## 5 Results and Discussion  
We commenced five simulations, where the model was subjected to the same acceleration loading in accordance with the C755-T2 test:  
* 2 simulations for MAT_VISCOELASTIC 2 (W and W/G)
* 1 simulation for MAT_HYPERELASTIC (W), as the data for grey matter is missing in the literature for this model of material. As the cranicerebiral injuries arise as a result of the relative displacement of the brain relative to the skull, we hypothesized that depending on the mechanical properties of the brain tissue, the displacements may be significantly different. In practice, this can change the degree of brain tissue damage. Thus, the study presents to what extent the application of the material model affects the displacement of brain tissue. At the same time, the effect of grey matter and white matter separation in the model on brain displacement is investigated. The research results showed that depending on the material model used, the brain kinematics are different. This phenomenon can be observed in Figures  
The obtained results for MAT_VISCOELASTIC 1 showed that taking into account the distinction in the numerical model of white and grey matter may have a significant impact on brain displacement, as shown in Figure 10, which depicts the markers placed in the brain model with only white matter (W) and the brain model with the separation between white and grey matter (W/G). It should be noted that in this simulation, both angular and linear velocities were implied as the mechanical loading. At this point, it should be mentioned that angular acceleration is the main cause of DAI. Interestingly, for MAT_VISCOELASTIC 2, the W/G matter separation does not significantly influence the kinematics of the 10 selected markers (FE nodes). The overlapping displacement-in-time characteristics for homogeneous and inhomogeneous MAT_VISCOELASTIC 2 are depicted in Figure 11. This issue needs some further research, yet the authors' hypothesis is that the Kelvin/Maxwell relaxation/decay constant plays a significant role. When the relaxation/decay constant parameter is lower, then tendency for relaxation behaviour in time increment is lower. Therefore, relaxation strain is much lower for both grey and white matter. As a consequence, the strain difference between grey and white matter do not expose such distinction in homogeneous and inhomogeneous MAT_VISCOELASTIC 2 models. Figure 12 depicts the relative resultant displacement of the brain for the C755-T2 test for the MAT_VISCOELASTIC 1 (W/G) inhomogeneous brain model. We can observe that the most displaced finite elements are located in the brain cortex as they are subjected to the highest angular acceleration. It is worth to notice again that DAI is usually caused by high rotational accelerations, leading to shear loads in the brain tissue [33]. A similar phenomenon is observed for all the considered configurations in this paper. Figure 8: Displacement-in-time characteristics of the markers in the rear (p) and frontal (a) columns in the X-direction using the homogeneous _MAT_VISCOELASTIC 1 (W/G)_ for the brain. Figure 9: Displacement-in-time characteristics of the markers in the rear (p) and frontal (a) columns in the X-direction using the homogeneous _MAT_VISCOELASTIC 2 (W/G)_ for the brain. Figure 11: Comparison between homogeneous and inhomogeneous for the displacement-in-time characteristics of the markers in the rear (p) and frontal (a) columns in the X and Z-direction _MAT_VISCOELASTIC 2_ for the brain. Figure 10: Comparison between homogeneous and inhomogeneous for the displacement-in-time characteristics of the markers in the rear (p) and frontal (a) columns and in the X and Z-direction _MAT_VISCOELASTIC 1_ for the brain. In all the respective simulations, we can see a noticeable pressure gradient at 10 ms after the loading, i.e., just after the 20 g linear acceleration inducement. The occurrence of brain contusions is associated with pressure gradients, correlated with linear acceleration during a head impact [95].