## Appendix A  
The attachment points and orientation of the elements modelling the ligaments were adopted from a previously published study, MySPINE [22]. All seven major spinal ligaments were modelled: anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), ligament flavour (LF), interspinous ligament (ISL), supraspinous ligament (SSL), intertransverse ligament (ITL), and capsular ligaments (CL). In the current study the ligaments were modelled with multiple spring elements in either parallel-series connection (ALL, PLL) or in parallel connection only (ISL, CL, ITL, LF, PLL, SSL) (Table A1) [44]. [PERSON] et al. defined the nonlinear characteristic for each ligament with two variables, stiffness, and strain. Data from [PERSON] et al. can be rewritten in the following form and units [47] (Table A2). As presented, [PERSON] et al. [47] defined the spring-like behaviour of the ligaments with strain dependent stiffness value of a single spring, describing the progressive characteristic. Nonlinear spring characteristic should be defined in Abaqus with force and \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ligament** & **No. Elements** & \
\begin{tabular}{c} **Length of 1 Element** \\ **(mm), L\({}_{\text{e}}\)** \\ \end{tabular} &
\begin{tabular}{c} **Length of 1 Chain (mm),** \\ **L\({}_{\text{chain}}\)** \\ \end{tabular} \\ \hline ALL & 5 parallel, 4 in series & 10.36 & 41.44 \\ ISL & 24 in parallel & 6.86 & 6.86 \\ CL & 20 in parallel & 6.54 & 6.54 \\ ITL & 20 in parallel & 22.50 & 22.50 \\ LF & 7 in parallel & 14.08 & 14.08 \\ PLL & 5 parallel, 4 in series & 8.56 & 34.24 \\ SSL & 6 in parallel & 15.14 & 15.14 \\ \hline \hline \end{tabular}
\end{table} 
Table A1: Nonlinear force-stiffness characteristics of the ligaments. elongation value pairs assigned to the corresponding SPRINGA element sets. To assign the material properties correctly, the following calculations were applied:  
\[F(\varepsilon)= \begin{cases}K_{1}L_{0}\varepsilon,&if\quad 0<\varepsilon\leq \varepsilon_{1}\\ K_{1}L_{0}\varepsilon_{1}+K_{2}L_{0}(\varepsilon-\varepsilon_{1}),&if\quad \varepsilon_{1}<\varepsilon\leq\varepsilon_{2}\\ K_{1}L_{0}\varepsilon_{1}+K_{2}L_{0}\varepsilon_{2}+K_{3}L_{0}(\varepsilon- \varepsilon_{2}),&if\quad\varepsilon_{2}<\varepsilon\leq 1\end{cases}  \tag{11}\]  
For the sake of simplicity, 1 was chosen as an upper limit of the ligament strains, since 100% strain is not reached during the simulation, thus the calculation remains stable. From this, the elementary force can be calculated (the force which is assigned to each element):  
\[F_{\varepsilon}=\frac{1}{p}F(\varepsilon) \tag{12}\]  
Beside the force values Abaqus requires the corresponding elongation values (strain dependent and elementary) as well:  
\[D(\varepsilon)=L_{chain}\varepsilon \tag{13}\]  
\[D_{\varepsilon}=\frac{1}{s}D(\varepsilon)=\frac{1}{s}L_{chain}\varepsilon, \tag{14}\]  
where:  
\(F\)--force (N)  
\(p\)--number of parallel chains (-)  
\(s\)--number of elements in a chain (-)  
\(K_{n}\)--stiffness (N/mm)  
\(\varepsilon_{n}\)--strain (-)  
\(D\)--elongation (mm)  
\(L_{0}\)--average length of one element (mm)  
The applied material properties defined by [PERSON] [47] were plotted in Figure 11, where the progressive behaviour of the ligaments is visualised. Figure 11: The nonlinear force-strain relationships of the seven spinal ligaments applied in the current study. Appendix B Calculation of the investigated variables from the finite element analysis is challenging. The current study considered two force, two pressure, and four rotation variables. The force (FJF, FJF_SEG) and pressure (IDP, IDP_SEG) variables can be calculated using average and maximum calculations after summary of the exported data. The calculation of the rotation variables (IVR, IVR_COMB, ROM, ROM_MAX) was based on virtual markers. The markers were nodes coupled to the vertebrae with rigid coupling.