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

Biophysical Approaches for Applying and Measuring Biological Forces

Over the past decades, increasing evidence has indicated that mechanical loads can regulate the morphogenesis, proliferation, migration, and apoptosis of living cells. Investigations of how cells sense mechanical stimuli or the mechanotransduction mechanism is an active field of biomaterials and biophysics. Gaining a further understanding of mechanical regulation and depicting the mechanotransduction network inside cells require advanced experimental techniques and new theories. In this review, the fundamental principles of various experimental approaches that have been developed to characterize various types and magnitudes of forces experienced at the cellular and subcellular levels are summarized. The broad applications of these techniques are introduced with an emphasis on the difficulties in implementing these techniques in special biological systems. The advantages and disadvantages of each technique are discussed, which can guide readers to choose the most suitable technique for their questions. A perspective on future directions in this field is also provided. It is anticipated that technical advancement can be a driving force for the development of mechanobiology.

Architecture of the cancellous bone in human proximal tibia based on P45 sectional plastinated specimens

PURPOSE

To reveal differences in the pattern of trabecular architecture in the epiphysis and metaphysis of the proximal tibia.

METHODS

The trabecular architecture of the proximal tibia was observed in 27 P45 plastinated knee specimens.

RESULTS

In the medial and lateral condyles, under the articular cartilage surrounded by the medial or lateral meniscus, the cancellous bone is formed by thick and dense trabecular bands, which run longitudinally in the epiphysis and then pass through the epiphyseal line to terminate on the slanted cortex of the metaphysis. In the intercondylar eminence, the trabeculae are arranged basically in a network. In the central portion of the tibial metaphysis, cancellous bone consists of fine arcuate trabeculae, which extend to the anterior and posterior cortices, respectively. These trabeculae are intersected sparsely and form trusses over the medullary cavity. Near the areas of attachment of the iliotibial tract, tibial collateral ligament, anterior and posterior cruciate ligaments, and patellar ligament, the cancellous bone is locally reinforced with patchy trabeculae, dense radiating trabeculae, or two orthotropic trabecular bands.

CONCLUSION

This study provides further accurate anatomical information on the trabeculae of the proximal tibia. The soft structures of knee joint, including the articular cartilage, menisci, and ligaments, and the slanted cortices of the metaphysis are important landmarks for the location of different arrangements of the cancellous architecture. The present results are beneficial for clinical diagnosis and treatment of pathologies of the knee joint, or the establishment of a finite element analysis model of the knee joint.

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.

Bone mineral density, mechanical properties, and trabecular orientation of cancellous bone within humeral heads affected by advanced shoulder arthropathy

The mechanical properties of cancellous bone in the humeral head are increasingly interesting due to the increased popularity of stemless prosthetic fixation in the cancellous bone of the metaphysis. Age or pathology-related systemic osteoporosis, inactivity, or pathology of the shoulder joint may influence the primary bonding of implants that rely on good cancellous bone quality. We assessed the bone mineral density (BMD) and anisotropy using micro-computed tomography (micro-CT) (0.04 mm voxel size) and correlated the results with indentation load/displacement response. Resected parts of humeral heads (from patients undergoing total shoulder replacement, n = 18) were used as probes. The region of interest was defined as 2 mm medial from the resection plane, presuming that it mirrored the bone quality lateral to the resection plane. The indentation tests were performed with a large probe (diameter 10 mm) in a single destructive loading procedure. The BMD and trabecular orientation were determined by micro-CT. Our results showed a correlation between the BMD and the slope of the load/displacement curve. Furthermore, the trabeculae were predominantly oriented orthogonal to the joint surface. In conclusion, the predominant factor determining the bone quality and mechanical resistance to pressure appears to be the BMD, while trabecular orientation could not be related to load/displacement response. Statement of clinical significance: Bone quality predominately determines the mechanical properties of cancellous bone. This might be crucial when prosthetic implants need to be anchored in metaphyseal bone. Therefore, clinical decision-making processes should also include local BMD measurements.

Effect of CT imaging on the accuracy of the finite element modelling in bone

The finite element (FE) analysis is a highly promising tool to simulate the behaviour of bone. Skeletal FE models in clinical routine rely on the information about the geometry and bone mineral density distribution from quantitative computed tomography (CT) imaging systems. Several parameters in CT imaging have been reported to affect the accuracy of FE models. FE models of bone are exclusively developed in vitro under scanning conditions deviating from the clinical setting, resulting in variability of FE results (< 10%). Slice thickness and field of view had little effect on FE predicted bone behaviour (≤ 4%), while the reconstruction kernels showed to have a larger effect (≤ 20%). Due to large interscanner variations (≤ 20%), the translation from an experimental model into clinical reality is a critical step. Those variations are assumed to be mostly caused by different “black box” reconstruction kernels and the varying frequency of higher density voxels, representing cortical bone. Considering the low number of studies together with the significant effect of CT imaging on the finite element model outcome leading to high variability in the predicted behaviour, we propose further systematic research and validation studies, ideally preceding multicentre and longitudinal studies.

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.

A comparison of density-modulus relationships used in finite element modeling of the shoulder

Subject- and site-specific modeling techniques greatly improve the accuracy of computational models derived from clinical-resolution quantitative computed tomography (QCT) data. The majority of shoulder finite element (FE) studies use density-modulus relationships developed for alternative anatomical locations. As such, the objectives of this study were to compare the six most commonly used density-modulus relationships in shoulder finite element (FE) studies. To achieve this, ninety-eight (98) virtual trabecular bone cores were extracted from uCT scans of scapulae from 14 cadaveric specimens (7 male; 7 female). Homogeneous tissue moduli of 20 GPa, and heterogeneous tissue moduli scaled by CT-intensity were considered. Micro finite element models (µ-FEMs) of each virtual core were compressively loaded to 0.5% apparent strain and apparent strain energy density (SED_app) was collected. Each uCT virtual core was then co-registered to clinical QCT images, QCT-FEMs created, and each of the 6 density-modulus relationships applied (6 × 98 = 588 QCT-FEMs). The loading and boundary conditions were replicated and SED_app was collected and compared to µ-FEM SED_app. When a homogeneous tissue modulus was considered in the µ-FEMs, SED_app was best predicted in QCT-FEMs with the density-modulus relationship developed from pooled anatomical locations (QCT-FEM SED_app = 0.979µ-FEM SED_app + 0.0066, r² = 0.933). A different density-modulus relationship best predicted SED_app (QCT-FEM SED_app = 1.014µ-FEM SED_app + 0.0034, r² = 0.935) when a heterogeneous tissue modulus was considered. This study compared density-modulus relationships used in shoulder FE studies using an independent computational methodology for comparing these relationships.