• sacrum;
  • statistical model;
  • fracture;
  • anatomy;
  • corridor


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The complex anatomy of the sacrum makes surgical fracture fixation challenging. We developed statistical models to investigate sacral anatomy with special regard to trans-sacral implant fixation. We used computed tomographies of 20 intact adult pelves to establish 3D statistical models: a surface model of the sacrum and the trans-sacral corridor S1, including principal component analysis (PCA), and an averaged gray value model of the sacrum given in Hounsfield Units. PCA demonstrated large variability in sacral anatomy markedly affecting the diameters of the trans-sacral corridors. The configuration of the sacral alae and the vertical position of the auricular surfaces were important determinants of the trans-sacral corridor dimension on level S1. The statistical model of trans-sacral corridor S1 including the adjacent parts of the iliac bones showed main variation in length; however, the diameter was the main criterion for the surgically available corridor. The averaged gray value model revealed a distinct pattern of bone mass distribution with lower density particularly in the sacral alae. These advanced 3D statistical models provide a thorough anatomical understanding demonstrating the impact of sacral anatomy on positioning trans-sacral implants. © 2014 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 32:1543–1548, 2014.

The sacrum exhibits a complex anatomy that is critical for treating sacral fractures. This is especially true in percutaneous minimally invasive osteosynthesis using sacroiliac screws[1] or trans-sacral implants,[2, 3] the latter being increasingly used in the treatment of sacral insufficiency fractures.[4] These fractures, occurring predominantly in osteoporotic patients, are isolated to the sacrum or a part of fragility fractures of the pelvic ring[5] and are typically located in the paraforaminal lateral region of the sacral ala.[6] Complex anatomy, reduced bone mass, and limited intraoperative visibility make adequate fixation difficult to achieve.

Trans-sacral implants must be placed through safe intraosseous pathways, also termed trans-sacral corridors. They extend laterally from the ilium, traversing the sacroiliac joint, passing through the vertebral body on level S1 or S2 to reach the contralateral side of the sacrum and the ilium. These pathways are bordered anteriorly by the cortex of the anterior sacrum, posteriorly by the vertebral canal, and superiorly and inferiorly by the adjacent neural foramen. In S1, the superior border is formed by the sacral ala.[7] The entrance and exit points are located on the outer surface of the iliac bone. In contrast to safe pathways for sacroiliac screws reaching the vertebral body, trans-sacral corridors are more limited in their critical diameter,[8, 9] exhibiting an oval shape.[7] Their 3D volume was previously computed in an automatic process.[7] The upper sacral anatomy was highly variable with up to 35% of the sacra called “dysmorphic”[10] providing only limited space to position implants on level S1. Surgical fracture fixation is further complicated by areas of different bone mass, especially in the osteoporotic, where screw anchorage is reduced due to decreased bone mass. An area of decreased bone mass (the “alar void”[11]) is located in the paraforaminal lateral region of the sacrum (the sacral ala), whereas in the vertebral bodies, bone mass is comparably higher.[12]

Trans-sacral safe pathways cover distinct anatomical volumes allowing dedicated implants to be placed safely. However, these volumes may display large inter-individual variation regarding size, shape, and available bone mass. These variables can significantly affect surgical decision making and hence the operative procedure.

We used innovative computed tomography (CT) based 3D statistical models to study the anatomy of the human sacrum, addressing the variability in size and shape and the impact on trans-sacral corridors. To assess bone mass distribution, we adopted methods of averaging CT gray values given in Hounsfield Units (HU).


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CT Imaging

A retrospective clinical series of 20 anonymized pelvic CT scans was used. Individuals with bony pathologies other than osteopenia or osteoporosis were excluded. The population consisted of 2 females and 18 males with a mean age of 57.2 years (28–78 years, std dev = ±12.5 years). Scans were performed with the multidetector CT scanners Siemens SOMATOM Sensation 64 and Siemens SOMATOM Definition (Siemens AG, Erlangen, Germany) using Kernel B45f. Data were saved in DICOM-format, CT values were given in HU, and the voxel size in x- and y-axis was 0.71–0.91 mm (mean 0.77) and 0.4–1 mm in z-axis (mean 0.91).

3D Statistical Modeling of the Sacrum

Processing, analysis, and visualization of the CT data was done using Amira software (Amira version 5.4.1, Visualization Science Group, Merignac Cedex, France). Image noise was reduced by applying a 3D median noise reduction filter. Subsequently, semiautomatic threshold segmentation of the sacrum was performed using predominantly axial slices (Fig. 1a). Osteopenic bone required manual segmentation, especially in the sacral foramina and canal. Triangulated meshed surface models of the sacrum were generated and saved in stl-format. These surfaces were processed with Geomagic Studio 2012 (Geomagic, Research Triangle Park, NC) using mesh repair and graphical smoothening.


