QCT-FE modeling of the proximal tibia: Effect of mapping strategy on convergence time and model accuracy.

Quantitative computed tomography (QCT) based finite element (FE) modeling, referred to as QCT-FE, has seen rapid growth and application for modeling bone mechanics. With this approach, varying bone material properties are set via experimentally-derived density-modulus equations. One challenge though associated with QCT-FE is to identify the appropriate mapping strategy for assigning elastic moduli to elements. The goal of this study was to evaluate different QCT-FE mapping strategies to identify the optimum approach with fastest convergence rate and highest accuracy. Four proximal tibial medial compartments were imaged using QCT and experimentally tested to characterize proximal tibial subchondral bone stiffness at four surface points, resulting in a total of 16 indentation measures. Three material mapping methods were analyzed: (1) constant-E where an average elastic modulus was assigned to each element; (2) node-based where the material properties were first mapped on nodes then interpolated to Gaussian integration points; and (3) element-based in which the material properties were directly assigned to Gaussian integration points. Different element sizes were assessed with edge-lengths ranging from 0.9 to 3 mm. Results indicated that all converged models showed similar coefficient-of-determination (R2) and normalized root-mean-square errors (RMSE%). Though, the constant-E and node-based methods converged with the element edge-length of 1.5 mm (prediction error of 4.8% and 2.5%, respectively) whereas the element-based method converged with a larger element having an edge-length 2.5 mm (error = 4.9%). In conclusion, the element-based method, with a larger element size, resulted in similar predictive accuracy, faster convergence and shorter run-times relative to the constant-E and node-based approaches. As such, we recommend the element-based method for future subject-specific QCT-FE modeling.

An exclusion approach for addressing partial volume artifacts with quantititive computed tomography-based finite element modeling of the proximal tibia.

INTRODUCTION: Quantitative computed tomography based finite element modeling (QCT-FE) has potential to clarify the role of subchondral bone stiffness in osteoarthritis. The limited spatial resolution of clinical QCT systems, however, results in partial volume (PV) artifacts and low contrast between cortical and trabecular bone, which adversely affects the accuracy of QCT-FE models. The objective of this research was to evaluate the agreement between stiffness predictions offered by QCT-FE models of proximal tibial subchondral bone (constructed with and without a new voxel-exclusion algorithm) with experimentally-derived local subchondral bone structural stiffness. METHODS: Thirteen proximal tibial compartments were obtained and imaged using QCT. Two types of QCT-FE models were developed: (1) standard model, which employed the standard procedure for QCT-FE modeling; and (2) "voxel exclusion (VE)" model, which addressed PV artifacts by excluding low density voxels during the material mapping stage of construction. We assessed agreement between QCT-FE stiffness estimates (using standard and VE approaches) with experimental stiffness by reporting predicted variance from linear regression and mean bias with 95% Limits of Agreement (LOA). RESULTS: The standard and VE models explained 81% and 84% of the variance in experimentally measured stiffness, respectively. The standard model showed a mean bias of -268 N/mm (LOA -1210 to 679 N/mm); the VE model showed a mean bias of +59 N/mm (LOA -762 to 910 N/mm). INTERPRETATION: The VE model explained more variance in subchondral bone stiffness with less bias. Our findings indicate that the VE method has potential to improve QCT-FE models of bone affected by PV artifacts.

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia.

INTRODUCTION: Previously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R2=0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia. METHODS: Local stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin's fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R2 and RMSE%. RESULTS: The uniform anisotropic FE model explained 53-74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76-79% of the variance in stiffness with RMSE% being 11.2-11.5%. CONCLUSIONS: Of the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin's fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness.