Orientated-quantitative computed tomography study on individualized axial safety target area of femoral neck screw channel and establishment of a stable spatial coordinate system based on anterior cortex of femoral neck basilar

Background:

Frequent in-out-in femoral neck screws were reported potential huge iatrogenic-injury risks, related to axial safe target area (ASTA) of femoral neck screws channel. However, orientated-quantitative ASTA based on stable coordinate system was unreported before.

Methods:

Three-dimensional reconstruction was performed on computed tomography (CT) images of 139 intact normal hips, and the intersection area, defined as ASTA, was obtained by superimposing the axial CT images of each femoral neck. Taking anterior cortex of femoral neck basilar (AC-FNB) as landmark, a coordinate system was established to measure the anterior–posterior diameter (D-AP), the superior–inferior diameter (D-SI) and the oblique angle respectively. Each intersection was overlaid up to the axial CT images to determine the coronal location of the ASTA boundaries.

Results:

Each ASTA presented an inclined rounded triangle with a flat anterior base coincided with AC-FNB. There were significant sex differences in D-SI (male: 33.6±2.3 vs. female: 29.4±1.9 mm) and D-AP (male: 25.3±2.1 vs. 21.9±1.9 mm), P<0.001. D-SI was found to be positively correlated with D-AP (R ²=0.6). All fluoroscopic visible border isthmus completely matched the corresponding ASTA boundaries. The oblique angle was 5–53° (male: 28.1±10.3°, female: 27.1±8.2°) without significant difference between sexes.

Conclusion:

The intersection method was employed to conveniently acquire orientated-quantitative individualized ASTA. Under this coordinate system, x-ray data of screws could be converted to axial coordinates in CT ASTA, which could help surgeons design combined screws configuration preoperatively and evaluate quantitatively their axial position intraoperatively.

Introduction

Highlights

• Get individualized axial safe target area (ASTA) of femoral neck by the intersection method.

• Axial safe target area was an inclined rounded triangle with a flat anterior base.

• A coordinate system was established to study orientated-quantitative safe area.

• The safe borders site on computed tomography (CT) were the same as those isthmus on simulated x-ray.

• X-ray data of screws could be converted to axial coordinates on visible CT safe area.

Inverted triangle with multiple cannulated screws, parallel dispersion, and intraosseous inclusions close to cortex remains preferred for hip-preserving treatment of femoral neck fractures1–4. However, successful implementation of intraoperative implanting screws of femur neck accurately-successfully at the first attempt (ISFNASFA) is difficult due to many uncertainties5, requiring multiple adjustments based on x-ray results. However, the position of the femoral neck guide pins cannot be quantitatively determined by fluoroscopy, and it varies with postural change or different viewing angles intraoperatively. Making such adjustments is difficult and often inaccurate, with a high 70% incidence of “In-Out-In (IOI)” screw4,6. These operations are associated with huge potential risks of iatrogenic injuries affecting the blood supply of the femoral head and neck and bone destruction, causing serious complications such as iatrogenic proximal femoral fracture, internal fixation failure, nonunion and femoral head necrosis6,7 and resulting in frequent reoperation4,8,9. The uncertainty of surgery is mainly due to ignorance of ASTA, which is the premise of safe-accurate screw placement, and placing screws without ASTA is blind and catastrophic. However, because of individual variations in femoral neck-shaft angle (FNSA), femoral neck torsion angle (FNTA), and femoral neck anteversion angle (FNAA)10,11, it is difficult to study orientated-quantitative ASTA for individualized screw implantation. So far, there are no relevant research about constant anatomical landmarks, determination of ASTA, establishment of a stable coordinate system, and x-ray data conversion into screw CT axial coordinates.

This study intended to acquire ASTA through the intersection method, seek constant anatomical landmarks, define a stable spatial rectangular coordinate system, and examine orientated-quantitative characteristics of ASTA to help surgeons in preoperative design and intraoperative evaluation of screw axial coordinates.

Methods

Study design and subjects

This observational study was conducted in our hospital. After obtaining ethical proof and institutional permission, CT scan data of 139 normal hips of 87 adults (at least 18 years of age with closed epiphysis line) from 443 cases whose CT data were recorded in our hospital from January 2020 to February 2023 were retrospectively and randomly selected for three-dimensional reconstruction. Hips with prior fractures and surgeries, skeletal dysplasia, degenerative changes, bone tumors, and any radiologically apparent pathological process were excluded. The work has been reported in line with the Consolidated Criteria for Reporting Qualitative Research (COREQ) criteria12.

Procedures

CT scan was performed with the 64-slice CT (Model SOMATOM; Siemens). Syngo Acquisition Workplace software was used for image postprocessing. The following parameters were selected: pelvis plus proximal femur, layer spacing 5 mm, layer thickness 5 mm, field of view from the upper pelvis to 180 mm below the lesser trochanter, kV p130, effective mAs 106, and matrix 512×512.

