Joint Torque Errors Induced by Quasi-Static Assumptions in Lower Limb Biomechanics

Background/Objectives: Quasi-static inverse dynamics is widely used in biomechanical analyses due to its computational simplicity; however, neglecting inertial effects may introduce joint-specific torque estimation errors during dynamic movements. The purpose of this study was to quantify torque estimation errors introduced by quasi-static assumptions during bodyweight squats performed at different movement frequencies. Methods: A planar MATLAB-based (version R2022a) musculoskeletal model incorporating standard anthropometric parameters was developed to simulate squat motions at 1.00, 0.75, 0.50, and 0.25 Hz. Joint torques calculated using quasi-static inverse dynamics were compared with fully dynamic inverse dynamics at the ankle, knee, and hip. Model agreement was evaluated using Root Mean Square Error (RMSE), normalized percentage error relative to peak dynamic torque, and bootstrapped 95% confidence intervals (CI). Results: Quasi-static modeling produced negligible torque estimation errors at the ankle and knee across all movement frequencies, with percentage errors consistently below 0.1% and narrow confidence intervals. In contrast, the hip joint demonstrated a clear frequency-dependent underestimation of torque when inertial effects were neglected. At 1.00 Hz, the hip RMSE reached 14.4 Nm, corresponding to 14.01% of peak dynamic torque (95% CI: 13.97–14.06%). Error magnitude increased systematically with movement speed. Conclusions: The validity of quasi-static inverse dynamics strongly depends on joint location and movement frequency. While quasi-static models are appropriate for ankle and knee torque estimation during moderate-speed squats, accurate hip torque assessment during faster squats requires full dynamic modeling. These findings provide quantitative benchmarks to inform model selection in biomechanical research, rehabilitation engineering, and assistive device design.