The effect of three-dimensional geometrical changes during adolescent growth on the biomechanics of a spinal motion segment.

During adolescent growth, vertebrae and intervertebral discs undergo various geometrical changes. Although such changes in geometry are well known, their effects on spinal stiffness remains poorly understood. However, this understanding is essential in the treatment of spinal abnormalities during growth, such as scoliosis. A finite element model of an L3-L4 motion segment was developed, validated and applied to study the quantitative effects of changing geometry during adolescent growth on spinal stiffness in flexion, extension, lateral bending and axial rotation. Height, width and depth of the vertebrae and intervertebral disc were varied, as were the width of the transverse processes, the length of the spinous process, the size of the nucleus, facet joint areas and ligament size. These variations were based on average growth data for girls, as reported in literature. Overall, adolescent growth increases the stiffness with 36% (lateral bending and extension) to 44% (flexion). Two thirds of this increase occurs between 10 and 14 years of age and the last third between 14 years of age and maturity. Although the height is the largest geometrical change during adolescent growth, its effect on the biomechanics is small. The depth increase of the disc and vertebrae significantly affects the stiffness in all directions, while the width increase mainly affects the lateral bending stiffness. Hence, when analysing the biomechanics of the growing adolescent spine (for instance in scoliosis research), the inclusion of depth and width changes, in addition to the usually implemented height change, is essential.

The osteoporotic vertebral structure is well adapted to the loads of daily life, but not to infrequent "error" loads.

Osteoporotic vertebral fractures typically have a gradual onset, frequently remain clinically undetected, and do not seem to be related to traumatic events. The osteoporotic vertebrae may therefore be expected to display a less "optimal" bone architecture, leading to an uneven load distribution over the bone material. We evaluated the trabecular load distribution in an osteoporotic and a healthy vertebra under normal daily loading by combining three recent innovations: high resolution computed tomography (microCT) of entire bones, microfinite element analyses (microFEA), and parallel supercomputers. Much to our surprise, the number of highly loaded trabeculae was not higher in the osteoporotic vertebra than in the healthy one under normal daily loads (8% and 9%, respectively). The osteoporotic trabeculae were more oriented in the longitudinal direction, compensating for effects of bone loss and ensuring adequate stiffness for normal daily loading. The increased orientation did, however, make the osteoporotic structure less resistant against collateral "error" loads. In this case, the number of overloaded trabeculae in the osteoporotic vertebra was higher than in the healthy one (13% and 4%, respectively). These results strengthen the paradigm of a strong relationship between bone morphology and external loads applied during normal daily life. They also indicate that vertebral fractures result from actions like forward flexion or lifting, loads that may not be "daily" but are normally not traumatic either. If future clinical imaging techniques would enable such high-resolution images to be obtained in vivo, the combination of microCT and microFEA would produce a powerful tool to diagnose osteoporosis.

The influence of microcomputed tomography threshold variations on the assessment of structural and mechanical trabecular bone properties.

In this study, we investigate how morphological parameters and mechanical properties derived from microcomputed tomography (microCT) are affected by small errors in threshold value when variable bone structures and different bone volume fractions are involved. For this purpose, biopsies of vertebrae of 6-, 23-, and 230-week-old female pigs were scanned using microCT. For each specimen, five threshold values were determined within the range of thresholds that an observer could select realistically, in steps of 0.5%. The scans were converted to microfinite-element (microFE) models, used to determine the elastic moduli. A variation of 0.5% in threshold resulted in a 5% difference in bone volume fraction and 9% difference in maximal stiffness for bone cubes with a volume fraction of <0.15. When the volume fraction was >0.2, these differences were only 2% and 3%, respectively. For all bone cubes, the differences for trabecular thickness and bone surface density were <3%. The effects on morphological anisotropy and trabecular number were negligible for threshold variations of 0.5%. These findings suggest that threshold selection is important for the accurate determination of volume fraction and mechanical properties, especially for low bone volume fractions; the architectural directionality is less sensitive to changes in threshold.

Cancellous bone mechanical properties from normals and patients with hip fractures differ on the structure level, not on the bone hard tissue level.

Osteoporosis is currently defined in terms of low bone mass. However, the source of fragility leading to fracture has not been adequately described. In particular, the contributions of bone tissue properties and architecture to the risk or incidence of fracture are poorly understood. In an earlier experimental study, it was found that the architectural anisotropy of cancellous bone from the femoral heads of fracture patients was significantly increased compared with age- and density-matched control material (Ciarelli et al., J Bone Miner Res 15:32-40; 2000). Using a combination of compression testing and micro-finite element analysis on a subset of cancellous bone specimens from that study, we calculated the hard tissue mechanical properties and the apparent (macroscopic) mechanical properties. The tissue modulus was 10.0 GPa (SD 2.2) for the control group and 10.8 GPa (SD 3.3) for the fracture group (not significant). There were no differences in either the apparent yield strains, percentages of highly strained tissue, or the relationship between apparent yield stress and apparent elastic modulus. Hence, a difference in the tissue yield properties is unlikely. At the apparent level, the fracture group had a significantly decreased transverse stiffness, resulting in increased mechanical anisotropy. These changes suggest that bone in the fracture group was "overadapted" to the primary load axis, at the cost of fragility in the transverse direction. We conclude that individuals with a history of osteoporotic fractures do not have weaker bone tissue. Architectural and mechanical anisotropy alone renders their bone weaker in the nonprimary loading direction.

Osteoporosis changes the amount of vertebral trabecular bone at risk of fracture but not the vertebral load distribution.

