Simulation Mechanical 2016
The elderly are more likely to suffer from fracture because of age-related trabecular bone loss. Different bone loss locations and patterns have different effects on bone mechanical properties. Extended finite element method (XFEM) can simulate fracture process and was suited to investigate the effects of bone loss on trabecular bone. Age-related bone loss is indicated by trabecular thinning and loss and may occur at low-strain locations or other random sites. Accordingly, several ideal normal and aged trabecular bone models were created based on different bone loss locations and patterns; then, fracture processes from crack initiation to complete failure of these models were observed by XFEM; finally, the effects of different locations and patterns on trabecular bone were compared. Results indicated that bone loss occurring at low-strain locations was more detrimental to trabecular bone than that occurring at other random sites; meanwhile, the decrease in bone strength caused by trabecular loss was higher than that caused by trabecular thinning, and the effects of vertical trabecular loss on mechanical properties were more severe than horizontal trabecular loss. This study provided a numerical method to simulate trabecular bone fracture and distinguished different effects of the possible occurrence of bone loss locations and patterns on trabecular bone.
Simulation Mechanical 2016
Given rapid increase in the elderly population, age-related fracture has become an important public health issue [1, 2]. Many reasons explain why the elderly are susceptible to fracture; however, the main reason is the decreased bone strength caused by age-related trabecular bone loss [3, 4]. Investigating the effects of trabecular bone loss on the mechanical properties of bone structure may therefore assist in understanding the bone degeneration and fracture mechanism, which is meaningful for preventing age-related osteoporosis and fractures.
Since significant relationship between age-related changes in trabecular microstructure and its fracture risk has been found, it is therefore important to understand the effects of such changes on the mechanical properties of trabecular bone [11, 12]. To investigate the effects of various architectural deterioration factors on fracture characteristics, many studies focused on quantifying and comparing the morphological parameters of aged trabecular bones based on microcomputed tomography (micro-CT) images [5, 13]. However, in order to fully understand the effects of age-related changes, it is not sufficient to merely compare the morphological parameters for aged specimens. The degeneration process of trabecular bone with respect to trabeculae type and microstructure should also be investigated. With the development of structure modeling technique, several methods in modeling trabeculae microstructure were put forward. Individual trabecula segmentation technique, which can decompose the trabecular bone network into individual trabecular plates and rods, was developed [14, 15]; meanwhile, a method for subdividing a trabecular network into horizontal and vertical oriented trabeculae was also put forward . Although the type and orientation of trabeculae can be distinguished using above methods, it is also difficult to identify the changes in actual aged trabecular microstructure compared with the normal one. For example, bone loss locations and patterns in actual aged trabecular microstructures may not be determined. Instead, ideal trabecular bone model, which could artificially produce different bone loss locations and patterns for aged trabecular bone models based on the actual degeneration process, can solve this problem [6, 16]. Thus, ideal trabecular bone model can serve as a promising model to investigate the age-related changes in trabecular bone microstructure [17, 18].
Accordingly, this study aimed to simulate the fracture processes of ideal trabecular bone models based on XFEM analysis. Several ideal normal and aged trabecular bone models were first created based on different bone loss locations and patterns, and then the effects of these different locations and patterns of age-related bone loss on the mechanical properties of trabecular bone were compared. These simulations may assist in explaining the age-related fracture mechanism by analyzing the variations in trabecular microstructure and provide a theoretical basis for prevention of age-related fracture.
Regardless of the locations where trabeculae were lost, the process of age-related bone loss includes two steps: thinning of the trabecula and eventual loss [3, 16, 32]. BV/TV decreases significantly due to trabecular thinning. Trabecular loss has little effect on BV/TV, but it decreases the connectivity of trabecular bone to a great extent. It was unknown whether trabecular thinning would bring severer effects on trabecular bone than trabecular loss in terms of damage and fracture. Thus, it was necessary to compare the relative effects of trabecular thinning and loss on the mechanical properties of trabecular bone. Here trabecular loss was subdivided into loss of trabeculae along the vertical and horizontal directions. Therefore, three degeneration patterns were considered: thinning of trabecula was defined as degeneration pattern 1; loss of vertical trabecula was defined as degeneration pattern 2; loss of horizontal trabecula was defined as degeneration pattern 3. Based on the normal models (Model-rod A and Model-plate A), three sets of rod-like and plate-like models with different degeneration patterns were created: (1) As shown in Figure 3(a), Model-rod D and Model-plate D with degeneration pattern 1 were created by uniformly reducing the thickness of trabeculae from the normal models. (2) As shown in Figure 3(b), a quantity of vertical trabecular elements were randomly removed from the normal models, which formed Model-rod E and Model-plate E with degeneration pattern 2. (3) As shown in Figure 3(c), a quantity of horizontal trabecular elements were randomly removed from the normal models, which formed Model-rod F and Model-plate F with degeneration pattern 3. It was difficult to reduce too much BV/TV through loss of trabeculae alone. Given that the mechanical properties were obviously changed by at least a 5% reduction in BV/TV [16, 33], approximate 8% reduction in the original BV/TV of normal models was simulated for all the different degeneration pattern models.
