The interaction of muscle moment arm, knee laxity, and torque in a multi-scale musculoskeletal model of the lower limb

Abstract

Introduction: Musculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.

Methods: Two musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.

Results: Peak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).

Discussion: The large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.

Keywords: Finite element; Ligament; Musculoskeletal modeling; Torque.

Fig. 1.

Experimental and simulation setup for maximum isometric flexion and extension tasks.

Fig. 2.

Specimen-specific knee model illustrating the ligament representation (top left) (Harris et al., 2016) and tendon wrapping (bottom left) (Ali et al., 2016). Musculoskeletal model highlighting semimembranosus (SM), semitendonosus (ST), biceps femoris long head (BFL), rectus femoris (RF), vastus intermedius (VI), and multi-fiber representations of vastus medialis (VMs, VMm, VMi) and vastus lateralis (VLs, VLi) (right). Gastrocnemius and biceps femoris short head geometry not shown.

Fig. 3.

Maximum isometric flexion and extension torque of 12 subjects (red-female, blue-male) including mean curve (black) (left) and torque response of calibrated models during maximum isometric flexion and extension simulations compared to mean subject response (μ ± σ) (right).

Fig. 4.

Comparison between post-calibration passive knee flexion moment arms (solid) and moment arms calculated during maximum isometric torque simulations (dashed) compared with experimental bounds (μ ± σ) reported by Buford et al. (1997). Data from Buford et al. represent moment arms estimated from tendon excursion measurements in cadavers.

Fig. 5.

Changes in maximum isometric torque with (solid) and without (dashed) joint laxity representation.

Fig. 6.

Relative anterior-posterior (AP) tibial translation (passive knee extension AP subtracted from maximum isometric activity AP) for isometric flexion (dashed) and extension (solid). A negative value indicates a posterior translation.