equipment needed for the ex vivo work loop.
   1. Prepare a tissue-organ bath by inserting the oxytube needle valve into the water-jacket tissue bath (see Table of Materials). Connect the oxytube to a gas cylinder with 95% 0₂-5% CO₂. Allow 20 psi to fill the water-jacket tissue bath.
   2. Prepare the surgery area by running an additional oxytube from the gas line to a crystallizing dish filled with Krebs-Henseleit solution (step 2.1.3) near the surgery area. This will be used to keep the muscles aerated and hydrated during and after the surgeries.
      NOTE: Muscles can also be stored in this aerated solution up to 4 h, if more than one muscle is taken out of the mouse at a time.
   3. Prepare 1 L of Krebs-Henseleit solution containing (in mmol l^-1): NaCl (118); KCl (4.75); MgSO₄ (1.18); KH₂PO₄ (1.18); CaCl₂ (2.54); and glucose (10.0) at room temperature and pH to 7.4 using HCl and NaOH (see Table of Materials). When handling HCl and NaOH, wear the proper PPE of goggles and gloves.
   4. Fill the bath with Krebs-Henseleit solution at room temperature and pH 7.4. Submerge the muscle and the hook completely in the solution.
   5. Turn on all equipment; dual-mode muscle lever system, stimulator, and signal interface (DAQ board) (see Table of Materials).
2. EDL muscle dissection.
   1. Deeply anesthetize the mouse and then perform euthanasia by cervical dislocation. Lay the mouse in either a right or left lateral recumbent position with the top hindlimb stretched and toes touching the dissection board. Remove the fur from the ankle to above the knee joint.
   2. Tent the skin with forceps and cut from the ankle joint to the hip area. Once the muscle has been exposed, cut around the ankle like a "hem" of pants. Pull the skin up to expose the leg muscles more clearly.
   3. Locate the fascia line that separates the tibialis anterior (TA) and gastrocnemius, separate using dissection scissors to expose the knee tendons. Place dissection scissors between the two exposed knee tendons. Scissors will "catch" on a pocket just below the exposed knee tendons. Blunt dissect a "pocket" while pulling the scissors away from the leg until the scissors reach the ankle to expose the EDL.
   4. Using a pre-tied loop knot in size 4-0 silk surgical suture (see Table of Materials), lace one end of the suture under the tendon closest to the knee. Tie a double square knot above the proximal muscle-tendon junction without placing it on the muscle or including the tendon. Cut above the knot. Gently pull the loop tied to the tendon, and the EDL will emerge from the "pocket".
   5. Tape the loop to the dissection area to create tension in the EDL. Tie a double square knot using another pre-tied loop knot at the distal muscle-tendon junction without placing it on the muscle or including the tendon. Cut the knot on the side closer to the leg to remove the whole EDL from the mouse. Cut the extra suture away from the double square knots on the proximal and distal sides of the muscle and place the muscle in the aerated bath by the surgery area.
      NOTE: Ensure to note which side is proximal and/or distal if placing the muscle in an aerated bath.
   6. To place on the servomotor lever rig, attach EDL vertically between suspended platinum electrodes. Attach the distal loop knot to the stationary hook and attach the proximal loop knot to the hook attached to the servomotor arm. Raise the tissue bath to submerge the muscle in the aerated Krebs-Henseleit solution.
      NOTE: Aeration should not disturb the muscle when it is submerged. If it does, lower the pressure of the gas. Allow muscle to equilibrate for 10 minutes before beginning stimulation.
3. Measure the maximum isometric force of EDL muscle.
   NOTE: Refer to Table 1 for protocol on how to measure maximum isometric force using twitch and tetanus. See Supplementary Figure 1 for an illustration of the program used by the authors.
   1. Stimulate the muscle with a supramaximal twitch to ensure the muscle has not been damaged during surgery (80 V, 1 pps, 1ms; Table 1; see Supplementary Figure 2). If no damage has occurred, use the length knob on the muscle lever system to find a muscle length using twitch stimulation at which active tension is ~1V / 0.1271 N with less than ~0.1V / 0.01271N passive tension.
   2. Record the starting length of the muscle from suture knot to suture knot in Volts and millimeters. Input measurements into the calibration portion of the program for starting length (see Supplementary Figure 1).
   3. Find supramaximal twitch maximum isometric force at optimal length (L₀) of EDL (Table 1). No rest period is technically needed, but waiting 1 min between stimulations will stabilize passive tension. Record the length (in Volts) at which the supramaximal twitch is maximum. This is the muscle optimum length (L₀) for twitch.
   4. Measure the muscle with calipers at this length. Measure the muscle from suture knot to suture knot. Once L₀ has been found, shorten the muscle back to starting length (active tension ~1V / 0.1271 N).
   5. Find supramaximal tetanus maximum isometric force of EDL (80 V, 180 pps, 500 ms; Table 1). Record the length (in Volts and millimeters) of supramaximal tetanic force at L₀ and measure the fibers from suture knot to suture knot again with calipers.
      ​NOTE: Increasing the muscle length in 0.5 V/0.65 mm steps will result in more accurate L₀ for both twitch and tetanus.
   6. Find the submaximal isometric force of EDL (45 V, 110 pps, 500ms; Table 1) at L₀ before and after the experiment to ensure fatigue did not occur from the stimulation protocol. A 10% decrease in force is considered a "fatigued" muscle.

