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.

Separate modeling of cortical and trabecular bone offers little improvement in FE predictions of local structural stiffness at the proximal tibia.

Quantitative computed tomography-based finite element (QCT-FE) modeling has potential to clarify the role of altered subchondral bone stiffness in osteoarthritis. The objective of this research was to evaluate different QCT-FE modeling and thresholding approaches to identify the method which best predicted experimentally measured local subchondral structural stiffness with highest explained variance and least error. Our results showed that separate modeling of proximal tibial cortical and trabecular bone offered little improvement in QCT-FE-predicted stiffness (0% to +3% improvement in explained variance) when compared to modeling the proximal tibia as a single structure. Based on the results of this study, we do not recommend separate modeling of cortical bone and trabecular bone when developing QCT-FE models of the proximal tibia for predicting subchondral bone stiffness.

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.

Optimizing finite element predictions of local subchondral bone structural stiffness using neural network-derived density-modulus relationships for proximal tibial subchondral cortical and trabecular bone.

BACKGROUND: Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain. However, it is unclear what density-modulus equation(s) should be applied with subchondral cortical and subchondral trabecular bone when constructing finite element models of the tibia. Using a novel approach applying neural networks, optimization, and back-calculation against in situ experimental testing results, the objective of this study was to identify subchondral-specific equations that optimized finite element predictions of local structural stiffness at the proximal tibial subchondral surface. METHODS: Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using multiple density-modulus equations (93 total variations) then mapped to corresponding finite element models. For each variation, root mean squared error was calculated between finite element prediction and in situ measured stiffness at 47 indentation sites. Resulting errors were used to train an artificial neural network, which provided an unlimited number of model variations, with corresponding error, for predicting stiffness at the subchondral bone surface. Nelder-Mead optimization was used to identify optimum density-modulus equations for predicting stiffness. FINDINGS: Finite element modeling predicted 81% of experimental stiffness variance (with 10.5% error) using optimized equations for subchondral cortical and trabecular bone differentiated with a 0.5g/cm3 density. INTERPRETATION: In comparison with published density-modulus relationships, optimized equations offered improved predictions of local subchondral structural stiffness. Further research is needed with anisotropy inclusion, a smaller voxel size and de-blurring algorithms to improve predictions.

Quantifying trabecular bone material anisotropy and orientation using low resolution clinical CT images: A feasibility study.

Accounting for spatial variation of trabecular material anisotropy and orientation can improve the accuracy of quantitative computed tomography-based finite element (FE) modeling of bone. The objective of this study was to investigate the feasibility of quantifying trabecular material anisotropy and orientation using clinical computed tomography (CT). Forty four cubic volumes of interest were obtained from micro-CT images of the human radius. Micro-FE modeling was performed on the samples to obtain orthotropic stiffness entries as well as trabecular orientation. Simulated computed tomography images (0.32, 0.37, and 0.5mm isotropic voxel sizes) were created by resampling micro-CT images with added image noise. The gray-level structure tensor was used to derive fabric eigenvalues and eigenvectors in simulated CT images. For 'best case' comparison purposes, Mean Intercept Length was used to define fabric from micro-CT images. Regression was used in combination with eigenvalues, imaged density and FE to inversely derive the constants used in Cowin and Zysset-Curnier fabric-elasticity equations, and for comparing image derived fabric-elasticity stiffness entries to those obtained using micro-FE. Image derived eigenvectors (which indicated trabecular orientation) were then compared to orientation derived using micro-FE. When using clinically available voxel sizes, gray-level structure tensor derived fabric combined with Cowin's equations was able to explain 94-97% of the variance in orthotropic stiffness entries while Zysset-Curnier equations explained 82-88% of the variance in stiffness. Image derived orientation deviated by 4.4-10.8° from micro-FE derived orientation. Our results indicate potential to account for spatial variation of trabecular material anisotropy and orientation in subject-specific finite element modeling of bone using clinically available CT.

Individual and combined effects of OA-related subchondral bone alterations on proximal tibial surface stiffness: a parametric finite element modeling study.

The role of subchondral bone in OA pathogenesis is unclear. While some OA-related changes to morphology and material properties in different bone regions have been described, the effect of these alterations on subchondral bone surface stiffness has not been investigated. The objectives of this study were to characterize the individual (Objective 1) and combined (Objective 2) effects of OA-related morphological and mechanical alterations to subchondral and epiphyseal bone on surface stiffness of the proximal tibia. We developed and validated a parametric FE model of the proximal tibia using quantitative CT images of 10 fresh-frozen cadaveric specimens and in situ macro-indentation testing. Using this validated FE model, we estimated the individual and combined roles of OA-related alterations in subchondral cortical thickness and elastic modulus, and subchondral trabecular and epiphyseal trabecular elastic moduli on local surface stiffness. A 20% increase in subchondral cortical or subchondral trabecular elastic moduli resulted in little change in stiffness (1% increase). A 20% reduction in epiphyseal trabecular elastic modulus, however, resulted in an 11% reduction in stiffness. Our parametric analysis suggests that subchondral bone stiffness is affected primarily by epiphyseal trabecular bone elastic modulus rather than subchondral cortical and trabecular morphology or mechanical properties. Our results suggest that observed OA-related alterations to epiphyseal trabecular bone (e.g., lower mineralization, bone volume fraction, density and elastic modulus) may contribute to OA proximal tibiae being less stiff than normal.

Prediction of local proximal tibial subchondral bone structural stiffness using subject-specific finite element modeling: Effect of selected density-modulus relationship.

BACKGROUND: Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain initiation. Calculation of bone elastic moduli from image data is a basic step when constructing finite element models. However, different relationships between elastic moduli and imaged density (known as density-modulus relationships) have been reported in the literature. The objective of this study was to apply seven different trabecular-specific and two cortical-specific density-modulus relationships from the literature to finite element models of proximal tibia subchondral bone, and identify the relationship(s) that best predicted experimentally measured local subchondral structural stiffness with highest explained variance and least error. METHODS: Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using published density-modulus relationships and mapped to corresponding finite element models. Proximal tibial structural stiffness values were compared to experimentally measured stiffness values from in-situ macro-indentation testing directly on the subchondral bone surface (47 indentation points). FINDINGS: Regression lines between experimentally measured and finite element calculated stiffness had R(2) values ranging from 0.56 to 0.77. Normalized root mean squared error varied from 16.6% to 337.6%. INTERPRETATION: Of the 21 evaluated density-modulus relationships in this study, Goulet combined with Snyder and Schneider or Rho appeared most appropriate for finite element modeling of local subchondral bone structural stiffness. Though, further studies are needed to optimize density-modulus relationships and improve finite element estimates of local subchondral bone structural stiffness.