Comparison of the deformations and fracture patterns between the trabecular FE models and the corresponding RP models was shown in Figures 4(b) and 4(c). Because all the RP models were regular, the fracture processes and patterns under compression were nearly the same for the RP models with the same microarchitecture. It can be seen that fractures in both the FE models and RP models with the same microarchitecture appeared at the similar sites, which were at the intersections between vertical and horizontal trabeculae. Figure 5 shows the comparison of the apparent stress-strain curves predicted by the XFEM analysis for normal FE models and those obtained by the compressive tests for the corresponding RP models. Here the experimentally measured curves for the RP models with the same microarchitecture were averaged since no obvious differences in each curve of the same four RP models were observed. Not only did the predicted stress-strain curves show the same orders of magnitude in fracture strain, that is, the percentage difference between the simulated and experimentally measured fracture strains was less than 8%, but the similar patterns for the curve shapes and onsets of fracture between simulation and experiment were also observed. Thus, these comparisons showed the reliability of the method in modeling ideal trabecular bone and the XFEM analysis used in this study could accurately simulate the experimental results.
The apparent stress-strain curves of the three rod-like models were shown in Figure 6(a). Model-rod A had the highest apparent fracture strain and ultimate stress, Model-rod C was the lowest, and Model-rod B was between those two. Regardless of the locations where trabeculae were lost, bone loss resulted in negative effects on the mechanical properties of trabecular bone, particularly for Model-rod C, whose apparent fracture strain and ultimate stress were 30.93% and 37.89% lower than those in Model-rod A. A typical fracture process from crack initiation to complete failure in Model-rod A was shown in Figures 6(a) and 6(b). The deformation started with a linear elastic stage (A) and then entered yield stage (B). The crack was initiated at a quantity of trabeculae (C) and then continued to grow in the stiffness degradation stage, leading to a nonlinear relationship between stress and strain (CD). The stress continued to grow until it reached the ultimate stress (D), which led to a softening stage (DE) for the damaged trabeculae and in turn resulted in a shift from extensively continuous damage to localized permanent failure for the damaged trabeculae. The load was finally carried by the neighboring normal trabeculae, instead of the trabeculae that experienced localized permanent failure, until the complete fracture of the trabecular bone structure (E).
Different trabecular bone degeneration patterns caused by trabecular thinning or loss both led to decrease in the mechanical properties of normal trabecular bone models, whereas the mechanical properties were more sensitive to trabecular loss than to trabecular thinning; furthermore, the mechanical properties of trabecular bone were less affected by loss of horizontal trabeculae than by loss of vertical trabeculae (Figure 8). For the trabecular loss models, the localized fracture sites were all close to the disconnected trabeculae (Figure 9).
This study utilized a numerical simulation method to predict the fracture processes in normal and aged trabecular bone models. The fractures of these models were simulated using XFEM analysis embedded subroutine UDMGINI, in which the principal strains in tension and compression were used to control the crack initiation and propagation. In the simulation process, when the principal strain in the aged trabecular bone model exceeded the crack initiation strain of trabecular bone tissue, crack in the aged model would be initiated, and then the crack began to grow obeying the bone damage propagation law until complete fracture occurred in the aged model. According to the XFEM analyses in this study, different fracture processes from crack initiation to complete failure for the aged trabecular bone models were primarily observed; then, apparent ultimate stress and fracture strain of the aged trabecular bone models were obtained, and the mechanical properties of different aged trabecular bone models were compared; finally, the effects of bone degeneration locations and patterns on the mechanical properties of aged trabecular bone models were analyzed quantitatively.