The normalized axial CT parameter, perpendicular to the surgical central axis (SCA) of the femoral neck, were created after three-dimensional reconstruction. Images were taken outwards and downwards from the top of femoral head, with a slice thickness of 2 mm. This study defined SCA using the following criteria: (1) SCA was the midline of the two tangent to the isthmuses of the superior–inferior diameter of femoral neck in the coronal plane; (2) SCA was parallel to the anterior cortex of the femoral neck in the sagittal plane (AC-FN); (3) SCA passed through the midpoint of D-SI and D-AP of ASTA; and (4) SCA could be intraoperatively determined. True axial, sagittal, and coronal CT images of femoral necks were acquired (Fig. 1).

Figure 1.

Steps to acquire computed tomography (CT) images after CT three-dimensional reconstruction. Taking femoral neck as research object, stipulated that axial section was the section perpendicular to the central axis of the femoral neck. The sagittal and coronal planes were referenced to femoral neck, and three planes were perpendicular to each other. (A) Sagittal CT image of the femoral neck, the green line represented the coronal plane direction, parallel to both the anterior cortex and the central axis of the femoral neck. (B) Coronal CT image of the femoral neck, the orange line represented the sagittal plane direction, parallel to the central axis. (C) Axial CT image of the femoral neck, that is, the slice direction of the blue line in A and B, perpendicular to both the green and orange lines. The blue, green, and orange lines were perpendicular to each other, forming three vertical planes of the spatial coordinate system.

Determination of screw channel axial safe target area by intersection method

All axial CT images of each femoral neck were imported into the image processing software (Bridge, Photoshop CC), and two layers of images were sequentially superimposed in situ to remove non-intersecting areas, retaining the intersection (Figs. 2A–E). After superimposing relevant CT images, the common area of all axial CT images of femoral neck was obtained, which was defined as the ASTA of the screw channel.

Figure 2.

Schematic of steps to obtain the intersection of axial images, the union of the coronal computed tomography (CT) images and the union of the coronal CT images of the femoral neck. (A) The first slice axial CT image of femoral neck. (B) The second slice axial CT image of femoral neck. (C) Images overlaid, keeping the same scale and position. (D) The red overlapping part was the intersection of the images – axial safety target area (ASTA). (E) Building the coordinate system of ASTA. Taking the base AD of individualized ASTA as parallel line of the y-axis, drew a circumscribed rectangle ABCD, whose center O was the origin, and established a plane rectangular coordinate system YOZ. d1 and d2 were superior–inferior diameter (D-SI) and anterior–posterior diameter (D-AP) of ASTA under this coordinate system, respectively. (F–I) Schematic diagram of the steps to obtain the union of the coronal CT images of the femoral neck, superimposing coronal images in situ with keeping the same scale and position. (F) The first slice coronal CT image of femoral neck. (G) The second slice coronal CT image of femoral neck. (H) Images overlaid in situ, keeping the same scale and position. (I) The green part showed the union of the coronal images of femoral neck. The union of all the coronal images of femoral neck was equivalent to the projection of the femoral neck on its true coronal plane or meant simulated anteroposterior x-ray. (J–M) Schematic diagram of the steps to obtain the union of the sagittal CT images of the femoral neck, superimposing sagittal images in situ with keeping the same scale and position. (J) The first slice sagittal CT image of femoral neck. (K) The second slice sagittal CT image of femoral neck. (L) Images overlaid in situ, keeping the same scale and position. (M) The green part showed the union of the sagittal images of femoral neck. The union of all the sagittal images of femoral neck was equivalent to the projection of the femoral neck on its true sagittal plane or meant simulated lateral x-ray.

Acquisition of coronal–sagittal projection boundaries by union method

Analogously, all coronal CT images of each femoral neck were superimposed in situ to obtain their union, equivalent to the projection of the femoral neck on its true coronal plane or meant simulated anteroposterior x-ray, determining where the D-SI boundaries isthmus located at the femoral neck (Figs. 2F–I). Samely, the sagittal union was acquired to definite the position of D-AP boundaries isthmus at the femoral neck, which was equivalent to the projection of the femoral neck on its true sagittal plane or meant simulated lateral x-ray (Figs. 2J–M).

Data measurement

Establishment of the coordinate system. Taking the anterior base AD of the ASTA (AB-ASTA) as the y-axis parallel line, a circumscribed rectangle ABCD was drawn, and with the rectangle center O as the origin, a plane rectangular coordinate system YOZ belonging to the spatial rectangular coordinate system O-XYZ was established (Fig. 2E).

D-SI and D-AP measurement. Under the YOZ coordinate system, the CT images including ASTA were enlarged until the image scale became 1:1. Then D-SI (d1) and D-AP (d2) of ASTA were measured (Fig. 2E).

Determination of the position corresponding to the boundaries of ASTA on CT images. The red ASTA was overlapped on the axial CT images, and the axial CT images whose boundary coincided with one border of ASTA and their corresponding position layers in coronal images were determined (Figs. 3A–E).

Figure 3.