Figure 1. (a) 2D CT view illustrating the segmentation process of the sacrum with boundaries around the external bony surface and the sacral canal and foramina. (b) 3D view of a segmented sacrum with landmarks lying in the sacral canal and foramina, anatomical (red dots) and non-anatomical boundary (yellow dots) landmarks. (c) Homologous surface mesh.

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To establish anatomical correspondence in all sacra, 42 homologous anatomical landmarks were manually placed by mouse click on meaningful anatomical structures such as bony prominences or intervertebral disc spaces (Fig. 1b). At regions with sharp edges they were connected with additional non-homologous landmarks. These non-homologous landmarks were replaced by calculating equidistant interpolated landmarks. Another 32 anatomical landmarks were positioned within the sacral foramina and the sacral canal to define the internal surface of the sacrum containing the neural structures.

The innominate bones were segmented and processed accordingly. On the anterior pelvis, an additional six anatomical landmarks were placed bilaterally on the symphysis, the anterior inferior, and superior iliac spines.

First, the surface of a single sacrum was taken as reference. Based on the anatomical landmarks, its mesh structure was warped on each of the remaining sacra by matching the homologous landmarks using thin plate spline (TPS)[13] transformation. The computation resulted in sacral models with a homologous mesh structure including identically located and numbered vertices and triangles (i.e., 25,000 homologous vertices and 50,000 triangles, Fig. 1c). These homologous surfaces were controlled by visual judgment and aligned using a non-scaled procrustes fit method.[14] The overall mean sacral surface was computed, and principal component analysis (PCA)[13, 15, 16] was conducted to assess shape and size variability of the 3D statistical model. The mean shape was calculated by averaging the coordinates of the vertices. The use of PCA allowed the calculation of the principal modes of variation. They were ordered in descending manner of variation from the mean shape.[17] Visualization in a semitransparent lateral view was obtained to study the impact of the sacral anatomy on the trans-sacral corridors.

3D Statistical Modeling of the Trans-Sacral Corridor S1

The surface model of each pelvis including both innominate bones and the sacrum was aligned according to the outlet projection definition[18, 19] to create consistent orientation. Therefore, the pelvis was adjusted in the frontal plane such that the upper part of the symphysis projected halfway between the disk spaces S1/2 and S2/3 using the landmarks on the surface of the innominate bones. A mathematical best fit plane (sagittal plane) was calculated from the symmetrical landmarks on the surface of the innominate bones and the symmetrical landmarks on the sacrum. After projecting the pelvis onto the sagittal plane, landmarks were positioned defining the limits of the trans-sacral corridor S1. The corridor volume was defined by laterally extending to both sides rectangularly until the outer border of the iliac bone was reached.

A cylindrical parameterization of the corridor surfaces in the pelvic outlet alignment was conducted to determine homologous vertices of the corridor triangles. On the mid-sagittal cross-section of the corridor, the intersection points of equiangular radial lines emanating from the center of the cross-section to the corridor's diameter limits were computed. Horizontal lines through these points intersecting with the outer surface of the iliac bone defined a homologous triangulation of each corridor (Fig. 2c). Additionally, the lateral parts of the corridor surfaces included the intersection points of the iliac bone surfaces with the horizontal lines through equidistant points on the radial lines connecting the center of the mid-sagittal cross-section and their intersection with the lateral corridor surface. Anatomical correspondence of vertices was defined by outlet alignment and cylindrical parameterization. Subsequently, standard PCA of the homologous horizontal corridor surfaces was computed.


Figure 2. Trans-sacral corridor visualized in oblique (a) and lateral (b) views. (c) Trans-sacral corridor model demonstrating the homologous triangulated structure; for illustrative purposes, rendered with a reduced number of triangles.

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The dimensions of trans-sacral corridors S1 and S2 were measured in the crancio-caudal and the antero-posterior (ap) diameter of the irrespective corridors on the 3D model of each sacrum after manually orientating it to obtain the largest possible corridor in a semitransparent lateral view.

