Bayesian Calibration of Computational Knee Models to Estimate Subject-Specific Ligament Properties, Tibiofemoral Kinematics, and Anterior Cruciate Ligament Force With Uncertainty Quantification.

High-grade knee laxity is associated with early anterior cruciate ligament (ACL) graft failure, poor function, and compromised clinical outcome. Yet, the specific ligaments and ligament properties driving knee laxity remain poorly understood. We described a Bayesian calibration methodology for predicting unknown ligament properties in a computational knee model. Then, we applied the method to estimate unknown ligament properties with uncertainty bounds using tibiofemoral kinematics and ACL force measurements from two cadaver knees that spanned a range of laxities; these knees were tested using a robotic manipulator. The unknown ligament properties were from the Bayesian set of plausible ligament properties, as specified by their posterior distribution. Finally, we developed a calibrated predictor of tibiofemoral kinematics and ACL force with their own uncertainty bounds. The calibrated predictor was developed by first collecting the posterior draws of the kinematics and ACL force that are induced by the posterior draws of the ligament properties and model parameters. Bayesian calibration identified unique ligament slack lengths for the two knee models and produced ACL force and kinematic predictions that were closer to the corresponding in vitro measurement than those from a standard optimization technique. This Bayesian framework quantifies uncertainty in both ligament properties and model outputs; an important step towards developing subject-specific computational models to improve treatment for ACL injury.

Tekscan analysis programs (TAP) for quantifying dynamic contact mechanics.

This short communication provides details on customized Tekscan Analysis Programs (TAP) which extract comprehensive contact mechanics metrics from piezoelectric sensors in articulating joints across repeated loading cycles. The code provides functionality to identify regions of interest (ROI), compute contact mechanic metrics, and compare contact mechanics across multiple test conditions or knees. Further, the variability of identifying ROIs was quantified between seven different users and compared to an expert. Overall, the contribution of four variables were studied: two knee specimens; two points in the gait cycle; two averaging methods; and seven observers, to determine if variations in these values played a role in accurately quantifying the ROI. The relative error between the force ratio from each observer's ROI and the expert ROI was calculated as the output of interest. A multivariate linear mixed effects model was fit to the four variables for the relative error with an observer- and knee-specific random intercept. Results from the fitted model showed a statistically significant difference at the 0.05 level in the mean relative errors at the two gait points. Additionally, variability in the relative errors attributed to the observer, knee, and random errors was quantified. To reduce variability amongst users, by ensuring low inter-observer variability and increasing segmentation accuracy of knee contact mechanics, a training module and manual have been included as supplemental material. By sharing this code and training manual, we envisage that it can be used and modified to analyze outputs from a range of sensors, joints, and test conditions.

Reducing uncertainty when using knee-specific finite element models by assessing the effect of input parameters.

Little is known about knee-specific factors that influence contact mechanics. Finite Element (FE) models offer a powerful tool to study contact mechanics, but there often exists ambiguity in the exact values of the inputs (e.g., tissue properties), which can result in a range of output values. Our objective was to quantify the reduction in the range of output values (defined herein as "uncertainty") from FE models of the human knee joint when known pre-defined values are used for clinically measurable inputs. To achieve this goal, we applied a statistically augmented FE approach to three human cadaveric knees for which full geometric and kinematic data were available. Two sets of conditions were simulated: All model inputs, clinically measurable or not, were varied to represent a "normal" patient population (Condition 1); subsets of clinically measurable variable inputs were fixed at specific values (called "patient derived inputs," or PDIs) while the other variables were varied over "normal" values (Condition 2). We found that by fixing body mass index and the anterior-posterior position of the meniscal-bony insertion points, model output uncertainty was reduced by one- to three-fifths. The magnitude of uncertainty reduction was strongly influenced by the individual knee. It was observed that knees with great anterior-posterior translation during gait had greater reductions in uncertainty when PDIs were used. This study represents the first step in developing FE models of the human knee joint based on inputs that can be derived from patients in a clinical setting. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2233-2242, 2017.

A statistically-augmented computational platform for evaluating meniscal function.

