Correlation of sagittal conguration of the sacrum and pelvic incidence evaluated by computed tomography measurements

Objective To measure the sagittal congurations of the sacrum using computed tomography (CT), and to investigate the correlation between the sagittal conguration of the sacrum and pelvic incidence. Methods The computed topographies of complete pelvic imaging between 2006 and 2018 was retrospectively studied. Measurements of pelvic and sacral morphological parameters were performed on the midsagittal plane of the 2D reconstruction images of computed tomography. Pelvic incidence (PI) (STA) were measured as previously described, and sacral table angle, sacral incidence (SI), sacral segmental vertebral angle (SSVA), sacral segmental kyphosis (SSK), central angle (SCA), arc length (SAL) as well as arc radius (SAR) were introduced to describe the segmental morphology of sacrum. Pearson Correlation Coecient and Stepwise Regression Analysis were used to determine the relationship between PI and sacral morphological parameters.


Introduction
The measurements of sagittal balance have become an important consideration for many spinal disorders such as lumbar disc herniation and spondylolisthesis 1 . Pelvic incidence (PI) is one of the most studied radiologic measurements which was initially introduced by Duval-Beaupère 2 . As a positionindependent parameter that quanti es the sagittal angle between the perpendicular axis of the sacral endplate and a line from the center of the sacral endplate to the femoral head axis, the unique value of PI represents pelvic morphology for every individual 3 . An association between PI and spondylolisthesis has been in numerous studies, and PI has been found to be increased in adults with low-grade isthmic spondylolisthesis and correlated with the severity of slippage 4 .
Similarly, morphological characteristics of the sacrum have also been studied within the context of spinopelvic pathologies, and various studies indicate that the sagittal con guration of the sacrum might be an important factor related to spondylolisthesis 5 . Sacral table angle (STA) has been found to be related with the occurrence rate of spondylolysis. Besides the measurement of STA, two methods have also been reported in the literature to measure sacral kyphosis, using either the Cobb angle method or the Ferguson technique 6 . A more curved sacrum has been associated with degenerative and developmental spondylolisthesis as well as lumbar disc herniation 7,8 . Although a large number of studies reported the radiographic measurements of the sacral morphology, di culties still exists regarding the limited visibility of sacrum on X-rays 9 . Different methods have described the measurement of sacral kyphosis, however, there is still no consensus on a standard method, since all the existing techniques have their own limitations 6 .
Since both PI and the sacral morphology correlate with spondylolisthesis, how these two measurements relate to each other stated to gain interest recently. Abola et al reported that PI is associated with a highly angulated and curved sacrum through an anatomical comparative study of cadaveric specimens 10 , however, no further studies supports this nding, and there has been no radiologic study about the impact of sacral morphology on pelvic incidence yet.
The purpose of this study was therefore to measure the sagittal con gurations of the sacrum using computed tomography (CT), trying to establish a set of standard method for the measurement of sacral morphology, and also to investigate the correlation between the sagittal con guration of the sacrum and pelvic incidence.

Study Population
The computed topographies of complete pelvic imaging between 2006 and 2018 was retrospectively studied from the database of Shanghai Ninth People's Hospital, Shanghai Jiao Tong University School of Medicine. This study has been approved by the institutional review board of Shanghai Ninth People's Hospital, and written informed consents were obtained from the all patients. Inclusion criteria were as follows: (1) age between 20 and 80 years old; (2) complete pelvic imaging including the whole sacrum; (3) no pelvic or femoral fracture; (4) no surgical history of the spine, pelvis, or hip joints. Exclusion criteria include: (1) anatomical anomalies of the sacrum. (2) history of any disease that may affect bone growth.
(3) severe osteoporosis or arthritis. A total of 304 subjects were nally enrolled in this study. The CT scans were performed using Siemens SOMATOM De nition Flash 128 scanners (Somatom De nition FLASH, Siemens Healthcare, Forchheim, Germany) with a mean voxel size of 0.98×0.98×1.00 mm.
Imaging data were exported as DICOM (Digital Imaging and Communications in Medicine) les for further analysis.

