(D-142) Ultrasound Elastography to Measure In Vivo Muscle Forces Compared to Static Optimization Calculation Methods

Muscles are a major part of internal loads acting at joints and understanding the amount of force each individual muscle contributes to the overall load is critical to predicting the dynamics of the body during movement. Determining individual muscle forces and their motion can aid in optimized training for athletes, more personalized rehabilitation programs, and further insight into injury prevention [1]. Current methods to calculate muscle forces include in-vivo methods such as sEMGs, invasive methods utilizing transducers, and cadavers, or using computational modeling; all of which include their own limitations [2], [3]. A new method being researched is using shear wave elastography (SWE) ultrasound, benefits of which are not relying on invasive methods or noisy signals. Given this is a fairly novel approach, continuation of result validation is highly important.  As a method of validation, a model utilizing traditional methods of computations focused on force equations and static optimization can be used [3]. To test this theory, the elbow is isolated due to it being a simple hinge joint with a clear understanding of elbow muscle mechanics during flexion; specifically of the biceps brachii, brachioradialis, and brachialis. The aim of this study is to create a model that calculates forces of these muscles to understand how their contribution changes with differing flexion angles and effort, as well as a way to validate ultrasound as a prospective method of measuring these forces.  

Ultrasound: The Supersonic Imagine Ultrasound used SWE to take resting images of the biceps brachii, brachialis, and brachioradialis at 0°, 45°, and 90° of elbow flexion. Cross sectional area (CSA) images were taken using B-mode. A maximum volumetric contraction (MVC) test was performed at 0°, 45°, and 90° to find maximum torque for the participant using the Humac Norm. From the MVC torques, 10%, 20%, and 30% efforts were calculated for each flexion angle. 27 total trials were completed during muscle activation. During these trials, the three muscles were imaged independently at each percent effort and flexion angle. Using the Q-box technology of SWE images, shear wave velocity(c) was found then using the equation, c2=k′μ+σ/ρ [4], stress(σ) was calculated. Stress was multiplied by CSA to calculate force for each muscle. 

Model: The forces were calculated using a MATLAB model that utilized the following equation: Fm=q*Fmax*F(l)*F(v). Static optimization using the fmincon function was utilized to minimize stress and muscle activations to compare different optimization techniques. Muscle activation boundary conditions were 0≥q≥1. Parameters for tendon slack length, optimal muscle fiber length, and maximum isometric force were found [1], [5]. Computations were performed for elbow flexion angles of 0°, 45°, and 90° degrees as well as the 10%, 20%, and 30% of this participant’s specific MVC. Forces were multiplied by the moment arm to find torque for individual muscles [6]. A constraint on the static optimization was that the total torque of all muscles must match the patient’s torque, specific for each trial.  

Results/Discussion:  

It was expected at 0° and 45° that the brachioradialis (longest muscle fiber lengths and moment arm) would have the highest force contribution, but due to a small CSA as torque increases, brachialis and bicep contribution would increase, which matches ultrasound results [1], [2]. At 0°, biceps and brachioradialis contributions decreased in the stress model across MVC levels but brachioradialis activity dominated in all levels in the activation model, like the ultrasound. At 45°, biceps have the closest contribution across MVC levels for all methods, at other angles biceps activity greatly varied compared to other methods. As flexion angle increased, bicep contribution increased within the models but not with the ultrasound, this occurred at all MVC levels. This could be due to the biceps maximizing at the same value for effort independent of angle which isn’t reflected in models. Trends don’t follow at 90° for ultrasound, possibly due to imaging difficulties.  

When comparing static optimization techniques, there was the highest variation between methods at 0°. At 0°, there was extremely low brachialis contribution, but at 45° and 90° brachialis tended to contribute about 50% of the force which indicates model error. The stress models always have the highest levels of bicep activity with little to no brachioradialis contribution. Overall, the models tended to not change muscle contribution ratios as MVC level increased, this was consistent across all degree angles except at 0°. This is because stress models did not consider the force-length relationship at 0° so there’s high brachialis activity whereas the activation models incorporate this relationship where there’s high brachioradialis activity. 

Conclusions:  

The most used static optimization models are stress squared and activation squared. These models have considerable variation between muscle contributions, highlighting the difficulty in using a model to validate ultrasound results. However, ultrasound results fall in range of model results, suggesting it is a similarly valid method of calculating muscle force to static optimization. Ultrasound results also seem to reflect a strategy that follows logically from muscle architecture. Future work should include an increased number of participants for comparison and creating a subject specific model. 

This material is based upon work supported by the National Science Foundation under Grant No. 1950507. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Special thanks to the East Carolina Summer REU faculty that lead the program: Dr. Chris Venters, Dr. Nicholas Murray, and Dr. Stacey Meardon. I would also like to thank Mackenzie Hoey for her contribution to the models.