Multibody muscle driven model of an instrumented prosthetic knee during squat and toe rise motions

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.

Ligamentous influence in pelvic load distribution

BACKGROUND CONTEXT

The influence of the posterior pelvic ring ligaments on pelvic stability is poorly understood. Low back pain and sacroiliac joint (SIJ) pain are described being related to these ligaments. Computational approaches involving finite element (FE) modeling may aid to determine their influence. Previous FE models lacked in precise ligament geometries and material properties, which might have influence on the results.

PURPOSE AND STUDY DESIGN

The aim of this study is to investigate ligamentous influence in pelvic stability by means of FE using precise ligament material properties and morphometries.

METHODS

An FE model of the pelvis bones was created from computer tomography, including the pubic symphysis joint (PSJ) and the SIJ. Ligament data were used from 55 body donors: anterior (ASL), interosseous (ISL), and posterior (PSL) sacroiliac ligaments; iliolumbar (IL), inguinal (IN), pubic (PL), sacrospinous (SS), and sacrotuberous (ST) ligaments; and obturator membrane (OM). Stress-strain data were gained from iliotibial tract specimens. A vertical load of 600 N was applied. Pelvic motion related to altered ligament and cartilage stiffness was determined in a range of 50% to 200%. Ligament strain was investigated in the standing and sitting positions.

RESULTS

Tensile and compressive stresses were found at the SIJ and the PSJ. The center of sacral motion was at the level of the second sacral vertebra. At the acetabula and the PSJ, higher ligament and cartilage stiffnesses decrease pelvic motion in the following order: SIJ cartilage>ISL>ST+SS>IL+ASL+PSL. Similar effects were found for the sacrum (SIJ cartilage>ISL>IL+ASL+PSL) but increased ST+SS stiffnesses increased sacral motion. The influence of the IN, OM, and PL was less than 0.1%. Compared with standing, total ligament strain was reduced to 90%. Increased strains were found for the IL, ISL, and PSL.

CONCLUSIONS

Posterior pelvic ring cartilage and ligaments significantly contribute to pelvic stability. Their effects are region- and stiffness dependent. While sitting, load concentrations occur at the IL, ISL, and PSL, which goes in coherence with the clinical findings of these ligaments serving as generators of low back pain.

Surrogate articular contact models for computationally efficient multibody dynamic simulations

Contact occurs in a wide variety of multibody dynamic systems, including the human musculoskeletal system. However, sensitivity and optimization studies of such systems have been limited by the high computational cost of repeated contact analyses. This study presents a novel surrogate modeling approach for performing computationally efficient three-dimensional elastic contact analyses within multibody dynamic simulations. The approach fits a computationally cheap surrogate contact model to data points sampled from a computationally expensive elastic contact model (e.g., a finite element or elastic foundation model) and resolves several unique challenges involved in applying surrogate modeling techniques to elastic contact problems. As an example application, we performed multibody dynamic simulations of a Stanmore wear simulator machine using surrogate and elastic foundation (EF) contact models of a total knee replacement. Accuracy was assessed by performing eleven dynamic simulations with both types of contact models utilizing large variations in motion and load inputs to the machine. Wear volumes predicted with the surrogate contact models were within 1.5% of those predicted with the EF contact models. Computational speed was assessed by performing five Monte Carlo analyses (over 1000 dynamic simulations each) with surrogate contact models utilizing realistic variations in motion and load inputs. Computation time was reduced from an estimated 284 h per analysis with the EF contact models to 1.4 h with the surrogate contact models (i.e., 17 min vs. 5 s per simulation), with higher wear sensitivity observed for motion variations than for load variations. The proposed surrogate modeling approach can significantly improve the computational speed of multibody dynamic simulations incorporating three-dimensional elastic contact models with general surface geometry.