Automated 2D and 3D finite element overclosure adjustment and mesh morphing using generalized regression neural networks.

Computer representations of three-dimensional (3D) geometries are crucial for simulating systems and processes in engineering and science. In medicine, and more specifically, biomechanics and orthopaedics, obtaining and using 3D geometries is critical to many workflows. However, while many tools exist to obtain 3D geometries of organic structures, little has been done to make them usable for their intended medical purposes. Furthermore, many of the proposed tools are proprietary, limiting their use. This work introduces two novel algorithms based on Generalized Regression Neural Networks (GRNN) and 4 processes to perform mesh morphing and overclosure adjustment. These algorithms were implemented, and test cases were used to validate them against existing algorithms to demonstrate improved performance. The resulting algorithms demonstrate improvements to existing techniques based on Radial Basis Function (RBF) networks by converting to GRNN-based implementations. Implementations in MATLAB of these algorithms and the source code are publicly available at the following locations: https://github.com/thor-andreassen/femors; https://simtk.org/projects/femors-rbf; https://www.mathworks.com/matlabcentral/fileexchange/120353-finite-element-morphing-overclosure-reduction-and-slicing.

Deciphering the "Art" in Modeling and Simulation of the Knee Joint: Assessing Model Calibration Workflows and Outcomes.

Model reproducibility is a point of emphasis for the National Institutes of Health (NIH) and in science, broadly. As the use of computational modeling in biomechanics and orthopedics grows, so does the need to assess the reproducibility of modeling workflows and simulation predictions. The long-term goal of the KneeHub project is to understand the influence of potentially subjective decisions, thus the modeler's "art", on the reproducibility and predictive uncertainty of computational knee joint models. In this paper, we report on the model calibration phase of this project, during which five teams calibrated computational knee joint models of the same specimens from the same specimen-specific joint mechanics dataset. We investigated model calibration approaches and decisions, and compared calibration workflows and model outcomes among the teams. The selection of the calibration targets used in the calibration workflow differed greatly between the teams and was influenced by modeling decisions related to the representation of structures, and considerations for computational cost and implementation of optimization. While calibration improved model performance, differences in the postcalibration ligament properties and predicted kinematics were quantified and discussed in the context of modeling decisions. Even for teams with demonstrated expertise, model calibration is difficult to foresee and plan in detail, and the results of this study underscore the importance of identification and standardization of best practices for data sharing and calibration.

Reproducibility in modeling and simulation of the knee: Academic, industry, and regulatory perspectives.

Stakeholders in the modeling and simulation (M&S) community organized a workshop at the 2019 Annual Meeting of the Orthopaedic Research Society (ORS) entitled "Reproducibility in Modeling and Simulation of the Knee: Academic, Industry, and Regulatory Perspectives." The goal was to discuss efforts among these stakeholders to address irreproducibility in M&S focusing on the knee joint. An academic representative from a leading orthopedic hospital in the United States described a multi-institutional, open effort funded by the National Institutes of Health to assess model reproducibility in computational knee biomechanics. A regulatory representative from the United States Food and Drug Administration indicated the necessity of standards for reproducibility to increase utility of M&S in the regulatory setting. An industry representative from a major orthopedic implant company emphasized improving reproducibility by addressing indeterminacy in personalized modeling through sensitivity analyses, thereby enhancing preclinical evaluation of joint replacement technology. Thought leaders in the M&S community stressed the importance of data sharing to minimize duplication of efforts. A survey comprised 103 attendees revealed strong support for the workshop and for increasing emphasis on computational modeling at future ORS meetings. Nearly all survey respondents (97%) considered reproducibility to be an important issue. Almost half of respondents (45%) tried and failed to reproduce the work of others. Two-thirds of respondents (67%) declared that individual laboratories are most responsible for ensuring reproducible research whereas 44% thought that journals are most responsible. Thought leaders and survey respondents emphasized that computational models must be reproducible and credible to advance knee M&S.

Modeling of active skeletal muscles: a 3D continuum approach incorporating multiple muscle interactions.

