Patient selection

This is a retrospective, cross-sectional analysis of the patients in Qilu Hospital. Computed tomography (CT) data of the pelvis of patients who visited our hospital between January 1, 2020, and December 31, 2020, were collected. The inclusion criteria were (i) patients aged 18–60 years and (ii) those with CT scans of the complete pelvis and the greater trochanter of the femur. Exclusion criteria included patients with (i) a fracture present on a CT image, (ii) hip arthritis, (iii) pelvic deformity or osteolytic disease such as a bone tumor, and (iv) a 7.3-mm screw difficult to be placed transversely to the S1.

Processing and reconstruction of CT data

Anonymized CT raw data were post-processed using the Mimics 25.0 software (Mimics, Materialise N.V., Belgium). The appropriate range of Hounsfield units (HU) was selected to locate the boundaries of the cortical bone or soft tissue during reconstruction. The 3D reconstruction function was used to construct a 3D model of bone tissue, fill the space of the bone tissue samples after construction, and smooth the process. The soft tissue model, in this case, was constructed using a similar method.

Surgical intervention

The ipsilateral ASIS and the greater trochanter were marked. The ASIS was selected as the highest point of the pelvis in the sagittal position in a supine position (Fig. 2a). The greater trochanter was marked at the center of the gluteus minimus insertion in the middle of the plane of the most lateral vertex of the greater trochanter toward the cephalic end (Fig. 2a). This point was selected because it is more accurate to touch the plane of the greater trochanter, where the gluteus minimus points during actual surgery.

Fig. 2

Measurement of anatomical data

(a) The ASIS and the greater trochanter position, (b) safe access for iliosacral screws, (c) concentric circles of the femoral head and neck, (d) the femoral neck axis, and (e) the femoral rotation angle

ASIS, anterior superior iliac spine

To simulate the placement of iliosacral screws, the bone tissue was rendered semitransparent (Fig. 2b), and the 3D model was adjusted to the standard lateral view (bilateral ASIS and alignment of the high-density line). The shadow formed by the first sacral pedicle, which was roughly oval, was visible. The upper and lower limits of the ellipse were the sacral alar, and the posterior and lower boundaries indicated the sacral nerve canal. The length of the short axis of the shadow was measured. Additionally, the short shaft was at least > 7.3 mm in length. Samples with short axis lengths < 7.3 mm were excluded. The midpoint of the short axis was the best position for the placement of iliosacral screws. The two ends of the simulated screw were extended, and the intersection point between the extension line and the skin was the skin entry point. Furthermore, the linear distances between the skin entry point, the greater trochanter, and the ASIS were measured.

Measurement of the angle of the femoral neck axis and the coronal plane

In the 3D reconstruction model of bone tissue, the view angle was adjusted such that the unilateral femoral head and femoral neck were observed as concentric circles (Fig. 2c), and the center of the concentric circle from the inner and outer sides of the femoral neck was marked (Fig. 2d). The inner and outer sides of the concentric circle center were connected by a line defined as the femoral neck axis. Furthermore, the angle of the femoral neck axis between the horizontal projection and coronal plane was measured (Fig. 2e) and defined as the femoral rotation angle.

Data processing and rectangular plane coordinate system

To compensate for individual differences, the distance between the ASIS and the greater trochanter of the femur was defined as standard length 1, and the distance between the simulated needle entry point and the ASIS and the greater trochanter of the femur was standardized.

On the plane determined using the ASIS, the greater trochanter, and the skin entry point, the ASIS was used as the origin, the ASIS to the greater trochanter of the femur was used as the X-axis, and the injection point was simulated as the positive side of the Y-axis to establish a rectangular plane coordinate system (Fig. 3). The distance between the simulated needle entry point and the ipsilateral ASIS and the greater trochanter of the femur was measured. Trigonometric functions were used to calculate the position of the simulated entry point of the needle using X- and Y-coordinates, which were statistically analyzed. This operation yielded 182 scatter points, and normality tests were performed using the X- and Y-coordinates. The point in the plane of the coordinate system with the shortest distance from all scatter points was defined as the average point to calculate the median center, as follows:

Fig. 3

Rectangular plane coordinate system

The plane cartesian coordinate system is established in the plane where the three points, namely, the greater trochanter, the ASIS, and the SEP, are located

ASIS, anterior superior iliac spine; SEP, skin entry point

$$f\left(x\right)=\sum\limits_^n\sqrt_-a)}^+_-b)}^}$$

When the function takes its minimum value, (a, b) is the average point of the scatter. This operation was performed using Python, version 3.9 (Python Software Foundation, Delaware, USA) software.

We used kernel density estimation, which is a non-parametric probability density estimation method, for calculating the aggregation of scatter points in the plane, and we constructed a density distribution map using Python version 3.9 software (Python Software Foundation, Delaware, USA).

Statistical analysis

A Shapiro–Wilk test was used to determine the normal distribution of quantitative data. Student’s t-test or Welch’s nonparametric test was used to compare the means or data distributions between the different groups. Statistical significance was set at P < 0.05. All statistical analyses were performed using IBM SPSS Statistics for Windows, version 26.0 (IBM Corp., Armonk, N.Y., USA).