PSI - Issue 28

Juan Du et al. / Procedia Structural Integrity 28 (2020) 577–583 J. Du et al./ Structural Integrity Procedia 00 (2019) 000–000

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4. Discussion In this study, a multi-material model representing realistic density distribution in trabecular bone was applied according to the GV distribution and compared with the traditional single-material scheme. Results for different density distributions obtained with these two material models were compared. Similar histograms of the occurrence of density in the element of trabecular bone from a femur head also showed the same highest number of element in the density rage from 1.25 to 1.35 g/cm3. Furthermore, the evolution of volume fractions also demonstrated a trend similar to that from the literature. The initial material distributions assigned to the FE model using multi- and single-material property resulted in a similar inhomogeneous density distribution. The multi-material model produced structures similar to those in the single-material model. This outcome indicates that previous simplified models based on single-material properties can still be used. However, some morphological changes in single trabeculae are different, and the single-material model might lead to a structure with a higher trabecular number and lower thickness. The effect of initial density distribution on simulation result can be more specifically analysed with the histogram of Fig. 2. Elements with the density in the range of 1.25-1.35 g/cm 3 were predominate in both models. The result indicates that density changes due to remodelling may correlated with variations of the loading conditions more than the effect of initial density distribution. These results were in agreement with a two-year follow-up human study, showing that the sites of bone formation and resorption correlated with the strain energy density distribution [18]. The difference of using multi- and single-material models were even more vague in terms of volume fraction development. The respective curves largely overlapped; initially the volume fraction rase sharply, overshoot and then stabilized. Results of the study with pigs demonstrated a similar behaviour of bone’s morphological development to that in our simulations [19]. It indirectly validated our approach and indicated that both models could be used in the future to simulate the bone remodelling process. The major limitation of this study was that the calculated absolute value of density might not resemble the realistic bone density. First, the initial density assigned to each element in the FE model of trabecular bone was not calibrated with a phantom. Second, the applied load was rather simple and did not represent the whole set of loads the femur is subjected to during the daily activity. However, the aim of this study was to compare results for different material distributions in the simulation of bone remodelling process, while the actual density was not its objective. For this reason, only a simple load and the same density calculation method were employed to compare the simulation results, so, the comparison results were reliable. 5. Conclusion This paper investigated the sensitivity of trabecular bone remodelling to different material properties in FE simulation. Results obtained for different trabecular morphologies with density distributions were analysed for two material models. Similar histograms of the occurrence of density in the elements of trabecular bone from a femur head were found, with the highest number of elements in the density rage from 1.25 to 1.35 g/cm 3 for both cases. These outcomes indicate that previous schemes employing the simplification of single-material properties can still be used. References 1. Dirschl D.R., Henderson R.C., Oakley W.C. Accelerated bone mineral loss following a hip fracture: a prospective longitudinal study. Bone. 1997;21(1), 79–82. 2. Maïmoun L., Fattal C., Micallef J.P., Peruchon E., Rabischong P. Bone loss in spinal cord-injured patients: From physiopathology to therapy. Spinal Cord. 2006;44(4), 203–10. 3. Du J., Brooke-Wavell K., Paggiosi M.A., Hartley C., Walsh J.S., Silberschmidt V. V., et al. Characterising variability and regional correlations of microstructure and mechanical competence of human tibial trabecular bone: An in-vivo HR-pQCT study. Bone. 2019;121, 139–48. 4. Martínez-reina J., Ojeda J., Mayo J. On the use of bone remodelling models to estimate the density distribution of bones Uniqueness of the solution. Plos One,2016; 1–17. 5. Li S., Denirci E., Silberschmidt V. V. Variability and anisotropy of mechanical behavior of cortical bone in tension and compression. J Mech Behav Biomed Mater. 2013;21, 109–20. 6. Rubin C.T., Recker R., Cullen D., Ryaby J., McCabe J., McLeod K. Prevention of postmenopausal bone loss by a low-magnitude, high frequency mechanical stimuli: A clinical trial assessing compliance, efficacy, and safety. J Bone Miner Res. 2004;19(3), 343–51. 7. Shackelford L.C. Resistance exercise as a countermeasure to disuse-induced bone loss. J Appl Physiol. 2004;97(1), 119–29.