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

Biomechanics of the Human Osteochondral Unit: A Systematic Review

The damping system ensured by the osteochondral (OC) unit is essential to deploy the forces generated within load-bearing joints during locomotion, allowing furthermore low-friction sliding motion between bone segments. The OC unit is a multi-layer structure including articular cartilage, as well as subchondral and trabecular bone. The interplay between the OC tissues is essential in maintaining the joint functionality; altered loading patterns can trigger biological processes that could lead to degenerative joint diseases like osteoarthritis. Currently, no effective treatments are available to avoid degeneration beyond tissues' recovery capabilities. A thorough comprehension on the mechanical behaviour of the OC unit is essential to (i) soundly elucidate its overall response to intra-articular loads for developing diagnostic tools capable of detecting non-physiological strain levels, (ii) properly evaluate the efficacy of innovative treatments in restoring physiological strain levels, and (iii) optimize regenerative medicine approaches as potential and less-invasive alternatives to arthroplasty when irreversible damage has occurred. Therefore, the leading aim of this review was to provide an overview of the state-of-the-art-up to 2022-about the mechanical behaviour of the OC unit. A systematic search is performed, according to PRISMA standards, by focusing on studies that experimentally assess the human lower-limb joints' OC tissues. A multi-criteria decision-making method is proposed to quantitatively evaluate eligible studies, in order to highlight only the insights retrieved through sound and robust approaches. This review revealed that studies on human lower limbs are focusing on the knee and articular cartilage, while hip and trabecular bone studies are declining, and the ankle and subchondral bone are poorly investigated. Compression and indentation are the most common experimental techniques studying the mechanical behaviour of the OC tissues, with indentation also being able to provide information at the micro- and nanoscales. While a certain comparability among studies was highlighted, none of the identified testing protocols are currently recognised as standard for any of the OC tissues. The fibril-network-reinforced poro-viscoelastic constitutive model has become common for describing the response of the articular cartilage, while the models describing the mechanical behaviour of mineralised tissues are usually simpler (i.e., linear elastic, elasto-plastic). Most advanced studies have tested and modelled multiple tissues of the same OC unit but have done so individually rather than through integrated approaches. Therefore, efforts should be made in simultaneously evaluating the comprehensive response of the OC unit to intra-articular loads and the interplay between the OC tissues. In this regard, a multidisciplinary approach combining complementary techniques, e.g., full-field imaging, mechanical testing, and computational approaches, should be implemented and validated. Furthermore, the next challenge entails transferring this assessment to a non-invasive approach, allowing its application in vivo, in order to increase its diagnostic and prognostic potential.

Systematic review of computed tomography parameters used for the assessment of subchondral bone in osteoarthritis

OBJECTIVE

To systematically review the published parameters for the assessment of subchondral bone in human osteoarthritis (OA) using computed tomography (CT) and gain an overview of current practices and standards.

DESIGN

A literature search of Medline, Embase and Cochrane Library databases was performed with search strategies tailored to each database (search from 2010 to January 2023). The search results were screened independently by two reviewers against pre-determined inclusion and exclusion criteria. Studies were deemed eligible if conducted in vivo/ex vivo in human adults (>18 years) using any type of CT to assess subchondral bone in OA. Extracted data from eligible studies were compiled in a qualitative summary and formal narrative synthesis.

RESULTS

This analysis included 202 studies. Four groups of CT modalities were identified to have been used for subchondral bone assessment in OA across nine anatomical locations. Subchondral bone parameters measuring similar features of OA were combined in six categories: (i) microstructure, (ii) bone adaptation, (iii) gross morphology (iv) mineralisation, (v) joint space, and (vi) mechanical properties.

CONCLUSIONS

Clinically meaningful parameter categories were identified as well as categories with the potential to become relevant in the clinical field. Furthermore, we stress the importance of quantification of parameters to improve their sensitivity and reliability for the evaluation of OA disease progression and the need for standardised measurement methods to improve their clinical value.

