2.1 CT-data

For this study, 17 axial CT scans of the thorax and abdomen were analyzed from a mixed-gender patient cohort (Patients 1–17, P1–P17). Patient ages ranged from 54 to 88 years. The CT data were retrospectively selected from existing images at the radiology department, where scans were originally performed for other medical purposes but incidentally showed spinal deformations, as confirmed by a senior orthopedic specialist. The data was accessed from 2017 until 2025 and was collected by the radiology department. The sole inclusion criterion was a visually lean patient habitus, resulting in a random distribution of deformity types and severities. They were anonymized prior to transfer to the research team, ensuring that the authors had no access to information that could identify the patient during or after the data collection. No additional CT scans were performed for this study.

To provide a comprehensive cohort description, each scan was classified by the same senior orthopedic specialist according to two criteria: curvature severity and affected spinal region. The severity classification used four categories based on Cobb angle measurements: spinal curve (<10°), mild (10–20°), moderate (20–40°), and severe (>40°) [46]. The affected spinal regions were categorized as: (a) high thoracic (apex between ), (b) thoracic (apex between ), (c) thoraco-lumbar (apex around ), (d) lumbar (apex between ). The detailed distribution of patients across these categories is provided in Table A1 in S1 Supplementary Information. However, due to the limited sample size of 17 patients resulting in single-subject representation in certain subgroups, the cohort was analyzed as a single entity.

All CT data were anonymized by the radiology department, and the study protocol was approved by the ethics committee of the Faculty of Medicine of the Technical University of Munich (Eth.nr. 569/16 S).

2.2 Independent implementation of the backshape-to-spine approach based on the principles described by Drerup

The backshape-to-spine approach, developed by Drerup and Hierholzer [6] and commercially implemented in the DIERS Formetric system, reconstructs the internal spinal alignment (ISL) directly from surface topography. The process begins with establishing a body-fixed coordinate system (Fig 1(1)) based on the automatically localized Posterior Superior Iliac Spines (PSIS) and the Vertebra Prominens [47]. Within this frame, the method automatically identifies the line of symmetry along the back surface [47], which serves as an approximation of the Spinous Process Line (SPL) (Fig 1(2)). The coordinates of the vertebral body centroids, which define the ISL, are subsequently derived using a trigonometric relationship that relates surface trunk rotation (STR) to ISL (Fig 1(3 and 4)):

(1)

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Fig 1. Step by step overview of Drerup’s backshape-to-spine approach.

(1) Reference coordinate system definition. (2) Estimation of the spinous process line (SPL). (3) Calculation of the surface trunk rotation (STR) angle. (4) Estimation of distance L and factor K. (5) Calculation of the internal spinal alignment (ISL) and Cobb angle.

https://doi.org/10.1371/journal.pone.0353213.g001

Here, represents the STR angle along the SPL, and K serves as a correction factor that accounts for the difference between surface rotation measured on the skin and the actual vertebral rotation. L(z) denotes the anatomical distance between the spinous process and the vertebral body centroid and can be calculated as follows:

(2)

where S represents the total spine length (). Finally, the reconstructed ISL is smoothed using analytical functions such as fifth order polynomials and frequency modulated sines (FMS), and the Cobb angle is calculated from the inflection points of the resulting curve in the coronal plane (Fig 1(5)). A detailed description of fundamental principles relating to the implementation of the complete backshape to spine approach by Drerup is provided in Text A2 of S1 Supplementary Information.

2.3 From CT image to dataset for backshape-to-spine-approach validation

Generating a validation dataset from CT images involves two distinct steps: extracting 3D surface models of the skin and vertebrae, and measuring relevant anatomical parameters from the extracted surfaces. While the first step utilizes established open-source tools for surface extraction from CT images, the second required the development of a novel algorithm to automatically define vertebral poses in accordance with standard recommendations.

2.3.1 Extraction of skin and vertebrae surfaces from CT data.

The data extraction from CT images focuses on two key anatomical structures: the patient’s skin surface and and the vertebrae from T₁ to L₅. Drerup’s method [6] ideally performs spinal analysis between C₇ and S₁; however, due to the limited field of view in the CT scans, the present analysis was restricted to the T1 to L5 range.

For skin contour extraction, we generate a surface mesh based on the CT data that serves as an equivalent to the rasterstereography-derived skin surface used in Drerup’s method [6]. This is accomplished by applying a marching cubes algorithm [48] to the CT scan’s scalar field, using an isosurface threshold that corresponds to the grayscale value of skin (Fig 2 (a)).

