Mathieu Charlebois

Improvements in vertebral body strength under teriparatide treatment assessed in vivo by finite element analysis: results from the EUROFORS study.

Monitoring of osteoporosis therapy based solely on DXA is insufficient to assess antifracture efficacy. Estimating bone strength as a variable closely linked to fracture risk is therefore of importance. Finite element (FE) analysis–based strength measures were used to monitor a teriparatide therapy and the associated effects on whole bone and local fracture risk. In 44 postmenopausal women with established osteoporosis participating in the EUROFORS study, FE models based on high‐resolution CT (HRCT) of T12 were evaluated after 0, 6, 12, and 24 mo of teriparatide treatment (20 μg/d). FE‐based strength and stiffness calculations for three different load cases (compression, bending, and combined compression and bending) were compared with volumetric BMD (vBMD) and apparent bone volume fraction (app. BV/TV), as well as DXA‐based areal BMD of the lumbar spine. Local damage of the bone tissue was also modeled. Highly significant improvements in all analyzed variables as early as 6 mo after starting teriparatide were found. After 24 mo, bone strength in compression was increased by 28.1 ± 4.7% (SE), in bending by 28.3 ± 4.9%, whereas app. BV/TV was increased by 54.7 ± 8.8%, vBMD by 19.1 ± 4.0%, and areal BMD of L1–L4 by 10.2 ± 1.2%. When comparing standardized increases, FE changes were significantly larger than those of densitometry and not significantly different from app. BV/TV. The size of regions at high risk for local failure was significantly reduced under teriparatide treatment. Treatment with teriparatide leads to bone strength increases for different loading conditions of close to 30%. FE is a suitable tool for monitoring bone anabolic treatment in groups or individual patients and offers additional information about local failure modes. FE variables showed a higher standardized response to changes than BMD measurements, but further studies are needed to show that the higher response represents a more accurate estimate of treatment‐induced fracture risk reduction.

A three-dimensional elastic plastic damage constitutive law for bone tissue

Motivated by mechanical analysis of bones and bone-implant systems, a 3D constitutive law describing the macroscopic mechanical behaviour of both cortical and trabecular bone in cyclic (not fatigue) overloads is developed. The proposed model which mathematical formulation is established within the framework of generalized standard materials accounts for three distinct material evolution modes where elastic, plastic and damage aspects are closely related. The anisotropic elasticity of bone is described by a morphology-based model and distinct damage behaviour in tension and compression by a halfspacewise generalized Hill criterion. The plastic criterion is based on the intact elastic compliance tensor. The algorithm applies three distinct projections based on the relationship between the internal variables and criteria. Their respective consistent tangent operators are presented. Numerical resolutions of several boundary value problems and a biomechanical application are presented to illustrate the potential of the constitutive model and demonstrate the expected quadratic convergence of the algorithm.

Cement distribution, volume, and compliance in vertebroplasty: some answers from an anatomy-based nonlinear finite element study.

Study Design. The biomechanics of vertebral bodies augmented with real distributions of cement were investigated using nonlinear finite element (FE) analysis. Objectives. To compare stiffness, strength, and stress transfer of augmented versus nonaugmented osteoporotic vertebral bodies under compressive loading. Specifically, to examine how cement distribution, volume, and compliance affect these biomechanical variables. Summary of Background Data. Previous FE studies suggested that vertebroplasty might alter vertebral stress transfer, leading to adjacent vertebral failure. However, no FE study so far accounted for real cement distributions and bone damage accumulation. Methods. Twelve vertebral bodies scanned with high-resolution pQCT and tested in compression were augmented with various volumes of cements and scanned again. Nonaugmented and augmented pQCT datasets were converted to FE models, with bone properties modeled with an elastic, plastic and damage constitutive law that was previously calibrated for the nonaugmented models. The cement-bone composite was modeled with a rule of mixture. The nonaugmented and augmented FE models were subjected to compression and their stiffness, strength, and stress map calculated for different cement compliances. Results. Cement distribution dominated the stiffening and strengthening effects of augmentation. Models with cement connecting either the superior or inferior endplate (S/I fillings) were only up to 2 times stiffer than the nonaugmented models with minimal strengthening, whereas those with cement connecting both endplates (S + I fillings) were 1 to 8 times stiffer and 1 to 12 times stronger. Stress increases above and below the cement, which was higher for the S + I cases and was significantly reduced by increasing cement compliance. Conclusion. The developed FE approach, which accounts for real cement distributions and bone damage accumulation, provides a refined insight into the mechanics of augmented vertebral bodies. In particular, augmentation with compliant cement bridging both endplates would reduce stress transfer while providing sufficient strengthening.

A patient-specific finite element methodology to predict damage accumulation in vertebral bodies under axial compression, sagittal flexion and combined loads.

Due to the inherent limitations of DXA, assessment of the biomechanical properties of vertebral bodies relies increasingly on CT-based finite element (FE) models, but these often use simplistic material behaviour and/or single loading cases. In this study, we applied a novel constitutive law for bone elasticity, plasticity and damage to FE models created from coarsened pQCT images of human vertebrae, and compared vertebral stiffness, strength and damage accumulation for axial compression, anterior flexion and a combination of these two cases. FE axial stiffness and strength correlated with experiments and were linearly related to flexion properties. In all loading modes, damage localised preferentially in the trabecular compartment. Damage for the combined loading was higher than cumulated damage produced by individual compression and flexion. In conclusion, this FE method predicts stiffness and strength of vertebral bodies from CT images with clinical resolution and provides insight into damage accumulation in various loading modes.

The Role of Fabric in the Large Strain Compressive Behavior of Human Trabecular Bone

Osteoporosis-related vertebral body fractures involve large compressive strains of trabecular bone. The small strain mechanical properties of the trabecular bone such as the elastic modulus or ultimate strength can be estimated using the volume fraction and a second order fabric tensor, but it remains unclear if similar estimations may be extended to large strain properties. Accordingly, the aim of this work is to identify the role of volume fraction and especially fabric in the large strain compressive behavior of human trabecular bone from various anatomical locations. Trabecular bone biopsies were extracted from human T12 vertebrae (n=31), distal radii (n=43), femoral head (n=44), and calcanei (n=30), scanned using microcomputed tomography to quantify bone volume fraction (BV/TV) and the fabric tensor (M), and tested either in unconfined or confined compression up to very large strains (∼70%). The mechanical parameters of the resulting stress-strain curves were analyzed using regression models to examine the respective influence of BV/TV and fabric eigenvalues. The compressive stress-strain curves demonstrated linear elasticity, yielding with hardening up to an ultimate stress, softening toward a minimum stress, and a steady rehardening followed by a rapid densification. For the pooled experiments, the average minimum stress was 1.89 ± 1.77 MPa, while the corresponding mean strain was 7.15 ± 1.84%. The minimum stress showed a weaker dependence with fabric as the elastic modulus or ultimate strength. For the confined experiments, the stress at a logarithmic strain of 1.2 was 8.08 ± 7.91 MPa, and the dissipated energy density was 5.67 ± 4.42 MPa. The latter variable was strongly related to the volume fraction (R(2)=0.83) but the correlation improved only marginally with the inclusion of fabric (R(2)=0.84). The influence of fabric on the mechanical properties of human trabecular bone decreases with increasing strain, while the role of volume fraction remains important. In particular, the ratio of the minimum versus the maximum stress, i.e., the relative amount of softening, decreases strongly with fabric, while the dissipated energy density is dominated by the volume fraction. The collected results will prove to be useful for modeling the softening and densification of the trabecular bone using the finite element method.