Osteoarthritis (OA), a degenerative joint disease, is the most common chronic condition of the joints, which cannot be prevented effectively. Computational modeling of joint degradation allows to ...estimate the patient-specific progression of OA, which can aid clinicians to estimate the most suitable time window for surgical intervention in osteoarthritic patients. This paper gives an overview of the different approaches used to model different aspects of joint degeneration, thereby focusing mostly on the knee joint. The paper starts by discussing how OA affects the different components of the joint and how these are accounted for in the models. Subsequently, it discusses the different modeling approaches that can be used to answer questions related to OA etiology, progression and treatment. These models are ordered based on their underlying assumptions and technologies: musculoskeletal models, Finite Element models, (gene) regulatory models, multiscale models and data-driven models (artificial intelligence/machine learning). Finally, it is concluded that in the future, efforts should be made to integrate the different modeling techniques into a more robust computational framework that should not only be efficient to predict OA progression but also easily allow a patient's individualized risk assessment as screening tool for use in clinical practice.
Our objective was to identify precise mechanical metrics of the proximal tibia which differentiated OA and normal knees. We developed subject-specific FE models for 14 participants (7 OA, 7 normal) ...who were imaged three times each for assessing precision (repeatability). We assessed various mechanical metrics (minimum principal and von Mises stress and strain as well as structural stiffness) across the proximal tibia for each subject. In vivo precision of these mechanical metrics was assessed using CV%
. We performed parametric and non-parametric statistical analyses and determined Cohen's d effect sizes to explore differences between OA and normal knees. For all FE-based mechanical metrics, average CV%
was less than 6%. Minimum principal stress was, on average, 75% higher in OA versus normal knees while minimum principal strain values did not differ. No difference was observed in structural stiffness. FE modeling could precisely quantify and differentiate mechanical metrics variations in normal and OA knees, in vivo. This study suggests that bone stress patterns may be important for understanding OA pathogenesis at the knee.
Highlights • Evaluated different osteoarthritis-related bone alterations on surface stiffness. • Modeled proximal tibial surface stiffness using parametric finite element modeling. • Validated ...surface stiffness predictions using in situ macro indentation testing. • Surface stiffness not affected by subchondral cortical thickness or modulus. • Surface stiffness primarily affected by epiphyseal trabecular elastic modulus.
•Presented a novel “voxel exclusion” method to address partial volume artifacts in QCT-FE models of the proximal tibia.•Evaluated stiffness predictions at the proximal tibial subchondral surface in ...relation to experimental stiffness measures.•Voxel exclusion offered improved predictions of stiffness with less bias compared to the standard model (+3% in R2, mean bias difference of 209 N/mm).•Voxel exclusion has potential to improve QCT-FE models of bone affected by partial volume artifacts.
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.
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).
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).
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.
Abstract 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.
Highlights • Quantified fabric using grey-level structure tensor in upsized micro-CT images. • Derived anisotropic stiffness entries and main orientation using micro finite element. • Fabric ...explained 94% of the variance in anisotropic stiffness entries. • Fabric predicted main orientation with 4.8° mean error. • It is possible to estimate anisotropy in clinical CT images.
Abstract 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 0.5 g/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.
Abstract 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 R2 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.
Abstract This paper presents an effective patient-specific approach for prediction of failure initiation and growth in human vertebra using the general framework of the quantitative computed ...tomography (QCT)-based finite element method (FEM). The studies were carried out on 13 vertebrae (lumbar and thoracic), excised from 3 cadavers with the average age of 42 years old. Initially, 4 samples were QCT scanned and the images were directly converted into voxel-based 3D finite element models for linear and nonlinear analyses. The equivalent plastic strains obtained from the nonlinear analyses were used to predict the occurrence of local failures and development of the failure patterns. In the linear analyses, the strain energy density measure was used to identify the critical elements and predict the failure patterns. Subsequently, the samples were destructively tested in uniaxial compression and the experimental load–displacement diagrams were obtained. The plain radiographic images of the tested samples were also examined for observation of the failure patterns. In continuation, the presence of osteolytic defects in vertebrae was simulated by creation of artificial cavities within 9 remaining samples using a computer numerical control (CNC) milling machine. The same protocol was followed for scanning, modeling, and destructive testing of these samples. A strong correlation was found between the predicted and measured strengths. Finally, a typical vertebroplasty treatment was simulated by injection of low-viscosity bone cement within 3 compressed samples. The failure patterns and the associated load levels for these samples were also predicted using the QCT voxel-based FEM.
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