An open source software tool to assign the material properties of bone for ABAQUS finite element simulations

In silico assessment of the bone regeneration potential of complex porous scaffolds

Mechanical environment plays a crucial role in regulating bone regeneration in bone defects. Assessing the mechanobiological behavior of patient-specific orthopedic scaffolds in-silico could help guide optimal scaffold designs, as well as intra- and post-operative strategies to enhance bone regeneration and improve implant longevity. Additively manufactured porous scaffolds, and specifically triply periodic minimal surfaces (TPMS), have shown promising structural properties to act as bone substitutes, yet their ability to induce mechanobiologially-driven bone regeneration has not been elucidated. The aim of this study is to i) explore the bone regeneration potential of TPMS scaffolds made of different stiffness biocompatible materials, to ii) analyze the influence of pre-seeding the scaffolds and increasing the post-operative resting period, and to iii) assess the influence of patient-specific parameters, such as age and mechanosensitivity, on outcomes. To perform this study, an in silico model of a goat tibia is used. The bone ingrowth within the scaffold pores was simulated with a mechano-driven model of bone regeneration. Results showed that the scaffold's architectural properties affect cellular diffusion and strain distribution, resulting in variations in the regenerated bone volume and distribution. The softer material improved the bone ingrowth. An initial resting period improved the bone ingrowth but not enough to reach the scaffold's core. However, this was achieved with the implantation of a pre-seeded scaffold. Physiological parameters like age and health of the patient also influence the bone regeneration outcome, though to a lesser extent than the scaffold design. This analysis demonstrates the importance of the scaffold's geometry and its material, and highlights the potential of using mechanobiological patient-specific models in the design process for bone substitutes.

From computed tomography to finite element space: A unified bone material mapping strategy

BACKGROUND

The spatially varying mechanical properties in finite element models of bone are most often derived from bone density data obtained via quantitative computed tomography. The key step is to accurately and efficiently map the density given in voxels to the finite element mesh.

METHODS

The density projection is first formulated in least-squares terms and then discretized using a continuous and discontinuous variant of the finite element method. Both discretization variants are compared with the nodal and element approaches known from the literature.

FINDINGS

In terms of accuracy in the L2 norm, energy distance and efficiency, the discontinuous zero-order variant appears to be the most advantageous. The proposed variant sufficiently preserves the spectrum of density at the edges, while keeping computational cost low.

INTERPRETATION

The continuous finite element method is analogous to the nodal formulation in the literature, while the discontinuous finite element method is analogous to the element formulation. The two variants differ in terms of implementation, computational cost and ability to preserve the density spectrum. These differences cannot be described and measured by known indirect methods from the literature.

Bilateral asymmetry of bone density adjacent to pelvic sarcomas: A retrospective study using computed tomography

Limb-salvaging hemipelvectomy surgeries involving allograft or custom prosthesis reconstruction require high quality remaining pelvic bone for adequate device fixation. Modeling studies of custom pelvis prosthesis designs typically mirror contralateral pelvic bone material properties to the ipsilateral pelvis. However, the extent of bone material property and geometric symmetry, and thus the appropriateness of mirroring, remains unknown and should be considered when designing or analyzing the performance of pelvic prostheses. This study investigates preoperative differences between ipsilateral and contralateral pelvic bone for patients with a pelvic sarcoma. Computed tomography (CT) data were obtained retrospectively from eight patients with a pelvic sarcoma. Subject-specific computational models of the pelvic bones were constructed from the CT data. Bilateral asymmetry of bone material properties and cross-sectional areas between the ipsilateral and contralateral hemipelvis were quantified at points adjacent to the pelvic sarcoma. Large bilateral asymmetry (>20%) in trabecular but not cortical bone density was observed within 20 mm of the tumor location. Differences in trabecular bone density typically declined with increased distance from the tumor. The greatest bilateral difference in cross-sectional area occurred within 10 mm of the tumor boundary for three patients and within 40 mm from the tumor site for four patients. Our results suggest that pelvic sarcomas can cause significant bilateral asymmetries in trabecular bone density for patients with a pelvic sarcoma. These differences should be taken into account when designing custom implants for this patient population.