Mean Bone Mass Distribution

The mean bone mass distribution was calculated by averaging the HUs of each voxel. The mean sacral model served as container. After elastic transformation of the mean shape to each sacrum, based on TPS transforms of the homologous surface vertices, each voxel was referenced to a voxel within the mean shape allowing the mean HU to be calculated. This mean HU distribution was visualized analogous to a diagnostic CT in various planes. A 7 mm diameter region-of-interest was placed in the sacral alae and the vertebral bodies on the transversal section centrally through trans-sacral corridors S1 and S2. The resulting HUs were measured with synedra View Personal (Version, synedra information technologies GmbH, Innsbruck, Austria).


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3D Statistical Model of the Sacrum

A large anatomical variation was found in the 1st and 2nd principal component (PC) concerning size and shape. Different anatomical features exhibited variability in morphological characteristics. The auricular surfaces changed notably in their vertical position. The sacral curvature and height and the configuration of the sacral alae varied significantly (Fig. 3). Morphological changes in the upper sacrum affected the trans-sacral corridor S1 by limiting its ovoid cross-section in the lateral semitransparent view. Conversely, the dimensions of trans-sacral corridor S2 changed only minimally as seen in 1st and 2nd PC.


Figure 3. 3D statistical model of the sacrum in frontal and semitransparent lateral view with 20 sacra included. Mean model with variations according to PCA (±3 std devs) shown in the 1st and 2nd PC. In the lateral view, the trans-sacral corridors can be appreciated. A large variability exists in the sacral anatomy, particularly in the sacral curvature, the configuration of the sacral alae, and the vertical position of the auricular facets. The lateral view illustrates the impact on the trans-sacral corridors.

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3D Statistical Model of the Trans-Sacral Corridor S1

The horizontal length was the major variation in the trans-sacral corridor S1 demonstrated by the 1st PC. The 2nd PC revealed the shape and size of the cross-section to be highly variable; particularly, the size variation limited the availability of a trans-sacral corridor (Fig. 4).


Figure 4. 3D statistical model of the trans-sacral corridor S1. Mean model (gray transparent) and variations according to PCA (±3 std devs) shown in the 1st and 2nd PC. The main variation in the 1st PC was the length (frontal view); in the 2nd PC the cross-section showed the largest variability. Frontal and sagittal views are visualized in different scale for illustration.

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The cranio-caudal diameter in S1 measured in the individual sacra was 15.9 mm (9–21, std dev = ±3.9), the ap diameter in S1 averaged at 27.4 mm (21–32, std dev = ±2.3). On level S2, the cranio-caudal diameter was 14.7 mm (11–19, std dev = ±2.3), the ap diameter showed a mean of 18.4 mm (16–22, std dev = ±1.9). In S1 and S2, the cranio-caudal diameter was always smaller and hence limiting except in one individual, where the ap diameter in S2 was 2 mm smaller.

Mean Model of Bone Mass Distribution

The mean CT gray values in HU were displayed in sagittal and axial reconstructions (Fig. 5). The highest densities were located in the cortical bone. In the trabecular bone a zone of relatively high HU values occurred in the vertebral bodies, whereas the alar region revealed less dense bone. This was quantified in the region-of-interest in the vertebral body on S1 with 161 HU (std dev = ±39) compared to 44 HU (std dev = ±39) in the sacral ala. On level S2, the vertebral body had a mean of 113 HU (std dev = ±20), whereas the sacral alae showed a mean of −7 HU (std dev = ±7).


Figure 5. 3D averaged gray value model of the sacrum given in HU including 20 sacra. The mean sacral model in transparent red served as container for elastically matched gray values. The averaged gray values in axial slices on level S1 (a) and S2 (b) and in the midsagittal plane (c) reveal a lower density in the sacral ala with increased bone mass in the vertebral bodies.

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The sacrum is a complex bone, formed by the fusion of 4–6 vertebrae.[20] In many cases, the fusion site potentially permits trans-sacral implant positioning within safe pathways to fix sacral fractures. Such surgical procedures are complicated by the variation in sacral anatomy and by reduced bone mass in osteoporotic individuals. Here, we used 3D models of the sacrum, the trans-sacral corridor S1, and the mean bone mass by applying advanced computational techniques to provide an understanding of sacral anatomy.

