Optimizing Muscle Activations in Flight-Phase Sprinting at Different Speeds

Team Members

• Katie Marusich
• Kristen Steudel

Project Video

Sprinting_StaticOptimization.mp4

Project Files

Background

Hamstring muscle strain injuries (HSI) are one of the most common injuries in sprinting sports [2]. It has been found that hamstring injuries occur in the late swing phase of high speed running when the muscle-tendon unit reaches its peak length and develops a high force [12]. In the past eleven seasons of the UEFA professional men's soccer league, there has been an increase in hamstring injuries and they now constitute 24% of injuries [3]. The Nordic Hamstring Exercise (NHE) has been prescribed for decreasing rates of injury, but the UEFA has not seen an uptake in the exercise [3]. Sprint training could be a more agreeable training method because it has the potential to strengthen the elastic properties of connective tissue, increase motor unit activation, increase passive tension of the muscle-tendon complex and improve cross-bridge mechanics and it is sport specific [10].

Previous studies found that eccentric hamstring strength and biceps femoris long head fascicle length (BFlhFL) are modifiable risk factors for hamstring strain injury [10]. Both NHE and sprint training have been shown to increase the BFlhFL and eccentric hamstring strength [4,7,8,10]. However, it is still unclear how the exercises compare. For example, Ripley found that the NHE was superior to sprint training. Similarly, Freeman et al. found that the NHE group increased 9.8% in eccentric hamstring strength while the sprint training group increased by 6.2%. This experiment had no control for resistance training [4]. On the other hand, Mendiguchia et al. found that sprint training increased the BFlhFL by 16.21% whereas NHE training increased the BFlhFL by 7.38% [7]. In Mendiguchia’s study, the sprint training was quite intensive with multiple sessions of high volumes.

These studies demonstrate a need to know equivalent repetitions of NHE and sprinting. Until this is known, it is difficult to compare training programs' effects on HSI modifiable risk factors. 

A first step in determining the equivalence of NHE and sprinting is determining the hamstring muscle activations in the flight phase of sprinting, where the hamstring activations have a peak, via static optimization.

Research Question(s)

What are the muscle activations in the hamstrings muscles during sprinting at 50 to 95 percent of top speed during the flight phase, as determined by static optimization?

Methods

Data Collection & Model Preparation

1. Collect data files from experimental sprinting trials in the Human Performance Laboratory (HPL) at Stanford University. These files include motion capture, ground reaction force data, and raw EMG data. Trim data files to a single flight phase for each speed.
2. Scale an existing OpenSim sprinting model using AddBiomechanics and flight phase motion capture data
3. Adjust the muscle-tendon parameters of the scaled model to account for larger range of motion in sprinting
4. Filter raw EMG data and normalize using the peak voltage value for each muscle out of all the sprinting trials. 

Run Static Optimization in Custom Matlab Script

1. Calculate inverse kinematics to get generalized coordinates
2. Calculate  inverse dynamics to get the joint moments
3. Design joint moment equality constraints to include contributions from muscles and reserve actuators.
4. Implement an objective function that minimizes the sum of muscle activations squared and reserve actuator activations squared.
5.  Run the static optimization program for each speed

Analysis

1. Validate the solved muscle activations with the experimental EMG data.
2. Compare hamstring muscle forces with previous literature. 

Model: 

We used an existing OpenSim model for sprinting which included lower limb muscles and models the torso as a rigid body and allowed for greater range of motion than a traditional walking model. The model uses the Lai-Arnold model, a modified Rajagopal model with DeGrooteFregly2016 muscles [17].

This model was scaled via AddBiomechanics for the subject used for collecting pilot motion capture and EMG sprinting data. An additional Matlab script was run to modify muscle-tendon unit length parameters based on the maximum and minimum muscle-tendon lengths achieved in the study.

Static Optimization:

The following objective function and constraints were implemented to solve for the muscle activations (ai) and reserve joint actuator activations (aj) from the joint moments (Mj) computed during inverse dynamics:

Minimizing the sum of activations squared is consistent with previous literature [11]. The weight w in the objective function is used to penalize the activation of the reserve joint torque actuators.

Validation: 

The activations of muscles from the static optimization were validated with normalized EMG data collected during the pilot study. The EMG data was filtered and normalized using the peak voltage value for each muscle out of all the sprinting trials.

We also compared the muscle force results from the optimization to papers by Chumanov [2].

