Image-based biomechanical models of the musculoskeletal system

Finite element modeling is a precious tool for the investigation of the biomechanics of the musculoskeletal system. A key element for the development of anatomically accurate, state-of-the art finite element models is medical imaging. Indeed, the workflow for the generation of a finite element model includes steps which require the availability of medical images of the subject of interest: segmentation, which is the assignment of each voxel of the images to a specific material such as bone and cartilage, allowing for a three-dimensional reconstruction of the anatomy; meshing, which is the creation of the computational mesh necessary for the approximation of the equations describing the physics of the problem; assignment of the material properties to the various parts of the model, which can be estimated for example from quantitative computed tomography for the bone tissue and with other techniques (elastography, T1rho, and T2 mapping from magnetic resonance imaging) for soft tissues. This paper presents a brief overview of the techniques used for image segmentation, meshing, and assessing the mechanical properties of biological tissues, with focus on finite element models of the musculoskeletal system. Both consolidated methods and recent advances such as those based on artificial intelligence are described.

MRI-based assessment of proximal femur strength compared to mechanical testing

Half of the women who sustain a hip fracture would not qualify for osteoporosis treatment based on current DXA-estimated bone mineral density criteria. Therefore, a better approach is needed to determine if an individual is at risk of hip fracture from a fall. The objective of this study was to determine the association between radiation-free MRI-derived bone strength and strain simulations compared to results from direct mechanical testing of cadaveric femora. Imaging was conducted on a 3-Tesla MRI scanner using two sequences: one balanced steady-state free precession sequence with 300 μm isotropic voxel size and one spoiled gradient echo with anisotropic voxel size of 234 × 234 × 1500 μm. Femora were dissected free of soft-tissue and 4350-ohm strain-gauges were securely applied to surfaces at the femoral shaft, inferior neck, greater trochanter, and superior neck. Cadavers were mechanically tested with a hydraulic universal test frame to simulate loading in a sideways fall orientation. Sideways fall forces were simulated on MRI-based finite element meshes and bone stiffness, failure force, and force for plastic deformation were computed. Simulated bone strength metrics from the 300 μm isotropic sequence showed strong agreement with experimentally obtained values of bone strength, with stiffness (r = 0.88, p = 0.0002), plastic deformation point (r = 0.89, p < 0.0001), and failure force (r = 0.92, p < 0.0001). The anisotropic sequence showed similar trends for stiffness, plastic deformation point, and failure force (r = 0.68, 0.70, 0.84; p = 0.02, 0.01, 0.0006, respectively). Surface strain-gauge measurements showed moderate to strong agreement with simulated magnitude strain values at the greater trochanter, superior neck, and inferior neck (r = -0.97, -0.86, 0.80; p ≤0.0001, 0.003, 0.03, respectively). The findings from this study support the use of MRI-based FE analysis of the hip to reliably predict the mechanical competence of the human femur in clinical settings.

Stochastic analysis of a heterogeneous micro-finite element model of a mouse tibia

Finite element (FE) analysis can be used to predict bone mechanical environments that can be used for many important applications, such as the understanding of bone mechano-regulation mechanisms. However, when defining the FE models, uncertainty in bone material properties may lead to marked variations in the predicted mechanical environment. The aim of this study is to investigate the influence of uncertainty in bone material property on the mechanical environment of bone. A heterogeneous FE model of a mouse tibia was created from micro computed tomography images. Axial compression loading was applied, and all possible bone density-modulus relationships were considered through stochastic analysis. The 1st and 3rd principal strains (ε₁ and ε₃) and the strain energy density (SED) were quantified in the tibial volume of interest (VOI). The bounds of ε₁, ε₃, and SED were determined by the bounds of the density-modulus relationship; the bone mechanical environment (ε₁, ε₃, and SED) and the bone density-modulus relationship exhibit the same trend of change; the relative percentage differences caused by bone material uncertainty are up to 28%, 28%, and 21% for ε₁, ε₃, and SED, respectively. These data provide guidelines on the adoption of bone density-modulus relationship in heterogeneous FE models.

