Understanding individual muscle function requires quantification of their forces and velocities (Zajac et al., 2002, Zajac et al., 2003). Modeling and simulation are thus required because muscle force cannot be directly measured and the number of force actuators far exceeds the degrees-of-freedom of the musculoskeletal system. To solve the muscle redundancy problem, computationally efficient static optimization approaches have been used to estimate muscle forces that satisfy the inverse dynamics solution while applying a cost function with physiological criteria (e.g., Crowninshield and Brand, 1981, Herzog, 1987, Erdemir et al., 2007). However, muscle co-activation, which may increase joint stability, is not well predicted by static optimization (Binding et al., 2000, Kian et al., 2019, Zajac and Gordon, 1989, Zajac et al., 2002). In addition, muscle recruitment solutions are sensitive to properties such as individual muscle size or strength (Brand et al., 1986). Thus, the accuracy of predicted muscle force distributions may vary across individuals and tasks. There are alternative approaches that aim to address limitations of static optimization, such as Computed Muscle Control (CMC, Thelen et al., 2003, Thelen and Anderson, 2006). CMC uses static optimization within a forward dynamic simulation framework to estimate muscle forces, which can produce more realistic muscle recruitment than static optimization alone by incorporating activation and contraction dynamics when solving for muscle controls (Thelen et al., 2003, Thelen and Anderson, 2006). However, the challenge of solving the muscle force distribution solution remains.

Cost functions to solve muscle recruitment using CMC often minimize fatigue or energy expenditure represented by the weighted or non-weighted sum of muscle activations raised to a power (Ackermann and van den Bogert, 2010). In these formulations, force recruitment may be biased toward muscles with a better mechanical advantage, greater isometric strength, or operation closer to the optimal regions of the force–length curves and/or force–velocity curves relative to other muscles (Ackland et al., 2012, Brand et al., 1986, Carbone et al., 2016). Squared or cubed polynomials have demonstrated validity and robustness to a variety of movements and joints of interest, which suggests they reflect physiological muscle recruitment (Erdemir et al., 2007; McDonald et al., 2022). Commonly used Hill-type muscle models prescribe a homogenous muscle–tendon unit to represent the entire muscle between origin and insertion, which ignores non-uniformity in activation and tendon attachment. This generalization often reasonably approximates most lower extremity muscles excitations. However, muscles with more complex geometries like multi-headed (e.g., gastrocnemius) and fan-shaped muscles (e.g., gluteal muscles) are often represented with multiple model actuators (Arnold et al., 2010) to account for multiple attachment locations and regional differences in function.

Torso muscle geometries require complex representations as they have many attachments across multiple joints. For example, the lumbar multifidus consists of several bands attaching to individual lumbar vertebrae, each with multiple segments and/or layers leading to unique distal attachments (Macintosh and Bogduk, 1986, Rosatelli et al., 2008). In addition, forces in the lumbar spine are influenced by rigid torso assumptions in part due to the sensitivity of muscle force contributions to the assumed relative motions between vertebrae (Arshad et al., 2016, Ignasiak et al., 2016). Thus, to quantify muscle and joint forces in the spine, models with detailed skeletal and muscle geometries have been implemented (e.g., Bruno et al., 2015, Christophy et al., 2012, de Zee et al., 2007). These detailed torso models are combined with lower limb models to investigate how different daily tasks, such as static standing, rising, walking, lifting weight, and running, affect the lumbar spine and legs (e.g., Actis et al., 2018a, Actis et al., 2018b, Beaucage-Gauvreau et al., 2019, Beaucage-Gauvreau et al., 2020, Raabe and Chaudhari, 2016).

While the lowest attachment for most torso muscles may be the pelvis or sacrum, psoas attaches to the femur. Psoas, uniquely, can mobilize and stabilize the lumbar spine, pelvis, and leg, and these functional contributions may vary between tasks or postures (Andersson et al., 1995, Bogduk et al., 1992, Park et al., 2013, Penning, 2000, Penning, 2002, Santaguida and McGill, 1995). Psoas bundles or fascicles attach at multiple points at each vertebral level, including to the transverse process, vertebral body, and disc (Bogduk et al., 1992). In addition, regional differences in psoas activation may be related to task requirements and postures (Park et al., 2013). Thus, preservation of complex psoas geometry in full-body models is important. However, preserving psoas geometry creates imbalances among hip flexors in common muscle force sharing cost functions, as the individual model actuators representing psoas are small relative to iliacus, rectus femoris, adductor longus, and others, even though psoas overall is large. To meet hip flexion torque requirements, muscle recruitment optimizations will likely recruit greater force from these larger actuators rather than incurring greater cost from activating more actuators. In effect, different levels of geometric complexity between hip flexors may introduce a weighting bias against psoas muscle recruitment.

Thus, the purpose of this study was to quantify the effect of psoas muscle geometry on force recruitment using established movement simulation cost functions. We expected that greater psoas complexity (e.g., multi-actuator representations) would result in less total psoas force, requiring greater force from other hip flexors. In addition, we aimed to evaluate how well a cost function weighting scheme can restore psoas force to that of lower limb models. We developed movement simulations of downhill, level, and uphill walking, as these conditions have different hip mechanical demands (e.g., Lay et al., 2006), to evaluate psoas recruitment effects on clinically relevant outcome metrics.