In this study, a total of 13 loading conditions were analyzed and various crack patterns were obtained. The results demonstrate that even identical loading locations do not necessarily generate the same crack patterns. Additionally, some loading directions can produce different crack area size or a number of large cracks, while other directions cannot. This suggests that it is necessary to simulate crack formation using a FE skull model, and that the relationship between the crack shapes and loading conditions must be further clarified in order to be able to predict the loading conditions from the crack shapes. However, this relationship might not be generalizable, and could be specific to the subject in this study. Hence, it may only be useful to apply an FE model specific to a subject.
Under all of the studied loading conditions, small cracks developed radially in a circle around a loading point. These small cracks could be affected by the FLD, in which case the FLD would control the circle size or the appearance of cracks. On the other hand, a small crack occurring from the origin resulted in numerical errors, as the small cracks seemed to be random. Therefore, small cracks should not be evaluated individually, but by clusters of the small cracks and for each loading condition. In this study, crack shapes defined by clusters of small cracks were evaluated. Even though the shapes under different loading conditions could depend on the location and direction of the loading condition, obvious and typical formations were not observed in this study. In contrast, large cracks seemed to strongly depend on the structure of the skull and loading conditions, although these large cracks were certainly also derived from small cracks.
In this study, six loading conditions resulted in symmetrical crack formations: perpendicular, anterior, and posterior loads applied to the top, and perpendicular, superior, and inferior loads applied to the left. The shapes of small cracks were almost symmetrical for all conditions, while the large cracks did not necessarily demonstrate symmetry for the loads applied to the top of the cranium. We observed dents ahead of the directions of large cracks in Figs. 6, 7 and 8. Large cracks could run toward a dent on the cranial bones. The surfaces of actual skulls generally do not have a uniform thickness and have an uneven curved surface, but the size and location of small dents vary from person to person. Even though the FE model used in this study was symmetrized, since the model was constructed from CT images, surface geometry was preserved. Therefore, the present simulation results may have resulted from the skull shape specific to the subject. However, this means that the present results might not necessarily show the general cracking patterns of the skull. Because such structural unevenness can determine the direction of large cracks, the relationship between the crack direction and the locations of dents in the skull could be investigated.
In this study, the external and internal tables and the diploe were modeled with constant thickness, while the shape, hump, and dents of the cranial bones were preserved. Before the mesh model was constructed, the geometrical data of the skull were refined and smoothed with the original geometry. Even then, the model was likely subject-specific. To eliminate individual differences and evaluate the general relationship between crack shape and loading conditions, a smoother geometry model might be useful. However, smoothing like this risks eliminating important anatomical characteristics of the skull. To avoid this problem, it will be necessary to use and compare some subject-specific FE models.
When our results were compared with the previous experimental study in the same loading condition that the impactor was struct at the top of the skull , the large cracks were similar to each other in the size of approximately 60 mm and the direction toward the lateral. Also, the small size cracks were within the similar radius of approximately 30 mm, even though the previous experimental study showed less number of the small cracks. Therefore, our model could have a good validity about the accuracy to estimate the crack formation.
To validate the computational method, the crack sizes in the model were compared with the stress distribution in the previous FE analysis . Under the similar energy conditions of the impactor, the small cracks in this study showed the similar size to the stress concentration area in the previous analysis. Also, the directions of the large cracks had a good agreement with the stress distribution in the previous study. Therefore, our model could have an adequate validity and accuracy from the computational point of view.
In this study, the skull model was constructed based on CT images. The CT data proposed the skull shape, the width and thickness of the sutures on the skull. The anatomical information was used as the element properties. Especially, the cross-sectional structure of the skull, which consisted of the external and internal tables and the diploe, had different material properties. Therefore, our model should have the anatomical accuracy. Also, in this study, the X-FEM and FLD were embedded in the model. Using them, the model can produce the cracks at arbitrary locations and make the cracks developed toward arbitrary directions. These computational methods for FEM could reproduce the natural crack formation. Therefore, this study could improve the problems of the previous investigation.
This study had a few limitations. First, the model used here was from CT data from a single patient. The model was constructed while maintaining the anatomical structure of the skull and consisted of cross-sectional structures. However, structures specific to the subject might decrease the generality of the formation of hairline cracks of the cranial bones.
The second limitation was that the suture structure was simplified as a band. In reality, the sagittal suture follows a meandering path, and its micro-processes are complicated. However, the model did not reproduce this complex suture structure.
Finally, in this study, only the left side of the cranium was used to create the model. Neither the original subject-specific model nor a model made from the right side of the cranium was evaluated. Those models would not show the same results as in this study, and skull fractures from the different types of models would not be generalizable to each other.
Even though the present model has some limitations, the simulated results show that crack patterns may depend on the loading location and direction. By comparing our results with additional simulations, the relationship between loading conditions and the formation of hairline cracks on the cranial bones could be elucidated. Therefore, the model could be useful to estimate the loading conditions from the shapes of hairline cracks.