Introduction

Craniocervical junction abnormalities (CJA) are congenital bony anomalies of the occipital and atlantoaxial that occur in the craniocervical junction region, which is the transition between the skull and the cervical spine [1]. There is a possibility of quadriplegia in severe cases, and medulla oblongata compression may result in respiratory distress. Due to the special anatomical location of the atlantoaxial spine and the complex anatomical structures of the surrounding blood vessels and nerves, the treatment of atlantoaxial spine disorders can also be relatively difficult. With the introduction of modern imaging technologies—computer tomography (CT), magnetic resonance imaging (MRI)—there is better understanding of these abnormalities. However, the treatment of this pathology can be difficult. The goals of treatment of CJA are to restore the anatomy of the atlantoaxial spine, relieve the compression of the spinal cord, and stabilize the atlantoaxial complex [2]. A common surgical procedure to treat atlantoaxial disorders is atlantoaxial fusion, and biomechanical studies have shown that atlantoaxial screws and rods can provide excellent stability when combined with atlantoaxial lateral mass interarticular fusion devices [14] used calipers and a goniometer to measure bony specimens to determine the length, width, and inclination angle of the upper and lower articular surfaces of the lateral mass joint to provide data to support the placement of anterior transarticular screws. Dong and Rocha et al. [15,16,17] measured the mean thickness, width, height and coronal inclination of the lateral mass joint using cadavers and found a relatively low incidence of atlantoaxial articular cartilage degeneration. In vitro studies, X-rays were first applied to the anatomic radiological and morphological analysis of the lateral mass joint of the atlantoaxial spine. Xu et al. [18] confirmed the value of indicating the sagittal screw angle of the atlantoaxial spine by lateral X-ray measurements of the lateral mass joint. Ma et al. [19] applied CT and 3D reconstruction to measure the inclination and sliding type of the atlantoaxial lateral mass joint and proposed a staging system for congenital atlantoaxial subluxation to provide a basis for guiding surgical treatment. Other scholars used 3D reconstruction with software such as Mimics and Abaqus based on CT examination and generated finite element models to analyze and measure the range of motion, stress conditions and ligamentous changes of the lateral atlantoaxial mass by changing the model parameters. Accordingly, with the advancement of anatomy, imaging, and multidisciplinary synergy, it has become increasingly complex to study the anatomical morphology of the lateral mass of the atlantoaxial spine based on in vitro radiological images in comparison with anatomical studies on dry skeletal specimens and cadavers. In the future, the study of the anatomical morphology of the atlantoaxial spine will no longer be limited to X-rays, CT and other imaging examinations, but will make use of three-dimensional reconstruction, finite element analysis and other techniques to establish mathematical models and computer simulations of the articular surface of the lateral mass of the atlantoaxial spine. This is so that the morphological, functional and biomechanical studies of the articular surface of the lateral mass of the atlantoaxial spine can be carried out more precisely and accurately.

Significance of describing the articular surface of the lateral mass of the atlantoaxial spine using differential flow patterns

With the advancement of technology, it is often necessary in modern medicine to use medical imaging data to reconstruct anatomical structures, perform preoperative planning, perform virtual surgery, and simulate clinical surgical operations. It is difficult to form a good fit with the articular surface of the atlantoaxial lateral mass due to the planar end surfaces of all interarticular fusion devices reported in the literature. As a result, the fusion device may not be stable, and the bone graft might not fuse as easily as it should. In this study, the 3D reconstruction of atlantoaxial joint CT images was obtained, and the atlantoaxial articular surface was extracted by python software. The articular surface was fitted into an atlantoaxial surface formed by multiple points, and the “differential manifold” processing method was introduced for the first time to analyze and describe the atlantoaxial lateral mass articulation. The term, “manifold” is not much used in the medical field, but in the past, Zimmer et al. [20] applied manifold embedding to high-dimensional medical image data analysis techniques to automatically select functions and their associated parameters from a pool of candidate functions to generate the best manifold embedding. **a et al. [21] used low-dose CT to reconstruct manifold networks and achieved good results in terms of visualization and quantification. Maxime et al. [22] characterized the interaction between the heart shape and deformation by nonlinear manifold learning. This high latitude description of heart function is the key to determining heart disease and also confirmed the characteristics of right ventricular disease in the population.