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Fig 2. Three-dimensional surface meshes extracted from computed tomography data.

(a) Skin surface extraction. (b) Vertebrae extraction. Both structures are depicted in coronal anterior, coronal posterior, and sagittal right views.

https://doi.org/10.1371/journal.pone.0353213.g002

Vertebrae extraction requires an additional preprocessing step of individual vertebrae labeling before vertebral surface generation. This was accomplished using deep learning-powered segmentation [49]. The labeled vertebrae were then extracted as surface meshes using the same marching cubes approach (Fig 2 (b)).

2.3.2 Defining vertebra poses from extracted 3D vertebra surfaces.

Vertebral pose is defined by the centroid of the vertebra body, which specifies the vertebra’s spatial location, and by the orientation, which describes its rotations , as illustrated in Fig 3. These rotations indicate how the three axes of the vertebral coordinate system (, , ) are oriented relative to a reference coordinate system.

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Fig 3. Extracted skin surface, vertebrae, and thorax from CT data, with vertebrae shown alongside their local coordinate systems defining vertebral pose.

The intersegmental spinal line (ISL, magenta) connects vertebral centroids, while the spinal process line (SPL, blue) connects the projections of vertebral centroids along the axial rotation in the transverse plane. Right panel illustrates an example vertebra coordinate system , the reference CT coordinate system (x,y,z), and the corresponding rotation angles .

https://doi.org/10.1371/journal.pone.0353213.g003

Accurately determining vertebral pose presents significant challenges due to the complex, non-uniform geometry of vertebrae. Conventional approaches typically rely on manually marking landmarks from CT data using 2D cross-sectional analysis [50–52]. These methods are prone to errors, particularly in axial rotation measurements when significant sagittal and/or coronal rotations are present, which is often the case [53], and they suffer from human judgment variability. More sophisticated three-dimensional numerical methods have been proposed [54] which overcome these limitations; however, none of them provide publicly available implementations ready for direct application.

To address these limitations, we present a novel, fully automatic algorithm for vertebral pose extraction based on robust symmetry detection principles. This algorithm is specifically designed to account for the imperfect symmetry of biological structures and remains insensitive to noise and tessellation artifacts common in 3D surface data.

The extraction of vertebral body centroids and vertebral coordinate systems from the vertebrae surface meshes is performed using a fully automatic algorithm, which operates on 3D data in two main steps: symmetry plane estimation and definition of vertebral coordinate systems following the recommendations of the International Society of Biomechanics (ISB) [55,56].

Symmetry Plane Estimation.

Since no vertebra is perfectly symmetric and surface mesh objects inherently contain noise and tessellation dependencies, the algorithm estimates a symmetry plane (violet plane in Fig 4 (a)) using two complementary methods: a symmetry measure established for CT data [54] and a symmetry-finding approach based on generalized moments [57]. The symmetry measure evaluates the difference between the original object and its reflection by calculating the average distance between corresponding points on both surfaces. Ideally, the plane with the lowest average distance indicates the true symmetry plane. However, this approach can yield false positives—where an incorrect plane produces a low average distance—due to natural biological asymmetries (e.g., unequal transverse processes and deformed spinous processes), data noise, or uneven mesh tessellation. The moment-based approach, specifically designed for real objects without perfect symmetry, is robust against noise artifacts and mesh tessellation variations commonly found in scanned or CT-extracted geometries. This approach uses the moment function introduced by [57], which quantifies the spatial asymmetry of a 3D body. The function calculates the sum of the perpendicular distances from each surface face center to an arbitrary symmetry plane passing through the center of mass, weighting each distance by its respective face area. The orientation of this plane is defined by two input angles. Potential symmetry plane candidates are identified by finding minima of the moment function—a necessary but not sufficient condition for symmetry. After these potential candidates for symmetry planes are identified, the symmetry measure is then applied only to these preselected symmetry plane candidates, thereby compensating for the measure’s sensitivity to noise and data imperfections.

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Fig 4. Vertebral pose extraction algorithm: (a) estimation of the symmetry plane (violet plane), (b) segmentation of the vertebral body (red body) and identification of the top and bottom plates (grey planes), (c) definition of the vertebral centroid (red point) as the midpoint of the line connecting the midpoints of the top and bottom plates, and (d) establishment of the local coordinate system (xy-plane: red, yz-plane: violet, zx-plane: green).

https://doi.org/10.1371/journal.pone.0353213.g004

Definition of vertebral local coordinate system.

