Simulation of Skull Fracture Due to Falls

This study presents novel predictive equations for von Mises stress values of bones in the frontal and lateral regions of the skull. The equations were developed based on results of a finite element model developed during this research. The model was validated for frontal and lateral loading conditions with input values mimetic to fall scenarios. Using neural network processing of the information derived from the model achieved R 2 values of 0.9990 for both the stress and deflection. Based on the outcome of the fall victims, a threshold von Mises stress of 40.9 to 46.6 MPa was found to indicate skull fracture given a maximum input force of 26 kN and a load rate of 40 kN/ms.

been used in the past, however these are generally directed at soft tissue injury and model the skull itself at low resolutions. Other established head models contain a relatively small number of elements, such as a model developed in 1980 has 637 elements.9 More modern models include 19,417 elements and 17,651 nodes and the ULP model, which contains 10,500 elements and 12,000 nodes [15][16][17]. Not all these elements are included in analysis for the skull however; in both of these, elements are allocated for tissues other than the skull.

Materials and Methods
A converged finite element model was constructed to model the  [5]. Prony series analysis utilizes a minimization algorithm that corrects for errors between the predicted and measured values to represent the viscoelastic nature of the data. It then decomposes the data in a matter like that of a Fourier transform. Forces were uniformly distributed over a 300 mm 2 area in the "hat brim" region for the frontal and lateral locations to mimic the area impacted in falls as this is the most common region of the skull to be impacted in a fall. The area that the impact covers in a typical fall depends upon the object struck.
A sharper, more pronounced, or stiffer object would tend to present with a smaller impact area. The frequency with which different objects are struck was not available in literature at the time, so typical areas of impact in a fall are not agreed upon. The value of 300 mm 2 was chosen as a value that would be comparable to the size of the hat brim area. The lateral force distribution was centered 53.9 mm over the suprameatal triangle and 57.5 mm dorsal to the frontosphenoidal process. It consisted of a roughly elliptical shape following the contours of the element borders of the skull with a semi-major radius of 12.1 mm and a semi-minor radius of 7.65 mm. The frontal force profile was centered over and located 40.7 mm above the nasal spine and was likewise an ellipsoid following the contours of the elements on the skull. The semi-major radius was 12.28 mm and the semi-minor radius was 7.98 mm. These locations and approximate force areas can be seen in Figure 1. The magnitude used for the force was also designed to mimic the forces experienced in a fall. Fall data was reconstructed and several force versus time plots were created based on the differing situations.
Maximum forces for each simulation were found to range from 10 to 50 kN and maximum load rates between 10 to 100 kN/ms [11].
Forces in the simulation were assumed to be directed normal to the skull, pointing towards the interior. These plots were digitized in order to generate an equation for force as a function of time. The medium force value (case 2) was used here and fit to the 9 th degree polynomial seen in equation 1 from t=0 ms to t=2.5 ms with an R 2 of 0.998. This equation was then adjusted to account for changing load rates and maximum forces. These values were found to be significant at P<0.0001 for each variable. In addition, the combination terms of (load)*(load rate) (P=0.0001) and (load)*(location) (P<0.0001) were found to be significant to the calculation. Other variables did not show enough evidence for significance.  This created an initial model of the data with an R 2 value of 0.9997.   given that stress was found to accumulate in the region for lateral impacts, the proportion of frontal and lateral fractures was found to be approximately the same, with slightly more frontal fractures occurring than lateral. This data had a low sample size however (n=40) and few studies have reported the exact frequency with which different locations of the head are struck during an impact.
Given the data available, this result is supported. Lateral and frontal fracture thresholds were found to be relatively similar, with a 12% difference at the threshold fracture value (40.9 MPa for frontal and 46.6 for lateral). The further refined experimentation may uncover a difference in these values later.