## 2 Materials and Methods
### Morphometric Measurement  
Our CT imaging process involves utilizing a multi-detector CT scanner. The scan parameters include a slice thickness of 1-2 mm, covering the range from L3 to S1. During the procedure, patients were positioned in a supine position with a focus on maintaining a neutral alignment of the spine. The image acquisition followed a standard lumbar spine protocol, ensuring a systematic approach to data collection.  
CT scans of the patients were transformed using InVesalius, Meshmixer, 3D Builder, and GOM programs to obtain a three-dimensional image. In the obtained spatial visualization, the space of the root canal and the measurement planes were defined.  
The process of defining the root canal involved several steps. Since root canals can vary in their spatial arrangement depending on the evaluated motor segment, the primary factor used to define the root canal was the course of the long axis of the epiphysis that bordered the upper part of the canal. Subsequently, the cross-section of the root canal was determined to align with the axis of the pedicle, which formed the upper opening of the canal. The analysis specifically focused on the bony boundaries, disregarding any soft tissue contours like the intervertebral disc and joint capsule. To complete the outline of the root canal where the intervertebral disc outline was eliminated, a line was added, connecting the lower posterior edge of the upper vertebral body to the posterior upper edge of the lower vertebra.  
The obtained root canal contour was used to measure its maximum vertical dimension (MaxY). The maximum vertical dimension represents the longest section within the contour, perpendicular to the end plate of the vertebral body below (Figure 1).  
The two senior orthopedic surgeons had an average of 10 years' experience with CT.  
The surface area measurement method consisted of the following steps. In the first phase, the maximum vertical dimension of the L4/L5 root canal was determined. In the next stage of the measurement, the maximum vertical dimension of the root canal L4/L5 was applied to the visualization of the cross-section. Knowing the vertical dimension of the channel is expressed in mm, we calculated how many pixels fit in a square with a side equal to the vertical dimension. In this way, the scale was established as the number of pixels that fit in 1 mm\({}^{2}\) of the area in the cross-section visualization. In the last phase of the research, the cross-sectional area obtained was marked with a loop (Figure 2) and information on the number of pixels corresponding to the area of the selected area on the visualization was read. Then, using the proportion, the surface area of the intervertebral foramen cross section was calculated. We applied same procedure for L5/S1 root canal.  
Sections I-III were defined as follows:  
1. Halfway from the medial border of the root canal and the medial axis of the pedicle;
2. In the medial axis of the vertebral epiphysis;
3. Halfway from the lateral border of the root canal and the medial axis of the vertebral epiphysis  
Figure 1: Measurement method. Purple line represents the maximum vertical dimension [y1 wymiar max]; the yellow line represents the endplate of the vertebral body.  
Figure 2: Surface area; close-up of the measured area from Figure 1. Purple line represents boundries of calculated surface area.  
The dimensions of the cross-sections are given in mm, and the surface area in mm\({}^{2}\). The study population was divided into two age groups. The first was made up of people under 50, the second was made up of people over 50.