Peter J. Laz

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.

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.

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.

An Efficient Probabilistic Methodology for Incorporating Uncertainty in Body Segment Parameters and Anatomical Landmarks in Joint Loadings Estimated From Inverse Dynamics

Inverse dynamics is a standard approach for estimating joint loadings in the lower extremity from kinematic and ground reaction data for use in clinical and research gait studies. Variability in estimating body segment parameters and uncertainty in defining anatomical landmarks have the potential to impact predicted joint loading. This study demonstrates the application of efficient probabilistic methods to quantify the effect of uncertainty in these parameters and landmarks on joint loading in an inverse-dynamics model, and identifies the relative importance of the parameters and landmarks to the predicted joint loading. The inverse-dynamics analysis used a benchmark data set of lower-extremity kinematics and ground reaction data during the stance phase of gait to predict the three-dimensional intersegmental forces and moments. The probabilistic analysis predicted the 1-99 percentile ranges of intersegmental forces and moments at the hip, knee, and ankle. Variabilities, in forces and moments of up to 56% and 156% of the mean values were predicted based on coefficients of variation less than 0.20 for the body segment parameters and standard deviations of 2 mm for the anatomical landmarks. Sensitivity factors identified the important parameters for the specific joint and component directions. Anatomical landmarks affected moments to a larger extent than body segment parameters. Additionally, for forces, anatomical landmarks had a larger effect than body segment parameters, with the exception of segment masses, which were important to the proximal-distal joint forces. The probabilistic modeling approach predicted the range of possible joint loading, which has implications in gait studies, clinical assessments, and implant design evaluations.

Specimen-specific modeling of hip fracture pattern and repair

Hip fracture remains a major health problem for the elderly. Clinical studies have assessed fracture risk based on bone quality in the aging population and cadaveric testing has quantified bone strength and fracture loads. Prior modeling has primarily focused on quantifying the strain distribution in bone as an indicator of fracture risk. Recent advances in the extended finite element method (XFEM) enable prediction of the initiation and propagation of cracks without requiring a priori knowledge of the crack path. Accordingly, the objectives of this study were to predict femoral fracture in specimen-specific models using the XFEM approach, to perform one-to-one comparisons of predicted and in vitro fracture patterns, and to develop a framework to assess the mechanics and load transfer in the fractured femur when it is repaired with an osteosynthesis implant. Five specimen-specific femur models were developed from in vitro experiments under a simulated stance loading condition. Predicted fracture patterns closely matched the in vitro patterns; however, predictions of fracture load differed by approximately 50% due to sensitivity to local material properties. Specimen-specific intertrochanteric fractures were induced by subjecting the femur models to a sideways fall and repaired with a contemporary implant. Under a post-surgical stance loading, model-predicted load sharing between the implant and bone across the fracture surface varied from 59%:41% to 89%:11%, underscoring the importance of considering anatomic and fracture variability in the evaluation of implants. XFEM modeling shows potential as a macro-level analysis enabling fracture investigations of clinical cohorts, including at-risk groups, and the design of robust implants.

A multi-subject evaluation of uncertainty in anatomical landmark location on shoulder kinematic description.

An accurate assessment of shoulder kinematics is useful for understanding healthy normal and pathological mechanics. Small variability in identifying and locating anatomical landmarks (ALs) has potential to affect reported shoulder kinematics. The objectives of this study were to quantify the effect of landmark location variability on scapular and humeral kinematic descriptions for multiple subjects using probabilistic analysis methods, and to evaluate the consistency in results across multiple subjects. Data from 11 healthy subjects performing humeral elevation in the scapular plane were used to calculate Euler angles describing humeral and scapular kinematics. Probabilistic analyses were performed for each subject to simulate uncertainty in the locations of 13 upper-extremity ALs. For standard deviations of 4 mm in landmark location, the analysis predicted Euler angle envelopes between the 1 and 99 percentile bounds of up to 16.6°. While absolute kinematics varied with the subject, the average 1–99% kinematic ranges for the motion were consistent across subjects and sensitivity factors showed no statistically significant differences between subjects. The description of humeral kinematics was most sensitive to the location of landmarks on the thorax, while landmarks on the scapula had the greatest effect on the description of scapular elevation. The findings of this study can provide a better understanding of kinematic variability, which can aid in making accurate clinical diagnoses and refining kinematic measurement techniques.