Using the identified symmetry plane to isolate the vertebral body, a random sample consensus (RANSAC) algorithm [58] locates the vertebra’s top and bottom plates (grey planes in Fig 4 (b)).

Following ISB recommendations [55,56], the vertebral centroid is defined as the midpoint of the line connecting the geometric centers of the upper and lower endplates (red point in Fig 4 (c)).

While the standard ISB definition aligns the z-axis strictly with the endplate centers, we found this to be unstable for deformed vertebrae. To address this, we developed a novel modified orientation that incorporates the vertebral symmetry plane.

The coordinate system is then constructed as follows (Fig 4 (d)):

1. The y-axis is defined as the cross product of the symmetry plane normal and the mean of both endplate normals. Geometrically, this represents the intersection line between the symmetry plane and the average endplate planes.
2. The z-axis is calculated as the average of the mean of both endplate normals and the longitudinal vector within the symmetry plane (orthogonal to y).
3. The x-axis is determined as the cross product of the y and z axes.

This approach yields a more robust z-axis, particularly in complex and deformed vertebrae, and was validated by an orthopedic specialist through visual comparison of both definitions.

This completes the generation of the CT extracted dataset. By defining the skin surface, vertebral poses, centroids and endplate normals for each vertebra, the dataset now contains all necessary geometric information to derive any spinal and skin surface metric. The subsequent sections will focus specifically on calculating the parameters required to validate our CT extracted dataset using the Drerup’s backshape-to-spine approach [6].

2.4 Calculation of CT-derived ground truth parameters

To use Drerup’s backshape-to-spine approach to validate the applicability of our CT-derived dataset, we must first calculate the ground truth values for the key parameters identified in Section 2.2: the continuous parameters ISL, SPL, L, and as functions of the vertical coordinate z.

Although our vertebra pose extraction algorithm (Sec. 2.3.2) produces a set of discrete poses for each vertebra, the biomechanical constraints of the spine result in these poses naturally following a smooth, continuous path along the z-axis. This biological continuity allows us to construct accurate continuous representations along the z axis of both the vertebrae centroids (as ISL_true(z)) and the individual vertebrae rotations , using cubic Hermite spline interpolation between the discrete vertebral measurements. As a result, the continuous ISL_true(z) curve passes exactly through the vertebral centroids and inherits the tilts around the x- and y-axes from the individual vertebrae, since its derivatives at the centroids match those of the discrete vertebral orientations (Fig 3). Consequently, this approach yields an accurate and biomechanically plausible continuous representation of the internal spinal line obtained from discrete vertebra poses.

In Drerup’s model, vertebral rotation is approximated by the product of the STR angle and the factor K (Sec. 2.2). Consequently, the continuous vertebral rotation profile derived from the CT data defines the ground truth for this estimate. To provide a comprehensive validation, we also compute the ground truth STR angle, , directly along the true SPL derived from the CT surface. The reference parameter is derived through geometric projection of vertebral centroid coordinates () onto the skin surface, following the axial rotations measured from 3D vertebral orientations (Fig 3). The true anatomical distance between the spinous process and the vertebral centroid, , is then computed as the Euclidean distance between the SPL and ISL curves. The reference Cobb angle, , is computed according to Cobb’s definition [2] as the angle between the top and bottom plates of the two most inclined vertebrae—those exhibiting the greatest relative rotation around the y-axis—positioned above and below the apex, which is defined as the most laterally deviated vertebra.

2.5 Applying our Drerup-based implementation to the CT extracted skin surface

Since Drerup’s method solely uses surface topography, our Drerup-based implementation was applied to our CT-extracted skin surfaces to calculate the estimated parameters for each patient, following the procedure outlined in Section 2.2 using a constant factor K = 1. This yields a direct correspondence between the surface-derived estimates and the anatomical ground truth values calculated from the CT data, with the product of the STR angle and the factor K being the estimate for the vertebral rotation around the z-axis . The specific parameter pairs used for this comparative validation are summarized in Table 1.