Determine the position layer of each boundary of axial safety target area (ASTA) in the coronal computed tomography (CT) and the oblique angle. (A) Schematic in three-dimensional CT of axial-sections (C–F) selected. (B) Corresponding position-layer of each axis CT in the coronal image. (C) ASTA showed in approximately circular femoral head–neck junction. (D) D-SI boundaries of ASTA located at the axial-sectional CT layer 22, was consistent with the position of D-SI isthmuses in FNM on coronal plane (B). (E) Anterior–posterior diameter (D-AP) boundaries of ASTA located at the axial-sectional CT layer 27, was consistent with the position of D-AP isthmuses in FNB on sagittal plane (B). (F) Axial CT of proximal femur showed the oblique angle ∠α between N (anterior cortex of proximal femur almost parallel to the coronal central axis of axial plane of proximal femur) and M (the base of ASTA).

Oblique angle measurement. The oblique angle between the AB-ASTA (i.e. the y-axis) and the coronal central axis of the proximal femur cross-sectional image (approximately equal to the coronal plane of the proximal femur) was measured to evaluate the inclination degree of the ASTA triangle (Fig. 3F).

The position layers of ASTA boundaries in coronal CT were compared with those of the corresponding boundary isthmus of simulated x-ray projection (SXBI) to determine boundaries position consistency between both methods. Then the coordinate transformation relationship between the coordinate system O-XYZ, the CT ASTA, anteroposterior, and lateral x-ray were analyzed (Figs. 3 and 4).

Figure 4.

Schematic of correspondence relations between axial safe target area (ASTA) boundaries on computed tomography (CT) and boundary isthmus of simulated x-ray projection (SXBI) or fluoroscopic visible borders isthmuses on x-ray. (A) Space Cartesian Coordinate System O-XYZ built in the present study. x-axis was surgical central axis, while y-axis and z-axis were the same as the plane rectangular coordinate system YOZ. Ray 1 was anteroposterior x-ray along z-axis, Ray 2 was lateral x-ray along y-axis, and Ray 3 was axial view along x-axis only in CT. (B) Schematic of observing the XOY coordinate system along z-axis on three-dimensional -CT to get the projection of femoral neck on true coronal plane (XOY), that is, anteroposterior x-ray of femoral neck. (C) The union of coronal CT images, including collection of all femoral neck borders of coronal CT images and equivalent to simulated anteroposterior x-ray along z-axis, showed that the superior–inferior diameter (D-SI) isthmuses were located at FNM, the same as those on axial CT in Figures 3B and 4E. (D) Observing the XOY coordinate system along z-axis presented anteroposterior x-ray, and the visible borders isthmuses of D-SI in anteroposterior x-ray located at FNM and should be the same as boundary isthmus of simulated x-ray projection (SXBI) theoretically, whose diameter was d1. Anteroposterior perspective schematic was compared with the union of coronal CT images for convenient understanding. (E) Axial CT corresponding to D-SI isthmuses. Its position in the coronal plane was FNM in Figure 3B. Under this coordinate system, the positions in coronal CT images of D-SI boundaries of ASTA completely corresponded to D-SI boundary isthmus of simulated x-ray projection (SXBI) or the visible borders isthmuses of D-SI on anteroposterior x-ray. (F) Schematic on three-dimensional CT of observing the XOZ coordinate system along y-axis to get the projection of femoral neck on true sagittal plane (XOZ), that is, lateral x-ray of femoral neck. G The union of sagittal CT images, including collection of all femoral neck borders of sagittal CT images and equivalent to simulated lateral x-ray, showed that the anterior–posterior diameter (D-AP) isthmuses were located at FNB, the same as those on axial CT in Figures 3B and 4I. (H) Observing the XOZ coordinate system along y-axis got lateral x-ray, and the visible borders isthmuses of D-AP in lateral x-ray located at FNB and should be the same as boundary isthmus of simulated x-ray projection (SXBI) theoretically, whose diameter was d2. Lateral perspective schematic was compared with the union of sagittal CT images for convenient understanding. (I) Axial CT corresponding to D-AP isthmuses. Its position in the coronal plane was FNB in Figure 3B.Under this coordinate system, the positions in coronal CT images of D-AP boundaries of ASTA completely corresponded to D-AP boundary isthmus of simulated x-ray projection (SXBI) or the visible borders isthmuses of D-AP in lateral x-ray. (J and K) The boundaries and diameters of ASTA measured based on different coordinate systems were different. (J) The boundaries and diameters of ASTA measured based on FNTA coordinate systems O-XYZ. (K) The boundaries and diameters of ASTA measured based on coronal plane of proximal femur changed significantly, compared with FNTA coordinate systems O-XYZ.

Statistical analysis

The measurement data were analyzed using IBM SPSS Statistics software for Windows, Version 26·0 (IBM Corp.). The Student t-test was used to compare whether the parameters of D-SI, D-AP, and oblique angle were statistically different between sexes. Pearson’s correlation coefficients were calculated to assess the relationship between D-SI and D-AP. A P-value less than 0.05 was considered statistically significant.

Results

CT scan data of 139 normal hips (74 left and 65 right) of 87 adults (47 males and 40 females) were included. The patients had an average age of 55.1±17.8 years (range: 18–90 years). All data conformed to a normal distribution.