Skeletal muscles have a highly organized hierarchical structure, whose main function is to generate forces for movement and stability. To understand the complex heterogeneous behaviors of muscles, computational modeling has advanced as a non-invasive approach to evaluate relevant mechanical quantities. Aiming to improve musculoskeletal predictions, this paper presents a framework for modeling 3D deformable muscles that includes continuum constitutive representation, parametric determination, model validation, fiber distribution estimation, and integration of multiple muscles into a system level for joint motion simulation. The passive and active muscle properties were modeled based on the strain energy approach with Hill-type hyperelastic constitutive laws. A parametric study was conducted to validate the model using experimental datasets of passive and active rabbit leg muscles. The active muscle model with calibrated material parameters was then implemented to simulate knee bending during a squat with multiple quadriceps muscles. A computational fluid dynamics (CFD) fiber simulation approach was utilized to estimate the fiber arrangements for each muscle, and a cohesive contact approach was applied to simulate the interactions among muscles. The single muscle simulation results showed that both passive and active muscle elongation responses matched the range of the testing data. The dynamic simulation of knee flexion and extension showed the predictive capability of the model for estimating the active quadriceps responses, which indicates that the presented modeling pipeline is effective and stable for simulating multiple muscle configurations. This work provided an effective framework of a 3D continuum muscle model for complex muscle behavior simulation, which will facilitate additional computational and experimental studies of skeletal muscle mechanics. This study will offer valuable insight into the future development of multiscale neuromuscular models and applications of these models to a wide variety of relevant areas such as biomechanics and clinical research.

Three Dimensional Lower Extremity Musculoskeletal Geometry of the Visible Human Female and Male.

Models and simulations of human function impact medicine and medical technology. Particularly, musculoskeletal modeling provides an avenue for insight into the human body, which might not be otherwise possible. However, reaching the ultimate goal of functional multi-scale human models has been slowed by the lack of freely available datasets of anatomical models and geometries. Moreover, female-specific geometries have been neglected with a widespread emphasis on male geometry. To help realize this goal, we have developed and shared complete three-dimensional musculoskeletal geometries extracted from the National Libraries of Medicine Visible Human Female and Male cryosections. Muscle, bone, cartilage, ligament, and fat from the pelvis to the ankle were digitized and exported. These geometries provide a foundation for continued work in human musculoskeletal simulation with high-fidelity deformable tissues that enable a better understanding of normal function and the evaluation of pathologies and treatments. This work is novel as it includes both the male and female Visible Human specimens, outputs at multiple levels of post-processing for maximum data reuse, and is publicly available.

Assessment of reporting practices and reproducibility potential of a cohort of published studies in computational knee biomechanics.

Reproducible research serves as a pillar of the scientific method and is a foundation for scientific advancement. However, estimates for irreproducibility of preclinical science range from 75% to 90%. The importance of reproducible science has not been assessed in the context of mechanics-based modeling of human joints such as the knee, despite this being an area that has seen dramatic growth. Framed in the context of five experienced teams currently documenting knee modeling procedures, the aim of this study was to evaluate reporting and the perceived potential for reproducibility across studies the teams viewed as important contributions to the literature. A cohort of studies was selected by polling, which resulted in an assessment of nine studies as opposed to a broader analysis across the literature. Using a published checklist for reporting of modeling features, the cohort was evaluated for both "reporting" and their potential to be "reproduced," which was delineated into six major modeling categories and three subcategories. Logistic regression analysis revealed that for individual modeling categories, the proportion of "reported" occurrences ranged from 0.31, 95% confidence interval (CI) [0.23, 0.41] to 0.77, 95% CI: [0.68, 0.86]. The proportion of whether a category was perceived as "reproducible" ranged from 0.22, 95% CI: [0.15, 0.31] to 0.44, 95% CI: [0.35, 0.55]. The relatively low ratios highlight an opportunity to improve reporting and reproducibility of knee modeling studies. Ongoing efforts, including our findings, contribute to a dialogue that facilitates adoption of practices that provide both credibility and translation possibilities.

Integration of neural architecture within a finite element framework for improved neuromusculoskeletal modeling.

Neuromusculoskeletal (NMS) models can aid in studying the impacts of the nervous and musculoskeletal systems on one another. These computational models facilitate studies investigating mechanisms and treatment of musculoskeletal and neurodegenerative conditions. In this study, we present a predictive NMS model that uses an embedded neural architecture within a finite element (FE) framework to simulate muscle activation. A previously developed neuromuscular model of a motor neuron was embedded into a simple FE musculoskeletal model. Input stimulation profiles from literature were simulated in the FE NMS model to verify effective integration of the software platforms. Motor unit recruitment and rate coding capabilities of the model were evaluated. The integrated model reproduced previously published output muscle forces with an average error of 0.0435 N. The integrated model effectively demonstrated motor unit recruitment and rate coding in the physiological range based upon motor unit discharge rates and muscle force output. The combined capability of a predictive NMS model within a FE framework can aid in improving our understanding of how the nervous and musculoskeletal systems work together. While this study focused on a simple FE application, the framework presented here easily accommodates increased complexity in the neuromuscular model, the FE simulation, or both.

