Paul J. Rullkoetter

Comparison of Deformable and Elastic Foundation Finite Element Simulations for Predicting Knee Replacement Mechanics

Rigid body total knee replacement (TKR) models with tibiofemoral contact based on elastic foundation (EF) theory utilize simple contact pressure-surface overclosure relationships to estimate joint mechanics, and require significantly less computational time than corresponding deformable finite element (FE) methods. However, potential differences in predicted kinematics between these representations are currently not well understood, and it is unclear if the estimates of contact area and pressure are acceptable. Therefore, the objectives of the current study were to develop rigid EF and deformable FE models of tibiofemoral contact, and to compare predicted kinematics and contact mechanics from both representations during gait loading conditions with three different implant designs. Linear and nonlinear contact pressure-surface overclosure relationships based on polyethylene material properties were developed using EF theory. All other variables being equal, rigid body FE models accurately estimated kinematics predicted by fully deformable FE models and required only 2% of the analysis time. As expected, the linear EF contact model sufficiently approximated trends for peak contact pressures, but overestimated the deformable results by up to 30%. The nonlinear EF contact model more accurately reproduced trends and magnitudes of the deformable analysis, with maximum differences of approximately 15% at the peak pressures during the gait cycle. All contact area predictions agreed in trend and magnitude. Using rigid models, edge-loading conditions resulted in substantial overestimation of peak pressure. Optimal nonlinear EF contact relationships were developed for specific TKR designs for use in parametric or repetitive analyses where computational time is paramount. The explicit FE analysis method utilized here provides a unique approach in that both rigid and deformable analyses can be run from the same input file, thus enabling simple selection of the most appropriate representation for the analysis of interest.

Dynamic finite element knee simulation for evaluation of knee replacement mechanics

In vitro pre-clinical testing of total knee replacement (TKR) devices is a necessary step in the evaluation of new implant designs. Whole joint knee simulators, like the Kansas knee simulator (KKS), provide a controlled and repeatable loading environment for comparative evaluation of component designs or surgical alignment under dynamic conditions. Experimental testing, however, is time and cost prohibitive for design-phase evaluation of tens or hundreds of design variations. Experimentally-verified computational models provide an efficient platform for analysis of multiple components, sizes, and alignment conditions. The purpose of the current study was to develop and verify a computational model of a dynamic, whole joint knee simulator. Experimental internal-external and valgus-varus laxity tests, followed by dynamic deep knee bend and gait simulations in the KKS were performed on three cadaveric specimens. Specimen-specific finite element (FE) models of posterior-stabilized TKR were created from magnetic resonance images and CAD geometry. The laxity data was used to optimize mechanical properties of tibiofemoral soft-tissue structures on a specimen-specific basis. Each specimen was subsequently analyzed in a computational model of the experimental KKS, simulating both dynamic activities. The computational model represented all joints and actuators in the experimental setup, including a proportional-integral-derivative (PID) controller to drive quadriceps actuation. The computational model was verified against six degree-of-freedom patellofemoral (PF) and tibiofemoral (TF) kinematics and actuator loading during both deep knee bend and gait activities, with good agreement in trends and magnitudes between model predictions and experimental kinematics; differences were less than 1.8 mm and 2.2° for PF and TF translations and rotations. The whole joint FE simulator described in this study can be applied to investigate a wide range of clinical and research questions.

Development of subject-specific and statistical shape models of the knee using an efficient segmentation and mesh-morphing approach

Subject-specific finite element models developed from imaging data provide functional representation of anatomical structures and have been used to evaluate healthy and pathologic knee mechanics. The creation of subject-specific models is a time-consuming process when considering manual segmentation and hexahedral (hex) meshing of the articular surfaces to ensure accurate contact assessment. Previous studies have emphasized automated mesh mapping to bone geometry from computed tomography (CT) scans, but have not considered cartilage and soft tissue structures. Statistical shape modeling has been proposed as an alternative approach to develop a population of subject models, but still requires manual segmentation and registration of a training set. Accordingly, the aim of the current study was to develop an efficient, integrated mesh-morphing-based segmentation approach to create hex meshes of subject-specific geometries from scan data, to apply the approach to natural femoral, tibial, and patellar cartilage from magnetic resonance (MR) images, and to demonstrate the creation of a statistical shape model of the knee characterizing the modes of variation using principal component analysis. The platform was demonstrated on MR scans from 10 knees and enabled hex mesh generation of the knee articular structures in approximately 1.5h per subject. In a subset of geometries, average root mean square geometric differences were 0.54 mm for all structures and in quasi-static analyses over a range of flexion angles, differences in predicted peak contact pressures were less than 5.3% between the semi-automated and manually generated models. The integrated segmentation, mesh-morphing approach was employed in the efficient development of subject-specific models and a statistical shape model, where populations of subject-specific models have application to implant design evaluation or surgical planning.

