Automated Analysis of Vertebral Body Surface Roughness for Adult Age Estimation: Ellipse Fitting and Machine-Learning Approach

Abstract

Background/Objectives: Vertebral degenerative features are promising but often subjectively scored indicators for adult age estimation. We evaluated an objective surface roughness metric, the “average distance to the fitted ellipse” score (DS), calculated automatically for every vertebra from C7 to S1 on routine CT images. Methods: CT scans of 176 adults (94 males, 82 females; 21–94 years) were retrospectively analyzed. For each vertebra, the mean orthogonal deviation of the anterior superior endplate from an ideal ellipse was extracted. Sex-specific multiple linear regression served as a baseline; support vector regression (SVR), random forest (RF), k-nearest neighbors (k-NN), and Gaussian naïve-Bayes pseudo-regressor (GNB-R) were tuned with 10-fold cross-validation and evaluated on a 20% hold-out set. Performance was quantified with the standard error of the estimate (SEE). Results: DS values correlated moderately to strongly with age (peak r = 0.60 at L3–L5). Linear regression explained 40% (males) and 47% (females) of age variance (SEE ≈ 11–12 years). Non-parametric learners improved precision: RF achieved an SEE of 8.49 years in males (R² = 0.47), whereas k-NN attained 10.8 years (R² = 0.45) in women. Conclusions: Automated analysis of vertebral cortical roughness provides a transparent, observer-independent means of estimating adult age with accuracy approaching that of more complex deep learning pipelines. Streamlining image preparation and validating the approach across diverse populations are the next steps toward forensic adoption.

1. Introduction

Age estimation—alongside sex and stature assessment—is a critical step in establishing the identity of skeletal remains in forensic anthropological investigations [1]. Beyond this context, determining skeletal age is also essential in clinical forensic medicine [2], forensic radiology [3], and bio-archaeological research [1,4]. Accurate adult age attribution is far more than a taxonomic exercise: it underpins victim identification, informs medico-legal responsibility, and shapes demographic reconstructions. Casework experience shows that even a ±5- to 10-year misclassification can shift an unidentified skeleton into the wrong search stratum of missing persons databases or obscure a match when only partial antemortem information is available [1,5]. In the living, age estimates guide judicial decisions on criminal liability, asylum status and elite sport eligibility. Mansour et al. documented how erroneous age opinions in Hamburg led to both unwarranted detention and premature release of minors [2]. Radiology teams are therefore exploring automated pipelines that can infer age from routine imaging (e.g., chest radiographs [3]) or integrate multimodal deep learning forecasts [4] to tighten precision. However, classical morphoscopic methods remain limited by observer error and population specificity, prompting continuous refinement—such as transition analysis [6] and 3-D virtual validation of long-standing schemes in new populations [7]. Parallel biochemical, genetic, and epigenetic assays are now entering forensic practice, but they too report error bands that must be weighed against skeletal approaches [8]. Recent work even links inaccurate age estimation to biased interpretations of frailty and cause of death in paleopathological samples, illustrating how methodological drift can distort broader epidemiological narratives [9]. Collectively, these lines of evidence underscore the idea that improving the accuracy and transparency of adult age-estimation techniques—such as the surface roughness metric proposed here—is not merely an academic refinement but a prerequisite for ethical and legally defensible forensic science [10].

Although chronological age in subadults can be approximated with acceptable error margins by monitoring skeletal development [1,5,6], age estimation in adult populations remains a major practical challenge [1,10]. Adult methods exploit bone degeneration—so-called “wear-and-tear” changes—but the expression of these traits shows marked variability both among individuals and across populations [10]. Such heterogeneity stems from inter-individual and inter-population differences in genetic [7,8], environmental [7], and epigenetic influences [8], as well as variability in disease burden and overall health status [9], habitual physical activity [11], and body size [7]. Consequently, there is a substantial need for reliable alternative approaches to adult age estimation, and efforts to develop and standardize such methods are still ongoing [12,13].

Contemporary adult age-estimation protocols typically rely on skeletal indicators such as cranial suture closure, dental wear, auricular surface of the ilium, degenerative changes in the pubic symphysis, and the metamorphic stages observed at the sternal ends of the ribs [14]. Because current techniques do not yet yield sufficiently reliable results, the vertebrae have recently gained attention as one of the additional skeletal elements whose potential utility for age estimation is under active investigation [13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. Among vertebral indicators evaluated for adult age estimation, osteophyte formation has emerged as the most prominent feature [13,15,17,19,21,24,25,26,28,31]. Osteophytes are known to develop with advancing age at the margins of the intervertebral discs throughout the vertebral column. Additional age-related changes include deformation and increasing concavity of the vertebral bodies, as well as progressive ossification of the ligaments between adjacent vertebrae [17]. Additionally, cumulative micro-trauma, bone loss, and heightened osteoclastic activity with advancing age result in cortical thinning, increased porosity, and irregular indentations and protrusions. Collectively, these morphological alterations enhance the roughness of the bone surface [11].

Many techniques devised to characterize these vertebral surface changes still depend on subjective scoring systems [13,15,17,19,21,22,25,31]. Although numerous image-processing approaches could, in principle, provide an objective quantification of “roughness,” our literature survey revealed only a few studies that have addressed this issue directly [26,32,34]. One investigation explored the applicability of the convex-hull-derived volume ratio—a proxy metric for surface irregularity—and reported promising accuracy for vertebral age estimation [26]. In a separate study by the same team, the L4 vertebral body was smoothed using ITK-SNAP’s smoothing feature, and the maximum Hausdorff distance was then computed in MeshLab. This vertebral body roughness metric was subsequently used for age estimation [32]. In another study conducted by our group—designed as a preliminary investigation for the present project—we applied the newly proposed method to quantify roughness of the sacral base for age estimation and similarly obtained encouraging results [34].

