A multibody model of the knee was developed and the predicted ligament forces and kinematics during passive flexion corroborated subject-specific measurements obtained from a human cadaveric knee that was tested using a robotic manipulator. The model incorporated a novel strategy to estimate the slack length of ligament fibers based on experimentally measured ligament forces at full extension and included multifiber representations for the cruciates. The model captured experimentally measured ligament forces (≤ 5.7 N root mean square (RMS) difference), coupled internal rotation (≤ 1.6 deg RMS difference), and coupled anterior translation (≤ 0.4 mm RMS difference) through 130 deg of passive flexion. This integrated framework of model and experiment improves our understanding of how passive structures, such as ligaments and articular geometries, interact to generate knee kinematics and ligament forces.
Detailed knowledge of knee kinematics and dynamic loading is essential for improving the design and outcomes of surgical procedures, tissue engineering applications, prosthetics design, and rehabilitation. This study used publicly available data provided by the "Grand Challenge Competition to Predict in-vivo Knee Loads" for the 2013 American Society of Mechanical Engineers Summer Bioengineering Conference (Fregly et al., 2012, "Grand Challenge Competition to Predict in vivo Knee Loads," J. Orthop. Res., 30, pp. 503-513) to develop a full body, musculoskeletal model with subject specific right leg geometries that can concurrently predict muscle forces, ligament forces, and knee and ground contact forces. The model includes representation of foot/floor interactions and predicted tibiofemoral joint loads were compared to measured tibial loads for two different cycles of treadmill gait. The model used anthropometric data (height and weight) to scale the joint center locations and mass properties of a generic model and then used subject bone geometries to more accurately position the hip and ankle. The musculoskeletal model included 44 muscles on the right leg, and subject specific geometries were used to create a 12 degrees-of-freedom anatomical right knee that included both patellofemoral and tibiofemoral articulations. Tibiofemoral motion was constrained by deformable contacts defined between the tibial insert and femoral component geometries and by ligaments. Patellofemoral motion was constrained by contact between the patellar button and femoral component geometries and the patellar tendon. Shoe geometries were added to the feet, and shoe motion was constrained by contact between three shoe segments per foot and the treadmill surface. Six-axis springs constrained motion between the feet and shoe segments. Experimental motion capture data provided input to an inverse kinematics stage, and the final forward dynamics simulations tracked joint angle errors for the left leg and upper body and tracked muscle length errors for the right leg. The one cycle RMS errors between the predicted and measured tibia contact were 178 N and 168 N for the medial and lateral sides for the first gait cycle and 209 N and 228 N for the medial and lateral sides for the faster second gait cycle. One cycle RMS errors between predicted and measured ground reaction forces were 12 N, 13 N, and 65 N in the anterior-posterior, medial-lateral, and vertical directions for the first gait cycle and 43 N, 15 N, and 96 N in the anterior-posterior, medial-lateral, and vertical directions for the second gait cycle.
Detailed knowledge of knee joint kinematics and dynamic loading is essential for improving the design and outcomes of surgical procedures, tissue engineering applications, prosthetics design, and rehabilitation. The need for dynamic computational models that link kinematics, muscle and ligament forces, and joint contacts has long been recognized but such body-level forward dynamic models do not exist in recent literature. A main barrier in using computational models in the clinic is the validation of the in vivo contact, muscle, and ligament loads. The purpose of this study was to develop a full body, muscle driven dynamic model with subject specific leg geometries and validate it during squat and toe-rise motions. The model predicted loads were compared to in vivo measurements acquired with an instrumented knee implant. Data for this study were provided by the "Grand Challenge Competition to Predict In-Vivo Knee Loads" for the 2012 American Society of Mechanical Engineers Summer Bioengineering Conference. Data included implant and bone geometries, ground reaction forces, EMG, and the instrumented knee implant measurements. The subject specific model was developed in the multibody framework. The knee model included three ligament bundles for the lateral collateral ligament (LCL) and the medial collateral ligament (MCL), and one bundle for the posterior cruciate ligament (PCL). The implanted tibia tray was segmented into 326 hexahedral elements and deformable contacts were defined between the elements and the femoral component. The model also included 45 muscles on each leg. Muscle forces were computed for the muscle driven simulation by a feedback controller that used the error between the current muscle length in the forward simulation and the muscle length recorded during a kinematics driven inverse simulation. The predicted tibia forces and torques, ground reaction forces, electromyography (EMG) patterns, and kinematics were compared to the experimentally measured values to validate the model. Comparisons were done graphically and by calculating the mean average deviation (MAD) and root mean squared deviation (RMSD) for all outcomes. The MAD value for the tibia vertical force was 279 N for the squat motion and 325 N for the toe-rise motion, 45 N and 53 N for left and right foot ground reaction forces during the squat and 94 N and 82 N for toe-rise motion. The maximum MAD value for any of the kinematic outcomes was 7.5 deg for knee flexion-extension during the toe-rise motion.
Knowledge of the forces acting on musculoskeletal joint tissues during movement benefits tissue engineering, artificial joint replacement, and our understanding of ligament and cartilage injury. Computational models can be used to predict these internal forces, but musculoskeletal models that simultaneously calculate muscle force and the resulting loading on joint structures are rare. This study used publicly available gait, skeletal geometry, and instrumented prosthetic knee loading data [1] to evaluate muscle driven forward dynamics simulations of walking. Inputs to the simulation were measured kinematics and outputs included muscle, ground reaction, ligament, and joint contact forces. A full body musculoskeletal model with subject specific lower extremity geometries was developed in the multibody framework. A compliant contact was defined between the prosthetic femoral component and tibia insert geometries. Ligament structures were modeled with a nonlinear force-strain relationship. The model included 45 muscles on the right lower leg. During forward dynamics simulations a feedback control scheme calculated muscle forces using the error signal between the current muscle lengths and the lengths recorded during inverse kinematics simulations. Predicted tibiofemoral contact force, ground reaction forces, and muscle forces were compared to experimental measurements for six different gait trials using three different gait types (normal, trunk sway, and medial thrust). The mean average deviation (MAD) and root mean square deviation (RMSD) over one gait cycle are reported. The muscle driven forward dynamics simulations were computationally efficient and consistently reproduced the inverse kinematics motion. The forward simulations also predicted total knee contact forces (166 N < MAD < 404 N, 212 N < RMSD < 448 N) and vertical ground reaction forces (66 N < MAD < 90 N, 97 N < RMSD < 128 N) well within 28% and 16% of experimental loads respectively. However the simplified muscle length feedback control scheme did not realistically represent physiological motor control patterns during gait. Consequently, the simulations did not accurately predict medial/lateral tibiofemoral force distribution and muscle activation timing.
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