Verification of predicted specimen-specific natural and implanted patellofemoral kinematics during simulated deep knee bend.

Verified computational models represent an efficient method for studying the relationship between articular geometry, soft-tissue constraint, and patellofemoral (PF) mechanics. The current study was performed to evaluate an explicit finite element (FE) modeling approach for predicting PF kinematics in the natural and implanted knee. Experimental three-dimensional kinematic data were collected on four healthy cadaver specimens in their natural state and after total knee replacement in the Kansas knee simulator during a simulated deep knee bend activity. Specimen-specific FE models were created from medical images and CAD implant geometry, and included soft-tissue structures representing medial-lateral PF ligaments and the quadriceps tendon. Measured quadriceps loads and prescribed tibiofemoral kinematics were used to predict dynamic kinematics of an isolated PF joint between 10 degrees and 110 degrees femoral flexion. Model sensitivity analyses were performed to determine the effect of rigid or deformable patellar representations and perturbed PF ligament mechanical properties (pre-tension and stiffness) on model predictions and computational efficiency. Predicted PF kinematics from the deformable analyses showed average root mean square (RMS) differences for the natural and implanted states of less than 3.1 degrees and 1.7 mm for all rotations and translations. Kinematic predictions with rigid bodies increased average RMS values slightly to 3.7 degrees and 1.9 mm with a five-fold decrease in computational time. Two-fold increases and decreases in PF ligament initial strain and linear stiffness were found to most adversely affect kinematic predictions for flexion, internal-external tilt and inferior-superior translation in both natural and implanted states. The verified models could be used to further investigate the effects of component alignment or soft-tissue variability on natural and implant PF mechanics.

Verification of Predicted Knee Replacement Kinematics During Simulated Gait in the Kansas Knee Simulator

Evaluating total knee replacement kinematics and contact pressure distributions is an important element of preclinical assessment of implant designs. Although physical testing is essential in the evaluation process, validated computational models can augment these experiments and efficiently evaluate perturbations of the design or surgical variables. The objective of the present study was to perform an initial kinematic verification of a dynamic finite element model of the Kansas knee simulator by comparing predicted tibio- and patellofemoral kinematics with experimental measurements during force-controlled gait simulation. A current semiconstrained, cruciate-retaining, fixed-bearing implant mounted in aluminum fixtures was utilized. An explicit finite element model of the simulator was developed from measured physical properties of the machine, and loading conditions were created from the measured experimental feedback data. The explicit finite element model allows both rigid body and fully deformable solutions to be chosen based on the application of interest. Six degrees-of-freedom kinematics were compared for both tibio- and patellofemoral joints during gait loading, with an average root mean square (rms) translational error of 1.1 mm and rotational rms error of 1.3 deg. Model sensitivity to interface friction and damping present in the experimental joints was also evaluated and served as a secondary goal of this paper. Modifying the metal-polyethylene coefficient of friction from 0.1 to 0.01 varied the patellar flexion-extension and tibiofemoral anterior-posterior predictions by 7 deg and 2 mm, respectively, while other kinematic outputs were largely insensitive.

Development of a statistical shape model of the patellofemoral joint for investigating relationships between shape and function

Patellofemoral (PF)-related pathologies, including joint laxity, patellar maltracking, cartilage degradation and anterior knee pain, affect nearly 25% of the population. Researchers have investigated the influence of articular geometry on kinematics and contact mechanics in order to gain insight into the etiology of these conditions. The purpose of the current study was to create a three-dimensional statistical shape model of the PF joint and to characterize relationships between PF shape and function (kinematics and contact mechanics). A statistical shape model of the patellar and femoral articular surfaces and their relative alignment was developed from magnetic resonance images. Using 15 shape parameters, the model characterized 97% of the variation in the training set. The first three shape modes primarily described variation in size, patella alta-baja and depth of the sulcus groove. A previously verified finite element model was used to predict kinematics and contact mechanics for each subject. Combining the shape and joint mechanics data, a statistical shape-function model was developed that established quantitative relations of how changes in the shape of the PF joint influence mechanics. The predictive capability of the shape-function model was evaluated by comparing statistical model and finite element predictions, resulting in kinematic root mean square errors of less than 3° and 2.5 mm. The key results of the study are dually in the implementation of a novel approach linking statistical shape and finite element models and the relationships elucidated between PF articular geometry and mechanics.