Superior–inferior diameter and anterior–posterior diameter

Under the coordinate system, D-SI of males (33.6±2.3 mm, range: 29–38 mm) differed significantly from that of females (29.4±1.9 mm, range: 26–34 mm). D-AP of males was 25.3±2.1 mm (range: 19–29 mm), while that of females was 21.9±1.9 mm (range: 17–25 mm), with a statistical difference between sexes (P<0.001, Table S1, Supplemental Digital Content 1, http://links.lww.com/JS9/A350 and Table S2, Supplemental Digital Content 2, http://links.lww.com/JS9/A351).

Axial safe target area boundaries position-layer located at the coronal computed tomography

Both the medial-inferior boundary (anterior-inferior vertex of the ASTA triangle) and the lateral-superior boundary (anterior-superior vertex of the ASTA triangle) were located in the FNM, which was consistent with the position of the D-SI isthmus on the simulated anteroposterior x-ray, but the isthmus was not necessarily on the same CT section. The AB-ASTA coincided with AC-FNB, while the posterior vertex of the ASTA triangle was located behind FNB, coinciding with the position of the D-AP isthmus on simulated lateral radiography (Fig. 3).

Correlation between superior–inferior diameter and anterior–posterior diameter

There was a significant positive correlation between D-SI and D-AP (R ²=0.6, P<0.05). The regression equation was expressed as (D-AP)=0.71×(D-SI)+1.35 mm.

Oblique angle

The oblique angle was 28.1±10.3° in males and 27.1±8.2° in females, ranging from 5 to 53°. There was no significant difference between sexes (P=0.56), but individual variations were large.

Discussion

This study for the first time reported orientated-quantitative determination of individualized ASTA of femoral neck screw channel through the intersecting method. The results revealed that ASTA presented an inclined rounded triangle forming an oblique angle with individual differences. The base of the ASTA triangle coincided with flat AC-FNB, which could be taken as a reference landmark to build the FNTA coordinate system. Under this coordinate system, the border isthmus on SXBI could match the ASTA boundaries on CT, so the axial coordinates of all pins in the femoral neck could be stably calculated from the x-ray for intraoperative positioning. The findings could help surgeons to design the spatial configuration of combined screws preoperatively, and establish a new ASTA geometric model and X-CT criteria to intuitively evaluate the positions and spatial configurations of guide pins intraoperatively.

Methods to acquire individualized axial safe target area

Due to the serious clinical consequences of IOI screws, research on the femoral neck safety zone has received increasing attention in recent years13,14. Nakanishi et al. 11 selected the axial CT image the medicervical isthmus located on anteroposterior x-ray as the safe zone. Zhang et al. 15 obtained the safe and risk zones on axial graphs by using the projection method. However, there was no evidence that all isthmuses were located at the same transverse plane. Previous studies did not find out constant anatomical landmarks as a reference to define a quantitative safe zone and its direction and position its safety boundaries. Without considering the orientated-quantitative-stable individualized ASTA, the help for ISFNASFA was extremely limited. So far, there is no consensus on how to determine individualized ASTA.

The current consensus is that the cannulated screws should be placed in all bony stenoses, parallel to the central axis, running in a straight line1–4. However, the contour of the femoral neck is irregular, the shape of different cross-sections varies greatly, and not all the stenoses are in the same plane. Therefore, in this study, all axial CT images of the same femoral neck were superimposed to obtain the intersection, and the common stenosis area of all cross-sections was determined as the individualized ASTA. Then constant-flat AC-FNB was defined as the anatomical landmark reference of the coordinate system. This study not only clarified the specific positions of ASTA boundaries in the femoral neck on CT and their relationship with SXBI but also quantitatively evaluated D-SI and D-AP. The ASTA acquisition method was simple and noninvasive, and the data were accurate and intuitive.

Characteristics of axial safe target area

This study first showed that ASTA presented an oblique rounded triangle with a constant-flat AB-ASTA coincided with the AC-FNB, which could be used as an important anatomical reference mark, both in CT study and in surgery.

In the present study, different from Zhang et al. 16, the oblique angle between the AB-ASTA and the coronal central axis of the proximal femur cross-section was used to evaluate the inclination degree of the ASTA triangle (Fig. 3F). ASTA inclination degree refers to the torsion angle of the anterior contour of FNB relative to the proximal femoral coronal plane through rotating around femoral neck central axis, which is also called contour-FNTA. This angle can be determined as an inherent anatomical characteristic, but large individual variations exist. The oblique angle was different from the FNAA, which formed by femoral neck rotating around the proximal femur axis17,18, FNTA was a very important but often overlooked parameter in evaluating the anatomical morphology of femoral neck, which could directly affect the screw entry point and screw arrangement on the lateral wall of the proximal femur16, and the correct fluoroscopic direction was also closely related to FNTA.

In addition, this study also found that the ASTA varied in different individuals in terms of D-SI, D-AP, oblique angle, and shape, so an individualized plan considering the screw entry points and screw spacing should be developed on acquired individualized ASTA, instead of the average parameters, achieving accurate screw placement and avoiding IOI screws.