The Effect of Material Heterogeneity, Element Type, and Down-Sampling on Trabecular Stiffness in Micro Finite Element Models

Preclinical and clinical bone strength predictions can be elucidated by understanding bone mechanics at a variety of hierarchical levels. As such, down-sampled micro-CT images are often used to make comparisons across image resolutions or used to reduce computational resources in micro finite element models (µFEMs). Therefore, the objectives of this study were to compare trabecular apparent modulus among (i) hexahedral and tetrahedral µFEMs, (ii) µFEMs generated from 32, 64, and 64 µm down-sampled from 32 µm µCT scans, and (iii) µFEMs with homogeneous and heterogeneous tissue moduli. Trabecular µFEMs were generated from scans at the three spatial resolutions taken from the glenoid vault of 14 cadaveric specimens. Simulated unconstrained compression was performed and used to calculate and compare the apparent modulus of each µFEM. It was found that models derived from high-resolution images that account for material heterogeneity are nearly equivalent whether hexahedral or tetrahedral elements are used. However, translation of stiffness from down-sampled scans are not equivalent to scans performed at the down-sampled resolution, or that account for trabecular material heterogeneity. Material heterogeneity is most representative of in vivo trabecular bone and to accurately model trabecular mechanical properties, material heterogeneity should be considered in future µFEM development.

Effects of Scan Resolutions and Element Sizes on Bovine Vertebral Mechanical Parameters from Quantitative Computed Tomography-Based Finite Element Analysis

Quantitative computed tomography-based finite element analysis (QCT/FEA) has been developed to predict vertebral strength. However, QCT/FEA models may be different with scan resolutions and element sizes. The aim of this study was to explore the effects of scan resolutions and element sizes on QCT/FEA outcomes. Nine bovine vertebral bodies were scanned using the clinical CT scanner and reconstructed from datasets with the two-slice thickness, that is, 0.6 mm (PA resolution) and 1 mm (PB resolution). There were significantly linear correlations between the predicted and measured principal strains (R² > 0.7, P < 0.0001), and the predicted vertebral strength and stiffness were modestly correlated with the experimental values (R² > 0.6, P < 0.05). Two different resolutions and six different element sizes were combined in pairs, and finite element (FE) models of bovine vertebral cancellous bones in the 12 cases were obtained. It showed that the mechanical parameters of FE models with the PB resolution were similar to those with the PA resolution. The computational accuracy of FE models with the element sizes of 0.41 × 0.41 × 0.6 mm³ and 0.41 × 0.41 × 1 mm³ was higher by comparing the apparent elastic modulus and yield strength. Therefore, scan resolution and element size should be chosen optimally to improve the accuracy of QCT/FEA.

Quantitative Computed Tomography (QCT) derived Bone Mineral Density (BMD) in finite element studies: a review of the literature

BACKGROUND

Finite element modeling of human bone provides a powerful tool to evaluate a wide variety of outcomes in a highly repeatable and parametric manner. These models are most often derived from computed tomography data, with mechanical properties related to bone mineral density (BMD) from the x-ray energy attenuation provided from this data. To increase accuracy, many researchers report the use of quantitative computed tomography (QCT), in which a calibration phantom is used during image acquisition to improve the estimation of BMD. Since model accuracy is dependent on the methods used in the calculation of BMD and density-mechanical property relationships, it is important to use relationships developed for the same anatomical location and using the same scanner settings, as these may impact model accuracy. The purpose of this literature review is to report the relationships used in the conversion of QCT equivalent density measures to ash, apparent, and/or tissue densities in recent finite element (FE) studies used in common density-modulus relationships. For studies reporting experimental validation, the validation metrics and results are presented.

RESULTS

Of the studies reviewed, 29% reported the use of a dipotassium phosphate (K2HPO4) phantom, 47% a hydroxyapatite (HA) phantom, 13% did not report phantom type, 7% reported use of both K2HPO4 and HA phantoms, and 4% alternate phantom types. Scanner type and/or settings were omitted or partially reported in 31% of studies. The majority of studies used densitometric and/or density-modulus relationships derived from different anatomical locations scanned in different scanners with different scanner settings. The methods used to derive various densitometric relationships are reported and recommendations are provided toward the standardization of reporting metrics.

CONCLUSIONS

This review assessed the current state of QCT-based FE modeling with use of clinical scanners. It was found that previously developed densitometric relationships vary by anatomical location, scanner type and settings. Reporting of all parameters used when referring to previously developed relationships, or in the development of new relationships, may increase the accuracy and repeatability of future FE models.