In this cross-sectional study, we analyzed CT images of all 19 vertebral bodies from C7 to S1 in 176 living adults (21–94 years, 94 males and 82 females) using our previously introduced ellipse-fitting roughness algorithm. We hypothesized that vertebral cortical roughness would correlate positively with chronological age, providing a reliable indicator for adult skeletal age estimation. Furthermore, we aimed to show that this automated metric offers a repeatable, objective alternative to existing subjective scoring systems and can be readily adopted in future research and forensic practice.

The remainder of this article is structured as follows: Section 2 (Materials and Methods) describes the study cohort, CT acquisition parameters, the DS extraction workflow (image preparation, contour detection, ellipse fitting), and the statistical learning framework—each in its own numbered sub-section. Section 3 (Results) reports the descriptive statistics, sex-specific correlation patterns, and the comparative performance of linear, LASSO, and four machine learning regressors. Section 4 (Discussion) interprets the findings under nine thematic sub-headings: main results, comparison with conventional scores, contrast with deep learning pipelines, population/sex patterns, model diagnostics, practical applications, ethical–legal issues, biological rationale, and taphonomic considerations (Section 4.1, Section 4.2, Section 4.3, Section 4.4, Section 4.5, Section 4.6, Section 4.7, Section 4.8 and Section 4.9). Section 5 (Limitations) summarizes methodological constraints and avenues for improvement, while Section 6 (Conclusions) distills the key take-home messages and outlines future work. Appendix figures, full diagnostic plots, and the open-access dataset/code are provided in the Appendix A and Zenodo repository referenced at the end of the manuscript.

2. Materials and Methods

2.1. Sample Size and Demographics

A total of 176 adult CT examinations (94 males, 82 females) were included. Chronological age ranged from 21 to 94 years (Mean ± SD = 58.5 ± 14.0 y; males 57.0 ± 13.2 y, females 60.2 ± 14.7 y). Detailed age/sex distribution is provided in Figure A1, Figure A2 and Figure A3 and

Table A1. Descriptive statistics and age-group distribution of the study sample by sex. The upper panel summarizes central tendency measures (mean ± SD, median (IQR), and range) for age, while the lower panel lists absolute case counts in decadal age bins.

Measures of Central Tendency for Age
	Total Sample	Males		Females
N	176	94		82
Mean ± SD	58.5 ± 14.0	57.0 ± 13.2		60.2 ± 14.7
Median (IQR)	60.0 (18.8)	58.5 (17.3)		60.0 (20.3)
Range	21–95	21–85		25–95
Distribution of Cases According to Age Groups
Age Group	Males		Females
21–29	3		1
30–39	6		6
40–49	19		10
50–59	21		20
60–69	30		22
70–79	10		17
80–89	5		4
90–99	0		2

N: number of cases; SD: standard deviation; IQR: interquartile range.

.

2.2. Case Selection

This retrospective study was conducted at Van Yüzüncü Yıl University Dursun Odabaş Medical Center. Spine CT examinations performed between 1 January 2020 and 31 October 2023 were retrieved from the hospital picture-archiving and communication system. Adults aged ≥ 21 years who had a single thoracic–lumbar scan encompassing vertebrae C7 through S1 on the index date were screened for inclusion.

Inclusion criteria: (1) age ≥ 21 years; (2) CT series demonstrating the entire vertebral column from C7 to S1.

Exclusion criteria: (1) metabolic, endocrine, or neoplastic disorders—or prior fracture, surgery, or instrumentation—expected to alter bone density or morphology; (2) congenital anomalies affecting any vertebra between C7 and S1; (3) motion, metallic, or other artefacts obscuring cortical detail; (4) CT studies that omitted one or more of the target vertebrae.

Only individuals ≥ 21 years were eligible, because the vertebral ring-apophyses (secondary ossification centers) normally fuse with the vertebral body by 18–20 y in females and 19–23 y in males; after this epiphyseal closure, cortical topography reflects degenerative rather than growth-related remodeling, which is the biological signal our DS metric is intended to capture [15,30,35].

Electronic health record data were reviewed, under institutional ethics approval, to verify that no candidate met any exclusion criterion. To achieve random case selection, CT examinations were screened in reverse chronological order beginning on 31 October 2023 and working backwards until equal numbers of male and female adults (≥21 years), roughly equally distributed in age groups, with a single thoracic–lumbar series covering C7–S1 were found. The target of 100 men and 100 women was reached with scans dated 15 August 2022 or later. These 200 cases were then scrutinized for the predefined exclusion criteria, resulting in the removal of 18 women and 6 men. The final analytic cohort therefore comprised 176 individuals—82 women and 94 men.

2.3. Radiologic Imaging

In this study, surface roughness was quantified by scaling the boundary coordinates of the anterior half of the vertebral corpus superior end plate, isolated from 2D tomographic slices. The surface roughness metric is derived from the antero-superior end-plate cortex because:

(i)

This surface bears the highest compressive and shear loads during standing and flexion;

(ii)

Cortical porosity and scalloping on this face have been shown to increase monotonically with age [15,16];

(iii)

The outline of the intact anterior half approximates an ellipse in young adults, providing a mathematically convenient reference shape. The posterior half was purposefully excluded to avoid pedicle interference and because its load path is dominated by trabecular rather than cortical bone. By fitting a least-squares ellipse to the intact anterior rim and computing the mean orthogonal distance of every boundary node to that ellipse, we obtain a single, observer-independent roughness index that quantifies cumulative cortical remodeling.