Heterogeneous material mapping methods for patient-specific finite element models of pelvic trabecular bone: A convergence study

Patient-specific finite element (FE) models of bone require the assignment of heterogeneous material properties extracted from the subject's computed tomography (CT) images. Though node-based (NB) and element-based (EB) material mapping methods (MMMs) have been proposed, the sensitivity and convergence of FE models to MMM for varying mesh sizes are not well understood. In this work, CT-derived and synthetic bone material data were used to evaluate the effect of MMM on results from FE analyses. Pelvic trabecular bone data was extracted from CT images of six subjects, while synthetic data were created to resemble trabecular bone properties. The numerical convergence of FE bone models using different MMMs were evaluated for strain energy, von-Mises stress, and strain. NB and EB MMMs both demonstrated good convergence regarding total strain energy, with the EB method having a slight edge over the NB. However, at the local level (e.g., maximum stress and strain), FE results were sensitive to the field type, MMM, and the FE mesh size. The EB method exhibited superior performance in finer meshes relative to the voxel size. The NB method converged better than did the EB method for coarser meshes. These findings may lead to higher-fidelity patient-specific FE bone models.

OPTIMAL MESH CRITERIA IN FINITE ELEMENT MODELING OF HUMAN FOOT: THE DEPENDENCE FOR MULTIPLE MODEL OUTPUTS ON MESH DENSITY AND LOADING BOUNDARY CONDITIONS

The use of finite element models has gained popularity in the field of foot and footwear biomechanics to predict the stress–strain distribution and the treatment effectiveness of therapeutic insoles for pathological foot conditions. However, a comprehensive evaluation of mesh quality is often ignored, meanwhile no golden standard exists for the mesh density and selection of element size at an acceptable accuracy. Here, we make a convergence test and established anatomically-realistic foot models at different mesh densities. The study compared the discrepancy in output variables to the changes of element type and mesh density under barefoot and footwear conditions with compressive and shear loads, which are commonly encountered in foot and footwear biomechanics simulations. For a range of loading conditions simulated in 125 finite element models, the peak plantar pressure consistently converged with optimal mesh size determined at 2.5[Formula: see text]mm. The convergence variable of principal strains and stress tensors, however, varies significantly. The max von-Mises stress showed strong sensitive behavior to the changes of the mesh density. The pattern for contact pressure distribution became less accurate when the element sizes increase to 6.0[Formula: see text]mm; in particular, the locations of the pressure peak do not show remarkable changes, but the size of the area of contact still changes. The current study could offer a general guideline when generating a reasonable accurate finite element models for the analysis of plantar pressure distributions and stress/strain states employed for foot and footwear biomechanics evaluations.

Mechano-driven regeneration predicts response variations in large animal model based on scaffold implantation site and individual mechano-sensitivity

It is well founded that the mechanical environment may regulate bone regeneration in orthopedic applications. The purpose of this study is to investigate the mechanical contributions of the scaffold and the host to bone regeneration, in terms of subject specificity, implantation site and sensitivity to the mechanical environment. Using a computational approach to model mechano-driven regeneration, bone ingrowth in porous titanium scaffolds was simulated in the distal femur and proximal tibia of three goats and compared to experimental results. The results showed that bone ingrowth shifted from a homogeneous distribution pattern, when scaffolds were in contact with trabecular bone (max local ingrowth 12.47%), to a localized bone ingrowth when scaffolds were implanted in a diaphyseal location (max local ingrowth 20.64%). The bone formation dynamics revealed an apposition rate of 0.37±0.28%/day in the first three weeks after implantation, followed by limited increase in bone ingrowth until the end of the experiment (12 weeks). According to in vivo data, we identified one animal whose sensitivity to mechanical stimulation was higher than the other two. Moreover, we found that the stimulus initiating bone formation was consistently higher in the femur than in the tibia for all the individuals. Overall, the dependence of the osteogenic response on the host biomechanics means that, from a mechanical perspective, the regenerative potential depends on both the scaffold and the host environment. Therefore, this work provides insights on how the mechanical conditions of both the recipient and the scaffold contribute to meet patient and location-specific characteristics.

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.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

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.