Trent M. Guess

A subject specific multibody model of the knee with menisci

The menisci of the knee play an important role in joint function and our understanding of knee mechanics and tissue interactions can be enhanced through computational models of the tibio-menisco-femoral structure. Several finite element models of the knee that include meniscus-cartilage contact exist, but these models are typically limited to simplified boundary conditions. Movement simulation and musculoskeletal modeling can predict muscle forces, but are typically performed using the multibody method with simplified representation of joint structures. This study develops a subject specific computational model of the knee with menisci that can be incorporated into neuromusculoskeletal models within a multibody framework. Meniscus geometries from a 78-year-old female right cadaver knee were divided into 61 discrete elements (29 medial and 32 lateral) that were connected through 6x6 stiffness matrices. An optimization and design of experiments approach was used to determine parameters for the 6x6 stiffness matrices such that the force-displacement relationship of the meniscus matched that of a linearly elastic transversely isotropic finite element model for the same cadaver knee. Similarly, parameters for compliant contact models of tibio-menisco-femoral articulations were derived from finite element solutions. As a final step, a multibody knee model was developed and placed within a dynamic knee simulator model and the tibio-femoral and patello-femoral kinematics compared to an identically loaded cadaver knee. RMS errors between finite element displacement and multibody displacement after parameter optimization were 0.017 mm for the lateral meniscus and 0.051 mm for the medial meniscus. RMS errors between model predicted and experimental cadaver kinematics during a walk cycle were less than 11 mm translation and less than 7 degrees orientation. A small improvement in kinematics, compared to experimental measurements, was seen when the menisci were included versus a model without the menisci. With the menisci the predicted tibio-femoral contact force was significantly reduced on the lateral side (937 N peak force versus 633 N peak force), but no significant reduction was seen on the medial side.

Considerations for reporting finite element analysis studies in biomechanics.

Simulation-based medicine and the development of complex computer models of biological structures is becoming ubiquitous for advancing biomedical engineering and clinical research. Finite element analysis (FEA) has been widely used in the last few decades to understand and predict biomechanical phenomena. Modeling and simulation approaches in biomechanics are highly interdisciplinary, involving novice and skilled developers in all areas of biomedical engineering and biology. While recent advances in model development and simulation platforms offer a wide range of tools to investigators, the decision making process during modeling and simulation has become more opaque. Hence, reliability of such models used for medical decision making and for driving multiscale analysis comes into question. Establishing guidelines for model development and dissemination is a daunting task, particularly with the complex and convoluted models used in FEA. Nonetheless, if better reporting can be established, researchers will have a better understanding of a models value and the potential for reusability through sharing will be bolstered. Thus, the goal of this document is to identify resources and considerate reporting parameters for FEA studies in biomechanics. These entail various levels of reporting parameters for model identification, model structure, simulation structure, verification, validation, and availability. While we recognize that it may not be possible to provide and detail all of the reporting considerations presented, it is possible to establish a level of confidence with selective use of these parameters. More detailed reporting, however, can establish an explicit outline of the decision-making process in simulation-based analysis for enhanced reproducibility, reusability, and sharing.

A multibody knee model with discrete cartilage prediction of tibio-femoral contact mechanics

Combining musculoskeletal simulations with anatomical joint models capable of predicting cartilage contact mechanics would provide a valuable tool for studying the relationships between muscle force and cartilage loading. As a step towards producing multibody musculoskeletal models that include representation of cartilage tissue mechanics, this research developed a subject-specific multibody knee model that represented the tibia plateau cartilage as discrete rigid bodies that interacted with the femur through deformable contacts. Parameters for the compliant contact law were derived using three methods: (1) simplified Hertzian contact theory, (2) simplified elastic foundation contact theory and (3) parameter optimisation from a finite element (FE) solution. The contact parameters and contact friction were evaluated during a simulated walk in a virtual dynamic knee simulator, and the resulting kinematics were compared with measured in vitro kinematics. The effects on predicted contact pressures and cartilage–bone interface shear forces during the simulated walk were also evaluated. The compliant contact stiffness parameters had a statistically significant effect on predicted contact pressures as well as all tibio-femoral motions except flexion–extension. The contact friction was not statistically significant to contact pressures, but was statistically significant to medial–lateral translation and all rotations except flexion–extension. The magnitude of kinematic differences between model formulations was relatively small, but contact pressure predictions were sensitive to model formulation. The developed multibody knee model was computationally efficient and had a computation time 283 times faster than a FE simulation using the same geometries and boundary conditions.

