## 4 Discussion
### Locally Defined Material Properties  
Clinical application of bone imaging for the in vivo assessment of structural properties involves, among others, dual X-ray absorptiometry (DXA), quantitative computed tomography (QCT), quantitative ultrasonography (QUS), and high-resolution magnetic resonance (HR-MR) [62]. These non-invasive and non-destructive techniques are coupled with different advantages and disadvantages. DXA and QCT need ionising radiation, while HR-MR and QUS apply no radiation load on the patient [63]. Using the QUS technique in vivo, the number of measurement sites is limited; there is also little opportunity for calibration standardisation [63, 64]. In contrast to QUS, the QCT technique can provide accurate data on the 3D BMD of the trabecular and cortical compartments via calibration. HR-MR acquisition takes much more time and is technically demanding, although, in contrast to DXA, the apparent microstructure of the bone is assessable, likewise with QCT [62, 65].  
In addition to these techniques, finite element models employing locally defined material properties have been used to evaluate fracture risk and ultimate strength and have shown superior results in comparison with densitometry measurements alone [62, 65]. Due to the relative availability of QCT scans and the possibility of accurately modelling locally defined material properties in FE models, the current study employed QCT-derived materials in the patient-specific model.  
Multiple studies have defined empirical relationships for assigning local material properties based on QCT for different anatomic sites by comparing the QCT-based bone density with the results of mechanical testing [40, 66, 67, 68]. According to [PERSON] et al. [69], the QCT-based bone density can be directly converted into local mechanical properties when using calibration phantoms, which approach has been used in several finite element studies in various anatomical areas [19, 37, 70, 71, 72]. The finite element models typically used voxel-based hexahedral elements [37, 72, 73, 74] or tetrahedral elements that follow the smoothed geometry [19, 36, 70, 71, 75]. Density assignment is more directly implemented in voxel-based models, where voxels are directly converted into hexahedral elements, and thus the density of an element is equal to the density of the corresponding voxel of the QCT scan [37]. On the contrary, tetrahedral-based models better approximate the complex structure and geometry of vertebrae than hexahedral ones [76]. However, as [PERSON] et al. [77] stated, in these models, the density of an element is the average density of the voxels contained in one element, which clearly shows why QCT resolution and mesh resolution is important [11]. Furthermore, [PERSON] et al. [40] concluded that modulus-density relationships depend on the anatomic site, which means there is no universal modulus-density relationship, so it is essential that the used relationship comes from the same anatomical site as the one being investigated. Accordingly, in our research, besides applying a thin-sliced QCT imaging protocol [22] and accurate tetrahedral mesh resolution [11], we implemented a commonly used, well-established correlation that has been determined based on in vitro measurements of vertebrae [40].