Experiment			Simulation Intensity (V)		Pulse Frequency (pps / Hz)		Stimulation Duration (ms)		Yorumlar
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

1. Set up the software necessary to complete "avatar" work loop techniques (see Table of Materials).
   NOTE: An input file (.csv or similar) that specifies the muscle length at each time step is needed (see step 1.4). Inputs for the percentage of the cycle at which the stimulation starts and for the duration of stimulation are necessary (see Supplementary Figure 3 for example).
2. Complete "avatar" work loop technique.
   NOTE: While we use a custom LabView program, researchers can use any program that allows control of length changes in mouse EDL on a servomotor lever, control of the onset (% cycle) and duration (ms) of stimulation at specified times, and measurement of muscle force. See Supplementary Figure 3 for an illustration of the program authors use.
   1. Upload the scaled strain changes with scaled length excursion into the program from step 1.4. See steps 1.4, 3.3, and the Discussion section for more on "scaled strain changes".
   2. Adjust the starting length of the muscle if needed (see section 3.3). Input the starting length in V and mm to calibrate results (see Supplementary Figure 3).
   3. Use stimulation onset and duration calculated in step 1.3.
   4. Run the muscle through the scaled length changes with determined length excursion for two cycles.
   5. Save data. If several stimulation protocols are collected on the same muscle, wait 3 min between each stimulation.
   6. Stimulate at optimal length (L₀) using submaximal activation to determine if fatigue has occurred. If force decreases by more than 10%, muscles are considered fatigued. See Table 1 for stimulation protocols.
   7. Remove the muscle from the bath. Cut-loop knots from the muscle and dab the excess solution off the muscle. Weigh the muscle. Determine physiological cross-sectional area using the standard formula: muscle mass/(L₀*1.06)¹⁹.
3. Tune parameters for "avatar" work loop technique (see Discussion section).
   1. Determine the starting length and length excursion by matching the ex vivo passive tension rise to the passive tension rise observed in vivo (Figure 2).
      NOTE: This study used percent L₀ to scale starting length (mm) and excursion (% L₀; see step 1.4 and Discussion section). For matching the tension rise in ex vivo mouse EDL to that of the in vivo rat MG, the authors found that starting length at L₀ produced the best fit (Figure 2).
   2. Choose three starting lengths (e.g., -5% L₀, L_0, and +5% L₀). Perform the "avatar" work loop at each of these starting lengths with a specified length excursion (e.g., 10% L₀).
      NOTE: In the present "avatar" experiments using mouse EDL, a length excursion of 10% L₀ was used.
   3. Repeat with new starting lengths and/or excursion until the rate of ex vivo passive tension rise is similar to the rate of in vivo passive tension rise (see Figure 2B).
   4. Depending on fiber types and activation dynamics of the muscles used, increase or decrease the duration of stimulation to optimize the match between ex vivo and in vivo force. Thus, it may be necessary to change the onset and/or duration of stimulation to best match in vivo force production during "avatar" experiments.
   5. To decide whether this is necessary (see Discussion section), plot force over time of "avatar" and in vivo muscle (Figure 3) and calculate the coefficient of determination R² by squaring the scaled correlation between target and "avatar" muscle force (see Representative results).

