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Anoosha Pai S
Six Skov

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Background

Note: During the final revision of this submission, it came to our attention that there is an error in our simulation. While the model’s muscle strengths and masses were doubled, the inertia values were not. This likely impacts the results presented in this report. This error is being addressed for a future report. An updated version of the code, which addresses this error, is included above.

Background

Hamstring strains are one of the most prevalent injuries that occur in sports involving high-speed running. Hamstring strain injuries account for 37% of all muscle injuries in sports [1, 3] and have increased by about 4% annually in the last decade [3]. Recently, eccentric Nordic Hamstring Exercise (NHE) has attracted a lot of attention in the world of biomechanics and sports science for its potential in reducing muscle injury risk among athletes and non-athletes alike [4]–[7]. To understand the mechanism behind the preventive action of NHE against injury, it is important to understand what physical stimuli NHE applies to the muscle, and how the muscle responds.

Many studies have focused on the second half of this question— how the muscle is responding. Several investigate the changes in bulk force and torque outputs after NHE training to characterize the muscle response [8], [9]. A few others have investigated muscle level adaptations through volume changes of individual hamstring muscles [9] and fascicle length changes in the biceps femoris muscles [10] after NHE training. However, there is little work that has emphasized the stimulus causing these changes. Van Hooren et al. characterized the force in the knee flexors during a rep of NHE [11]. Therefore, with our work, we aim to recreate these findings and expand on them by characterizing the power and workloads experienced by the knee flexors during NHE

Research Question(s)

Are the results found in Van Hooren et. al. (2022) consistent with new data?
What is the power load on each of the hamstring muscles during the Nordic Hamstring Exercise?
What is the distribution of workload on each of the hamstrings during one rep of a Nordic Hamstring Exercise?

Methods

Data

Our data consisted of the following:

Marker locations of one subject performing NHE repetitions, from 34 marker-set captured by an 11-camera motion capture system (Motion Analysis Corporation, Santa Rosa, CA, USA).
External load measured proximal (0.06 m) to the ankle joint using uniaxial load cells (HT Sensor Technology, Shaanxi, China) mounted on a customized Nord board (Fig. 1).
EMG (Delsys, Natick, MA, USA) of 10 muscles in the lower limb, including Biceps Femoris Long Head (lateral sensor), Medial Semimembranosus, and Semitendinosus (medial sensor) on the left leg (Fig. 2).

External load measured from load cells of the right and left legs were added (to represent equivalent load acting on a single leg in the simplified model, explained below). Furthermore, the point of this load application with respect to the ankle joint was also computed, based on the distance of the ankle strap from the lateral malleolus.

We preprocessed the raw EMG data by applying a bandpass filter (30–500 Hz, 4th order, zero-phase shift Butterworth), followed by rectifying, and low-pass filtering (0.5 Hz, 4th order, zero-phase shift Butterworth). EMG data was then normalized to the maximum value of all recorded trials, which also included sprinting at 50%, 80%, and 90% of top speed.

Figure 1: Side view of rep on Nord Board. Force gauges can be seen on the ankle strap.

Figure 2: Front (left) and back (right) view of marker and EMG placements.

Modeling

We used OpenSim 4.0 [12] with a custom static optimization code in MATLAB R2021a (Mathworks, Inc., Natick MA, USA) for the simulation. We modeled the lower extremities and torso using the musculoskeletal model described by Arnold et. al., [13] with 20 degrees of freedom and 42 musculotendon actuators spanning the pelvis and lower extremities. This model was linearly scaled to match the anthropometric measurements from the static Motion Capture trial. Model scaling automatically adjusted the muscle optimal fiber lengths and moment arms, and tendon slack lengths.

We then simplified the scaled model by removing the left leg, while doubling the inertial and muscle properties. We fixed the tibia segment as the ground segment for our model, such that residual forces were applied to the tibia rather than the pelvis. Model kinematics and joint moments were estimated using the Inverse Kinematics and Inverse Dynamics tools in OpenSim, respectively. We preprocessed the kinematic data with a low-pass filter at a cut-off frequency of 0.5 Hz (NHE trial lasted about 5s), 6th order, zero-phase shift Butterworth in OpenSim.

