Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

A combined experimental and computational study of mechanical properties after balloon kyphoplasty

Vertebral compression fractures rank among the most frequent injuries to the musculoskeletal system, with more than 1 million fractures per annum worldwide. The past decade has seen a considerable increase in the utilisation of surgical procedures such as balloon kyphoplasty to treat these injuries. While many kyphoplasty studies have examined the risk of damage to adjacent vertebra after treatment, recent case reports have also emerged to indicate the potential for the treated vertebra itself to re-collapse after surgery. The following study presents a combined experimental and computational study of balloon kyphoplasty which aims to establish a methodology capable of evaluating these cases of vertebral re-collapse. Results from both the experimental tests and computational models showed significant increases in strength and stiffness after treatment, by factors ranging from 1.44 to 1.93, respectively. Fatigue tests on treated specimens showed a 37% drop in the rate of stiffness loss compared to the untreated baseline case. Further analysis of the computational models concluded that inhibited PMMA interdigitation at the interface during kyphoplasty could reverse improvements in strength and stiffness that could otherwise be gained by the treatment.

A Multiscale Finite Element Analysis of Balloon Kyphoplasty to Investigate the Risk of Bone-Cement Separation In Vivo

BACKGROUND

During the past decade there has been a significant increase in the number of vertebral fractures being treated with the balloon kyphoplasty procedure. Although previous investigations have found kyphoplasty to be an effective treatment for reducing patient pain and lowering cement-leakage risk, there have been reports of vertebral recollapse following the procedure. These reports have indicated evidence of in vivo bone-cement separation leading to collapse of the treated vertebra.

METHODS

The following study documents a multiscale analysis capable of evaluating the risk of bone-cement interface separation during lying, standing, and walking activities following balloon kyphoplasty.

RESULTS

Results from the analysis found that instances of reduced cement interlock could initiate both tensile and shear separation of the interface region at up to 7 times the failure threshold during walking or up to 1.9 times the threshold during some cases for standing. Lying prone offered the best protection from interface failure in all cases, with a minimum safety factor of 2.95.

CONCLUSIONS

The results of the multiscale analysis show it is essential for kyphoplasty simulations to take account of the micromechanical behavior of the bone-cement interface to be truly representative of the in vivo situation after the treatment. The results further illustrate the importance of ensuring adequate cement infiltration into the compacted bone periphery during kyphoplasty through a combination of new techniques, tools, and biomaterials in a multifaceted approach to solve this complex challenge.

Inverse finite element modeling for characterization of local elastic properties in image-guided failure assessment of human trabecular bone

The local interpretation of microfinite element (μFE) simulations plays a pivotal role for studying bone structure–function relationships such as failure processes and bone remodeling.In the past μFE simulations have been successfully validated on the apparent level,however, at the tissue level validations are sparse and less promising. Furthermore,intra trabecular heterogeneity of the material properties has been shown by experimental studies. We proposed an inverse μFE algorithm that iteratively changes the tissue level Young's moduli such that the μFE simulation matches the experimental strain measurements.The algorithm is setup as a feedback loop where the modulus is iteratively adapted until the simulated strain matches the experimental strain. The experimental strain of human trabecular bone specimens was calculated from time-lapsed images that were gained by combining mechanical testing and synchrotron radiation microcomputed tomography(SRlCT). The inverse μFE algorithm was able to iterate the heterogeneous distribution of moduli such that the resulting μFE simulations matched artificially generated and experimentally measured strains.

The importance of intrinsic damage properties to bone fragility: a finite element study

As the average age of the population has increased, the incidence of age-related bone fracture has also increased. While some of the increase of fracture incidence with age is related to loss of bone mass, a significant part of the risk is unexplained and may be caused by changes in intrinsic material properties of the hard tissue. This investigation focused on understanding how changes to the intrinsic damage properties affect bone fragility. We hypothesized that the intrinsic (μm) damage properties of bone tissue strongly and nonlinearly affect mechanical behavior at the apparent (whole tissue, cm) level. The importance of intrinsic properties on the apparent level behavior of trabecular bone tissue was investigated using voxel based finite element analysis. Trabecular bone cores from human T12 vertebrae were scanned using microcomputed tomography (μCT) and the images used to build nonlinear finite element models. Isotropic and initially homogenous material properties were used for all elements. The elastic modulus (E(i)) of individual elements was reduced with a secant damage rule relating only principal tensile tissue strain to modulus damage. Apparent level resistance to fracture as a function of changes in the intrinsic damage properties was measured using the mechanical energy to failure per unit volume (apparent toughness modulus, W(a)) and the apparent yield strength (σ(ay), calculated using the 0.2% offset). Intrinsic damage properties had a profound nonlinear effect on the apparent tissue level mechanical response. Intrinsic level failure occurs prior to apparent yield strength (σ(ay)). Apparent yield strength (σ(ay)) and toughness vary strongly (1200% and 400%, respectively) with relatively small changes in the intrinsic damage behavior. The range of apparent maximum stresses predicted by the models was consistent with those measured experimentally for these trabecular bone cores from the experimental axial compressive loading (experimental: σ(max) = 3.0-4.3 MPa; modeling: σ(max) = 2-16 MPa). This finding differs significantly from previous studies based on nondamaging intrinsic material models. Further observations were that this intrinsic damage model reproduced important experimental apparent level behaviors including softening after peak load, microdamage accumulation before apparent yield (0.2% offset), unload softening, and sensitivity of the apparent level mechanical properties to variability of the intrinsic properties.