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Table 1. Parameter pairs used for comparative validation.

https://doi.org/10.1371/journal.pone.0353213.t001

Because the original software for Drerup’s method is not publicly available, we developed an independent implementation based on the primary literature [6,41,47]. To successfully apply this framework to our specific patient cohort, we introduced three necessary adaptations to the standard protocol. First, the standard protocol relies on a body-fixed coordinate system defined by the posterior superior iliac spine (PSIS) and the vertebra prominens (C7). However, soft tissue deformation and age-related skin laxity in our older cohort rendered these surface landmarks unreliable in ten patients. Consequently, all parameters were calculated directly within the intrinsic CT coordinate system. To validate this adaptation, we quantified the alignment between the standard body-fixed frame and the CT coordinate system in the seven patients with clearly identifiable landmarks. This analysis demonstrated a strong correspondence, with average angular deviations below five degrees (Fig A3 in S1 Supplementary Information), confirming the validity of the CT coordinate frame for this analysis. Second, because the PSIS was frequently obscured, we bypassed the automated localization of the PSIS and C7. Beyond defining the body-fixed coordinate system, Drerup’s method utilizes these markers solely to calculate the parameter L (Eq. 2) and to guide the internal criterion for automated symmetry line detection. As the most suitable anatomical substitute, we instead utilized L4 and C7 coordinates that were manually identified and marked by an orthopedic specialist. Third, in one patient with severe thoracic scoliosis, the automated symmetry line identification [47] failed because the extreme lateral curve deviation extended too far beyond the standard longitudinal axis connecting the pelvis and C7. To resolve this, we manually traced a preliminary initialization line approximating the expected symmetry line. The algorithm then successfully identified the final symmetry line points based on this manually adapted initialization.

2.6 Validation

The method of automatically extracting datasets for verifying the backshape-to-spine approach is validated through two evaluations: (1) comparing automatically extracted vertebral poses using our algorithm with expert-annotated poses, and (2) applying our implementation of a well-established backshape-to-spine approach (Drerup’s method) on the CT-extracted dataset and comparing the results to existing literature values. The first evaluation assesses whether the extracted values fall within the range of expert annotations, despite their limitations as imperfect ground truth, which is discussed in Section 2.6.1. The second evaluation assesses the applicability of the CT extracted dataset for the validation of our Drerup-based implementation. If applying a well-established method to the extracted skin surfaces and validating the output against the CT ground truth yields results consistent with existing literature, it establishes its suitability for verifying backshape-to-spine approaches.

2.6.2 Evaluating CT dataset applicability for the validation of backshape to spine approaches using our Drerup-based implementation.

In this section, we use the extracted parameters summarized in Table 1 to calculate error metrics of the estimated values obtained from applying our Drerup-based implementation to the CT-extracted skin surface and the true values calculated from the CT data. For quantitative assessment, root mean square error (RMSE), mean absolute error (MAE) and standard deviation (STD) are used as metrics to evaluate deviations between estimated and true parameter values.

The error metrics are chosen so that they are comparable with previous validation studies of Drerup’s method, which are summarized and grouped according to types of ground truth parameters in Table 2.

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Table 2. Summary of validation studies of Drerup’s method. The table presents MAE and STD of Cobb angle, vertebral rotation and SPL(coronal) as well as RMSE for axial vertebra rotation and ISL(coronal). “Th” and “Lu” indicate that the results belong to the thoracic and lumbar curve regions, respectively. The categories “All,” “Mild,” and “Med./Sev.” refer to all types of spine curves, mild curves, and moderate to severe curves, respectively.

https://doi.org/10.1371/journal.pone.0353213.t002

To ensure a robust evaluation, we define the estimated Cobb angles as non-interpretable if the identified apex deviates from the true apex by more than one vertebral level, thus excluding anatomically implausible results.

At first, the deviation between estimated and true values of input and output parameters are analysed for each individual patient. Then, RMSE, MAE and STD are calculated for the continuous parameters ISL, SPL, L, and , by evaluating the functions along the spine at each true vertebral position from T1 to L5. For the Cobb angle, the absolute deviation between estimated and true values is reported for individual patients, and the MAE and STD of these deviations are calculated across all patients.

To enable comparison with prior work, RMSE is reported for ISL and axial rotation, while MAE and STD are presented for the remaining parameters.

To demonstrate the full utility of the CT-extracted dataset, a comprehensive analysis of parameter dependencies and error propagation in Drerup’s approach was conducted. As this detailed analysis falls outside the primary scope of this paper, the complete methodology and results are provided in the Text A4 in S1 Supplementary Information.