STUDY DESIGN: A finite-element study to investigate the amount of trabecular bone at risk of fracture and the distribution of load between trabecular core and cortical shell, for healthy, osteopenic, and osteoporotic vertebrae. OBJECTIVES: To determine differences between healthy, osteopenic, and osteoporotic vertebrae with regard to the risk of fracture and the load distribution. SUMMARY OF BACKGROUND DATA: The literature contains no reports on the effects of osteopenia and osteoporosis on load distribution in vertebral bodies, nor any reports on the amount of trabecular bone at risk of fracture. METHODS: Computed tomography data of vertebral bodies were used to construct patient-specific finite-element models. These models were then used in finite-element analyses to determine the physiologic stresses and strains in the vertebrae. RESULTS: For all three classes of vertebrae the contribution of the trabecular core to the total load transfer decreased from about 70% near the endplates to about 50% in the midtransverse region. The amount of trabecular bone that is at risk of fracture was about 1% for healthy vertebrae, about 3% for osteopenic vertebrae, and about 16% for osteoporotic vertebrae. CONCLUSIONS: Our finite-element models indicated that neither osteopenia nor osteoporosis had any effect on the contribution of the trabecular core to the total load placed on the vertebra. The trabecular core carried about half the load. Our finite-element models indicated that osteoporosis had a significant effect on the amount of trabecular bone at risk of fracture, which increased from about 1% in healthy vertebrae to about 16% for osteoporotic vertebrae.

Increase in bone volume fraction precedes architectural adaptation in growing bone.

In mature trabecular bone, both density and trabecular orientation are adapted to external mechanical loads. Few quantitative data are available on the development of architecture and mechanical adaptation in juvenile trabecular bone. We studied the hypothesis that a time lag occurs between the adaptation of trabecular density and the adaptation of trabecular architecture during development. To investigate this hypothesis we used ten female pigs at 6, 23, 56, 104, and 230 weeks of age. Three-dimensional morphological and mechanical parameters of trabecular bone samples from the vertebra and proximal tibia were studied using microcomputed tomography and micro-finite element analysis. Both bone volume fraction and stiffness increased rapidly in the initial growth phase (from 6 weeks on), whereas the morphological anisotropy started increasing only after 23 weeks of age. In addition, the anisotropy reached its highest value much later in the development than did bone volume fraction. Hence, the alignment of trabeculae was still progressing at the time of peak bone mass. Therefore, our hypothesis was supported by the time lag between the increase in trabecular density and the adaptation of the trabecular architecture. The rapid increase of bone volume fraction in the initial growth phase can be explained by the enormous weight increase of the pigs. The trabeculae aligned at later stages when the increase in weight, and thus the loading, was slowed considerably compared with the early growth stage. Hence, the trabecular architecture was more efficient in later years. We conclude that density is adapted to external load from the early phase of growth, whereas the trabecular architecture is adapted later in the development.

Mechanical consequences of bone loss in cancellous bone.

The skeleton is continuously being renewed in the bone remodeling process. This prevents accumulation of damage and adapts the architecture to external loads. A side effect is a gradual decrease of bone mass, strength, and stiffness with age. We investigated the effects of bone loss on the load distribution and mechanical properties of cancellous bone using three-dimensional (3D) computer models. Several bone loss scenarios were simulated. Bone matrix was removed at locations of high strain, of low strain, and random throughout the architecture. Furthermore, resorption cavities and thinning of trabeculae were simulated. Removal of 7% of the bone mass at highly strained locations had deleterious effects on the mechanical properties, while up to 50% of the bone volume could be removed at locations of low strain. Thus, if remodeling would be initiated only at highly strained locations, where repair is likely needed, cancellous bone would be continuously at risk of fracture. Thinning of trabeculae resulted in relatively small decreases in stiffness; the same bone loss caused by resorption cavities caused large decreases in stiffness and high strain peaks at the bottom of the cavities. This explains that a reduction in the number and size of resorption cavities in antiresorptive drug treatment can result in large reductions in fracture risk, with small increases in bone mass. Strains in trabeculae surrounding a cavity increased by up to 1,000 microstrains, which could lead to bone apposition. These results give insight in the mechanical effects of bone remodeling and resorption at trabecular level.

Introduction and evaluation of a gray-value voxel conversion technique.

In micro finite element analyses (microFEA) of cancellous bone, the 3D-imaging data that the FEA-models are based on, contain a range of gray-values. In the construction of the eventual FEA-model, these gray-values are commonly thresholded. Although thresholding is successful at small voxel sizes, at larger voxel sizes there is substantial loss of trabecular connectivity. We propose a new method: the gray-value method, where the microFEA-models use the information within the 3D-imaging data directly, without prior thresholding. Our question was twofold. First, how does the gray-value method compare to both plain and mass-compensated thresholding? Second, what is the effect of element size on the results obtained with the gray-value method? We used nine microCT-scans of human vertebral cancellous bone. These were degraded to represent different resolutions, and converted into microFEA-models using plain thresholding, mass-compensated thresholding, and the gray-value method. The apparent elastic moduli of the specimens were determined using microFEA. The different methods were compared on the basis of the apparent elastic moduli, compared to those calculated for a 28 microm reference model. The results showed that the gray-value method greatly improves the results relative to other methods. The gray-value method gives accurate predictions of the apparent elastic moduli, for voxel sizes up to one trabecular thickness (Tb.Th.). For voxel sizes greater than one Tb.Th. the accuracy, although still better than for both thresholding methods, becomes increasingly worse.