The significance of establishing the coordinate system

Accurate judgment of matching intraoperative x-ray borders with corresponding ASTA CT boundaries was a prerequisite to ensure safe screw trajectory4,19. Without evidence, most surgeons defaulted to boundary matching, which was objected by Kumar et al. 10. The present study confirmed that ASTA had an irregular shape with a certain direction. When the parameters, such as D-SI, D-AP, and boundaries, were measured from different directions, inconsistent data would be generated (Figs. 4J and K). Thus, constant anatomical landmarks must be sought to define the coordinate system direction to acquire objective-accurate-stable ASTA, to match intraoperative fluoroscopic borders with corresponding ASTA boundaries, and to provide effective help for clinical surgery.

In previous studies on ASTA, no constant anatomical reference landmark of the coordinate systems were established20. Those coordinate systems were constructed with the approximate proximal femoral coronal plane as the longitudinal axis15. However, the longitudinal axis was neither parallel nor perpendicular to ASTA with an individualized oblique angle (Figs. 5A1 and A2), inevitably causing uncontrollable rotational deviation between the coordinate system and the entity. Therefore, ASTA boundaries were inconsistent with SXBI, which elicited great intraoperative difficulty to accurately locate and adjust the guide pins by x-ray alone, resulting in IOI screws, similar to previous findings10.

Figure 5.

Clinical significance of axial safe target area (ASTA). (A) Schematic of preoperative design of individualized screws spatial configuration based on the individualized ASTA. Recommend three screws should be arranged parallel to the central axis and distributed in the three vertices of the ASTA triangle with scattered welt. A1: The ASTA and its coordinate system were projected to the lateral side of the proximal femur to facilitate a visual understanding of the spatial location and orientation of the ASTA. A2: There was an individual angle between the anterior base of ASTA (AB-ASTA) and the coronal plane of proximal femur (PFCP). A3: Comparing with the actual ASTA, the hypothetical oval safe zone (HOSZ) used in the navigation system had a certain error, which could cause IOI screws. A4: The spatial configuration of the screws scattered at the three vertices of the ASTA was projected to the lateral wall of the proximal femur to facilitate a visual understanding of the spatial location and layout of the screws. A5: The inverted triangular distribution of the screws was projected to the lateral wall of the proximal femur. A6: The triangular distribution of the screws was projected to the lateral wall of the proximal femur. A7: Axial computed tomography (CT) of the spatial configuration of screws scattered at three vertices of ASTA corresponding to A4, and its fixed cross-sectional area was larger than those of the inverse-triangular and triangular configuration. A8: Axial CT of the distribution configuration of the inverted triangular screws, corresponding to A5. A9: Axial CT of the distribution configuration of the triangular screws, corresponding to A6. (B–D) Taking the screw guide pin S2 as an example, the process of calculating their coordinates in ASTA through intraoperative anteroposterior and lateral x-rays was demonstrated. (B) Measure the distances from S2 center to the superior–inferior borders respectively in anteroposterior x-ray (a1, a2), y2=(a2−a1)×d1/[2×(a1+a2)]. d1 was superior–inferior diameter (D-SI) of ASTA measured in CT. (C) Measure the distances from S2 center to the anterior–posterior edges respectively in lateral x-ray (b1, b2), z2=(b2−b1)×d2/[2×(b1+b2)]. d2 was anterior–posterior diameter (D-AP) of ASTA measured in CT. (D) In ASTA on the YOZ coordinate system, the coordinates point S2 (y2, z2) calculated above was marked to obtain the coordinate position of S2 center in ASTA and to judge whether the screw or guild pin penetrates cortical bone or not intuitively. The same as S1 and S3. (E) Axial CT postoperative showed the coordinate position of each guide pin, which was consistent with the calculation result in (D). Due to metal interference, there were guide pin diameter enlargement and artifacts.

This study defined the constant-flat AC-FNB or AB-ASTA as a reference mark for establishing a coordinate system to eliminate the interference of FNSA, FNAA, and FNTA. Through observing along the x-axis direction, that is, the simulated projection of the spatial coordinate system O-XYZ on the YOZ plane coordinate system, the axial CT images of ASTA were acquired, which could not be accomplished by x-ray (Figs. 4A, E, I). Through perspective along the z-axis (Figs. 4B–E) the projection of O-XYZ on the XOY coordinate system, anteroposterior radiographs were acquired and the superior and inferior SXBI completely matched to the corresponding D-SI boundaries of ASTA. Through perspective along the y-axis direction (Figs. 4F–I), the projection of O-XYZ on the XOZ, lateral radiographs were acquired, and the anterior and posterior SXBI completely matched to the corresponding D-AP boundaries of ASTA. Therefore, the boundaries of ASTA revealed by CT were completely consistent with the corresponding SXBI detected by x-ray, indicating quantitative correspondence of point coordinates between x-ray and axial CT results. Using the coordinate system O-XYZ constructed in this study, the coordinates of each point could be stably located, and the x-ray data of the screws could be converted to axial coordinates on CT images.

However, attention should be paid to the conditions of boundaries matching. Only when anteroposterior fluoroscopy was perpendicular to AC-FNB, did D-SI CT boundaries correspond to superior–inferior SXBI of FNM. When lateral fluoroscopy was parallel to AC-FNB, D-AP CT boundaries corresponded to anterior–posterior SXBI of FNB.