Biomechanical analysis of internal fixation system stability for tibial plateau fractures

Background: Complex bone plateau fractures have been treated with bilateral plate fixation, but previous research has overemphasized evaluating the effects of internal fixation design, plate position, and screw orientation on fracture fixation stability, neglecting the internal fixation system's biomechanical properties in postoperative rehabilitation exercises. This study aimed to investigate the mechanical properties of tibial plateau fractures after internal fixation, explore the biomechanical mechanism of the interaction between internal fixation and bone, and make suggestions for early postoperative rehabilitation and postoperative weight-bearing rehabilitation. Methods: By establishing the postoperative tibia model, the standing, walking and running conditions were simulated under three axial loads of 500 N, 1000 N, and 1500 N. Accordingly, finite element analysis (FEA) was performed to analyze the model stiffness, displacement of fractured bone fragments, titanium alloy plate, screw stress distribution, and fatigue properties of the tibia and the internal fixation system under various conditions. Results: The stiffness of the model increased significantly after internal fixation. The anteromedial plate was the most stressed, followed by the posteromedial plate. The screws at the distal end of the lateral plate, the screws at the anteromedial plate platform and the screws at the distal end of the posteromedial plate are under greater stress, but at a safe stress level. The relative displacement of the two medial condylar fracture fragments varied from 0.002-0.072 mm. Fatigue damage does not occur in the internal fixation system. Fatigue injuries develop in the tibia when subjected to cyclic loading, especially when running. Conclusion: The results of this study indicate that the internal fixation system tolerates some of the body's typical actions and may sustain all or part of the weight early in the postoperative period. In other words, early rehabilitative exercise is recommended, but avoid strenuous exercise such as running.

Finite Element Analysis of Different Osseocartilaginous Reconstruction Techniques in Animal Model Knees

Lesions of the articular cartilage are frequent in all age populations and lead to functional impairment. Multiple surgical techniques have failed to provide an effective method for cartilage repair. The aim of our research was to evaluate the effect of two different compression forces on three types of cartilage repair using finite element analysis (FEA). Initially, an in vivo study was performed on sheep. The in vivo study was prepared as following: Case 0-control group, without cartilage lesion; Case 1-cartilage lesion treated with macro-porous collagen implants; Case 2-cartilage lesion treated with collagen implants impregnated with bone marrow concentrate (BMC); Case 3-cartilage lesion treated with collagen implants impregnated with adipose-derived stem cells (ASC). Using the computed tomography (CT) data, virtual femur-cartilage-tibia joints were created for each Case. The study showed better results in bone changes when using porous collagen implants impregnated with BMC or ASC stem cells for the treatment of osseocartilaginous defects compared with untreated macro-porous implant. After 7 months postoperative, the presence of un-resorbed collagen influences the von Mises stress distribution, total deformation, and displacement on the Z axis. The BMC treatment was superior to ASC cells in bone tissue morphology, resembling the biomechanics of the control group in all FEA simulations.

The effect of postmenopausal osteoporosis on subchondral bone pathology in a rat model of knee osteoarthritis

This study aimed to investigate the additional effect of ovariectomy-induced osteoporosis (OP) on the pathology of knee osteoarthritis (OA) in a rat meniscectomized model, particularly focusing on subchondral bone changes and pain behaviour. Rats were divided into four groups, sham, OP, OA, OP plus OA, and assessed for histology, osteoclast activity, subchondral bone microstructure, and pain-related behaviour. Rats with OP plus OA had significantly increased calcified cartilage and subchondral bone damage scores, increased densities of subchondral osteoclasts in the weight-bearing area, and more porous subchondral trabecular bone compared with rats with OA. Loss of tidemark integrity was observed most frequently in rats with OP plus OA. The density of subchondral osteoclasts correlated with the calcified cartilage and subchondral bone damage score in rats with OA (OA and OP plus OA). No significant differences in the receptor activator of nuclear factor-kappa B ligand (RANKL)/osteoprotegerin (OPG) expression ratio in subchondral bone and pain-related behavioural tests were observed between rats with OA and rats with OP plus OA. In rats with OA, coexisting OP potentially aggravated OA pathology mainly in calcified cartilage and subchondral trabecular bone by increasing subchondral osteoclast activity.

Stability of internal fixation systems based on different subtypes of Schatzker II fracture of the tibial plateau: A finite element analysis

Background: Schaztker II fracture is the most common type of the tibial plateau fractures (TPF). There has been a large number of cadaveric biomechanical studies and finite element simulation studies to explore the most stable fixation methods for this type of fracture, which were based on a single fracture morphology. But differences among fracture morphologies could directly affect the stability of internal fixation systems. In this sense, we verified the stability of existing internal fixation modalities by simulating Schatzker II fractures with different fracture morphologies.

Objectives: To compare the stability of different filler types combined with locked compression plate/screw in different subtypes of Schatzker II TPF.