Meniscal implants have been developed in an attempt to provide pain relief and prevent pathological degeneration of articular cartilage. However, as yet there has been no systematic and comprehensive analysis of the effects of the meniscal design variables on meniscal function across a wide patient population, and there are no clear design criteria to ensure the functional performance of candidate meniscal implants. Our aim was to develop a statistically-augmented, experimentally-validated, computational platform to assess the effect of meniscal properties and patient variables on knee joint contact mechanics during the activity of walking. Our analysis used Finite Element Models (FEMs) that represented the geometry, kinematics as based on simulated gait and contact mechanics of three laboratory tested human cadaveric knees. The FEMs were subsequently programmed to represent prescribed meniscal variables (circumferential and radial/axial moduli-Ecm, Erm, stiffness of the meniscal attachments-Slpma, Slamp) and patient variables (varus/valgus alignment-VVA, and articular cartilage modulus-Ec). The contact mechanics data generated from the FEM runs were used as training data to a statistical interpolator which estimated joint contact data for untested configurations of input variables. Our data suggested that while Ecm and Erm of a meniscus are critical in determining knee joint mechanics in early and late stance (peak 1 and peak 3 of the gait cycle), for some knees that have greater laxity in the mid-stance phase of gait, the stiffness of the articular cartilage, Ec, can influence force distribution across the tibial plateau. We found that the medial meniscus plays a dominant load-carrying role in the early stance phase and less so in late stance, while the lateral meniscus distributes load throughout gait. Joint contact mechanics in the medial compartment are more sensitive to Ecm than those in the lateral compartment. Finally, throughout stance, varus-valgus alignment can overwhelm these relationships while the stiffness of meniscal attachments in the range studied have minimal effects on the knee joint mechanics. In summary, our statistically-augmented, computational platform allowed us to study how meniscal implant design variables (which can be controlled at the time of manufacture or implantation) interact with patient variables (which can be set in FEMs but cannot be controlled in patient studies) to affect joint contact mechanics during the activity of simulated walking.

Using a statistically calibrated biphasic finite element model of the human knee joint to identify robust designs for a meniscal substitute.

This paper describes a methodology for selecting a set of biomechanical engineering design variables to optimize the performance of an engineered meniscal substitute when implanted in a population of subjects whose characteristics can be specified stochastically. For the meniscal design problem where engineering variables include aspects of meniscal geometry and meniscal material properties, this method shows that meniscal designs having simultaneously large radial modulus and large circumferential modulus provide both low mean peak contact stress and small variability in peak contact stress when used in the specified subject population. The method also shows that the mean peak contact stress is relatively insensitive to meniscal permeability, so the permeability used in the manufacture of a meniscal substitute can be selected on the basis of manufacturing ease or cost. This is a multiple objective problem with the mean peak contact stress over the population of subjects and its variability both desired to be small. The problem is solved by using a predictor of the mean peak contact stress across the tibial plateau that was developed from experimentally measured peak contact stresses from two modalities. The first experimental modality provided computed peak contact stresses using a finite element computational simulator of the dynamic tibial contact stress during axial dynamic loading. A small number of meniscal designs with specified subject environmental inputs were selected to make computational runs and to provide training data for the predictor developed below. The second experimental modality consisted of measured peak contact stress from a set of cadaver knees. The cadaver measurements were used to bias-correct and calibrate the simulator output. Because the finite element simulator is expensive to evaluate, a rapidly computable (calibrated) Kriging predictor was used to explore extensively the contact stresses for a wide range of meniscal engineering inputs and subject variables. The predicted values were used to determine the Pareto optimal set of engineering inputs to minimize peak contact stresses in the targeted population of subjects.

Changes in dynamic medial tibiofemoral contact mechanics and kinematics after injury of the anterior cruciate ligament: a cadaveric model.

The effects of tears of the anterior cruciate ligament on knee kinematics and contact mechanics during dynamic everyday activities, such as gait, remains unclear. The objective of this study was to characterize anterior cruciate ligament-deficient knee contact mechanics and kinematics during simulated gait. Nine human cadaveric knees were each augmented with a sensor capable of measuring dynamic normal contact stresses on the tibial plateau, mounted on a load-controlled simulator, and subjected to physiological, multidirectional, dynamic loads to mimic gait. Using a mixed model with random knee identifiers, confidence intervals were constructed for contact stress before and after anterior cruciate ligament transection at two points in the gait cycle at which axial force peaked (14% and 45% of the gait cycle). Kinematic and contact mechanics changes after anterior cruciate ligament transection were highly variable across knees. Nonetheless, a statistically significant increase in contact stress in the posterior-central aspect of the medial tibial plateau at 45% of the gait cycle was identified, the location of which corresponds to the location of degenerative changes that are frequently found in patients with chronic anterior cruciate ligament injury. The variability in the contact stress in other regions of the medial plateau at 45% of the gait cycle was partly explained by the variations in osseous geometry across the nine knees tested. At 14% of gait, there was no significant change in peak contact stress after anterior cruciate ligament transection in any of the four quadrants, and none of the possible explanatory variables showed statistical significance. Understanding the variable effect of anterior cruciate ligament injury on contact mechanics based on geometric differences in osseous anatomy is of paramount clinical importance and may be invaluable to select the best reconstruction techniques and counsel patients on their individual risk of subsequent chondral degeneration.

Hip resurfacing increases bone strains associated with short-term femoral neck fracture.