Thoracic and lumbar CT scans were obtained in helical mode on either a 16-slice SOMATOM Emotion^® (software VA40A, Siemens Healthineers, Erlangen, Germany) or a 64-slice SOMATOM Sensation^® multidetector scanner (software VB10B, Siemens Healthineers, Erlangen, Germany) under the following parameters: 120 kVp, 120–150 mAs, collimation 16 × 1.5 mm, pitch = 1.1, and rotation time = 0.5 s. Raw data were acquired at 0.6–1 mm slice thickness and reconstructed as 1 mm axial and 2 mm sagittal/coronal multiplanar reformations using bone (B70) and soft-tissue (B30) kernels. The resulting DICOM datasets were reviewed in multiplanar mode on an ENLIL PACS^® workstation (v2.5.32.b622, ENLIL Yazılım ve Bilişim A.Ş., Istanbul, Turkey). The “Adjust Window” tool was used to set the window level (WL) to 162 HU and the window width (WW) to 16 HU. This narrow window compresses the gray-scale mapping so that cortical bone densities above 170 HU appear as high-contrast white (255 gray level), while densities below 150 HU appear as black (0 gray level), thereby sharpening the bone margins. Windowing was performed solely via a lookup table (LUT) transformation; neither the underlying CT attenuation values nor the geometric resolution were modified.

Scanner calibration and QC: Daily air calibration and weekly water-phantom checks are performed on both scanners. A Catphan 500 phantom is run monthly; water HU remains within 0 ± 4, high-contrast MTF is ≥50% at 0.5 Lp/mm, and geometric distortion is <1 mm across a 200 mm field.

Native resolution and resampling: Helical data are reconstructed to 0.6 mm isotropic voxels (512 × 512 matrix, FOV 320–380 mm; in-plane pixel ≈ 0.63–0.74 mm). For surface roughness analysis, volumes are resampled to 0.5 mm³ using third-order B-spline interpolation to standardize point-cloud density.

Noise suppression and artefact handling: A 3 × 3 median filter suppresses quantum mottle. Beam-hardening streaks are mitigated with Siemens iMAR (level 2) and residual outliers removed by HU sigma-clipping (μ ± 3 σ). Scans showing ring artefacts wider than one pixel were discarded (n = 6).

Surface-extraction pipeline: (i) Threshold > 170 HU → (ii) marching-cubes mesh → (iii) Laplacian smoothing, 3 iterations, λ = 0.5 → (iv) PCA alignment to the vertebral mid-sagittal plane → (v) ellipse fitting to the superior endplate. All steps run in Python 3.10 (scikit-image 0.23); average processing time ≈ 9 s per case.

For each of the 19 vertebral bodies from C7 through S1, the field of view was adjusted to the individual corpus orientation; an axial plane parallel to the superior endplate of each vertebra was identified, and that slice was exported for further analysis (Figure 1). A reference measurement was also recorded when saving each vertebral body’s superior endplate image to allow later standardization of measurements to millimeters.

2.4. Image Preparation

Each image was then imported into the ImageJ^® (Version 1.54g, National Institutes of Health, Bethesda, MD, USA) environment [36]. Because the anterior half of the vertebral body more closely resembles an ellipse—and because the pedicles would interfere with subsequent automatic edge detection—only the anterior surface was analyzed. To that end, a perpendicular scale line was drawn to span the anteroposterior length of the vertebral body, and from its midpoint the anterior half of the image was isolated. The physical length of the reference line (in millimeters) was noted, then its pixel length was measured using ImageJ’s straight-line length tool; these values completed the image-scaling step. Finally, all other bony and vascular structures falling within the field of view were removed via freehand selection and cutting, yielding an isolated anterosuperior endplate image ready for automated edge detection and further processing (Figure 2).

2.5. Image Processing

Numerous image-processing techniques have been developed to quantify the roughness of a surface or profile [37,38,39]. The “ellipse-fit + mean deviation” approach was first reported for laser-PBF-fabricated micro-struts. Hossain et al. [39] fitted an ellipse to micro-CT-derived strut cross-sections using a least-squares algorithm and defined $S_a$as the mean absolute orthogonal distance of each network node from the ellipse; they demonstrated that this roughness score increased systematically with build angle.

In the present study, we adapted this concept to quantify the anterior vertebral end-plate roughness, drawing on the observation that the end-plate geometry in young adults approximates an ellipse. By using the idealized ellipse as a “young/healthy” reference surface, the mean deviation reduces complex surface irregularities to a single, reproducible quantitative indicator. This adaptation of Hossain et al.’s [39] method to bone biomechanics provides a novel metric for vertebral aging studies.