Radiographic Measurements
Measurements of pelvic and sacral morphological parameters were performed on the midsagittal plane of the 2D reconstruction images of computed tomography (Fig.1, Table 1). Hip axis was determined on the midsagittal plane based on a 3D pelvic surface using Mimics software ( Fig.1) (Materialise, Leuven, Belgium). We measured the pelvic incidence (PI) and sacral table angle (STA) as previously described 9 , and also introduced several radiographic parameters to delineate sacral morphology, the de nition of which were listed in Table 2. A circle tting method was developed based on the morphology of S1, S2, S3 to simulate the sacral curvature, and the central angle (SCA), arc length (SAL) as well as arc radius (SAR) of the simulated sacral arc were calculated. A positive central angle was de ned if the arc central sat in front of the sacrum. The intraobserver and interobserver reliabilities of the measurements were determined using the intraclass correlation coe cient (ICC). The segmental morphology and curvature of sacrum were measured as sacral segmental vertebral angle (SSVA) and sacral segmental kyphosis (SSK) respectively, and a positive SSVA was de ned if vertex of the angle sat in front of the sacrum. The measurements of the sacral parameters were demonstrated in Fig. 2.

Statistics Analysis
Statistical analysis was performed using the Statistical Package for the Social Sciences (SPSS) for Windows, version 22 (Armonk, NY: IBM Corp). All data were expressed as mean ± standard deviation (SD). Kolmogorov-Smirnov test was employed to determine whether the parameters were normally distributed in the male and female cohorts. Variance discrepancy analysis was used to compare the difference among three or more groups. Differences in parameters between groups were evaluated by the t-test. Pearson Correlation Coe cient and Stepwise Regression Analysis were used to determine the relationship between PI and sacral morphological parameters. Statistically signi cant Pearson correlation coe cient was considered strong if greater than 0.5, moderate if larger than 0.3, and weak if greater than 0.1 11 . Differences were considered signi cant when p was <0.05.

Results
A total of 304 subjects were nally included in this study. The average age of the patients were 46.22 ± 15.92 years, and the average PI was 45.24±8.68°. The demographic data of the patients was shown in Table 1.

Radiographic measurements of pelvic incidence and sacral morphology
De nition and abbreviations of the radiographic measurements were listed in Table 2. Besides commonly used PI and STA, we introduced sacral incidence (SI), sacral segmental vertebral angle (SSVA) and sacral segmental kyphosis (SSK) to describe the segmental morphology of sacrum, and SCA, SAL as well as SAR to describe the overall sacral kyphosis. Most of the parameters were not different as affected by gender or age as shown in Table 3. However, by a correlation analysis strati ed by PI, almost all these sacral parameters were somewhat correlated with PI ( Table 4). The strongest correlation was identi ed between PI and S 1 I (r=0.791, p<0.01), and a multivariate regression analysis was performed to further con rm these correlations. As shown in Table 5, three parameters were nally con rmed to be closely correlated with PI: S 1 I, SSVA 1 and STA. Since S 1 I was most signi cantly correlated with PI, a linear regression equation between PI and S 1 I using the scatter diagram ( Fig 3A).