We propose for the first time an implicit surface reconstruction algorithm based on the differential manifold in the processing of atlantoaxial spine image data to measure relevant anatomical parameters on a model with higher accuracy of output. The ROI labeling and measurement portion of this study was completed by three experienced radiologists, and an ICC consistency test of their measurements revealed strong consistency among the three radiologists’ measurements. This means that the algorithm is less affected by human factors and has a certain reliability in clinical extension. Compared with the manual measurement of traditional bony specimens or sagittal and coronal measurements based on image data reconstruction, the error is significantly reduced and the efficiency is significantly improved, which can more accurately characterize the morphology, size, orientation, curvature and other anatomical features of the articular surfaces of the lateral mass of the atlantoaxial spine and provide a deeper understanding of the interaction, motion patterns, stability and function of the articular surfaces of the lateral mass of the atlantoaxial spine. Aside from eliminating the need for expensive commercial software like mimics, this method enables a mathematical model and computer simulation of the atlantoaxial mass’s articular surface that provides tools for further research into its pathological and biomechanical characteristics. By measuring the anatomical morphology of the articular surface of the lateral atlantoaxial mass, this study provides a personalized preoperative assessment for patients undergoing surgery for CJA, provides a database for the individualized design of 3D printed fusion devices, and provides a reference for clinical diagnosis and surgery to reduce surgical risks for the benefit of such patients.

Measurement and significance of data related to the atlantoaxial articular surface

In previous anatomical studies of the articular surface of the lateral atlantoaxial mass, the sagittal lengths of the articular surface of the atlantoaxial spine measured from cadaveric specimens were (15.7–18.7 mm) and (17.0–17.7 mm), and the coronal lengths were (15.2–16.5 mm) and (16.6–17.3 mm), respectively, and Li et al. [3] measured CT images of 46 adults and obtained The sagittal and transverse diameters of the articular surface of the lateral atlantoaxial mass were 16.96 mm and 16.27 mm, respectively, and the sagittal and transverse diameters of the articular surface of the lateral cardinal mass were 17.69 mm and 16.32 mm, respectively, and similar results were obtained in this study with other anatomical data on the measurement of parameters related to the articular surface of the lateral atlantoaxial mass, which demonstrates that the method used in this study has a high degree of reliability and reliability. The results of this study are similar to the anatomical data of other atlantoaxial mass (Table 5).

Table 5 Comparison of measured parameters between previous studies and the present study
Full size table

In our study, the reconstructed joint gaps were divided into anterior, middle and posterior and internal, middle and external regions by means of differential flow reconstruction surfaces, and it was found that the morphological characteristics of the gaps showed a general trend of anteriorly wide, moderately narrow and posteriorly wide in the sagittal position and internally narrow, moderately wide and externally narrow in the coronal position. This was consistent with the findings of Gu et al. [24]. Meanwhile, the study of the lateral mass of the atlantoaxial spine found that its articular surface curvature has a certain degree of curvature, its projection and depression are different, and there is no exact coincidence or complementary relationship between the two articular bony surfaces. The results of the coronal position with the superior surface vertex generally located in the middle and medial sides were: 93.75% (75/80) and 97.50% (78/80) for the left and right sides of the atlantoaxial spine, respectively, and 97.50% (78/80) and 95.00% (76/80) for the left and right sides of the pivot spine, respectively, with the inferior surface vertex generally located in the middle and lateral sides. In the sagittal position, the results of the vertex of the articular surface in the middle 1/3 were: 81.25% (65/80) and 73.75% (59/80) for the left and right sides of the atlantoaxial spine, respectively, and 76.25% (61/80) and 71.25% (57/80) for the left and right sides of the pivot spine, respectively.