Image segmentation and automatic contour extraction were implemented entirely in Python 3 using the OpenCV and NumPy libraries as follows:

First, each CT slice was loaded as a matrix I(x,y) of 8-bit grayscale pixel intensities (0–255). Otsu’s method was then applied to determine an optimal threshold θ, producing a binary mask

$$m\left(x,y\right)=\left\{\begin{array}{c}1, I\left(x,y\right)\ge \theta ,\\ 0, I\left(x,y\right)<\theta .\end{array}\right.$$

(1)

Next, external contour points

$$c={\left\{\left(x_i, y_i\right)\right\}}_{i=1}^L$$

(2)

were extracted via cv2.findContours(…, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_NONE) and only the largest contour—identified by ${arg max}_c Area\left(C\right)$ was retained to remove small noisy contours. To eliminate the effect of a perfectly horizontal baseline, we computed the most frequent contour y-coordinate

$$y^{\ast }=\genfrac{}{}{0pt}{}{argmax}{y}\left|\left\{\left(x_i,y_i\right) ϵ C:y_i=y\right\}\right|$$

(3)

and filtered out all points lying within τ = 2 pixels of that line:

$$C^{\prime }=\left\{\left(x_i,y_i\right)ϵ C: \left|y_i-y\ast \right|>\mathsf{\tau }\right\}.$$

(4)

This step preserves only the true surface undulations for subsequent analysis. The extracted coordinate points for each vertebral image of every subject were saved in separate CSV files. These CSV datasets were then parsed and passed on to the subsequent ellipse-fitting procedure.

Ellipse fitting was implemented in a Python 3 environment using NumPy, pandas, matplotlib, and SciPy.optimize as follows:

Each coordinate CSV was read into a data matrix

$$PϵR^{n\times 2}$$

(5)

via pandas. A coarse initial estimate of the ellipse parameters—center $(x_0,y_0)$, semi-axis lengths $a_0$ and $b_0$, and rotation angle ${\phi }_0$—was obtained by performing PCA on the covariance of P.

To prepare for optimization, the semi-axis lengths were log-transformed while preserving the center and rotation information, yielding an initial parameter vector $q_0$.

The trust-region-reflective least-squares algorithm (least_squares (…, method = ‘trf’)) was used to minimize a composite residual function comprising: the ellipse equation residual

$$r_i={\left({\displaystyle \frac{\left(x_i-x_c\right)cos\phi +\left(y_i-y_c\right)sin\phi }{a}}\right)}^2+{\left({\displaystyle \frac{-\left(x_i-x_c\right)sin\phi +\left(y_i-y_c\right)cos\phi }{b}}\right)}^2-1;$$

(6)

tangential penalties, which quantify how closely the contour endpoints satisfy the ellipse’s tangency condition; curvature penalties, enforcing adherence to the expected curvature at reference points; and an eccentricity constraint, penalizing any value of

$$\log \left({\displaystyle \frac{b}{a}}\right)$$

(7)

that exceeds a predefined threshold $r_{max}$. From the optimized parameters ($x_c,y_c, a, b, \phi$), the nearest-point Euclidean distance of each contour point to the fitted ellipse was computed, and the mean error was reported as the average of these distances. The resulting mean error was adopted as a quantitative roughness index for the anterior surface of the superior endplate and termed the “average distance to the fitted ellipse” score (DS) (Figure 3 and Figure 4).

2.6. Statistical Analysis

The analyses were conducted in two complementary environments. First, IBM SPSS Statistics v27.0 (IBM Corp., Armonk, NY, USA) was used to screen the data for normality, identify extreme outliers (±3 SD), and compute Spearman correlation coefficients between chronological age and each of the 19 anterior-vertebral metrics.

All predictive models were then implemented in Python v3.10 (Python Software Foundation, Wilmington, DE, USA) with scikit-learn 1.4 and statsmodels 0.14. For each sex, the data were split once into an 80% training set and a 20% hold-out test set, after which 10-fold cross-validation (shuffled, random_state = 42) was applied inside the training portion for hyper-parameter tuning. Continuous predictors were z-standardized within every fold to avoid information leakage; tree-based algorithms, although scale-invariant, were embedded in the same pipeline for consistency.

Before modelling, the entire sample (n = 176) was subjected to an analysis of covariance (ANCOVA) in which chronological age was regressed on (1) sex as a fixed factor, (2) the 19 vertebral metrics as covariates, and (3) all first-order sex × metric interaction terms. The joint Wald test indicated that at least one sex-related coefficient differed significantly from zero (min p = 0.007). Consequently, all subsequent regressions were fitted separately for men and women. Within each sex, the modelling sequence began with multiple linear regression in SPSS to establish a classical benchmark (adjusted R² and the standard error of the estimate, SEE). A LASSO model was then trained in Python; its α regularization parameter was selected from a log-spaced grid (10⁻³–10¹) that minimized cross-validated mean absolute error. LASSO’s coefficient shrinkage provided a sparse predictor subset that guided the interpretation of non-parametric learners.

Four machine learning algorithms were evaluated in parallel. Support vector regression (SVR) mapped the scaled input into a high-dimensional Gaussian kernel space, where ε-insensitive loss produced a smooth regression surface; the cost (C), kernel width (γ), and ε parameters were grid-searched. Random forest (RF) regression aggregated 100–250 boot-strapped decision trees, with maximum depth varied to balance bias and variance; the method captures nonlinear interactions without explicit parametric assumptions. The k-nearest neighbors (KNN) regression provided a purely instance-based model in which each prediction is the mean age of the k nearest (Euclidean) neighbors; k was tuned between three and seven. Finally, a custom Gaussian naïve-Bayes regressor discretized age into equal-frequency bins, fitted a Gaussian-NB classifier to the binned labels, and projected its probabilistic output back to the continuous scale via bin mid-points—an approach suited to small samples when normality is plausible.

Model performance was quantified on the unseen test sets with mean absolute error (MAE), root mean squared error (RMSE), and the coefficient of determination (R²). In addition, the standard error of the estimate was reported, computed for every model as

$$SEE=\sqrt{{\displaystyle \frac{\sum _{i=1}^n\left(y_i-{\mathrm{ý}}_i\right)}{n-k-1}}}$$

(8)

where n is the number of cases in the relevant sex-specific subsample and k is the number of retained predictors (for LASSO, the non-zero coefficients). Separate SEE values facilitated direct comparison with earlier vertebral age-estimation studies that present sex-specific error bands. All analyses were executed with fixed random seeds and fully version-controlled scripts, ensuring complete reproducibility.

