## 3 Results
### Stress Distributions  
The ECDF plots of the estimated cumulative distribution showed noteworthy differences between the models developed by two bone material assignment strategies (Figure 7a-d). Generally, the cumulative distribution of stress values in the low-stress range, from 0 MPa to 1 MPa, shows the same characteristics. It is also observed that the stress values in the LBM are more spread out and have a less steep curve than in the PSM. This difference in the curve steepness also means that proportionally, the LBM contains more high-stress elements.  
Figure 3: Results of the FE models against pure bending of 7.5 Nm. (**a**) Predicted total ROM values in flexion-extension, lateral bending, and axial rotation for the LBM and LSP models. The white bars and their ranges correspond to the median and the range of an in vitro measurement [57]. The grey bars and their range represent the median and the range of multiple published FE results [2]. (**b**) Load-deflection curves of the LBM and PSM. The median results of an in vitro experiment are shown with a black dashed line, while the black error bars represent the range of results at 7.5 Nm [57]. The minimum and maximum values of the in silico results are shown as a grey band [2]. (**c**) The mean FJF values at all spinal levels for the LBM and the LSP models. The black error bars correspond to the range of facet joint forces measured in vitro [58]. The grey bars and their ranges show the median, the minimum, and maximum values of the in silico results [2]. (**d**) IDP values of the nucleus pulposus at L4-L5 against compressive follower load for both FE models. The black dashed line shows the median result of an in vitro measurement, while the black error bars represent the minimum and maximum values for 0 N, 300 N, and 1000 N [59]. The range of validated FE results is shown as a grey band [2].  
The strain values characterise the most compressed state of the bony tissues, as nodes with the smallest minimum principal (equivalent to highest compressive) strain were included in this analysis. In the LBM, the median compressive strain values were calculated as \(-0.0053\), \(-0.0040\), \(-0.0059\), and \(-0.0023\) for flexion, extension, lateral bending, and axial rotation, respectively. In contrast to the LBM, the PSM decreased median compressive strain values, and the strain values are calculated as \(-0.0053\), \(-0.0040\), \(-0.0059\), and \(-0.0023\) for flexion, extension, lateral bending, and axial rotation. The results of the LBM and PSM at different strain values are presented in Table 1. The results of the LBM and PSM at different strain values are presented in Table 2. The results of the LBM and PSM  
strain values by 77.3%, 62.5%, 79.7%, and 39.1%, respectively (Figure 8). Although the outlier values reveals that the PSM spreads the strain values more evenly, as the box and whiskers are narrow, and contains more outliers than the LBM. While the median values are lower in the LBM, the outliers are even lower in the PSM, indicating that the PSM includes more nodes with higher compression.  
Figure 5: Predicted IDP values at different spinal levels for combined loads in (**a**) flexion, (**b**) extension, (**c**) lateral bending, and (**d**) axial rotation. The white bars correspond to the median values of an in vivo measurement [56]. The grey bars and their range illustrate the median and range of multiple validated and published FE models result [2].  
Figure 6: Predicted FJF values at different spinal levels for (**a**) extension, (**b**) lateral bending, and (**c**) axial rotation for the FE models. The grey bars and their range illustrate the median, the minimum, and maximum results of multiple FE models [2].