Theoretical bounds for the influence of tissue-level ductility on the apparent-level strength of human trabecular bone

The role of tissue-level post-yield behavior on the apparent-level strength of trabecular bone is a potentially important aspect of bone quality. To gain insight into this issue, we compared the apparent-level strength of trabecular bone for the hypothetical cases of fully brittle versus fully ductile failure behavior of the trabecular tissue. Twenty human cadaver trabecular bone specimens (5mm cube; BV/TV=6-36%) were scanned with micro-CT to create 3D finite element models (22-micron element size). For each model, apparent-level strength was computed assuming either fully brittle (fracture with no tissue ductility) or fully ductile (yield with no tissue fracture) tissue-level behaviors. We found that the apparent-level ultimate strength for the brittle behavior was only about half the value of the apparent-level 0.2%-offset yield strength for the ductile behavior, and the ratio of these brittle to ductile strengths was almost constant (mean±SD=0.56±0.02; n=20; R(2)=0.99 between the two measures). As a result of this small variation, although the ratio of brittle to ductile strengths was positively correlated with the bone volume fraction (R(2)=0.44, p=0.01) and structure model index (SMI, R(2)=0.58, p<0.01), these effects were small. Mechanistically, the fully ductile behavior resulted in a much higher apparent-level strength because in this case about 16-fold more tissue was required to fail than for the fully brittle behavior; also, there was more tensile- than compressive-mode of failure at the tissue level for the fully brittle behavior. We conclude that, in theory, the apparent-level strength behavior of human trabecular bone can vary appreciably depending on whether the tissue fails in a fully ductile versus fully brittle manner, and this effect is largely constant despite appreciable variations in bone volume fraction and microarchitecture.

Towards patient-specific material modeling of trabecular bone post-yield behavior

Bone diseases such as osteoporosis are one of the main causes of bone fracture and often result in hospitalization and long recovery periods. Researchers are aiming to develop new tools that consider the multiple determinants acting at the different scales of bone, and which can be used to clinically estimate patient-specific fracture risk and also assess the efficacy of new therapies. The main step towards this goal is a deep understanding of the bone organ, and is achieved by modeling the complexity of the structure and the high variability of the mechanical outcome. This review uses a hierarchical approach to evaluate bone mechanics at the macroscale, microscale, and nanoscale levels and the interactions between scales. The first section analyzes the experimental evidence of bone mechanics in the elastic and inelastic regions, microdamage generation, and post-yield toughening mechanisms from the organ level to the ultrastructural level. On the basis of these observations, the second section provides an overview of the constitutive models available to describe bone mechanics and predict patient-specific outcomes. Overall, the role of the hierarchical structure of bone and the interplay between each level is highlighted, and their effect is evaluated in terms of modeling biological variability and patient specificity.

Method of Determining the Initial Stiffness Modulus for Trabecular Bone under Stepwise Load

In this work was presented method of initial stiffness modulus E0 calculation based on fatigue tests of trabecular bone under stepwise load. The investigation was performed on 61 cylindrical bone samples obtained from the neck of different femur heads. The bone sample fatigue tests were carried out under compression with stepwise increases of the applied load. The obtained values of the initial stiffness modulus E0 were consistent with literature data and can be used to determine the S-N curve for trabecular bone using the hypotheses of fatigue damage accumulation. It was also an unsuccessful attempt to find a statistical relationship between the values of the initial stiffness modulus E0 and indices of bone structure.

Role of trabecular microarchitecture in the formation, accumulation, and morphology of microdamage in human cancellous bone

Alterations in microdamage morphology and accumulation are typically attributed to impaired remodeling, but may also result from changes in microdamage initiation and propagation. Such alterations are relevant for cancellous bone with high metabolic activity and numerous bone quality changes. This study investigates the role of trabecular microarchitecture on morphology and accumulation of microdamage in human cancellous bone. Trabecular bone cores from donors of varying ages and bone volume fraction (BV/TV) were separated into high and low BV/TV groups. Samples were subjected to no load or uniaxial compression to 0.6% (pre-yield) or 1.1% (post-yield) strain. Microdamage was stained with lead uranyl acetate and specimens were imaged via microcomputed tomography to quantify microdamage and determine its morphology in three-dimensions (3D). Donors with high BV/TV had greater post-yield strain and were tougher than low BV/TV donors. High BV/TV bone had less microdamage than low BV/TV bone under post- but not pre-yield loading. Microdamage under both loading conditions showed significant correlations with microarchitecture and BV/TV, but the key predictor was structure model index (SMI). As SMI increased (more trabecular rods), microdamage morphology became crack-like. Thus, low BV/TV and increased SMI have strong influences on microdamage accumulation in bone through altered initiation. 