A schematic overview of the entire six-step pipeline, from CT retrieval to statistical validation, is presented in Figure 5.

3. Results

3.1. Descriptive Statistics

The overall mean age of the sample was 58.5 years (median = 60.0; range = 21–95; SD = 13.9). Mean age was 56.9 years for men (median = 58.5; range = 21–85; SD = 13.2) and 60.2 years for women (median = 60.0; range = 25–95; SD = 14.7). The age distributions of male and female participants did not differ significantly (p = 0.128) (Appendix A Figure A1, Figure A2 and Figure A3).

Table 1. Sex-specific descriptive statistics for distance to fitted ellipse roughness score.

Variable	Male (N = 94)				Female (N = 82)				p
	Mean ± SD	Median	Min–Max	95% CI	Mean ± SD	Median	Min–Max	95% CI
C7 DS	0.33 ± 0.34	0.24	0.09–2.93	0.26–0.40	0.35 ± 0.34	0.26	0.09–2.23	0.28–0.43	0.917
T1 DS	0.30 ± 0.15	0.27	0.08–1.02	0.27–0.33	0.34 ± 0.28	0.27	0.08–1.68	0.28–0.40	0.991
T2 DS	0.33 ± 0.22	0.26	0.06–1.73	0.28–0.37	0.30 ± 0.20	0.24	0.06–1.17	0.25–0.34	0.136
T3 DS	0.33 ± 0.16	0.30	0.10–1.22	0.29–0.36	0.27 ± 0.15	0.25	0.08–1.03	0.24–0.30	0.005 *
T4 DS	0.35 ± 0.16	0.31	0.10–0.90	0.32–0.38	0.27 ± 0.18	0.22	0.08–1.19	0.23–0.31	0.000 *
T5 DS	0.33 ± 0.18	0.28	0.09–1.28	0.29–0.36	0.32 ± 0.47	0.24	0.09–4.30	0.22–0.42	0.022 *
T6 DS	0.35 ± 0.20	0.31	0.12–1.24	0.30–0.39	0.29 ± 0.23	0.24	0.02–1.54	0.24–0.34	0.003 *
T7 DS	0.30 ± 0.19	0.23	0.10–1.16	0.26–0.34	0.27 ± 0.17	0.23	0.06–0.96	0.24–0.31	0.374
T8 DS	0.32 ± 0.22	0.25	0.08–1.13	0.27–0.36	0.28 ± 0.21	0.22	0.06–1.34	0.23–0.32	0.135
T9 DS	0.31 ± 0.17	0.27	0.09–0.94	0.27–0.34	0.33 ± 0.25	0.23	0.07–1.43	0.28–0.39	0.801
T10 DS	0.39 ± 0.29	0.30	0.08–1.62	0.33–0.45	0.33 ± 0.22	0.25	0.09–1.01	0.28–0.38	0.073
T11 DS	0.48 ± 0.30	0.40	0.08–1.41	0.41–0.54	0.36 ± 0.30	0.27	0.07–1.68	0.29–0.42	0.000 *
T12 DS	0.46 ± 0.31	0.39	0.11–1.64	0.40–0.52	0.41 ± 0.46	0.28	0.08–3.18	0.31–0.51	0.021 *
L1 DS	0.41 ± 0.25	0.33	0.03–1.13	0.36–0.46	0.31 ± 0.16	0.25	0.07–0.88	0.28–0.35	0.009 *
L2 DS	0.57 ± 0.39	0.46	0.10–1.79	0.49–0.65	0.49 ± 0.38	0.35	0.10–1.97	0.41–0.58	0.112
L3 DS	0.62 ± 0.40	0.50	0.13–2.02	0.54–0.70	0.62 ± 1.13	0.41	0.12–10.25	0.38–0.87	0.094
L4 DS	0.74 ± 0.55	0.61	0.13–2.58	0.63–0.85	0.68 ± 0.47	0.53	0.12–1.93	0.58–0.78	0.633
L5 DS	0.61 ± 0.36	0.52	0.15–1.63	0.54–0.68	0.65 ± 0.56	0.47	0.13–3.57	0.53–0.78	0.622
S1 DS	0.56 ± 0.31	0.47	0.15–1.96	0.50–0.63	0.66 ± 0.43	0.53	0.20–2.61	0.57–0.76	0.079

DS: the score of average distance to fitted ellipse. *: p value < 0.05; there is a statistically significant difference between the two sex groups in terms of the relevant variable.

presents sex-specific descriptive statistics for the DS. With the exception of the upper thoracic levels, the central tendency and spread of DS values are broadly similar in men and women (e.g., C7: 0.33 ± 0.34 vs. 0.35 ± 0.34).

Statistically significant sex differences are confined to a contiguous mid-thoracic band—T3 through T6, as well as T11, T12, and L1—where women show systematically lower roughness than men (mean gap ≈ 0.05–0.08 DS units). No significant differences emerge in the lumbar bodies L2–L5 or in S1, and variability (min–max range and SD) is comparable across sexes except at T5 and L3, whose female distributions are widened by a few high-roughness outliers. These findings indicate that sexually dimorphic surface ageing is most pronounced in the mid-thoracic region, whereas lumbar roughness—key to the predictive models—does not differ between males and females.