Methods: Four subtypes of Schatzker II were created based on 3D map of TPF. Each of the subtypes was fixed with LCP/screw or LCP/screw combined with different fill types. Stress distribution, displacement distribution, and the load sharing capacity of the filler were assessed by applying the maximum load during gait. In addition, repeated fracture risks of depressed fragment were evaluated regarding to the ultimate strain of bone.

Results: The stress concentration of the implant in each scenario was located on the screw at the contact site between the plate and the screw, and the filler of the defect site significantly reduced the stress concentration of the implant (Subtype A: Blank group 402.0 MPa vs. Experimental group 315.2 ± 5.5 MPa; Subtype C: Blank group 385.0 MPa vs. Experimental group 322.7 ± 12.1 MPa). Displacement field analysis showed that filler significantly reduced the reduction loss of the depressed fragment (Subtype A: Blank group 0.1949 mm vs. Experimental group 0.174 ± 0.001 mm; Subtype C: 0.264 mm vs. 0.253 ± 0.002 mm). Maximum strain was in subtype C with the value of 2.3% ± 0.1% indicating the greatest possibility of failure risk. And with the increase of its modulus, the bearing capacity of filler increased.

Conclusion: The existence of filler at the defect site can effectively reduce the stress concentration of the implant and the reduction loss of the collapsed block, thus providing good stability for Schatzker II fracture. In subtype A fracture, the modulus of filler presented the slightest influence on the stability, followed by subtype C, while the stability of subtype B was most influenced by the modulus of filler. Therefore, it is necessary to evaluate the preoperative patient imaging data adequately to select the appropriate stiffness of the filler.

Knee Pain from Osteoarthritis: Pathogenesis, Risk Factors, and Recent Evidence on Physical Therapy Interventions

For patients presenting knee pain coming from osteoarthritis (OA), non-pharmacological conservative treatments (e.g., physical therapy interventions) are among the first methods in orthopedics and rehabilitation to prevent OA progression and avoid knee surgery. However, the best strategy for each patient is difficult to establish, because knee OA's exact causes of progression are not entirely understood. This narrative review presents (i) the most recent update on the pathogenesis of knee OA with the risk factors for developing OA and (ii) the most recent evidence for reducing knee pain with physical therapy intervention such as Diathermy, Exercise therapy, Ultrasounds, Knee Brace, and Electrical stimulation. In addition, we calculated the relative risk reduction in pain perception for each intervention. Our results show that only Brace interventions always reached the minimum for clinical efficiency, making the intervention significant and valuable for the patients regarding their Quality of Life. In addition, more than half of the Exercise and Diathermy interventions reached the minimum for clinical efficiency regarding pain level. This literature review helps clinicians to make evidence-based decisions for reducing knee pain and treating people living with knee OA to prevent knee replacement.

The causal association between bone mineral density and risk of osteoarthritis: A Mendelian randomization study

OBJECTIVES

The causal direction and magnitude of the association between total body bone mineral density (TB-BMD) and osteoarthritis (OA) risk is uncertain owing to the susceptibility of observational studies to confounding and reverse causation. The study aimed to explore the relationships between TB-BMD concentration and OA using Mendelian randomization (MR).

METHODS

In this study, we used two-sample MR to obtain unconfounded estimates of the effect of TB-BMD on hip and knee OA. Single nucleotide polymorphisms (SNPs) strongly associated with TB-BMD in a large genome-wide association study (GWAS) were identified and selected as instrumental variables (IVs). In addition to the main analysis using inverse-variance weighted (IVW) method, we applied 2 additional methods to control for pleiotropy(MR-Egger regression, weighted median estimator) and compared the respective MR estimates.

RESULTS

MR analyses suggested that genetically predicted higher TB-BMD is associated with risks of hip OA (For IVW: OR=1.199, 95%CI: 1.02-1.42, P=0.032; for WM: OR=1.257, 95%CI: 1.09-1.45, P=0.002). There was no evidence that the observed causal effect between TB-BMD and the risk of hip OA was affected by genetic pleiotropy(P=0.618). Additionally, our study didn't support causal effects of a genetically increased TB-BMD risk on knee OA risk(OR=1.121, 95%CI: 0.99-1.28, P=0.084 using IVW; OR=1.132, 95%CI: 0.99-1.29, P=0.068 using WM; OR=1.274, 95%CI: 0.88-1.85, P=0.217 using MR-Egger).

CONCLUSIONS

Our findings support a causal effect that a genetic predisposition to systematically higher TB-BMD was associated with the risk of OA. And, TB-BMD likely exerts an effect on the risk of hip OA not knee OA.