3.1 Comparison between expert annotated and automatically extracted vertebra poses

Table 3 presents the deviations between expert-annotated and automatically extracted vertebral poses. The similarity in MAE and STD values indicates consistent performance among annotators. Good agreement is observed between manual and automatic poses for the ISL parameter, while larger deviations are noted in vertebral rotations. Specifically, sagittal inclination () exhibits greater deviation compared to axial rotation and coronal tilt ( and ), which show comparable deviations.

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Table 3. Mean absolute error (MAE) and standard deviation (STD) of vertebra body centroids and vertebral rotations around the z, y, and x axes (, , ) across all patients. Annotators 1, 2, and 3 are the computational engineer, the mathematician, and the orthopedic specialist, respectively.

https://doi.org/10.1371/journal.pone.0353213.t003

3.2 Deviations of our drerup-based implementation on CT-extracted skin surfaces

Fig 5 details the deviations between the estimates (SPL, ISL, axial vertebral rotation and L) of our Drerup-based implementation applied to the CT-extracted skin surfaces and the CT ground truth parameters across all vertebral levels. The mean deviations for parameters (SPL, ISL and axial vertebral rotation) range around near zero, indicating an absence of systematic bias, while the L parameter shows a large negative bias. The results show high consistency across the cohort, with all individual trajectories falling within ±3 standard deviations of the mean.

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Fig 5. Deviations of SPL, ISL axial vertebral rotation and L between our Drerup-based implementation applied to CT-extracted skin surfaces and CT ground truth across vertebral levels.

The plots display individual patient data alongside the overall mean, ±1 and ±3 standard deviation.

https://doi.org/10.1371/journal.pone.0353213.g005

The MAE of SPL and L, as well as the RMSE of ISL and axial vertebra rotation calculated for each patient across vertebral levels T₁ to L₅ are shown in Fig 6. The mean MAE of SPL is 6.8 mm with a standard deviation of 2.8 mm, and the mean RMSE of axial vertebra rotation is 5.8° with a standard deviation of 2.0°. Both metrics show a relatively compact error distribution. In contrast, the mean RMSE of ISL is notably higher at 11.3 mm with a standard deviation of 5.0 mm. The ISL distribution shows significantly larger variance, including a prominent extreme value near 24 mm. The parameter L exhibits the largest errors, with a mean MAE of 27.3 mm and a standard deviation of 6.5 mm.

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Fig 6. MAE of SPL and L, and RMSE of ISL and axial vertebra rotation evaluated from vertebral levels T₁ to L₅ for each patient.

https://doi.org/10.1371/journal.pone.0353213.g006

The absolute errors of the coronal Cobb angle estimated using two fitting methods (described in detail in Text A2 in S1 Supplementary information), separated by the interpretability criterion defined in Sec 2.6.2 are presented in Fig 7. When considering all cases, the FMS fitting method () results in a lower MAE of 11.6° with a standard deviation of 8.5°, compared to the polynomial fit () which has an MAE of 13.5° and a standard deviation of 8.4°. Both error distributions in the unrestricted cohort show large variance and contain extreme outliers approaching 38°.

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Fig 7. Absolute deviations of coronal Cobb angle across the patient cohort for polynomial and FMS fitting methods.

The left panel: unrestricted cohort. The right panel: restricted cohort, obtained by excluding non-interpretable estimates of Cobb angle, defined as apex deviations exceeding one vertebral level from the anatomical reference established via the standard radiographic Cobb method.

https://doi.org/10.1371/journal.pone.0353213.g007

Excluding non-interpretable cases (apex deviations exceeding one vertebral level) significantly reduces the variance and eliminates extreme outliers across both fitting methods. In this restricted subset, the polynomial fit shows a similar MAE of 13.6° as when considering all cases but with a narrower standard deviation of 5.4°. The FMS fitting method demonstrates the highest overall accuracy on interpretable cases, reducing the MAE to 9.1° with a standard deviation of 4.2° and keeping all absolute errors at or below 15°.

4.1 Comparison with expert annotations

Deviations between expert-annotated and automatically extracted vertebral poses can be directly attributed to several specific factors. The deviation in the vertebral body centroid appears solely due to differences in endplate segmentation between expert and automatic methods, as the underlying approach for centroid calculation is identical in both methods. These differences are minimal, as reflected by small MAE values of 0.17 mm, 0.20 mm, and 0.25 mm for annotators (1), (2), and (3), respectively (see Table 3).