Simulation

We implemented a custom static optimization pipeline in MATLAB, using the OpenSim API, to solve for muscle redundancies during NHE. We chose metabolic cost, i.e., the sum of squared muscle activations as the objective function for the static optimization. Our model did not require the addition of reserve actuators.

Results

Verification

We verified the solutions of our solver by comparing the joint moments calculated with the OpenSim Inverse Dynamics tool (Fig 3). The solution identified is able to match the torques demanded by the dynamics throughout the region of interest— the region before free fall— without reserve actuators.

Figure 3: Inverse Dynamics and Muscle Driven torque for the 3 sagittal plane joints

Validation

In addition to being dynamically consistent without reserve actuators, our results show some agreement with the results presented by van Hooren et. al. The normalized hip extension and knee flexion moments for our subject closely match the average found in their study (Fig. 4).

Figure 4: (Left) Muscle Driven flexion moment about knee and hip, normalized by subject body weight. (Right) Van Hooren et al., (2022) normalized hip extension and knee flexion moment.

Our results for activation of the semitendinosus and the biceps femoris showed close alignment as well, with the two muscles increasing to 40% and 30% of activation respectively (Fig. 5).

Figure 5: (Left) Computed activations of biceps femoris short head and semitendinosus. (Right) Van Hooren et al., (2022) computed activations of biceps femoris and semitendinosus

However, the normalized force profiles of the involved muscles differed somewhat from those presented by van Hooren. Our model shows the primary force is always provided by the semimembranosus, the largest muscle of the Hamstrings (Fig. 6).

Figure 6: (Left) Computed activations of biceps femoris short head and semitendinosus. (Right) Van Hooren et al., (2022) computed activations of biceps femoris and semitendinosus.

In addition to checking our data with findings in the literature, we validated the computed muscle activations of 10 muscles against collected EMG data. The knee extensors and soleus show low activations consistent with the solutions from static optimization (Fig. 7).

Figure 7: Computed activations and experimentally measured muscle activations of 10 muscles.

Figure 8: (Left) Work per rep of the knee flexors. (Right) Work per rep normalized by PCSA of the knee flexors.

These results show the relative overperformance of the hamstrings compared to the gastrocnemius muscles. This is consistent with the fact that the hamstrings are a much larger muscle group, thus providing a higher force. Additionally, gastrocnemius activation is limited by ankle plantar flexion. To activate the gastrocnemius muscles, the tibialis anterior also needs to activate. Meanwhile, the four hamstring muscles are also contributing to the hip extension moment, and have no need for hip flexion moment to counteract them.

The semimembranosus also dissipates the most work, by far (Fig. 8 Left). When normalizing the work by the PCSA, a proxy for the work per muscle fiber, we find this difference is less drastic. Semimembranosus continues to outperform all other muscles, but semitendinosus outperforms biceps femoris long head after normalization (Fig .8 Right) .

Limitations

Single leg model does capture asymmetries between legs.
EMG of all hamstring muscles are not available. Furthermore, EMG data during maximum voluntary contraction trials was not acquired. Hence exact comparison was not possible.
Static optimization ignores muscle activation dynamics, which might vary the nature of muscle work and power as observed in our results, especially in the give-up region that involves rapid motion.
Our model neglects tendon compliance, which may be a major contributor to the NHE.
Minimizing activation squared may not fully capture the muscle coordination strategy during NHE.

Future Work

One area for future work is improving the accuracy of the model. Future work should include muscle activation dynamics and tendon compliance to give more realistic and accurate muscle activations, forces, and power during the NHE, especially post the give-up point. Dynamic optimization is a promising tool for this future direction. Furthermore, future studies could test whether MRI-informed subject-specific models can better explain the loading seen in these muscles during NHE.

It is also important to tie this work back to the original goal of understanding the impact of NHE on the hamstrings. Identifying the relationship between the physical stimuli, calculated with methods outlined in this paper, and the adaptation in the muscle is an area of study that still needs work.

Acknowledgments

We thank Reed Gurchiek, Nicos Haralabidis, Nick Bianco, Jon Stingel, Carmichael Ong, and Scott Delp for providing countless hours of technical support and encouragement. We also thank Kristen Steudel and Katie Marusich for their experimental data.

References

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