The clinical significance of axial safe target area

Obviously, the preoperative design of the spatial configuration of multiple cannulated screws should be based on the individualized ASTA to ensure the safety of screw placement and the effectiveness of fixation. If three cannulated screws were arranged in a triangle or inverted triangle along the femoral longitudinal axis, considering 1–2 mm safety corridor of screws21, both the fixed cross-sectional area and the safety of screw placement would be greatly reduced. Therefore, this study recommended that three hollow screws should be arranged in parallel to the central axis and distributed in three vertices of the ASTA triangle with scattered welt, which might enable to generate the largest safe containment cross-sectional area and fixed strength. Hence, an inverted triangle might not be preferred, and an optimal spatial configuration remained explored further (Fig. 5A).

An intraoperative x-ray can merely provide anteroposterior and lateral two-dimensional images of the screws, but their axial coordinates which were critical for screws-placement could not be directly obtained. The present study clarified the conditions under which SXBI could match the corresponding boundaries of ASTA on CT. Through preoperative measurements on CT images, the geometric model map of individualized ASTA based on the coordinate system could be drawn, the measured D-SI and D-AP data were assigned to anteroposterior and lateral x-ray, and then x-ray data could be quantified to conveniently calculate the axial coordinates of guide pins (y, z). After the coordinate points were marked in the ASTA map of the YOZ coordinate system, it could be intuitive to determine their accurate positions in ASTA and to judge whether they penetrated the boundaries of ASTA (Figs. 5B–E). The research results can be applied to the computerized navigation system to avoid systematic errors caused by the false premise that individualized ASTA was round or oval20,22 and to improve the security and accuracy of screw placement (Fig. 5A3).

Since D-SI boundaries or isthmus were located at FNM, while D-AP boundaries or isthmus were located at FNB, D-SI and D-AP could be measured respectively on the corresponding axial CT images, and then the corresponding data of the intersection could be easily estimated. In addition, for femoral neck fractures, when only either of D-SI and D-AP could be measured, a regression equation could be used to roughly estimate the other parameter.

Limitations

It was a single-center study. There might be racial differences in contour and diameter. At present, there was no recognized standard for the central axis of the femoral neck, so FNSA and FNAA selected in this study might represent a certain deviation (within ±5°). Of course, this deviation scope was acceptable in surgical practice. This study employed a simulated perspective to theoretically infer the x-ray border isthmuses coinciding with ASTA boundaries on CT, and further direct radiological experimental evidence should be required.

Conclusions

The orientated-quantitative individualized ASTA was easily acquired through the intersection method and a coordinate system based on the constant-flat AC-FNB was established. Under this coordinate system, the x-ray borders could match the boundaries of ASTA, while the coordinates of all pins and screws in the femoral neck could be stably located.

Ethical approval

Ethics approval was obtained from the hospital’s institutional review board. The registered clinical study code was SC20200233. CT data were analyzed in this study, and no patients were directly involved.

Sources of funding

Supported by unrestricted grants from Hainan Provincial Natural Science, Foundation of China (Grant No. 821MS160) and the Hainan Province Health Commission (Grant No. 20A200517).

Author contribution

Y.-S.D., G.-L.J., and Y.-F.C. co-designed the study. Y.-S.D., H.-Y.D., G.-L.J., and Y.-F.C. participated in conducting the experiments, performed the statistical evaluation of the data and determined their interpretation, and drafted and revised the manuscript. H.-P.Y., Z.-B.Z., and D.-Q.W. contributed to conducting the experiments and drafted the manuscript. Q.-G.W. supervised the study and revised the manuscript. All authors have read and approved the final version of the submitted manuscript.

Conflicts of interest disclosure

The authors declare that they have no financial conflict of interest with regard to the content of this report.

Research registration unique identifying number (UIN)

1. Name of the registry.

2. Unique Identifying number or registration ID.

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Guarantor

Ying-Sheng Deng.

Provenance and peer review

Not commissioned, externally peer-reviewed.

Data availability statement

None.

