student University of Colorado Denver, United States
Introduction: Finite element analysis (FEA) is a computational method used to analyze complex structures and predict their response under specific conditions. Two well-known methods that implement this technique to examine the response of bone structures under applied forces. The Crawford method, developed by Dr. Richard Crawford, takes a displacement-based approach to understanding how bones respond to external loads by focusing on the displacement and deformation patterns within the bone structure. The Keyak method, developed by Dr. Joyce Keyak, predicts the ultimate strength of a bone sample by examining a limited number of finite elements that represent the behavior of the entire bone sample. Although both the Crawford and Keyak methods are well known, there is still not a comparison of the two methods. An experiment was conducted to compare the results from each analysis method when applied to a vertebral model, to get insight concerning the reliability of results obtained by each method, allowing for method validation and highlighting any discrepancies in results.
Materials and
Methods: Computed tomography (CT) scans of a female lumbar spine model were imported and calibrated in Matlab for segmentation. L1, L2 , L3, and T12 vertebrae were segmented in Simpleware Scan IP imaging software, and finite element analysis was conducted in Abaqus to compare each analysis method. Since the Keyak method was originally developed for the femur, Keyak's density-Young's modulus and density-ultimate strength conversion equations were utilized and failure of the vertebral body was assumed when 23.5% of the elements exceeded their ultimate strength. Data for the fracture force values for the Keyak method had been previously calculated and were obtained for comparison from the Smart Materials and Biomechanics Lab at the University of Colorado Denver. Actual fracture force values were also obtained for comparison from the Smart Materials and Biomechanics Lab at the University of Colorado Denver. The donor spine was dissected, individual vertebrae were potted in urethane, and each model was loaded until failure using an MTS insight 30 with a 1%/s global strain.
Results, Conclusions, and Discussions: It was found that the average difference in fracture forces between the two methods was 772.1 N, while the standard deviation of difference was 387.0 N, signifying considerable discrepancy and variability between results. However, the obtained regression value of 0.98 suggests similar overall trends between data sets and a strong linear relationship. Interestingly, both methods overestimated fracture force values, however, the Keyak Method overestimated to a higher degree. The percent overestimation by the Crawford method was 34.9 percent, while the Keyak Method overestimated by 53.6 percent. These values indicate that the Keyak method may be favorable for applications where fracture force needs to be overestimated to provide larger safety margins. The Crawford method may be favorable to applications where it is desirable to underestimate fracture force values. A detailed comparison of these two methods may have implications for various applications of FEA, such as surgical planning, implant design, and other fracture risk assessments. Understanding the strengths and limitations of each method can help us interpret FEA results more accurately, make informed decisions regarding FEA results, as well as promote intentionality when choosing an FEA method for achieving desired goals and objectives.
It is important to consider that these results were obtained from a very small-scale study with a limited set of comparison data. Thus, there is not sufficient data to draw definitive results, but can be used to draw insight and motivation for further studies.
Acknowledgements (Optional): I would like to acknowledge Dr. Dana Carpenter, PhD, at the University of Colorado Denver who mentored me throughout this project and the Smart Materials and Biomechanics Lab where data used in this experiment was obtained.