Quantification of trabecular bone microdamage using the virtual internal bond model and the individual trabeculae segmentation technique

Trabecular bone microdamage significantly influences the skeletal integrity and bone remodelling process. In this paper a novel constitutive model, called the virtual internal bond model (VIB), was adopted for simulating the damage behaviour of bone tissue. A unique 3D image analysis technique, named individual trabeculae segmentation, was used to analyse the effects of microarchitectures on the damage behaviours of trabecular bone. We demonstrated that the process of initiation and accumulation of microdamage in trabecular bone samples can be captured by the VIB-embedded finite-element method simulation without a separate fracture criterion. Our simulation results showed that the microdamage can occur at as early as about 0.2-0.4% apparent strain, and a large volume of microdamage was accumulated around the apparent yield strain. In addition we found that the plate-like trabeculae, especially the longitudinal ones, take crucial roles in the microdamage behaviours of trabecular bone.

Early stage disc degeneration does not have an appreciable affect on stiffness and load transfer following vertebroplasty and kyphoplasty

Vertebroplasty and kyphoplasty have been reported to alter the mechanical behavior of the treated and adjacent-level segments, and have been suggested to increase the risk for adjacent-level fractures. The intervertebral disc (IVD) plays an important role in the mechanical behavior of vertebral motion segments. Comparisons between normal and degenerative IVD motion segments following cement augmentation have yet to be reported. A microstructural finite element model of a degenerative IVD motion segment was constructed from micro-CT images. Microdamage within the vertebral body trabecular structure was used to simulate a slightly (I = 83.5% of intact stiffness), moderately (II = 57.8% of intact stiffness), and severely (III = 16.0% of intact stiffness) damaged motion segment. Six variable geometry single-segment cement repair strategies (models A-F) were studied at each damage level (I-III). IVD and bone stresses, and motion segment stiffness, were compared with the intact and baseline damage models (untreated), as well as, previous findings using normal IVD models with the same repair strategies. Overall, small differences were observed in motion segment stiffness and average stresses between the degenerative and normal disc repair models. We did however observe a reduction in endplate bulge and a redistribution in the microstructural tissue level stresses across both endplates and in the treated segment following early stage IVD degeneration. The cement augmentation strategy placing bone cement along the periphery of the vertebra (model E) proved to be the most advantageous in treating the degenerative IVD models by showing larger reductions in the average bone stresses (vertebral and endplate) as compared to the normal IVD models. Furthermore, only this repair strategy, and the complete cement fill strategy (model F), were able to restore the slightly damaged (I) motion segment stiffness above pre-damaged (intact) levels. Early stage IVD degeneration does not have an appreciable effect in motion segment stiffness and average stresses in the treated and adjacent-level segments following vertebroplasty and kyphoplasty. Placing bone cement in the periphery of the damaged vertebra in a degenerative IVD motion segment, minimizes load transfer, and may reduce the likelihood of adjacent-level fractures.

Modeling the onset and propagation of trabecular bone microdamage during low-cycle fatigue

Relatively small amounts of microdamage have been suggested to have a major effect on the mechanical properties of bone. A significant reduction in mechanical properties (e.g. modulus) can occur even before the appearance of microcracks. This study uses a novel non-linear microdamaging finite-element (FE) algorithm to simulate the low-cycle fatigue behavior of high-density trabecular bone. We aimed to investigate if diffuse microdamage accumulation and concomitant modulus reduction, without the need for complete trabecular strut fracture, may be an underlining mechanism for low-cycle fatigue failure (defined as a 30% reduction in apparent modulus). A microCT constructed FE model was subjected to a single cycle monotonic compression test, and constant and variable amplitude loading scenarios to study the initiation and accumulation of low-cycle fatigue microdamage. Microcrack initiation was simulated using four damage criteria: 30%, 40%, 50% and 60% reduction in bone element modulus (el-MR). Evaluation of structural (apparent) damage using the four different tissue level damage criteria resulted in specimen fatigue failure at 72, 316, 969 and 1518 cycles for the 30%, 40%, 50% and 60% el-MR models, respectively. Simulations based on the 50% el-MR model were consistent with previously published experimental findings. A strong, significant non-linear, power law relationship was found between cycles to failure (N) and effective strain (Deltasigma/E(0)): N=1.394x10(-25)(Deltasigma/E(0))(-12.17), r(2)=0.97, p<0.0001. The results suggest that microdamage and microcrack propagation, without the need for complete trabecular strut fracture, are mechanisms for high-density trabecular bone failure. Furthermore, the model is consistent with previous numerical fatigue simulations indicating that microdamage to a small number of trabeculae results in relatively large specimen modulus reductions and rapid failure.