				D-SI			D-AP
					Border location			Border location
Case	Sex	Year	R/L	Distance (mm)	ASTA border	Simulated X-ray isthmus	Distance (mm)	ASTA border	Simulated X-ray isthmus	Oblique angle (°)
				27	FNM	FNM	21	FNB	FNB	24
2	F	75	L	30	FNM	FNM	25	FNB	FNB	35
3	M	52	R	33	FNM	FNM	27	FNB	FNB	30
4	M	52	L	33.5	FNM	FNM	27	FNB	FNB	31
5	M	37	L	34.5	FNM	FNM	27.5	FNB	FNB	26
6	M	44	R	35	FNM	FNM	27.5	FNB	FNB	44
7	F	70	R	28.5	FNM	FNM	20.5	FNB	FNB	36
8	M	60	R	37	FNM	FNM	29	FNB	FNB	20
9	M	60	L	37	FNM	FNM	29	FNB	FNB	21
10	M	77	R	30	FNM	FNM	22.3	FNB	FNB	34
11	F	48	L	30	FNM	FNM	22	FNB	FNB	25
12	M	51	L	33	FNM	FNM	23	FNB	FNB	15
13	M	55	L	35	FNM	FNM	24	FNB	FNB	20
14	F	62	R	28	FNM	FNM	20	FNB	FNB	22
15	F	62	L	29	FNM	FNM	20	FNB	FNB	19
16	M	56	R	32.5	FNM	FNM	23	FNB	FNB	10
17	M	54	R	34	FNM	FNM	24.5	FNB	FNB	24
18	M	54	L	34.5	FNM	FNM	25	FNB	FNB	23
19	F	80	R	29	FNM	FNM	23.5	FNB	FNB	21
20	F	80	L	29	FNM	FNM	22	FNB	FNB	18
21	M	69	L	32	FNM	FNM	23.5	FNB	FNB	27
22	F	83	L	29	FNM	FNM	19	FNB	FNB	34
23	M	30	R	35.5	FNM	FNM	24	FNB	FNB	12
24	M	30	L	36	FNM	FNM	23.5	FNB	FNB	12
25	M	54	L	31	FNM	FNM	26	FNB	FNB	28
26	F	66	R	30	FNM	FNM	24.5	FNB	FNB	20
27	F	67	L	34	FNM	FNM	25	FNB	FNB	18
28	F	60	L	28	FNM	FNM	20.5	FNB	FNB	25
29	F	67	L	30	FNM	FNM	21	FNB	FNB	15
30	F	80	R	27	FNM	FNM	17	FNB	FNB	21
31	m	53	R	33	FNM	FNM	25.5	FNB	FNB	15
32	m	53	L	33	FNM	FNM	25	FNB	FNB	17
33	m	74	L	33	FNM	FNM	23	FNB	FNB	18.5
34	F	32	R	32	FNM	FNM	25	FNB	FNB	22
35	F	32	L	33.6	FNM	FNM	23.2	FNB	FNB	10
36	F	87	L	28.5	FNM	FNM	19.5	FNB	FNB	20
37	F	56	R	28	FNM	FNM	20	FNB	FNB	26
38	F	56	L	29	FNM	FNM	21	FNB	FNB	23
39	F	69	R	30.3	FNM	FNM	23	FNB	FNB	28
40	F	69	L	29.5	FNM	FNM	24	FNB	FNB	32
41	F	80	R	26	FNM	FNM	22	FNB	FNB	24
42	M	55	L	30	FNM	FNM	24	FNB	FNB	8
43	M	39	R	35	FNM	FNM	27	FNB	FNB	30
44	F	41	R	26	FNM	FNM	18	FNB	FNB	17
45	F	18	L	26.5	FNM	FNM	18.5	FNB	FNB	25
46	F	73	R	33	FNM	FNM	22.5	FNB	FNB	12
47	F	73	L	30	FNM	FNM	20.5	FNB	FNB	18
48	M	80	L	34	FNM	FNM	29	FNB	FNB	6
49	F	54	R	29	FNM	FNM	21	FNB	FNB	33
50	F	54	L	27.5	FNM	FNM	21	FNB	FNB	26
51	F	73	R	28	FNM	FNM	19	FNB	FNB	23
52	F	32	R	29.5	FNM	FNM	20	FNB	FNB	22
53	F	32	L	28	FNM	FNM	20	FNB	FNB	15
54	F	75	L	30	FNM	FNM	23.5	FNB	FNB	33
55	F	77	R	28	FNM	FNM	20.5	FNB	FNB	20
56	F	77	L	28	FNM	FNM	20.5	FNB	FNB	21
57	F	84	R	29	FNM	FNM	20	FNB	FNB	19
58	m	46	R	34	FNM	FNM	22.5	FNB	FNB	16
59	m	46	L	34	FNM	FNM	22.5	FNB	FNB	13
60	M	90	L	33.5	FNM	FNM	26	FNB	FNB	25
61	M	33	L	35.5	FNM	FNM	28	FNB	FNB	20
62	M	43	L	35	FNM	FNM	24	FNB	FNB	5
63	F	73	L	30	FNM	FNM	20	FNB	FNB	27
64	M	79	R	38	FNM	FNM	26	FNB	FNB	19
65	m	35	R	30.3	FNM	FNM	25	FNB	FNB	30
66	m	35	L	30.2	FNM	FNM	23.6	FNB	FNB	22
67	M	55	R	32.5	FNM	FNM	24	FNB	FNB	45
68	M	55	L	33	FNM	FNM	23.5	FNB	FNB	45
69	F	50	R	28	FNM	FNM	21	FNB	FNB	38