3.2. Correlation Between Age and Vertebral Surface Roughness (

Table 2. Correlation between chronological age and vertebral metrics in males and females.

	Males		Females
Variable	r	p	r	p
C7 DS	0.089	0.395	0.194	0.081
T1 DS	−0.108	0.301	0.096	0.392
T2 DS	−0.039	0.711	0.355	<0.01 (*)
T3 DS	0.078	0.453	0.334	<0.01 (*)
T4 DS	0.014	0.893	0.362	<0.001 (**)
T5 DS	0.059	0.575	0.314	<0.01 (*)
T6 DS	0.129	0.214	0.287	<0.01 (*)
T7 DS	0.279	<0.01 (*)	0.352	<0.01 (*)
T8 DS	0.324	<0.01 (*)	0.522	<0.001 (**)
T9 DS	0.322	<0.01 (*)	0.459	<0.001 (**)
T10 DS	0.352	<0.001 (**)	0.471	<0.001 (**)
T11 DS	0.284	<0.01 (*)	0.367	<0.001 (**)
T12 DS	0.175	0.092	0.324	<0.01 (*)
L1 DS	0.280	<0.01 (*)	0.495	<0.001 (**)
L2 DS	0.424	<0.001 (**)	0.553	<0.001 (**)
L3 DS	0.600	<0.001 (**)	0.509	<0.001 (**)
L4 DS	0.448	<0.001 (**)	0.538	<0.001 (**)
L5 DS	0.395	<0.001 (**)	0.588	<0.001 (**)
S1 DS	0.403	<0.001 (**)	0.074	0.508

* p < 0.01; ** p < 0.001; DS: the score of average distance to the fitted ellipse.

; Figure 6 and Figure 7)

In males, 11 of the 19 DS variables correlated significantly with age (p < 0.05). The strongest association was observed at L3 (r = 0.60, p < 0.001), followed by L4, L2, S1, and L5 (r = 0.40–0.45, p < 0.001). Mid-thoracic roughness (T8–T11) showed weaker but still meaningful correlations (r ≈ 0.32–0.35), whereas DS for the upper thoracic and cervical levels (C7, T1–T5) was essentially unrelated to age (r ≤ 0.13, p > 0.20).

Female results displayed the same cranio-caudal gradient but with uniformly higher coefficients: 15 DS variables were significant, the top five again belonging to the lumbar spine—L5 (r = 0.59), L2, L4, L3, and L1 (all r ≥ 0.49, p < 0.001). Thoracic DS at T8–T11 ranked next (r ≈ 0.36–0.52). Cervical (C7) and upper-thoracic (T1) scores remained nonsignificant, mirroring the male findings. Of note, the sacral base (S1) correlated with age in males (r = 0.40, p < 0.001) but not in females (p = 0.51).

Taken together, the results demonstrate a moderate-to-strong, sex-specific monotonic increase in vertebral surface roughness—quantified by DS—from the mid-thoracic region down to the lumbar spine, with the lumbar levels providing the clearest chronological signal.

3.3. Multiple Linear Regression (

Table 3. Multiple linear regression of average distance to the fitted ellipse scores (DS) on chronological age.

Statistic	Females (n = 81)	Males (n = 94)
R	0.685	0.631
R2	0.469	0.399
Adjusted R2	0.304	0.244
SEE (years)	12.29	11.44
F (df)	2.84 (19, 61)	2.58 (19, 74)
Model p	0.001	0.002
Max VIF (variable)	3.22 (L2 DS)	2.36 (T8 DS)
Min tolerance (variable)	0.311 (L2 DS)	0.424 (T8 DS)
Max condition index	17.3	17.6
Collinearity flag	none	none

)

The sex-specific linear models explained a moderate share of age variance. In women, the 19 DS predictors jointly accounted for 47% of the variability (adjusted R² = 0.304) with a standard error of the estimate (SEE) of 12.3 years, whereas the male equation explained 40% (adjusted R² = 0.244; SEE = 11.4 years). Both regressions were highly significant (F = 2.8–2.6, p ≤ 0.002).

Collinearity diagnostics indicated that redundancy among the vertebral DS scores was mild and well below critical thresholds in both sexes: the highest variance-inflation factor was 3.22 (tolerance = 0.311) in females and 2.36 (tolerance = 0.424) in males, and the largest condition indices were 17–18 (far short of 30). Consequently, no predictor was removed.

At the individual coefficient level, none of the female DS terms reached the 0.05 threshold, suggesting that age information is distributed across several lumbar and lower-thoracic sites rather than concentrated in a single level. In the male model, only the L3 score (β = 0.43, p = 0.002) remained significant after mutual adjustment, reinforcing the univariable finding that the caudal lumbar surface contributes most strongly to male age estimation. Despite these differences in term-level significance, the overall SEE values for both sexes lie within the 11–12-year band that is considered acceptable in previous vertebral age-estimation studies.

3.4. LASSO Regression

LASSO regression—with the same optimal penalty (α = 2.06) for both sexes—reduced the 19-level DS panel to a very compact set of age predictors. In men, the algorithm retained only the upper-lumbar surfaces, L3 (β = 4.27) and L2 (β = 0.68); this two-variable equation explained 30% of the test-set variance (R² = 0.30) with a root mean square error of 11.2 years (SEE = 12.2 y on the test fold; 11.4 y when refitted to the full sample). In contrast, the female solution was more diffuse, keeping eight coefficients—four lower-thoracic (T2, T4, T8, T9) and four lumbar (L1, L2, L4, L5)—all positively signed, with T8 and T9 carrying the largest weights (β ≈ 2.0). This broader lumbar-plus-thoracic set captured 47% of the test variance (R² = 0.47), yielding a test SEE of 13.5 years (12.5 y on the combined dataset). Thus, while LASSO confirmed the primacy of lumbar roughness in males, it highlighted a mixed thoracolumbar ageing pattern in females; in both cases, the shrinkage approach produced SEE values comparable to—and slightly lower than—the corresponding multilinear models, but with far fewer parameters.