Results

The following plots show the hamstring muscles (biceps femoris long head, semimembranosus, and semitendinosus) forces and hamstring muscle activations in the sprinting flight phase at 50%, 70%, and 90% of the subject’s top speed. The right leg was the leading front leg in these flight phases. There is no ground contact during these trials.

Figure 1. Hamstring muscle activations in the biceps femoris long head (UL), semimembranosus (UR),  semitendinosus (LL)  for sprinting at 50%, 70%, and 90% of the subject’s top speed. The experimental EMG data is included for the biceps femoris and semitendinosus at the 50% and 90% of top speed trials.

The results in Figure 1 show the hamstring muscle activations between 50% and 90% of top speed sprinting. Additionally, the experimental EMG profiles for the biceps femoris and semitendinosus at 50% and 70% top speed trials are plotted. 

The relative activations of the muscles increase as the speed increases in both the EMG and solved muscle activations.

Since we are limited to the EMG sensors that were used in the pilot study, we do not have EMG to compare for the semitendinosus. Additionally, EMG sensors are difficult to validate with because there can be cross talk between muscle voltage signals.

Figure 2. Hamstring muscle forces in the bicep femoris long head (UL), semimembranosus (UR),  semitendinosus (LL), total (LR) for sprinting at 50%, 70%, and 90% of the subject’s top speed. The hamstring muscle force results from [2] are also included for comparison.

The results in Figure 2 show the hamstring muscle forces between 50% and 90% of top speed sprinting. Additionally, the muscle force results at 100% of top speed from the Chumanov paper [2]–which have been scaled from the originally reported force per mass–are shown. 

In each of the individual hamstring muscles, and in the total muscle force, the muscle force generally increases as the sprinting speed increases. Interestingly, the force profiles of the higher speed (70% and 90%) trials are more similar to each other than the lower speed (50%) trial. 

The profiles for the biceps femoris long-head and semitendinosus generally match the Chumanov results, although there are discrepancies in the result magnitudes. The semimembranosus, however, did not match the profile well. Of the hamstrings, the semimembranosus has the longest tendon and the highest compliance ratio of tendon slack length to optimal muscle fiber length [16], so the rigid tendon assumption of static optimization is worse in this muscle. This may explain why the profile does not match as well as the other two muscles.

However, there are fundamental differences in the methods of this project and those of the Chumanov paper. Chumanov used computed muscle control (CMC) dynamic optimization of the entire sprinting gait cycle to solve for muscle forces. We solve static optimization only during the flight phase of sprinting. Differences in static vs dynamic optimization, different muscle models, and test subjects could explain the differences such as the magnitude of forces and profiles.

Limitations

Optimization was used to solve the muscle redundancy problem and determine muscle activations. Static optimization only considers individual instants in time and, for this problem, we were limited to the flight phase of sprinting due to too noisy ground reaction force data for the stance phases of the gait cycle. Additionally, static optimization cannot include activation dynamics and tendon compliance. Dynamic optimization, on the other hand, 

However, static optimization is computationally faster which is why it was used for this project.

We want to solve the muscle redundancy problem. Static optimization only looks at individual time points and in this problem we were limited to using static optimization during solely the flight phase of sprinting. The ground reaction force data is too noisy to use static optimization to solve for the activations and forces in the muscles over the entire gait cycle. Dynamic optimization solves for all times, muscles, and controls simultaneously. 

Another limitation we encountered was the need to include reserve actuators at each joint. These reserve actuators were included to allow the optimization to converge  within our constraints and were necessary due to noise and a muscle model that was not strong enough. The left hip joint rotation was the most difficult to track and had the largest activations  in the reserve actuators. However, our analysis only considered the hamstring muscles in the right leg which used much smaller reserve torques. 

Future Work

This project determined the hamstring muscle activation patterns during the flight phase of sprinting using static optimization. As discussed above, there are limitations to using static optimization in a highly dynamic activity. Frequently, in biomechanics dynamic optimization strategies include single shooting, multiple shooting, and direct collocation. In future work, we plan to use direct collocation to solve the muscle redundancy problem for an entire gait cycle at each sprinting speed. Tools such as OpenSim MoCo would allow us to determine muscle activations while expanding to consider the dynamics of the full gait cycle. Additionally, activation dynamics and tendon compliance could be integrated into the analysis.