70	F	50	L	28	FNM	FNM	21	FNB	FNB	33
71	M	55	R	31.5	FNM	FNM	24	FNB	FNB	44
72	M	55	L	30.5	FNM	FNM	24	FNB	FNB	39
73	F	40	R	32.5	FNM	FNM	24.5	FNB	FNB	37
74	F	40	L	32.5	FNM	FNM	23.5	FNB	FNB	38
75	M	59	R	36.5	FNM	FNM	28.5	FNB	FNB	39
76	M	59	L	35.5	FNM	FNM	28.5	FNB	FNB	32
77	F	50	R	29	FNM	FNM	22	FNB	FNB	32
78	F	50	L	29	FNM	FNM	22	FNB	FNB	29
79	M	20	R	30.5	FNM	FNM	24.5	FNB	FNB	29
80	M	20	L	29	FNM	FNM	23	FNB	FNB	32
81	M	55	R	29.5	FNM	FNM	19.5	FNB	FNB	23
82	M	55	L	29.5	FNM	FNM	19	FNB	FNB	17
83	F	20	R	29	FNM	FNM	23	FNB	FNB	29
84	F	20	L	29	FNM	FNM	23.5	FNB	FNB	35
85	M	45	R	29	FNM	FNM	22	FNB	FNB	29
86	M	45	L	30	FNM	FNM	23	FNB	FNB	30
87	F	30	R	31.5	FNM	FNM	25	FNB	FNB	19
88	F	30	L	32	FNM	FNM	25	FNB	FNB	23
89	F	45	R	31	FNM	FNM	21	FNB	FNB	36
90	F	45	L	31	FNM	FNM	22	FNB	FNB	26
91	M	67	R	32.5	FNM	FNM	27	FNB	FNB	26
92	M	67	L	31.5	FNM	FNM	26	FNB	FNB	31
93	F	65	R	27	FNM	FNM	22	FNB	FNB	33
94	F	65	L	27.5	FNM	FNM	21	FNB	FNB	42
95	F	55	R	30.5	FNM	FNM	21.5	FNB	FNB	30
96	F	55	L	31.5	FNM	FNM	22	FNB	FNB	34
97	M	45	R	35	FNM	FNM	27.5	FNB	FNB	49
98	M	45	L	35.5	FNM	FNM	29	FNB	FNB	53
99	M	50	R	34.5	FNM	FNM	26.5	FNB	FNB	32
100	M	50	L	35.5	FNM	FNM	26.5	FNB	FNB	33
101	F	31	R	27.5	FNM	FNM	22.5	FNB	FNB	21
102	F	31	L	26	FNM	FNM	21	FNB	FNB	30
103	M	35	R	35.5	FNM	FNM	26.5	FNB	FNB	36
104	M	35	L	36	FNM	FNM	27	FNB	FNB	34
105	M	65	R	35.5	FNM	FNM	28	FNB	FNB	40
106	M	65	L	34.5	FNM	FNM	27	FNB	FNB	39
107	F	38	R	31	FNM	FNM	25	FNB	FNB	51
108	F	38	L	31.5	FNM	FNM	25	FNB	FNB	47
109	M	56	R	33.5	FNM	FNM	26	FNB	FNB	28
110	M	56	L	34	FNM	FNM	26	FNB	FNB	31
111	F	56	R	32	FNM	FNM	23	FNB	FNB	27
112	F	56	L	31	FNM	FNM	24	FNB	FNB	28
113	F	60	R	31	FNM	FNM	24	FNB	FNB	25
114	F	60	L	30	FNM	FNM	23	FNB	FNB	35
115	M	20	R	36.5	FNM	FNM	26	FNB	FNB	24
116	M	20	L	35.5	FNM	FNM	25	FNB	FNB	31
117	M	64	R	33	FNM	FNM	27	FNB	FNB	38
118	M	64	L	32.5	FNM	FNM	27	FNB	FNB	40
119	M	28	R	31	FNM	FNM	23	FNB	FNB	27
120	M	28	L	30	FNM	FNM	23	FNB	FNB	32
121	F	45	R	28	FNM	FNM	23	FNB	FNB	38
122	F	45	L	28.5	FNM	FNM	22	FNB	FNB	36
123	M	77	R	34	FNM	FNM	25	FNB	FNB	34
124	M	77	L	32.5	FNM	FNM	24.5	FNB	FNB	45
125	M	35	R	36	FNM	FNM	24	FNB	FNB	39
126	M	35	L	35	FNM	FNM	23	FNB	FNB	33
127	M	67	R	33	FNM	FNM	25	FNB	FNB	30
128	M	67	L	34.5	FNM	FNM	26	FNB	FNB	31
129	M	25	R	33.5	FNM	FNM	26	FNB	FNB	22
130	M	25	L	34	FNM	FNM	26	FNB	FNB	33
131	M	35	R	38	FNM	FNM	27	FNB	FNB	24
132	M	35	L	38	FNM	FNM	27.5	FNB	FNB	25
133	M	76	R	32	FNM	FNM	23	FNB	FNB	7
134	M	76	L	32	FNM	FNM	24	FNB	FNB	23
135	M	41	R	32.5	FNM	FNM	25	FNB	FNB	27
136	M	41	L	35.5	FNM	FNM	25	FNB	FNB	36
137	M	56	R	37	FNM	FNM	26.5	FNB	FNB	30
138	M	56	L	37	FNM	FNM	26	FNB	FNB	34
139	M	50	L	33.5	FNM	FNM	27	FNB	FNB	37

Supplementary Material

js9-109-1158-s001.docx ^{(21KB, docx)}

js9-109-1158-s002.docx ^{(22.5KB, docx)}