Purdue University Graduate School
Nathan_Knodel_PhD_Thesis_v3.pdf (35.91 MB)

Development and Validation of a Skeletal Muscle Force Model for the Purpose of Identifying Surrounding Musculoskeletal Tissue Loading

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posted on 2022-04-21, 19:46 authored by Nathan KnodelNathan Knodel

Musculoskeletal degradation and musculoskeletal injuries place a substantial burden on the healthcare system. Advancing the understanding and prevention of the injury potential associated with these injuries in various demographics as well as advancing performance optimization requires knowledge of the loading distribution among the various musculoskeletal tissues at the joints. Accurate muscle force estimates are needed for characterizing these distributions due to their influence on the loading of the system. This dissertation discusses

the development and validation of a physiologically-driven skeletal muscle force model that is suitable for application on an individualized level. The derivation of the skeletal muscle force model began with dimensional analysis and a selection of critical parameters that define muscle force generation. One of the key parameters included was measured muscle voltage using electromyography sensors. This provided the model with the ability to be easily used

in application-based studies. It also incorporated the muscle force-length, force-velocity, and force-frequency curves, providing an even stronger physiological basis to the model. Validation was performed by multiple studies using experimental data from subjects conducting exercises chosen to target specific muscles of interest. Data was collected from a Vicon Vero motion capture system, an instrumented Bertec treadmill, and Delsys Trigno electromyography sensors. The first study analyzed the ankle joint of seventeen subjects using the two Newton-Euler equations of rigid body motion and the skeletal muscle force model. The average percent error across all subjects was 8.2% and ranged from 4.2% to 15.5%. The second study analyzed the sensitivity of two sets of parameters within the model. The first was conducted on a set of observed and fitted constants from the dimensionless pi terms and aimed to identify which, if any, could be excluded from an optimization routine. Results indicated that only two of the nine constant parameters needed to be optimized. The second sensitivity analysis focused on the anatomical kinematic parameters in order to identify the impact that the incorporation of MRI scans for subject-specific anatomical models would have on the accuracy of the model’s output. Results demonstrated sensitivity to the muscle insertion points, suggesting that the use of MRI scans could increase the accuracy of the model. The third study was a case study focused on evaluating the assumption of a constant within the skeletal muscle force model remaining constant over time. Results indicated that the collection of maximum EMG recordings for these studies may not have been controlled to a desirable level and that the inclusion of specialized equipment for maximum EMG recordings would likely validate this assumption. The final study analyzed the

knee joint of ten subjects in a similar fashion to that of the ankle joint. The goal was to observe the model’s performance on a more anatomically complex joint. The average percent error across all subjects was 20.6%, approximately two times higher than the ankle joint.

However, the majority of the error associated with this study came from the deviation in calculated moments about an axis of much smaller importance and magnitude than the primary flexion/extension axis. When errors were excluded from this axis, the average percent error for all subjects was 8.8%, almost identical to that of the ankle joint application. These findings as a whole indicate that the model has predictive ability and is capable of providing reasonable estimates of both muscle forces and surrounding musculoskeletal tissue loading. Therefore, the model could be used in various biomechanical advancements and applications in injury prevention, performance optimization, tissue engineering, prosthetic design, and more.


Degree Type

  • Doctor of Philosophy


  • Mechanical Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Eric Nauman

Advisor/Supervisor/Committee co-chair

Charles Krousgrill

Additional Committee Member 2

Louis DiBerardino

Additional Committee Member 3

Shirley Rietdyk

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