Finally, we could examine the joint moments from existing papers with our joint moments from inverse dynamics. If these moments look similar and the activations are different with the same cost function, then we know the differences in profiles of activations originate from the optimization method rather than measurement error.

Acknowledgments

Thank you to Reed and Nicos who mentored us on the project. Thank you to our other teaching assistants including Nick Bianco, Carmichael Ong, and Jon Stingel, to our professor, Scott Delp, our classmates, and Julie Muccini for help collecting data and Scott Uhlrich for helping process EMG data.

References

[1] Bautista, Iker J., et al. "The effects of the Nordic hamstring exercise on sprint performance and eccentric knee flexor strength: A systematic review and meta-analysis of intervention studies among team sport players." Journal of Science and Medicine in Sport 24.9 (2021): 931-938.

[2] Chumanov, Elizabeth S., Bryan C. Heiderscheit, and Darryl G. Thelen. "The effect of speed and influence of individual muscles on hamstring mechanics during the swing phase of sprinting." Journal of biomechanics 40.16 (2007): 3555-3562.

[3] Ekstrand, Jan, et al. "Hamstring injury rates have increased during recent seasons and now constitute 24% of all injuries in men’s professional football: the UEFA Elite Club Injury Study from 2001/02 to 2021/22." British Journal of Sports Medicine 57.5 (2023): 292-298.

[4] Freeman, Brock W., et al. "The effects of sprint training and the Nordic hamstring exercise on eccentric hamstring strength." The Journal of sports medicine and physical fitness 59.7 (2019): 1119-25.

[5] Kalema, Rudy N., et al. "Sprinting technique and hamstring strain injuries: A concept mapping study." Journal of Science and Medicine in Sport 25.3 (2022): 209-215.

[6] Nagahara, Ryu, et al. "Alteration of swing leg work and power during human accelerated sprinting." Biology open 6.5 (2017): 633-641.

[7] Mendiguchia, Jurdan, et al. "Sprint versus isolated eccentric training: Comparative effects on hamstring architecture and performance in soccer players." PLoS One 15.2 (2020): e0228283.

[8] Pincheira, Patricio A., et al. "Biceps femoris long head sarcomere and fascicle length adaptations after 3 weeks of eccentric exercise training." Journal of sport and health science 11.1 (2022): 43-49.

[9] Rajagopal, Apoorva, et al. "Full-body musculoskeletal model for muscle-driven simulation of human gait." IEEE transactions on biomedical engineering 63.10 (2016): 2068-2079.

[10] Ripley, Nicholas J., et al. "Effect of additional Nordic hamstring exercise or sprint training on the modifiable risk factors of hamstring strain injuries and performance." Plos one 18.3 (2023): e0281966.

[11] Schache, Anthony G., et al. "Mechanics of the human hamstring muscles during sprinting." Medicine & science in sports & exercise 44.4 (2012): 647-658.

[12] Van den Tillaar, Roland, Jens Asmund Brevik Solheim, and Jesper Bencke. "Comparison of hamstring muscle activation during high-speed running and various hamstring strengthening exercises." International journal of sports physical therapy 12.5 (2017): 718.

[13] Van Hooren, Bas, et al. "Muscle forces and fascicle behavior during three hamstring exercises." Scandinavian Journal of Medicine & Science in Sports 32.6 (2022): 997-1012.

[14] Van Hooren, Bas, and Frans Bosch. "Is there really an eccentric action of the hamstrings during the swing phase of high-speed running? Part II: Implications for exercise." Journal of sports sciences 35.23 (2017): 2322-2333.

[15] Nigg, Benno M., RUUD W. De Boer, and V. E. R. O. N. I. C. A. Fisher. "A kinematic comparison of overground and treadmill running." Medicine and science in sports and exercise 27.1 (1995): 98-105.

[16] Arnold, Edith M., Scott L. Delp. “Fibre operating lengths of human lower limb muscles during walking.” Philos Trans R Soc Lond B Biol Sci. 2011;366(1570):1530-1539. doi:10.1098/rstb.2010.0345

[17] Lai, A.K.M., Arnold, A.S. & Wakeling, J.M. Why are Antagonist Muscles Co-activated in My Simulation? A Musculoskeletal Model for Analysing Human Locomotor Tasks. Ann Biomed Eng 45, 2762–2774 (2017). https://doi.org/10.1007/s10439-017-1920-7