To facilitate the smooth and accurate placement of the fusion device into the lateral atlantoaxial space and to obtain a stable bony fusion, the articular surface of the lateral atlantoaxial mass must be both concave and convex. According to the above measurements, the sagittal apex of the fusion device should be located in the middle 1/3 region, while the coronal apex should be located in the middle and medial regions on the upper surface and in the middle and lateral regions on the lower surface. Combining the results of the above anatomical measurements with the characteristics of the surgical operation during the actual clinical placement of the fusion device, attention should be paid to the design of the anatomical-type fusion device in the next stage with a length of no more than 13 mm, a width of no more than 10 mm, and a fusion device height of 4–6 mm. The overall shape should be that of a folding knife in the sagittal position with the upper surface up-convex and the lower surface up-concave. There should be a date pit shape in the coronal position with the upper surface up-convex in the middle and medial side and the lower surface down-convex in the middle and lateral side.

The sample size for this study was 80 cases, which is relatively small for a detailed anatomical study with individual variation, but is feasible when compared with previous studies due to the complexity of the anatomy at this site which limits the anatomical morphometric studies that can be performed. Previous solid anatomical studies performed on cadavers were limited by the collection of samples, and most current studies involve morphological measurements on digitized images such as CT. The reasons for the small sample size are as follows: First, the sample included in this study was 64-slice cervical spine CT images from a normal population during a physical examination, and not all physical examiners choose cervical spine CT, and even few asymptomatic people choose cervical spine CT to clarify the presence of abnormalities, which led to the limited collection of the sample size in this study. Second, the anatomy of atlantoaxial joint is complicated, which makes it difficult to carry out the study of anatomical morphometry in this region; third, the surface reconstruction algorithm based on differential manifolds needs to go through a series of complicated operations, such as ROI labeling, atlantoaxial surface extraction, and equivalent surface extraction, which are difficult and lengthy to process, again resulting in small sample sizes. Also, the age distribution of the sample included in this study was 20–54 years old, with a mean age of 37.8 years, which are mostly younger populations with less joint degeneration and hyperplasia, which could avoid the influence of joints with osteophytes due to aging in the older population on this measurement. However, sampling error due to small sample size is unavoidable, and larger sample sizes need to be further included to conduct the study, enabling the results of this study to be generalized in clinical settings.

Limitations

(i) For the results to be verified, the sample size included in the study is somewhat small, and further expansion of the sample size is required; (ii) Unlike the direct measurement of specimens, this study is an imaging anatomy study based on the reconstructed images of CT scans, and there may be a certain degree of error in the selection of thresholds and fitting of joint surfaces to the real object; (iii) Due to the selection and setting of the algorithm, there may be some errors in controlling grid accuracy and curvature determination.

Future research directions

It is necessary to further explore the optimization of data algorithms and to study the data related to the articular surface of the lateral mass of the atlantoaxial spine in patients with CJA by fitting models of the articular surface of the lateral mass of the atlantoaxial spine in conjunction with computer and other engineering, information engineering, biomechanics and other specialties. We will use the data from this study to further optimize the lateral atlantoaxial mass fusion device design and verify its implantability and safety, laying the foundation for the next animal experiments and clinical trials.

Conclusion

  1. 1.

    Clinical imaging data and differential flow algorithms can be used to better visualize the anatomical structure of the articular surfaces of the lateral atlantoaxial mass, measure all of the relevant parameters accurately, and provide data for the design of anatomical lateral atlantoaxial mass joint fusions.

  2. 2.

    The anatomical shape of the articular surface of the lateral atlantoaxial mass is irregular, with a certain curvature of the articular surface and different positions of the raised and depressed articular surfaces. The two bony surfaces do not show a strict coincidence and complementary relationship, and the positions of the upper and lower convexity can show a certain pattern in the population in general.

  3. 3.

    The atlantoaxial articular surface of most healthy adults is morphologically adequate to accept fusion devices up to 13 mm in length, 10 mm in width, and 4–6 mm in height. Based on the measured curvature pattern of the articular surface, anatomic fusion devices are generally shaped like a folding knife in the sagittal position and are more likely to fit the articular surface in the coronal position with a date palm shape.

  4. 4.

    There is a wide variation in the anatomical morphology of the lateral mass of the atlantoaxial spine which is large, and a thorough preoperative imaging examination of the atlantoaxial spine should be performed to provide a comprehensive preoperative evaluation of the patient, so that a reasonable surgical plan can be formulated and individualized treatment can be achieved.