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The aim of this study was to investigate how the forces required to stabilize the lumbar spine in the standing posture may be affected by variation in its shape. A two-dimensional model of the lumbar spine in the sagittal plane was developed that included a simplified representation of the lumbar extensor muscles. The shape of the model was varied by changing both the magnitude and distribution of the lumbar curvature. The forces required to produce a resultant load traveling along a path as close to the vertebral body centroids as possible (a follower load) were determined. In general,the forces required to produce a follower load increased as the curvature became larger and more evenly distributed. The results suggest that the requirements of the lumbar muscles to maintain spinal stability in vivo will vary between individuals. This has implications for understanding the role of spinal curvature and muscle atrophy in back pain.

Using a gradient-based numerical optimization routine, the force magnitudes required of 10 major sagittal plane leg muscles to create a constant magnitude isometric resultant force against a fixed surface at the toe directed anteriorly, posteriorly, superiorly, and inferiorly were quantitatively predicted for three sets of joint angles: a straight leg configuration, with the knee flexed, and with both the hip and knee flexed. Comparisons over the conditions studied for each individual system muscle found that the maximum variation occurred in knee and hip extensor forces (up to two orders of magnitude). Comparisons within the set of active muscles for each studied condition identified dominant muscles and muscle functions. All anteriorly-directed and posteriorly-directed resultants required a small number of muscles with common functions (mainly knee or hip extensors) and large force magnitudes (O(1000N)). In contrast, a large number of muscles, with wide-ranging synergistic and antagonistic functions, acting across multiple joints with relatively small magnitudes (O(100N)) were needed to create the superiorly-directed resultant with flexed hip and knee. With good correlation to experimentally measured trends in the interrelationships between leg joint angles and isometric forces, the systematic muscle force prediction and analysis presented in this work can be used to guide the design of targeted muscle strengthening exercises and study of muscle-specific injury.

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, $K_m$ [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.