No significant differences were observed between annotators, as their MAE values fall within each other’s standard deviation ranges, as summarized in Table 3. This consistency suggests that the manual pose extraction protocol is robust and reliable.

Two primary factors that contributed to deviations in vertebral rotations are differing definitions of the z-axis and y-axis. For the z-axis, expert annotations strictly followed the ISB recommendations [55,56], which, as confirmed by an orthopedic specialist reviewing visual comparisons, sometimes resulted in a z-axis orientation that does not visually align with the vertebral orientation. In contrast, our automatic method defines the z-axis more robustly by incorporating the full information of both vertebra endplates and the symmetry plane.

Regarding the y-axis, expert annotations rely on a single landmark at the dorsal central aspect of the vertebral foramen, whereas the automatic method defines the y-axis based on the overall symmetry of the vertebral body. This difference in definition resulted in angular deviations with MAE values ranging from 1.77° to 2.61° across all vertebra rotations and annotators.

4.2 Comparison with literature

For the SPL in the coronal plane, averaged across all patients the MAE of 6.8 mm and STD of 2.8 mm (Fig 6) aligned with literature values MAE of 5.8 mm and STD of 2.28 mm (Table 2). Similarly, axial vertebra rotation was estimated with the average RMSE of 5.8° and STD of 2.0° over all patients (Fig 6), which is consistent with the range reported in prior studies (RMSE: 2.7°–7.9°, Table 2). These results suggest, that our Drerup-based implementation can be successfully applied to CT extracted skin surface, because the SPL and STR error margins align with those reported in previous studies that used conventional 3D surface scans and reference radiographs.

The parameter L exhibited deviations with an overall MAE across all patients of 27.3 mm and STD of 6.2 mm (Fig 6) that unfortunately cannot be directly compared to literature due to the absence of prior validation studies. These errors are predominantly systematic, as evidenced by the notable bias in the deviations across all patients in Fig 5, likely stemming from demographic discrepancies and our necessary methodological adaptation of using the L4 marker instead of S1. The linear relationship used for the estimation of L in Eq. 2 was originally derived for AIS patients [6] –a population typically comprising children and adolescents [1]– while our dataset included adult spinal deformities. Additionally, the anatomical distance from L4 to C7 is inherently shorter than the standard distance from S1 to C7, meaning this substitution naturally results in the observed systematic underestimation of L.

The average RMSE of 11.3 mm and STD of 5.0 mm of the estimated ISL in the coronal plane across all patients (Fig 6) was higher than the largest deviation with an RMSE of 6.4 mm reported by [64] (Table 2). Unfortunately direct statistical comparison is impossible due to absent patient-to-patient standard deviations in prior studies. The higher average RMSE observed here can be explained by two main factors: first, the large errors in L with an MAE of 27.3 mm (Fig 6); and second, the use of a synchronized dataset, which for the first time directly links the reference ISL and back surface. This increased methodological precision likely reveals error components that previous studies, which did not use synchronized data, could not capture, explaining the remaining difference above literature values.

The average MAE across all patients of the estimated coronal Cobb angle (Fig 7) of 13.5° with an STD of 8.4° using polynomial fitting and 11.6° with an STD of 8.5° using FMS fitting, were consistent with literature values (MAE of 11.2° and STD of 7.9° for 3D-Xray, Table 2).

The consistent alignment with literature values of the deviations for estimated SPL, axial vertebral rotation, and Cobb angle derived from our CT-based dataset using Drerup’s established backshape-to-spine approach [6], demonstrates the validity of using CT images to extract perfectly synchronized skin and vertebral data. This provides a reliable alternative for the verification of backshape-to-spine approaches, unlike the traditional combination of surface scans and 2D X-rays, which suffers from posture-induced alignment errors.

Beyond the primary validation, the extended analysis of methodological discrepancies and parameter dependencies in Text A4 in S1 Supplementary Information showcases our dataset’s capacity for detailed error tracking in future algorithmic development.

4.3 Limitations of the study and future work

Taken together, the presented results demonstrate that our method enables the derivation of a synchronized back surface and spine dataset from CT images, opening up the way to a reliable foundation for the verification of back-shape to spine approaches. However, several limitations of the present study must be mentioned.