Computational Knee Ligament Modeling Using Experimentally Determined Zero-Load Lengths

This study presents a subject-specific method of determining the zero-load lengths of the cruciate and collateral ligaments in computational knee modeling. Three cadaver knees were tested in a dynamic knee simulator. The cadaver knees also underwent manual envelope of motion testing to find their passive range of motion in order to determine the zero-load lengths for each ligament bundle. Computational multibody knee models were created for each knee and model kinematics were compared to experimental kinematics for a simulated walk cycle. One-dimensional non-linear spring damper elements were used to represent cruciate and collateral ligament bundles in the knee models. This study found that knee kinematics were highly sensitive to altering of the zero-load length. The results also suggest optimal methods for defining each of the ligament bundle zero-load lengths, regardless of the subject. These results verify the importance of the zero-load length when modeling the knee joint and verify that manual envelope of motion measurements can be used to determine the passive range of motion of the knee joint. It is also believed that the method described here for determining zero-load length can be used for in vitro or in vivo subject-specific computational models.

Multiscale modeling in computational biomechanics

Biomechanics is broadly defined as the scientific discipline that investigates the effects of forces acting on and within biological structures. The realm of biomechanics includes the circulatory and respiratory systems, tissue mechanics and mechanotransduction, and the musculoskeletal system and motor control. As in many other biological phenomena, many spatial scales are crossed by biomechanics research: intracellular, multicellular, and extracellular matrices; and tissue, organ, and multiorgan systems. It is well established that the effect of forces at higher scales influence behavior at lower scales and that lower-scale properties influence higher-scale response. However, computational methods that incorporate these interactions in biomechanics are relatively rare. In general, computational models that include representation of multiple spatial or temporal scales are loosely defined as multiscale. The fact that multiscale modeling is not well defined lends the term to a variety of scenarios within the computational physiology community. In biomechanics, multiscale modeling may mean establishing a hierarchical link between the spatial and temporal scales, while the output of a larger-scale system is passed through a finely detailed representation at a lower scale (e.g., body-level movement simulations that provide net joint loading for tissue-level stress analysis). In reality, multiscale modeling may require more intricate representation of interactions among scales. A concurrent simulation strategy is inevitable to adequately represent nonlinear associations that have been known for decades [1].

Evaluation of a musculoskeletal model with prosthetic knee through six experimental gait trials

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 tibio-femoral 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 (166N<MAD<404N, 212N<RMSD<448N) and vertical ground reaction forces (66N<MAD<90N, 97N<RMSD<128N) 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 tibio-femoral force distribution and muscle activation timing.

Computational modeling of a dynamic knee simulator for reproduction of knee loading.

As a first step towards reproducing desired three-dimensional joint loading and motion on a dynamic knee simulator, the goal of this study was to develop and verify a three-dimensional computational model that generated control profiles for the simulator using desired knee loading and motion as model inputs. The developed model was verified by predicting tibio-femoral loading on an instrumented analog knee for given actuator forces and the ability to generate simulator control profiles was demonstrated using a three-dimensional walking profile. The model predicted axial tibia loading for a sagittal-plane dual-limb squat within 1% of measured peak loading. Adding out-of-sagittal-plane forces decreased the accuracy of load prediction. The model generated control profiles to the simulator that produced axial tibia loading within 16% of desired for walking. Discrepancies in predicted and measured quadriceps forces influenced the accuracy of the generated control profiles. Future work will replace the analog knee in both the model and machine with a prosthetic knee.