3.5. Machine Learning Models (

Table 4. Performance of four machine learning regressors for age prediction.

Sex	Model	Holdout R2	95% CI (R2)	SEE (y)	95% CI (SEE)	MAE (y)	RMSE (y)	CV R2	OOB R2 †
Male	RF	0.468	−0.01–0.67	8.49	5.8–10.9	6.69	8.49	0.432	0.446
Male	SVR-rbf	−0.184	−1.37–0.32	12.65	9.0–15.8	10.39	12.65	0.442	—
Male	SVR-lin	0.118	−0.70–0.41	10.92	7.6–14.0	8.77	10.92	0.098	—
Male	KNN	0.257	−0.79–0.66	10.03	6.3–13.5	7.12	10.03	0.367	—
Male	GNB-Reg	−1.147	−4.30–−0.13	17.04	13.0–21.0	14.46	17.04	−0.120	—
Female	RF	0.221	−0.74–0.73	12.83	5.9–18.4	9.06	12.83	0.374	0.418
Female	SVR-rbf	0.097	−0.69–0.42	13.81	9.6–17.5	10.85	13.81	0.311	—
Female	SVR-lin	−0.271	−2.10–0.41	16.39	9.9–22.5	12.11	16.39	0.153	—
Female	KNN	0.448	−0.26–0.77	10.80	6.3–14.8	7.98	10.80	0.304	—
Female	GNB-Reg	−0.202	−1.77–0.33	15.94	11.9–19.5	14.04	15.94	−0.080	—

R² = coefficient of determination; SEE = standard error of the estimate; MAE = mean absolute error; RMSE = root mean squared error; CV R² = mean 10-fold cross-validated R² calculated on the 80% training split; OOB R² = out-of-bag R² (internal validation metric computed only for random forest); CI (95%) = two-sided percentile bootstrap confidence interval based on 1000 resamples of the external test set; RF = random forest regressor; SVR = support vector regression; KNN = k-nearest neighbors regressor; GNB-Reg = discretized Gaussian naïve-Bayes pseudo-regressor. † Out of Bag R² is calculated only for the Random Forest model.

)

The discretized Gaussian naïve-Bayes (GNB) baseline performed worst in the male series, with a hold-out R² = −1.15 (95% CI −4.30 to −0.13) and a standard error of the estimate (SEE) of 17.0 y (MAE 14.5 y, RMSE 17.0 y). Internal 5 × 5 cross-validation (CV MAE 10.3 y; CV R² = −0.12) had predicted markedly smaller errors, confirming that the algorithm memorized the development set and systematically over-estimated younger males and under-estimated older ones.

The k-nearest neighbor (KNN) regressor provided an intermediate male result: hold-out R² = 0.26 (95% CI −0.79 to 0.66) with SEE = 10.0 y (MAE 7.1 y, RMSE 10.0 y). This is ≈ 2 years more precise than GNB. A slightly higher CV R² = 0.37 indicates a mild but acceptable optimism gap; KNN narrows the error margin by ~1 year relative to multiple linear regression.

After nested tuning (C = 100, γ = 0.01, ε = 0.1), the radial-kernel SVR (RBF-SVR) achieved a hold-out R² = −0.18 (95% CI −1.37 to 0.32) and SEE = 12.7 y (MAE 10.4 y, RMSE 12.6 y). Although CV R² rose to 0.44, the independent test split revealed substantial over-fitting and only marginal improvement over linear regression.

The linear-kernel SVR yielded modest explanatory power: hold-out R² = 0.12 (95% CI −0.70 to 0.41) with SEE = 10.9 y (MAE 8.8 y, RMSE 10.9 y). A similar CV R² = 0.10 shows the model captures little nonlinear structure and performs between KNN and RBF-SVR.

The random forest (RF) ensemble delivered the best male accuracy, achieving a hold-out R² = 0.47 (95% CI −0.01 to 0.67) and SEE = 8.5 y (MAE 6.7 y, RMSE 8.5 y). Internal validation was consistent (CV R² = 0.43; OOB R² = 0.45), indicating stable generalization with minimal optimism. Compared with KNN, the forest reduces the standard error by ~1.5 years and almost doubles explained variance, confirming it as the preferred male learner.

In the female sample, discretized GNB again failed to capture the ageing signal: hold-out R² = −0.20 (95% CI −1.77 to 0.33) with SEE = 15.9 y (MAE 14.0 y, RMSE 15.9 y). A slightly negative CV R² = −0.08 confirms that poor generalization stems from model bias rather than data scarcity.

The female KNN explained 45% of the external variance (hold-out R² = 0.45; 95% CI −0.26 to 0.77) with SEE = 10.8 y (MAE 7.98 y, RMSE 10.8 y) and a CV R² = 0.304. It halves the SEE relative to GNB and represents the current benchmark for women.

The female RBF-SVR offered only marginal benefit: hold-out R² = 0.10 (95% CI −0.69 to 0.42) with SEE = 13.8 y (MAE 10.9 y, RMSE 13.8 y). CV R² = 0.31 suggests a small optimism gap, yet the model remains ~3 years less precise than KNN and only slightly better than GNB.