First, a direct, isolated validation of our Drerup-based implementation—which was used to verify the applicability of our CT-based dataset—was not feasible. Such an isolated validation would necessitate reference data, such as the original datasets (or equivalent back-surface and X-ray cohorts) used in other validation studies, or pairs of commercial surface scan and CT scan from the same patients. This creates a coupled scenario where errors cannot be strictly isolated between our Drerup-based implementation and the variance introduced by our novel CT extracted dataset. However, we validated the system holistically: applying our implementation to our CT extracted data yielded error margins within reported ranges from literature. This consistency strongly supports both the accuracy of our implementation and the study’s main scope, the applicability of the CT data, despite the inability to perfectly decouple their individual error contributions. Second, all patients were scanned in the supine position, which leads to a different spinal alignment compared to the standing posture. This discrepancy may result in significant differences in Cobb angle measurements between supine and standing positions [66]. However, previous studies have shown that axial vertebral rotation remains largely unaffected by positional changes [59]. This suggests that, because the back surface and spine are captured simultaneously in a CT scan, any posture-induced spinal deformation is accompanied by corresponding changes in skin surface geometry. This synchronized adaptation preserves the fundamental relationship between the two structures. Consequently, analytical backshape-to-spine approaches like the one applied in this study, which rely on these geometric relationships, maintain their methodological validity despite the postural difference. However, the postural difference carries distinct clinical implications, as treatment decisions are strictly based on standing curve magnitudes. Statistical models trained exclusively on supine data would systematically underestimate curve severity if applied directly to standing patients. Therefore, any future clinical application of statistical algorithms developed using this dataset will require subsequent calibration or domain adaptation steps to translate supine-validated predictions into actionable, standing-equivalent metrics. Such adaptations are highly feasible given the established linear relationships between supine and standing measurements reported in the literature [67,68]. Third, direct contact between the back surface and the CT table can cause localized flattening of the skin, particularly in areas such as the hips and shoulder blades. While this effect was minimal in the lean patients of this cohort and did not impact SPL or rotation estimates, the obscuration of PSIS landmarks in individuals with higher body fat or age-related skin laxity represents a notable limitation.

Fourth, the limited sample size reduces the statistical power of the analysis, preventing a separate analysis of different scoliosis types and severity levels. Finally, the patients’ age range (54–88 years) does not correspond to the typical age range for adolescent idiopathic scoliosis (AIS) patients (10–18 years) [1]. Beyond limiting the direct generalizability of our findings to the AIS population, age-related skin laxity within this older cohort rendered standard anatomical landmarks unreliable in 10 patients. This forced a deviation from standard ISB recommendations, necessitating the use of the intrinsic CT coordinate system rather than a standard body-fixed coordinate system. However, within the context of a proof-of-concept validation, this skin laxity effectively served as a worst-case scenario. The observed error margins were comparable to the corresponding values from existing literature despite this tissue-level confounder, which demonstrates the robustness of our dataset generation method.

Based on the results of the present study, several directions for future work are planned to strengthen the validity and application of our approach. First, we will expand the patient cohort and CT extracted dataset to improve the statistical power and generalizability when used for STAM verification. Alongside this, we will also utilize Magnetic Resonance Tomography (MRT) scans, as outlined in the methods section 2, since the method requires only surface meshes of the vertebrae and skin, which can also be obtained from MRT imaging. Our initial reliance on a CT-based dataset rather than MRT was strictly driven by the lack of robust automated MRI segmentation tools during our study design in early 2024. Comprehensive whole-body MRI extraction tools, such as TotalSegmentator MRI, were not officially published until February 2025 [69], making their integration chronologically unfeasible for the current study. However, applying our approach to MRT data in the future not only increases the patient cohort size but, more importantly, allows inclusion of younger patients, as MRT scans are available for this group. Thus, we can extend the diversity of the patient cohort to better represent the targeted AIS population.

Finally, we believe that this work establishes a robust foundation for future research by providing a synchronized, CT-derived dataset that overcomes the limitations of unsynchronized back surface and spine alignment data as it was previously used [6,23,37–39,41,63–65]. Furthermore it enables reference measurements for all relevant parameters due to the comprehensive nature of CT imaging. The integration of validated biomechanical modeling with synchronized data will enable more precise error attribution to the analytical method itself, rather than to uncertainties in the underlying dataset, and will facilitate the development of next-generation, patient-specific analytical tools for spinal deformity assessment.