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.

Representative Results

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 muscles^20,21. 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, 25^th, and 75^th 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, 25^th, and 75^th 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, 25^th, and 75^th 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.

Discussion

While organisms move seamlessly across landscapes, the underlying loads and strains that the muscles experience vary drastically^1,6,23. During both in vivo locomotion^1,24 and in "avatar" experiments, muscles are stimulated submaximally under cyclical, non-steady conditions. The isometric force-length and isotonic force-velocity relationships are not well suited for predicting muscle force under these conditions². Understanding the effects of non-steady strain (i.e., transients) and loading is essential for predicting force production during in vivo movement, and therefore is the main rationale for developing these "avatar" experiments². "Avatar" experiments allow us to control muscle loading and strain trajectories while measuring force output. The "avatar" technique investigates the force response of muscles under in vivo-like conditions, without confounding factors of neural control and tendon compliance. To perform the "avatar" experiments, researchers will need a program that allows a muscle to go through prescribed length changes with the ability to stimulate at different starting lengths and for varying durations (see Supplementary Figure 3 for the program the authors use). Researchers need to specify starting muscle length (mm), length of excursion (mm), onset of stimulation (% of cycle duration) and duration of stimulation (ms) before doing experiments (see steps 1.3-1.4to obtain values for these parameters). In general, it is often desirable to select strides that are representative of all strides in the trial (e.g., start and end at a similar length, reach a similar peak force, have average EMG activity, etc.). Determining whether EMG/activation and force data from a selected stride is representative of other strides in the same trial can be helpful for "tuning" later, which can be done by plotting work loops (force versus length) of the entire trial using the target animal's muscle. During bipedal and quadrupedal locomotion, the shortest length to shortest length generally demarcates an entire stride (toe-off to toe-off), but EMG activation can vary. In some animals and muscles, EMG activation is closely correlated to foot contact, such as the rat MG shown here²². In other animals, such as the guinea fowl lateral gastrocnemius, EMG activation generally occurs at the longest length to achieve more stability during unknown terrain²⁵.

To perform "avatar" experiments, it is important to minimize the noise in the ex vivo force data. Force measurements are sensitive to several issues, including but not limited to tearing of the muscles during surgery, compliance of the sutures if the loop-knots are too long, improper scaling of the length inputs and excursion, and muscle fatigue. Tearing of the muscles often occurs when "dissecting the pocket" (step 2.2.3) and tying the loop-knot around the proximal portion of the tendon (step 2.2.4). While "dissecting the pocket", keeping the dissection scissors flat and horizontal to the muscle will prevent the tips from nicking the EDL. Additionally, pulling the dissection scissors away and distally while blunt dissecting will also limit contact between the dissection scissors and the EDL muscles. Additionally, muscles should be kept damp with Krebs-Henseliet solution during the surgery preparation and when being used on the rig.

Properly scaling length inputs is more complicated. Muscle passive and active force can be affected if the starting length and/or excursion are not scaled properly. The ex vivo rise in passive tension should match the in vivo rise in passive tension (see Figure 1). One scaling issue that has been observed in previous experiments is that both passive and active tension can be affected if the length excursion (starting length to longest length) is too small or too large. Theoretically, muscles should reach peak force near their optimal length (L₀)²⁶, which is why we use optimal length (L₀) to scale in vivo muscle lengths in ex vivo "avatar" experiments to accurately replicate in vivo force production. Architectural differences between muscles will play a role in determining the starting length and length excursion parameters. Although optimal length (L₀) is found during supramaximally stimulated isotonic and isometric conditions, using it as a scaling metric in "avatar" experiments can potentially highlight limitations of the force-length and force-velocity relationships during cyclical movement that need more investigation. In most steady-state conditions, muscle's instantaneous length, velocity, and activation (i.e., force-length and force-velocity properties) can be used to predict force and work output with reasonable accuracy^12,24,27. Under dynamic conditions with variable loading, the force increases as a function of velocity²⁸ and has a complex relationship with strain and activation^29,30. This contradicts the isotonic force-velocity and isometric force-length properties of muscles²⁸. In the rat MG, strain and velocity transients are evidence of loading, such as foot contact or interaction with the environment (i.e., rough terrain, wind, sudden change in direction for predation avoidance) (Figure 9). These rat MG strain trajectories, like most realistic conditions, have sudden changes in the applied load, force production, and work output^2,28. This experimental method aims to highlight these complex interactions among strain, velocity, and activation dynamics under in vivo conditions that are not well explained by traditional force-length and force-velocity relationships.