A Method to Compare Heterogeneous Types of Bone and Cartilage Meshes.

Accurately capturing the bone and cartilage morphology and generating a mesh remains a critical step in the workflow of computational knee joint modeling. Currently, there is no standardized method to compare meshes of different element types and nodal densities, making comparisons across research teams a significant challenge. The aim of this paper is to describe a method to quantify differences in knee joint bone and cartilages meshes, independent of bone and cartilage mesh topology. Bone mesh-to-mesh distances, subchondral bone boundaries, and cartilage thicknesses from meshes of any type of mesh are obtained using a series of steps involving registration, resampling, and radial basis function fitting after which the comparisons are performed. Subchondral bone boundaries and cartilage thicknesses are calculated and visualized in a common frame of reference for comparison. The established method is applied to models developed by five modeling teams. Our approach to obtain bone mesh-to-mesh distances decreased the divergence seen in selecting a reference mesh (i.e., comparing mesh A-to-B versus mesh B-to-A). In general, the bone morphology was similar across teams. The cartilage thicknesses for all models were calculated and the mean absolute cartilage thickness difference was presented, the articulating areas had the best agreement across teams. The teams showed disagreement on the subchondral bone boundaries. The method presented in this paper allows for objective comparisons of bone and cartilage geometry that is agnostic to mesh type and nodal density.

Deciphering the "Art" in Modeling and Simulation of the Knee Joint: Variations in Model Development.

The use of computational modeling to investigate knee joint biomechanics has increased exponentially over the last few decades. Developing computational models is a creative process where decisions have to be made, subject to the modelers' knowledge and previous experiences, resulting in the "art" of modeling. The long-term goal of the KneeHub project is to understand the influence of subjective decisions on the final outcomes and the reproducibility of computational knee joint models. In this paper, we report on the model development phase of this project, investigating model development decisions and deviations from initial modeling plans. Five teams developed computational knee joint models from the same dataset, and we compared each teams' initial uncalibrated models and their model development workflows. Variations in the software tools and modeling approaches were found, resulting in differences such as the representation of the anatomical knee joint structures in the model. The teams consistently defined the boundary conditions and used the same anatomical coordinate system convention. However, deviations in the anatomical landmarks used to define the coordinate systems were present, resulting in a large spread in the kinematic outputs of the uncalibrated models. The reported differences and similarities in model development and simulation presented here illustrate the importance of the "art" of modeling and how subjective decision-making can lead to variation in model outputs. All teams deviated from their initial modeling plans, indicating that model development is a flexible process and difficult to plan in advance, even for experienced teams.

ReadySim: A computational framework for building explicit finite element musculoskeletal simulations directly from motion laboratory data.

Musculoskeletal modeling allows researchers insight into joint mechanics which might not otherwise be obtainable through in vivo or in vitro studies. Common musculoskeletal modeling techniques involve rigid body dynamics software which often employ simplified joint representations. These representations have proven useful but are limited in performing single-framework deformable analyzes in structures of interest. Musculoskeletal finite element (MSFE) analysis allows for representation of structures in sufficient detail to obtain accurate solutions of the internal stresses and strains including complex contact conditions and material representations. Studies which performed muscle force optimization directly in a finite element framework were often limited in complexity to minimize computational time. Recent advances in computational efficiency and control schemes for muscle force prediction have made these solutions more practical. Yet, the formulation of subject-specific simulations remains a challenging problem. The objectives of this work were to develop an open-source computational framework to build and run simulations which (a) scale the size of MSFE models and efficiently estimate (b) joint kinematics and (c) muscle forces from human motion data collected in a typical gait laboratory. A computational framework was built using MATLAB and Python to interface with model input and output files. The software uses laboratory marker data to scale model segment lengths and estimate joint kinematics. Concurrent muscle force and tissue strain estimations are performed based on the estimated kinematics and ground reaction forces. This software will improve the usability and consistency of single-framework MSFE simulations. Both software and template model are made freely available on SimTK.Novelty Statement Single framework musculoskeletal modeling directly in a finite element environment for muscle force estimation and tissue strain analysis. Open dissemination of unilateral musculoskeletal finite element model and software used in manuscript.

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb.

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.

A lower extremity model for muscle-driven simulation of activity using explicit finite element modeling.