Short-term femoral neck fracture is a primary complication associated with contemporary hip resurfacing. Some fractures are associated with neck notching, while others occur in the absence of notching. These unexplained fractures may be due to large magnitude strains near the implant rim, which could cause bone damage accumulation and eventual neck fracture. We used statistically augmented finite element analysis to identify design and environmental variables that increase bone strains near the implant rim after resurfacing, and lead to strain magnitudes sufficient for rapid damage accumulation. After resurfacing, the compressive strains in the inferior, peripheral neck increased by approximately 25%, particularly when the implant shell was bonded. While the tensile strains in the peripheral neck were low in magnitude in the immediate postoperative models, they increased substantially following compressive damage accumulation. Low bone modulus, within the range of normal bone, and high head load contributed the most to large magnitude strains. Therefore, in some cases, hip resurfacing may cause a region of compressive bone damage to develop rapidly, which in turn leads to large tensile strains and potential neck fracture. Our study suggests that indications for surgery should account for bone material quality, and that rehabilitation protocols should avoid high-load activities.

Simultaneous Determination of Tuning and Calibration Parameters for Computer Experiments.

Tuning and calibration are processes for improving the representativeness of a computer simulation code to a physical phenomenon. This article introduces a statistical methodology for simultaneously determining tuning and calibration parameters in settings where data are available from a computer code and the associated physical experiment. Tuning parameters are set by minimizing a discrepancy measure while the distribution of the calibration parameters are determined based on a hierarchical Bayesian model. The proposed Bayesian model views the output as a realization of a Gaussian stochastic process with hyperpriors. Draws from the resulting posterior distribution are obtained by the Markov chain Monte Carlo simulation. Our methodology is compared with an alternative approach in examples and is illustrated in a biomechanical engineering application. Supplemental materials, including the software and a user manual, are available online and can be requested from the first author.

Demographic and behavioral modifiers of arsenic exposure pathways: a Bayesian hierarchical analysis of NHEXAS data.

We introduce a Bayesian hierarchical statistical model that describes subpopulation-specific pathways of exposure to arsenic. Our model is fitted to data collected as part of the National Human Exposure Assessment Survey (NHEXAS) and builds on the structural-equation-based analysis of the same data by Clayton et al. (Journal of Exposure Analysis and Environmental Epidemiology, 2002, 12, 29-43). Using demographic information (e.g., gender or age) and surrogates for environmental exposure (e.g., tobacco usage or the average number of minutes spent in an enclosed workshop), we identify subgroup differences in exposure routes. Missing and censored data, as well as uncertainty due to measurement error, are handled systematically in the Bayesian framework. Our analysis indicates that household size, amount of time spent at home, use of tapwater for drinking and cooking, number of glasses of water drunk, use of central air conditioning, and use of gas equipment significantly modify the arsenic exposure pathways.

Robust design for acetabular cup stability accounting for patient and surgical variability.

The stability of cementless acetabular cups depends on a close fit between the components and reamed acetabular cavities to promote bone ingrowth. Cup performance and stability are affected by both design and environmental (patient-dependent and surgical) factors. This study used a statistically based metamodel to determine the relative influences of design and environmental factors on acetabular cup stability by incorporating a comprehensive set of patient-dependent and surgical variables. Cup designs with 2 mm or 3 mm intended equatorial bone-implant interferences appeared to perform the best, improving implant stability with smaller mean and variability in cup relative motions and greater mean and smaller variability in ingrowth areas. Cup eccentricity was found to have no effect on implant performance. Design variables did not contribute as much to the variation in performance measures compared to the environmental variables, except for potential ingrowth areas.

Acetabular cup geometry and bone-implant interference have more influence on initial periprosthetic joint space than joint loading and surgical cup insertion.

Environmental variations in patient-dependent and surgical factors were modeled using robust optimization with a finite element acetabular cup-pelvis model. A previously developed statistical optimization scheme was used to: (1) determine the cup geometry and the optimal cup-bone interference that maximized bone-implant contact areas and minimized changes in the gap volume between the implant and bone surface during gait loading and unloading; and (2) determine the relative contributions of design, patient-dependent, and surgical factors to variations in bone-implant contact areas and a change in gap volume. The statistical analyses indicated that the design variables, namely the equatorial diameter and eccentricity, explained most of the variations in the performance measures. Further, the hemispherical designs performed better than the nonhemispherical designs. The 58 mm hemispherical cup, with 2 mm diametral interferences, minimized the change in gap volume and attained 82% and 81% of the maximum predicted total and rim contact areas, respectively. The equatorial diameter and eccentricity, not the patient-dependent and surgical factors, explained most of the variations in the performance measures. Perfect surface apposition was not attained with any of the cup designs.