Other issues can occur when the muscle starting length is too short or long. A too-short starting length will result in a reduced rate of rise in tension during the passive and active stretch (not shown), whereas a too-long starting length will result in an increased rate of rise in passive tension (see Figure 1B). Using the ratio of active to passive tension can be helpful. For example, in rat MG, passive tension (N) is generally around half the active tension (Figure 2). If a muscle starts at too long a length and/or is stretched to a length that is too long, the passive tension may be too high relative to the active tension (see Figure 1B), and the force may decrease quickly due to overstretching. Also, stretching to a length that is too long will potentially damage the muscle and can cause the muscle to fatigue more quickly. Additionally, active tension may appear unfused if the starting length is too short and/or the muscle is not stretched to a long enough length.

Preliminary experiments are necessary to determine starting length and excursion based on L₀. Additional preliminary experiments may be needed to adjust the duration of stimulation if the activation dynamics of the muscles used are different. These optimizations are needed because the fiber type composition and/or activation dynamics of in vivo and ex vivo muscles may be different. In our representative results (Figure 4 and Figure 5), we used two stimulation protocols for mouse EDL during ex vivo experiments to replicate in vivo rat MG force production. To optimize force production in the mouse EDL to best fit in vivo rat MG, stimulation duration was increased (Figure 2 and Figure 3). Rat MG is comprised of slower fiber types than mouse EDL^31,32,33. This was evident in "avatar" experiments because ex vivo mouse EDL muscles produced force faster after excitation, and force decreased at a faster rate after deactivation than observed in vivo in rat MG¹⁵ (Figure 2), even after accounting for excitation-contraction delay differences between in vivo and ex vivo conditions³⁴. Depending on the ex vivo and in vivo target muscles, optimization of stimulation might be needed in other "avatar" experiments as well. Either the mouse EDL or soleus (SOL) muscles may be used in this ex vivo work loop technique. EDL was chosen as an "avatar" for the rat MG due to the similarities in muscle fiber type and pennation structure. It is possible that some muscles may have a complex structure and cannot be emulated using muscles from laboratory rodents as an "avatar".

While "avatar" experiments do need some manual optimization to best replicate in vivo force production, the technique is applicable to a variety of different animals and locomotor modes. The "avatar" technique can be especially useful to understand in vivo force production in animals whose muscles are too large or otherwise inaccessible for ex vivo experiments. While only preliminary work has been done on larger animals³⁵, this work has shown potential for the applicability of this technique across animals, muscles, and locomotor gait using laboratory mice as "avatars". The usefulness of "avatar" experiments depends on how accurately a convenient, inexpensive, readily available, and well-characterized laboratory rodent model (i.e., mouse EDL) can be used for understanding in vivo mechanics of different muscles from varying species of vertebrates. Results from preliminary "avatar" experiments presented here (rat MG) and elsewhere (guinea fowl LG¹⁹), suggest this technique can be used to accurately predict in vivo forces and could be applied to other animals. Future applications of this method should expand the types of muscles and animals that have been used as both targets and "avatar" during ex vivo and in vitro experiments. "Avatar" experiments allow us to examine factors that affect muscle force and work output during in vivo locomotion when muscle loading and strain vary abruptly^1,2,19. Specifically, the "avatar" method allows us to examine the effects of strain and velocity transients on muscle force that are not captured by traditional muscle models or sinusoidal work loop experiments.

Materials

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