A key strength of computational modeling is that it can provide estimates of muscle, ligament, and joint loads, stresses, and strains through non-invasive means. However, simulations that can predict the forces in the muscles during activity while maintaining sufficient complexity to realistically represent the muscles and joint structures can be computationally challenging. For this reason, the current state of the art is to apply separate rigid-body dynamic and finite-element (FE) analyses in series. However, the use of two or more disconnected models often fails to capture key interactions between the joint-level and whole-body scales. Single framework MSFE models have the potential to overcome the limitations associated with disconnected models in series. The objectives of the current study were to create a multi-scale FE model of the human lower extremity that combines optimization, dynamic muscle modeling, and structural FE analysis in a single framework and to apply this framework to evaluate the mechanics of healthy knee specimens during two activities. Two subject-specific FE models (Model 1, Model 2) of the lower extremity were developed in ABAQUS/Explicit including detailed representations of the muscles. Muscle forces, knee joint loading, and articular contact were calculated for two activities using an inverse dynamics approach and static optimization. Quadriceps muscle forces peaked at the onset of chair rise (2174 N, 1962 N) and in early stance phase (510 N, 525 N), while gait saw peak forces in the hamstrings (851 N, 868 N) in midstance. Joint forces were similar in magnitude to available telemetric patient data. This study demonstrates the feasibility of detailed quasi-static, muscle-driven simulations in an FE framework.

Comparison of Marker-Based and Stereo Radiography Knee Kinematics in Activities of Daily Living.

Movement of the marker positions relative to the body segments obscures in vivo joint level motion. Alternatively, tracking bones from radiography images can provide precise motion of the bones at the knee but is impracticable for measurement of body segment motion. Consequently, researchers have combined marker-based knee flexion with kinematic splines to approximate the translations and rotations of the tibia relative to the femur. Yet, the accuracy of predicting six degree-of-freedom joint kinematics using kinematic splines has not been evaluated. The objectives of this study were to (1) compare knee kinematics measured with a marker-based motion capture system to kinematics acquired with high speed stereo radiography (HSSR) and describe the accuracy of marker-based motion to improve interpretation of results from these methods, and (2) use HSSR to define and evaluate a new set of knee joint kinematic splines based on the in vivo kinematics of a knee extension activity. Simultaneous measurements were recorded from eight healthy subjects using HSSR and marker-based motion capture. The marker positions were applied to three models of the lower extremity to calculate tibiofemoral kinematics and compared to kinematics acquired with HSSR. As demonstrated by normalized RMSE above 1.0, varus-valgus rotation (1.26), medial-lateral (1.26), anterior-posterior (2.03), and superior-inferior translations (4.39) were not accurately measured. Using kinematic splines improved predictions in varus-valgus (0.81) rotation, and medial-lateral (0.73), anterior-posterior (0.69), and superior-inferior (0.49) translations. Using splines to predict tibiofemoral kinematics as a function knee flexion can lead to improved accuracy over marker-based motion capture alone, however this technique was limited in reproducing subject-specific kinematics.

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

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.

Assessment of Knee Kinematics in Older Adults Using High-Speed Stereo Radiography.

PURPOSE: Quantification of knee motion is essential for assessment of pathologic joint function, such as tracking osteoarthritis progression and evaluating outcomes after conservative or surgical treatment, including total knee arthroplasty. Our purpose was to establish a useful baseline for the kinematic envelope of knee motion in healthy older adults performing movements of daily living. METHODS: A high-speed stereo radiography system was used to measure the three-dimensional tibiofemoral kinematics of eight healthy people over 55 yr of age (4 women/4 men; age, 61.7 ± 5.4 yr; body mass, 74.6 ± 7.7 kg; body mass index, 26.7 ± 4.4 kg·m; height, 168.2 ± 13.7 cm) during seated knee extension, level walking, pivoting, and step descent. RESULTS: Internal-external and varus-valgus rotation and anterior-posterior range of motion through stance in normal walking averaged 3.6° ± 1.1°, 2.3° ± 0.6°, and 3.4 ± 1.57 mm, respectively. Average range of motion across subjects was greater during the step-down in both internal-external rotation (average, 6.5° ± 3.1°) and anterior-posterior translation (average, 4.5 ± 1.1). Average internal-external range of motion increased to 13.5° ± 3.6° during pivoting. Range of motion of the knee in varus-valgus rotation was nearly the same for each subject across activities, rarely exceeding 6°. CONCLUSIONS: Pivoting and step descending during walking had greater internal-external rotation and anterior-posterior translation than normal gait. Internal-external rotation and anterior-posterior translation were shown to have greater activity dependence, whereas varus-valgus rotation was consistent across activities. These results were similar to prior measurements in younger cohorts, though a trend toward reduced range of motion in the older adults was observed.