Simulation of anterior cruciate ligament deficiency in a musculoskeletal model with anatomical knees.

Abnormal knee kinematics and meniscus injury resulting from anterior cruciate ligament (ACL) deficiency are often implicated in joint degeneration even though changes in tibio-femoral contact location after injury are small, typically only a few millimeters. Ligament reconstruction surgery does not significantly reduce the incidence of early onset osteoarthritis. Increased knowledge of knee contact mechanics would increase our understanding of the effects of ACL injury and help guide ACL reconstruction methods. Presented here is a cadaver specific computational knee model combined with a body-level musculoskeletal model from a subject of similar height and weight as the cadaver donor. The knee model was developed in the multi-body framework and includes representation of the menisci. Experimental body-level measurements provided input to the musculoskeletal model. The location of tibio-menisco-femoral contact as well as contact pressures were compared for models with an intact ACL, partial ACL transection (posterolateral bundle transection), and full ACL transection during a muscle driven forward dynamics simulation of a dual limb squat. During the squat, small changes in femur motion relative to the tibia for both partial and full ACL transection push the lateral meniscus in the posterior direction at extension. The central-anterior region of the lateral meniscus then becomes “wedged” between the tibia and femur during knee flexion. This “wedging” effect does not occur for the intact knee. Peak contact pressure and contact locations are similar for the partial tear and complete ACL transection during the deep flexion portion of the squat, particularly on the lateral side. The tibio-femoral contact location on the tibia plateau shifts slightly to the posterior and lateral direction with ACL transection.

Predicted loading on the menisci during gait: The effect of horn laxity

Radiographic measurements have established a link between meniscus extrusion and meniscus degeneration as well as with knee osteoarthritis. The presented work combines medical imaging with motion capture data from two healthy female subjects to create subject specific knee models that predict tibio-menisco-femoral contact forces and ligament forces during muscle driven simulations of barefoot gait. The developed computational models were used to explore the relationship between the extent of meniscal extrusion and biomechanical function by altering the laxity of the meniscal horn attachments during gait. The extrusion distance increased as laxity increased and the amount of contact force transferred through the menisci during gait decreased rapidly as the meniscal attachments became more lax. Horn attachment lengths that were 20% longer than MRI attachment lengths resulted in an almost complete loss of force transfer through the menisci during the gait cycle. Relatively small changes (2-3mm) in the lengths at which horn bundles first become taut, manifested in large changes in the capacity of the tissue to transmit forces. As meniscal horn attachment laxity increased from 80% to 120% of the MRI measured horn distance, medial meniscus extrusion increased 3.9mm for the first subject and 2.7mm for the second subject. For the same horn laxity changes, the percent of medial tibiofemoral contact force transmitted through the medial meniscus during early stance decreased from 51% to 8% and from 36% to 14% for the two subjects. The results of our study show that increased meniscal extrusion occurs with increased laxity of the meniscal tibia attachments and this increased laxity results in loss of meniscal function.

Application of neural networks for the prediction of cartilage stress in a musculoskeletal system

Traditional finite element (FE) analysis is computationally demanding. The computational time becomes prohibitively long when multiple loading and boundary conditions need to be considered such as in musculoskeletal movement simulations involving multiple joints and muscles. Presented in this study is an innovative approach that takes advantage of the computational efficiency of both the dynamic multibody (MB) method and neural network (NN) analysis. A NN model that captures the behavior of musculoskeletal tissue subjected to known loading situations is built, trained, and validated based on both MB and FE simulation data. It is found that nonlinear, dynamic NNs yield better predictions over their linear, static counterparts. The developed NN model is then capable of predicting stress values at regions of interest within the musculoskeletal system in only a fraction of the time required by FE simulation.