## 2 Materials and Methods  
### Geometry of the FE Models  
Two finite element models of the intact lumbar spine (L1-L5) were developed using quantitative computed tomography (QCT) images (Hitachi Presto, Hitachi Medical Corporation, Tokyo, Japan) of a 24-year-old male patient without any lumbar spine-related musculoskeletal pathology. The study involving the human participant was reviewed and approved by the National Ethics Committee of Hungary and the National Institute of Pharmacy and Nutrition (reference number: OGYEI/163-4/2019). Written informed consent was obtained from the individual for the publication of any potentially identifiable images or data included in this article. All methods were carried out in accordance with relevant guidelines and regulations. The QCT (voxel size of 0.6 \(\times\) 0.6 \(\times\) 0.6 mm\({}^{3}\)) scans were used to obtain the geometry of both FE models, with previously reported imaging protocol [22]. The QCT dataset (in DICOM extension) was acquired from the hospital's PACS and subsequently anonymised with Clinical Trial Processor software (Radiological Society of North America, [[https://www.rsna.org/ctp.aspx](https://www.rsna.org/ctp.aspx)]([https://www.rsna.org/ctp.aspx](https://www.rsna.org/ctp.aspx)), accessed on 10 August 2022) [23]. The 2D images of the QCT scans were imported into Materialise Mimics software (Mimics Research, Mimics Innovation Suite v23.0, Materialise, Leuven, Belgium) to create a patient-specific geometry model by Hounsfield Unit-based segmentation, setting the lower and upper threshold to 226 HU and 1712 HU, respectively. The surface mesh was then exported to 3-Matic software (Mimics Research, Mimics Innovation Suite v21.0, Materialise, Leuven, Belgium) in STL (stereolithography) format. The surface mesh was smoothed (smooth factor: 0.7, iteration no. : 6, shrinkage compensation: on) and remeshed with a target edge length of 1 mm to improve mesh quality and remove spikes and cavities on the vertebral surfaces [24] (Figure 1a). The current study applied two bone material assignment approaches to create the literature-based model (LBM) (Figure 2a) and the patient-specific model (PSM) (Figure 2b). In the LBM, the vertebral body consisted of a 1 mm thick cortical shell, trabecular core, 0.5 mm thick bony endplates, and posterior elements [25; 26]. The volumes were meshed adaptively with 1 mm linear tetrahedral elements in HyperWorks software (Altair Engineering, Inc., Troy, Michigan, United States) based on the surface mesh [27]. Vertebrae of the PSM were not further divided, but rather treated as a whole and were meshed with a uniform element size of 1 mm with linear tetrahedral elements. Soft tissues, such as the facet joints, were identical in both FE models and were modelled as a 0.25 mm thick cartilage layer with an initial gap of 0.5 mm between adjacent surfaces [28] and then meshed with 6-node wedge elements [29]. The intervertebral discs (IVD) consisted of the nucleus pulposus (NP), the annulus fibrosus (AF), including both the ground substance (GS), the fibres, and the 0.5 mm thick cartilaginous endplates (CEP). The AF GS was constructed as six concentric layers [14] around the NP, which accounted for 45% of the IVD [30] and was moved to the posterior direction in accordance with the literature and general anatomy [31]. The AF GS and the NP were represented with 8-node hybrid hexahedral elements [14], while CEP was meshed with linear tetrahedral and pyramid elements (Figure 1b). The fibres were modelled with tension-only truss elements in a criss-cross pattern with an alternating angle of \(\pm\)30\({}^{\circ}\) to the axial plane of the IVD [32]. The cross-sectional area values of the fibre layers were calculated from the volume ratio of the fibres to the ground substance: 23% (outermost), 20%, 17%, 13%, 9%, and 5% (innermost), respectively [33] (Figure 1b).