Discussion
The pelvis plays an important role as a mediator of sagittal balance in humans, and the sacrum is the junction which transfers loads from the spine to the lower extremity 13 . The anatomical characteristics of the sacrum must allow for the maintenance of bipedal posture as well as dynamic movements with minimal energy expenditure 14 . A more curved sacrum is considered to be a distinctive feature of homo sapiens 15,16 , and sacral curvature is minimal in tailed mammals and human infants, but increases with age in humans until reaches its skeletal maturity 17 . As pelvic incidence has also been reported to develop and change in a similar manner during human growth, which is thought as a result of erect posture and linked with numerous spinopelvic pathologies 18,19 , thus it's natural to relate the sacral curvature to PI together. There has been many reports showing that global sacral kyphosis correlates closely with increasing lumbosacral translation, sacral horizontal angle, lumbar lordosis, and lumbar index 6 . However, because of de ciencies in the conventional radiographic examination, the sacrum, acetabulum and hips were not included on spine radiograph in patients with lumbar spine disorders, and the association between pelvic incidence and sacral morphology is largely unknown.
As a parameter of the sagittal spine pro le, pelvic incidence describes the angulation of the sacrum in the pelvis in relation to the hip joints, and in uences force transmission thus has been associated with spondylolisthesis. Abola et al. 10 measured 120 cadaveric samples and found that a more curved sacrum, decreased sacral-ala width, and a more linear SI joint were related to an increased pelvic incidence.
However, we only found a weak correlation between sacrum curvature (SCA) and PI by the correlation coe cient analysis, and further regression analysis were not able to con rm the signi cance. Rather than the sacrum curvature, morphological parameters of S1: S 1 I, SSVA 1 and STA were found to be signi cantly correlated to PI. Morphological parameters of other sacral segments were also included in this study, but none of them were correlated to PI either.
STA is an anatomical parameter describing S1 rather than the curve of the sacrum. Inoue et al. 20 identi ed STA as a key anatomical sacral parameter in patients with spondylolisthesis. Compared to the control group, Wang et al. 21 revealed a signi cant decrease in STA in patients with L5-S1 spondylolisthesis, and that the slip grade is related to the decrease in STA. Whitesides et al. 22 indicated that STA may play a more important role than PI in the etiology of spondylolisthesis. We con rmed that STA is negatively correlated with PI, which corroborate the previous ndings and may serve as an explanation. For patients with high-grade spondylolisthesis, whose sacral endplate is always dome shaped, PI can be di cult to measure 12,23 . The newly suggested parameter (S 1 I) may have great potential in de ning the shape of the sacrum as well as the sagittal balance of the spine and may serve as an indirect parameter for the prediction of PI. However, more work is needed to validate the reliability of this new method.
Previously, two methods have been reported in the literature to measure, one using the standard Cobb angle method and the other with the Ferguson technique. Because the anterior and posterior aspects of the sacrum often appear eroded in spondylolisthesis, the Ferguson method has been thought more reliable than the Cobb method. Even so, manual tracing of standing lateral radiograph still have inherent error and aws, and reconstructed computed tomography scans would have given more information 24 . In this study, we introduced a new circle tting method based on the morphology of S1, S2, S3 to simulate the sacral curvature, and three parameters: SCA, SAL and SAR were used to describe the curvature of sacrum. Since SI joint involves primarily the rst three sacral vertebra and does not involve the last two sacral vertebra which curve is highly variable, we did not include S4 or S5. ICC analysis con rmed that this method has satisfactory intraobserver and interobserver reliabilities.

Conclusion
In this study, we introduced a new circle tting to measure the sacral curvature, and were not able to identify a signi cant correlation between sacral curvature and PI. The morphological parameters of S1 are more closely correlated with PI, and the sacral incidence of S1 might serve as a useful tool for the calculation of PI. This study has been approved by the institutional review board of Shanghai Ninth People's Hospital, and written informed consents were obtained from the all patients.

Consent for publication
All participants in this study have consent for publication.

Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests
Not applicable.

Funding
Not applicable.

Authors' contributions
Chen, Tian, Zhou and Zhang analyzed and interpreted the patient data. Chen and Tian were major contributors in writing the manuscript. Zhao designed this study. All authors read and approved the nal manuscript.
19. Mangione P, Gomez D, Senegas J. Study of the course of the incidence angle during growth.     Measurement of pelvic and sacral parameters. A. Measurement of PI, STA, S1I, SSK2 and SSVA3. Since S2 and S3 are ventrally wedged, the value of SSK2 and SSVA3 are de ned as positive. B. Measurement of SCA, SAL and SAR using the circle tting method. Direction of the curvature is de ned as positive in this schematic. C, D. Measurement of these above parameters on the CT images in the mid-sagittal plane.