Identifying alignment parameters affecting implanted patellofemoral mechanics

Complications of the patellofemoral (PF) joint remain a common cause for revision of total knee replacements. PF complications, such as patellar maltracking, subluxation, and implant failure, have been linked to femoral and patellar component alignment. In this study, a dynamic finite element model of an implanted PF joint was applied in conjunction with a probabilistic simulation to establish relationships between alignment parameters and PF kinematics, contact mechanics, and internal stresses. Both traditional sensitivity analysis and a coupled probabilistic and principal component analysis approach were applied to characterize relationships between implant alignment and resulting joint mechanics. Critical alignment parameters, and combinations of parameters, affecting PF mechanics were identified for three patellar designs (dome, modified dome, and anatomic). Femoral internal–external (I‐E) alignment was identified as a critical alignment factor for all component designs, influencing medial–lateral contact force and anterior–posterior translation. The anatomic design was sensitive to patellar flexion–extension (F‐E) alignment, while the dome, as expected, was less influenced by rotational alignment, and more by translational position. The modified dome was sensitive to a combination of superior–inferior, F‐E, and I‐E alignments. Understanding the relationships and design‐specific dependencies between alignment parameters can aid preoperative planning, and help focus instrumentation design on those alignment parameters of primary concern.

Statistical Modeling to Characterize Relationships Between Knee Anatomy and Kinematics

The mechanics of the knee are complex and dependent on the shape of the articular surfaces and their relative alignment. Insight into how anatomy relates to kinematics can establish biomechanical norms, support the diagnosis and treatment of various pathologies (e.g., patellar maltracking) and inform implant design. Prior studies have used correlations to identify anatomical measures related to specific motions. The objective of this study was to describe relationships between knee anatomy and tibiofemoral (TF) and patellofemoral (PF) kinematics using a statistical shape and function modeling approach. A principal component (PC) analysis was performed on a 20‐specimen dataset consisting of shape of the bone and cartilage for the femur, tibia and patella derived from imaging and six‐degree‐of‐freedom TF and PF kinematics from cadaveric testing during a simulated squat. The PC modes characterized links between anatomy and kinematics; the first mode captured scaling and shape changes in the condylar radii and their influence on TF anterior–posterior translation, internal‐external rotation, and the location of the femoral lowest point. Subsequent modes described relations in patella shape and alta/baja alignment impacting PF kinematics. The complex interactions described with the data‐driven statistical approach provide insight into knee mechanics that is useful clinically and in implant design.

A multi-platform comparison of efficient probabilistic methods in the prediction of total knee replacement mechanics

Explicit finite element (FE) and multi-body dynamics (MBD) models have been developed to evaluate total knee replacement (TKR) mechanics as a complement to experimental methods. In conjunction with these models, probabilistic methods have been implemented to predict performance bounds and identify important parameters, subject to uncertainty in component alignment and experimental conditions. Probabilistic methods, such as advanced mean value (AMV) and response surface method (RSM), provide an efficient alternative to the gold standard Monte Carlo simulation technique (MCST). The objective of the current study was to benchmark models from three platforms (two FE and one MBD) using various probabilistic methods by predicting the influence of alignment variability and experimental parameters on TKR mechanics in simulated gait. Predicted kinematics envelopes were on average about 2.6 mm for tibial anterior–posterior translation, 2.9° for tibial internal–external rotation and 1.9 MPa for tibial peak contact pressure for the various platforms and methods. Based on this good agreement with the MCST, the efficient probabilistic techniques may prove useful in the fast evaluation of new implant designs, including considerations of uncertainty, e.g. misalignment.