3D statistical modeling is a valid technique to analyze bony anatomy with its statistical variations.[17] PCA is a method in multivariate statistics clustering the 3D anatomical variability representing the largest variability in the 1st PC, the second most important variation in the 2nd PC and further PC having a gradually diminishing influence on the variability. Whitmarsh et al. published a 3D statistical model generated from 80 CT's of the proximal femur and confirmed main variations in the first three PC's to be the size of the bone, the neck-shaft-angle, and the neck length neck. Averaged bone mineral density (BMD) values were calculated within the mean shape, and a PCA was calculated demonstrating bone density variation.[21] Daruwalla et al. described a method using cylindrical parameterization in 21 CT scans of clavicles. They reported main variation in the 1st PC being length, width and thickness of the clavicles, and in the 2nd PC the anatomy varied in the lateral angle and depth.[22] van de Giessen et al. described a statistical shape model of the human lunate and scaphoid from 50 CT scans. The variations were less pronounced in the 1st and 2nd PC with ∼60% of the variation being covered by the first 5 PC's.[23] Kamer et al. studied the anatomy of the calvaria by calculating a statistical model using 80 CT scans. The 1st PC correlated significantly with the size, the 2nd and 3rd PC each with a spot of high variability in the temporal and the occipital region.[24] Using a TPS transformation to parameterize, Noser et al.[13] and Kamer et al.[15] reported scaled and unscaled evaluations of a fuzzy area typically affected in orbital fractures. In our study, TPS transformation was an appropriate method to parameterize the inside and outside surfaces of the sacrum. Semitransparent visualization allowed us to study the influence of the anatomy on the trans-sacral corridors by applying PCA. Due to the tube-like aspect of the trans-sacral corridors lacking distinct anatomical criteria, we adopted a cylindrical parameterization to calculate a 3D statistical model.

We consider PCA of the sacrum helpful in understanding size and shape variabilities and analyzing the impact on the trans-sacral corridors. The configuration of the sacral alae and the vertical position of the sacroiliac joints varied significantly. These were important anatomical structures narrowing the trans-sacral corridor S1, while trans-sacral corridor S2 was less influenced in the critical diameter. This was confirmed by manual measurements; however, our series did not contain a sacrum not allowing placement of a trans-sacral implant with a 7.3 mm diameter. Sacra offering only limited space for implant positioning in the upper sacrum were described as “dysmorphic,”[10] consisting of 14–35%[10, 25-27] in different series applying implants of 5–7.3 mm. A trans-sacral corridor was more consistently available on level S2 in these “dysmorphic” sacra[25-28] depending less on the variable 3D anatomy of the upper sacrum. The relationship between the upper sacral anatomy and the trans-sacral corridors was visualized in the PCA of the sacrum.

The 3D statistical model of the trans-sacral corridor S1 revealed length to be the main variable parameter as shown in 1st PC. The 2nd PC varied mainly in size and shape of the corridor's oval cross-section, hence affecting the dimensions to safely place trans-sacral implants. The knowledge about the previously described[7] oval cross-section, demonstrated by PCA to be relatively consistent in its shape, helps to position a trans-sacral implant using a radial safety zone to the limiting cortical structures.

The averaged gray value model of the sacrum revealed a distinct bone mass distribution. The trabecular bone displayed higher HU in the vertebral bodies and lower HU values located in the sacral ala (paraforaminal lateral) on the levels S1 and S2, correlating to findings with measurements in quantitative CT scans of 13 sacra.[12] Further, values in S2 were lower than in S1. The lower bone mass in the sacral ala impairs implant anchorage; hence, better purchase is given in the vertebral body.[29]

The use of routine clinical CT's to assess bone mass distribution represents a limitation in our study as there was no calibration to BMD values. However, in previous studies a good correspondence of HU in clinical CT's to BMD in dual-energy X-Ray absorption was demonstrated in the spine.[30-33] Further, due to limited spatial resolution[34] and the high content of yellow bone marrow,[35] bone density may be underestimated. The innominate bones, possibly also limiting trans-sacral corridors, were not incorporated into the statistical model of the sacrum. This study compromised a limited number of predominantly male sacra. For future work, increased information about sacral anatomy and the surgically important trans-sacral pathways could be provided by including more individuals into the statistical model and by investigating the influence of other factors, such as ethnicity, age and gender.

We conclude that 3D statistical modeling of the sacrum is a valuable approach to study the surgical anatomy relevant for trans-sacral fixation. The critical safe pathways are influenced by sacral anatomy and hence surgical decision making depends on analysis of the underlying sacral anatomy including the distinct bone mass. Trans-sacral implant positioning is often possible; however, screw purchase is best in the vertebral body and on level S1.


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We acknowledge the support of Dr. Karsten Schwieger. We thank Thomas Heldstab for his technical assistance and Dr. Jennifer Bara for revising the manuscript. Authors P.M. Rommens and T. Sawaguchi are members of the Pelvic Expert Group of the TK System, AO Foundation, Switzerland. D. Wagner received a research fellowship grant from the AO Research Institute Davos, Switzerland.


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