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Results and discussion

      The model was validated against data obtained from an impact speed of 4.4 m/s. Figure 3 shows the force-time and force-deflection curves from this simulation. Results fall well into the corridors of cadaver responses reported by Viano ([20]), with good correlation. Similar correlation with the experimental results was also observed when the pendulum speed was increased to 6.5 m/s. However, the time step of the simulation was greatly reduced for such a high severity impact. Limited by our computing resource, the simulation was cut down 32 ms. At this stage, the total energy lost at the end of a run, an indication of stability of the model, was less than 3%. Figure 4 illustrates force-time and force-deflection curves compared with experimental data.

     In order to correlate of the predictions of the model with typical automotive injuries, two more simulations were performed at speeds of 3.5 m/s and 5.5 m/s. These simulations served to study the relation between organ response severity and impact speed. The responses of the organs focused on the compression and surface velocity of the lung, the compression of the heart, the relative displacement between the attachments at both ends of the ligamentum arteriosum on the side of the aorta and on the side of pulmonary trunk along the impact direction, and the shear stresses at the isthmus of the aortic arch. The relative displacements of the attachments of the ligamentum arteriosum served to measure the deformation experienced by the ligament.

     The shear stresses at the isthmus of the aortic arch was used to measure aortic twisting and distortion in the coronal plane. Increasing impact speed generally correlated with increasing severity in these areas. This correlation has been clearly demonstrated by the in-vivo findings and inferences of previous studies ( [10]; [24]; [21]; [17]).  Figure 5 shows the compression and surface velocity of the lung at the four impact speeds. The percentages of heart compression are shown in Figure 6Figure 7 demonstrates the relative displacements of the attachments of the ligamentum arteriosum. The shear stresses at the isthmus of the aortic arch are shown in Figure 8.

     Although the model closely adheres to cadaver test data and demonstrates good correlation with typical in-vivo injuries, several concerns need to be addressed before it can be used to predict human injury. The first concern is related to the selection of material properties. Those properties were mainly from literature that employed only quasi-static tests. In some cases, where human tissues were not available, results from animal tests were used. More realistic material properties for human tissues are needed in order to justify predictions of organ injuries such as contusion and lacerations.

     The selection of a factor of 10 for the scaling of the heart and lung material properties is purely an assumption. A wide range of values may have been chosen for this factor. Many previous experimental studies did not report the strain rate employed. Judging from their experimental setup, it is estimated that the strain rate may have ranged from 3.5 to several hundred per second. Thus, it is not surprising to find out that the material properties reported for the same tissue varied widely from one study to another. In an experiment by Collins et al. ([4]), a maximum strain rate of 3.5 per second was used for testing aortic tissues. Their results showed that the dynamic material properties were more than two times greater than those obtained in quasi-static tests. The strain rate simulated in this study is close to several hundred per second, thus, a factor of 10 was selected. This selection also allowed us to complete the simulation without further numerical difficulties. Future research should be devoted to this area of study in order to further the understanding of this phenomenon.

     Additionally, the rib cage was modeled by one layer of rib solid elements and two layers of muscle shell elements. This simplification was made in order to reduce the model size and subsequently increase computing efficiency. Another problem not fully taken into consideration involves the selection of boundary conditions between organs and the surrounding tissues. Tissues such as small vessels, nerves and pleurae were not modeled. Instead, frictionless sliding interfaces were assumed, and additional interconnections were not considered.

     In summary, a three-dimensional finite element model of a 50th percentile male human thorax was developed. The model includes detailed descriptions of the skeleton and internal organs. At an impact speed of 4.4 m/s, the model correlated well with test data. Further improvements are necessary in order to achieve the original goal of using this model to study injuries of the viscera and other soft tissues.


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