The role of patient, surgical, and implant design variation in total knee replacement performance

Clinical studies demonstrate substantial variation in kinematic and functional performance within the total knee replacement (TKR) patient population. Some of this variation is due to differences in implant design, surgical technique and component alignment, while some is due to subject-specific differences in joint loading and anatomy that are inherently present within the population. Combined finite element and probabilistic methods were employed to assess the relative contributions of implant design, surgical, and subject-specific factors to overall tibiofemoral (TF) and patellofemoral (PF) joint mechanics, including kinematics, contact mechanics, joint loads, and ligament and quadriceps force during simulated squat, stance-phase gait and stepdown activities. The most influential design, surgical and subject-specific factors were femoral condyle sagittal plane radii, tibial insert superior-inferior (joint line) position and coronal plane alignment, and vertical hip load, respectively. Design factors were the primary contributors to condylar contact mechanics and TF anterior-posterior kinematics; TF ligament forces were dependent on surgical factors; and joint loads and quadriceps force were dependent on subject-specific factors. Understanding which design and surgical factors are most influential to TKR mechanics during activities of daily living, and how robust implant designs and surgical techniques must be in order to adequately accommodate subject-specific variation, will aid in directing design and surgical decisions towards optimal TKR mechanics for the population as a whole.

The influence of total knee arthroplasty geometry on mid-flexion stability: An experimental and finite element study

Fluoroscopic evaluation of total knee arthroplasty (TKA) has reported sudden anterior translation of the femur relative to the tibia (paradoxical anterior motion) for some cruciate-retaining designs. This motion may be tied to abrupt changes in the femoral sagittal radius of curvature characteristic of traditional TKA designs, as the geometry transitions from a large load-bearing distal radius to a smaller posterior radius which can accommodate femoral rollback. It was hypothesized that a gradually reducing radius may attenuate sudden changes in anterior-posterior motion that occur in mid-flexion with traditional discrete-radius designs. A combined experimental and computational approach was employed to test this hypothesis. A previously developed finite element (FE) model of the Kansas knee simulator (KKS), virtually implanted with multiple implant designs, was used to predict the amount of paradoxical anterior femoral slide during a simulated deep knee bend. The model predicted kinematics demonstrated that incorporating a gradually reducing radius in mid-flexion reduced the magnitude of paradoxical anterior translation between 21% and 68%, depending on the conformity of the tibial insert. Subsequently, both a dual-radius design and a modified design incorporating gradually reducing radii were tested in vitro in the KKS for verification. The model-predicted and experimentally observed kinematics exhibited good agreement, while the average experimental kinematics demonstrated an 81% reduction in anterior translation with the modified design. The FE model demonstrated sufficient sensitivity to appropriately differentiate kinematic changes due to subtle changes in implant design, and served as a useful pre-clinical design-phase tool to improve implant kinematics.

Relative contributions of design, alignment, and loading variability in knee replacement mechanics

Substantial variation in total knee replacement (TKR) outcomes exists within the patient population. Some of this variability is due to differences in the design of the implanted components and variation in surgical alignment, while other variability is due to differences in the applied forces and torques due to anatomic and physiological differences within a patient population. We evaluated the relative contributions of implant design, surgical alignment, and patient‐specific loading variability to overall tibiofemoral joint mechanics to provide insight into which measures can be influenced through design and surgical decisions, and which are inherently dependent on variation within the patient population and should be considered in the robustness of the implant design and surgical procedure. Design, surgical, and loading parameters were assessed using probabilistic finite element methods during simulated stance‐phase gait and squat activities. Patient‐specific loading was found to be the primary contributor to joint loading and kinematics during low flexion, particularly under conditions of high external loads (for instance, the gait cycle with high internal–external torque), while design and surgical factors, particularly femoral posterior radius and posterior slope of the tibial insert became increasingly important in TKR performance in deeper flexion.

Comparison of patellar bone strain in the natural and implanted knee during simulated deep flexion

Instances of anterior knee pain and patellar fracture are significant complications following total knee replacement (TKR). Bone strain measured in the patella can provide an indication of patellar fracture risk and may also be related to anterior knee pain. The objective of this study was to develop subject‐specific finite element models of the patellofemoral (PF) joint including density‐mapped material properties to gain insight into the patellar bone strain distribution in the natural and implanted knee. In eight subjects, the volume of bone experiencing strains >0.5% in the implanted condition was ∼200% larger, on average, than the natural condition. An inverse relationship with a correlation of −0.74 was established between postoperative bone volume and strain in the implanted specimens, suggesting that patellar geometry may be a useful indicator of postoperative strain. Comparing strains between regions (superior, inferior, medial, and lateral), it was found that although highly strained bone was evenly distributed between medial and lateral regions in the natural case, the implanted specimens demonstrated significantly larger volumes of highly strained bone medially as a result of substantially lower modulus bone in the medial compartment. Understanding distributions of PF strain may aid in preoperative identification of those patients at risk for patellar fracture or anterior knee pain, guidance regarding altered component placement for at‐risk patients, and design of components considering the implications of PF load transfer and patellar strain distribution.