Subchondral bone microarchitecture and mineral density in human osteoarthritis and osteoporosis: A regional and compartmental analysis

Osteoarthritis (OA) and osteoporosis (OP) are historically considered to be inversely correlated but there may be an overlap between the pathophysiology of the two diseases. This study aimed to investigate the subchondral bone microarchitecture and matrix mineralization, and the association between them in OA and OP in relation to the degree of cartilage degeneration. Fifty-six osteochondral plugs were collected from 16 OA femoral heads. They were graded on a regional basis according to the stages of cartilage degeneration, as evaluated by a new macroscopic and a modified microscopic grading system. Twenty-one plugs were collected from seven femoral heads with OP. Plugs were scanned by microcomputed tomography and the microarchitectural and mineral properties were obtained for both subchondral plate and trabecular bone. Microarchitecture and material and apparent densities of subchondral bone in OP were similar to regions with early cartilage degeneration but different from regions with advanced cartilage degradation in OA femoral heads. Subchondral trabecular bone was more mineralized than subchondral plate in both OP and OA, and this compartmental difference varied by severity of cartilage degradation. Furthermore, the relationship among trabecular bone volume fraction, tissue mineral density, and apparent bone density was similar in OP and different stages of OA. Subchondral bone microarchitecture and mineral properties in OP are different from OA in a regionalized manner in relation to stages of cartilage degeneration. Both regional and compartmental differences at structural, material, and cellular levels need to be studied to understand the transition of OA subchondral bone from being osteoporotic to sclerotic.

Morphological and Apparent-Level Stiffness Variations Between Normal and Osteoarthritic Bone in the Humeral Head

Osteoarthritis (OA) is characterized by morphological changes that alter bone structure and mechanical properties. This study compared bone morphometric parameters and apparent modulus between humeral heads excised from end-stage OA patients undergoing total shoulder arthroplasty (n = 28) and non-pathologic normal cadavers (n = 28). Morphometric parameters were determined in central cores, with regional variations compared in four medial to lateral regions. Linear regression compared apparent modulus, morphometric parameters, and age. Micro finite element models estimated trabecular apparent modulus and derived density-modulus relationships. Significant differences were found for bone volume fraction (p < 0.001) and trabecular thickness (p < 0.001) in the most medial regions. No significant differences occurred between morphometric parameters and apparent modulus or age, except in slope between groups for apparent modulus versus trabecular number (p = 0.021), and in intercept for trabecular thickness versus age (p = 0.040). Significant differences occurred in both slope and intercept between density-modulus regression fits for each group (p ≤ 0.001). The normal group showed high correlations in the power-fit (r²  = 0.87), with a lower correlation (r²  = 0.61) and a more linear relationship, in the OA group. This study suggests that alterations in structure and apparent modulus persist mainly in subchondral regions of end-stage OA bone. As such, if pathologic regions are removed during joint replacement, computational models that utilize modeling parameters from non-pathologic normal bone may be applied to end-stage OA bone. An improved understanding of humeral trabecular bone variations has potential to improve the surgical management of end-stage OA patients. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 38:503-509, 2020.

Use of Computational Modeling to Study Joint Degeneration: A Review

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.

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.

Intraarticular Ligament Degeneration Is Interrelated with Cartilage and Bone Destruction in Osteoarthritis

Osteoarthritis (OA) induces inflammation and degeneration of all joint components including cartilage, joint capsule, bone and bone marrow, and ligaments. Particularly intraarticular ligaments, which connect the articulating bones such as the anterior cruciate ligament (ACL) and meniscotibial ligaments, fixing the fibrocartilaginous menisci to the tibial bone, are prone to the inflamed joint milieu in OA. However, the pathogenesis of ligament degeneration on the cellular level, most likely triggered by OA associated inflammation, remains poorly understood. Hence, this review sheds light into the intimate interrelation between ligament degeneration, synovitis, joint cartilage degradation, and dysbalanced subchondral bone remodeling. Various features of ligament degeneration accompanying joint cartilage degradation have been reported including chondroid metaplasia, cyst formation, heterotopic ossification, and mucoid and fatty degenerations. The entheses of ligaments, fixing ligaments to the subchondral bone, possibly influence the localization of subchondral bone lesions. The transforming growth factor (TGF)β/bone morphogenetic (BMP) pathway could present a link between degeneration of the osteochondral unit and ligaments with misrouted stem cell differentiation as one likely reason for ligament degeneration, but less studied pathways such as complement activation could also contribute to inflammation. Facilitation of OA progression by changed biomechanics of degenerated ligaments should be addressed in more detail in the future.

