This study investigated the predictive ability of the skeletal muscle force model presented by Knodel et al. [Knodel NB, Lawson LB, Nauman EA, “An emg-based constitutive law for force generation in skeletal muscle-part i: Model development,” J Biomech Eng (in press), doi: 10.1115/1.4053568] on the knee joint. It has previously been validated on the ankle joint [Knodel NB, Calvert LB, Bywater EA, Lamia JP, Patel SN, Nauman EA, “An emg-based constitutive law for force generation in skeletal muscle-part ii: Model validation on the ankle joint complex,” Submitted for Publication] and this paper aimed to identify how well it, and the solution process, performed on a more complex articulation. The knee joint’s surrounding musculoskeletal tissue loading was also identified. Ten subjects (five male and five female) performed six exercises targeting the muscles that cross the knee joint. Motion capture, electromyography, and force plate data was collected during the exercises for use in the analysis program written in MATLAB and magnetic resonance images were used to observe subject-specific ligament and tendon data at the knee articulation. OpenSim [Delp, SL, Anderson FC, Arnold AS, Loan P, Habib A, John CT, Guendelman E, Thelen DG, “Opensim: Open-source software to create and analyze dynamic simulations of movement,” IEEE Trans Biomed Eng 54(11):1940–1950, 2007, doi: 10.1109/TBME.2007.901024] was used for scaling a generic lower extremity anatomical model of each subject. Five of the six exercises were used to calculate each muscle’s constant, [Formula: see text] [Knodel NB, Lawson LB, Nauman EA, “An emg-based constitutive law for force generation in skeletal muscle-part i: Model development,” J Biomech Eng (in press), doi: 10.1115/1.4053568; Knodel NB, Calvert LB, Bywater EA, Lamia JP, Patel SN, Nauman EA, “An emg-based constitutive law for force generation in skeletal muscle-part ii: Model validation on the ankle joint complex,” Submitted for Publication], and the sixth was used as a testing set to identify the model’s predictive ability. Average percent errors ranged from 9.4% to 26.5% and the average across all subjects was 20.6%. The solution process produced physiologically relevant muscle forces and the surrounding tissue loading behaved as expected between the various exercises without approaching respective tensile strength values.

Purpose: This paper proposes a new method for estimating skeletal muscle forces using a model derived from dimensional analysis. It incorporates electromyography signals and muscle force-length, force-velocity, and force frequency relationships as inputs. The purpose of this model is to provide more accurate estimates of individualized muscle forces to better predict surrounding musculoskeletal tissue and joint contact loading. Theory: The derivation begins with dimensional analysis and a selection of critical parameters that define muscle force generation. The resulting constitutive equation gives way to a unique application of inverse-dynamics, one which avoids the issue of indeterminacy when reaction moments and ligament loading are minimized in a joint. The ankle joint is used as an example for developing the equations that culminate into a system of linear equations. Discussion: A muscle force model capable of being calibrated and then used to predict joint contact and surrounding tissue loading is critical in advancing biomechanics research areas like injury prevention, performance optimization, and tissue engineering, among others. This model's foundation in dimensional analysis, along with its inclusion of electromyography signals, gives promise that it will be physiologically relevant and suitable for application-based studies.

This study evaluates the predictive ability of the skeletal muscle force model derived previously within the ankle joint complex. The model is founded in dimensional analysis, using electromyography and the muscle force-length, force-velocity, and force-frequency curves as inputs. Seventeen subjects (8 males, 9 females) performed five different exercises that activated the primary muscles crossing the ankle joint. Motion capture, force plate, and electromyography data were collected during these exercises. A constant, Km, was calculated for each muscle of each subject using four of the five exercises. The fifth exercise was used to validate the results by treating the moments due to muscle forces as known and all other components in Euler's second law as unknown. While muscle forces cannot be directly validated in vivo, methods can be developed to test these values with reasonable confidence. This study compared moments about the ankle joint due to the calculated muscle forces to the sum of the moments due to all other sources and the kinematic terms in the second Newton-Euler equation of rigid body motion. Average percent errors for each subject ranged from 4.2% to 15.5% with an average percent error across all subjects of 8.2% while maximum percent errors for each subject ranged from 33.3% to 78.0% with an overall average maximum of 52.4%. Future work will examine sensitivity analyses to identify potential simplifications to the model and solution process and will validate the model on a more complex joint.