Mechanical Metrics of the Proximal Tibia are Precise and Differentiate Osteoarthritic and Normal Knees: A Finite Element Study

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%RMS. 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%RMS 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.

Utility of cement injection to stabilize split-depression tibial plateau fracture by minimally invasive methods: A finite element analysis

BACKGROUND

Treatment for fractures of the tibial plateau is in most cases carried out by stable fixation in order to allow early mobilization. Minimally invasive technologies such as tibioplasty or stabilization by locking plate, bone augmentation and cement filling (CF) have recently been used to treat this type of fracture. The aim of this paper was to determine the mechanical behavior of the tibial plateau by numerically modeling and by quantifying the mechanical effects on the tibia mechanical properties from injury healing.

METHODS

A personalized Finite Element (FE) model of the tibial plateau from a clinical case has been developed to analyze stress distribution in the tibial plateau stabilized by balloon osteoplasty and to determine the influence of the cement injected. Stress analysis was performed for different stages after surgery.

FINDINGS

Just after surgery, the maximum von Mises stresses obtained for the fractured tibia treated with and without CF were 134.9 MPa and 289.9 MPa respectively on the plate. Stress distribution showed an increase of values in the trabecular bone in the treated model with locking plate and CF and stress reduction in the cortical bone in the model treated with locking plate only.

INTERPRETATION

The computed results of stresses or displacements of the fractured models show that the cement filling of the tibial depression fracture may increase implant stability, and decrease the loss of depression reduction, while the presence of the cement in the healed model renders the load distribution uniform.

Proximal tibial trabecular bone mineral density is related to pain in patients with osteoarthritis

Background

Our objective was to examine the relationships between proximal tibial trabecular (epiphyseal and metaphyseal) bone mineral density (BMD) and osteoarthritis (OA)-related pain in patients with severe knee OA.

Methods

The knee was scanned preoperatively using quantitative computed tomography (QCT) in 42 patients undergoing knee arthroplasty. OA severity was classified using radiographic Kellgren-Lawrence scoring and pain was measured using the pain subsection of the Western Ontario and McMaster Universities Arthritis Index (WOMAC). We used three-dimensional image processing techniques to assess tibial epiphyseal trabecular BMD between the epiphyseal line and 7.5 mm from the subchondral surface and tibial metaphyseal trabecular BMD 10 mm distal from the epiphyseal line. Regional analysis included the total epiphyseal and metaphyseal region, and the medial and lateral epiphyseal compartments. The association between total WOMAC pain scores and BMD measurements was assessed using hierarchical multiple regression with age, sex, and body mass index (BMI) as covariates. Statistical significance was set at p < 0.05.

Results

Total WOMAC pain was associated with total epiphyseal BMD adjusted for age, sex, and BMI (p = 0.013) and total metaphyseal BMD (p = 0.017). Regionally, total WOMAC pain was associated with medial epiphyseal BMD adjusted for age, sex, and BMI (p = 0.006).

Conclusion

These findings suggest that low proximal tibial trabecular BMD may have a role in OA-related pain pathogenesis.

Electronic supplementary material

The online version of this article (doi:10.1186/s13075-017-1415-9) contains supplementary material, which is available to authorized users.

Assessment of fracture risk in proximal tibia with tumorous bone defects by a finite element method

There has not been a satisfying method to predict the fracture risk in tumorous bone lesions. To tackle this challenge, we used a finite element method to assess the fracture risk in the proximal tibia (pT) when the size and location of the tumorous defects are varied in bone. Towards this end, the circular cortical defects, mimicking the tumorous lesions by forming cortical window defects, with a diameter (Ф) of 20, 30, 40, or 50 mm, are structured on the anteromedial, lateral, posterior wall of pT, which is located 5, 15, and 25 mm below articular margin, respectively. We found that under walking conditions, the Von Mises Stress of each defective tibia model was larger than that of the intact tibia model and also showed a positive linear correlation with the sizes of the defects. A notable fracture risk was not observed until the defect was Ф30 mm or larger. When the defect emerged, the anteromedial wall resisted fracture risk more than the rest of wall. Our results show that the size and location of the bone tumors are important factors affecting the fracture risk of pT. Our findings will be beneficial to clinicians when deciding what treatment to use for pT lesions.

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.