The female linear SVR was weaker still, returning a negative hold-out R² = −0.27 (95% CI −2.10 to 0.41) and SEE = 16.4 y (MAE 12.1 y, RMSE 16.4 y). With CV R² = 0.15, it ranks at the bottom of the female hierarchy.

The female random forest provided a middle-ground solution: hold-out R² = 0.22 (95% CI −0.74 to 0.73) and SEE = 12.8 y (MAE 9.1 y, RMSE 12.8 y). Internal metrics were stronger (CV R² = 0.374; OOB R² = 0.418), indicating honest generalization. The forest trims the SEE by ~3 years compared with RBF-SVR and ~4 years compared with GNB or linear SVR yet remains ≈ 2 years less precise than KNN.

In sum, random forest is the clear winner for men, whereas KNN remains the top performer for women. SVR variants offer only incremental gains, and both naïve-Bayes and linear SVR are unsuitable as stand-alone forensic tools.

Across the male sample, diagnostic panels converged on a clear performance hierarchy. Random forest (RF) emerged as the only algorithm that balanced bias and variance: L3–L4 dominated its permutation importance profile, residuals were tight and unbiased, and learning curves showed high but not perfect training R² (~0.9) with steadily rising CV R², yielding the narrowest limits of agreement (≈±17 y). K-nearest neighbor (KNN) relied on a broader lumbar-plus-lower-thoracic pattern; its residuals were symmetric and homoscedastic, but a plateauing CV R² (~0.25) revealed variance limitation, placing KNN as a serviceable—but clearly inferior—fallback to RF. In contrast, both support vector regressors were hampered by bias: the RBF kernel latched onto upper-lumbar levels, dramatically over-aged young men and under-aged older ones, and displayed a steep residual slope, while the linear kernel compressed predictions into a 50–65 y band, leaving large age-dependent errors; their learning curves showed either near-perfect memorization (RBF) or persistent under-fit (linear). The discretized Gaussian naïve-Bayes (GNB) fared worst: it effectively used a single mid-lumbar predictor and produced age “plateaus,” a funnel-shaped residual pattern, bimodal error distribution, and extreme over-fitting (train R² > 0.95, CV R² < 0.10). Taken together, RF is the only model with real forensic promise, KNN provides a bias-free but variance-limited alternative, both SVR variants add little value, and GNB serves only as a comparative baseline to be discarded in practice.

In the female cohort, diagnostics again revealed a clear pecking order: k-nearest neighbor (KNN) remained the standout, explaining ~45% of external variance with the narrowest error band (SEE ≈ 10.8 y) and minimal age-dependent bias, its learning curve indicating variance—not bias—limits that further data could remedy. The random forest (RF) ensemble offered the next-best trade-off: cross-validated R² approached 0.40, residuals were near-normal and largely unbiased (median ≈ −1 y), and although one extreme outlier inflated the upper Bland–Altman limit, overall dispersion (SEE ≈ 12.8 y) was ~3 y tighter than either support vector model; permutation importance highlighted a diffuse upper-thoracic/upper-lumbar pattern (T7, T9, L4) rather than the male L3/L4 focus. Both support vector regressors were hampered by bias: the RBF kernel compressed ages into 55–75 y, under-ageing the oldest woman and widening limits to ±27 y, while the linear kernel fared worst—predictions squeezed into 50–75 y, negative hold-out R² (−0.27), and the broadest limits (≈−38 y to +27 y). Finally, the Gaussian naïve-Bayes (GNB) baseline catastrophically over-fitted (train R² ≈ 0.9, CV ≤ 0), yielded bimodal residuals and limits of ±26 y, underscoring its unsuitability. In sum, KNN remains the only truly forensic-grade option for women at present, RF provides a robust but slightly less precise alternative, both SVR variants offer marginal utility, and GNB is best retained solely as a comparative benchmark. The learning curve panels, Bland–Altman plots, permutation importance plots, predicted vs. true scatter plots, residual vs. fitted plots, and residual histograms for both male and female cases are presented in detail—and interpreted—in Appendix A.

3.6. Post Hoc Power Analysis

Using the observed coefficients of determination from the multiple linear regression benchmarks (Table 3) and the exact sample sizes of the final data sets (male n = 94, female n = 82), we calculated the achieved power for the overall regression F-test. With 19 predictors, the denominator degrees of freedom were 74 (males) and 61 (females). Converting the observed fits to effect-size indices

$$(Cohen’s f^2={\displaystyle \frac{R^2}{\left[1-R^2\right]}})$$

(9)

yielded f² = 0.66 for men and 0.88 for women. The corresponding non-centrality parameters

(λ = f² · df₂)

(10)

were 49.1 and 53.9. At α = 0.05, the critical F value is ≈ 1.73; the non-central F distribution therefore gives an achieved power of 0.992 for the male model and 0.995 for the female model. In other words, the study had >99% probability of detecting the observed age-related variance if it was present in the source population.

However, the power to estimate individual regression coefficients or to generalize the SEE to new samples is appreciably lower. Each sex provides only ~4.3 (male) and ~3.9 (female) observations per predictor, well below the commonly recommended 10–15 cases per variable. This shortfall is reflected in the wide 95% confidence intervals of the SEE, the learning curve analyses, and the large permutation importance uncertainties (Appendix A).

4. Discussion

4.1. Synopsis of the Main Findings

Accurately estimating adult age or age at death remains one of the most persistent challenges in forensic anthropology, clinical forensic medicine, forensic radiology, and bio-archaeology because most protocols still depend on semi-subjective scoring of heterogeneous degenerative features. In the present study, we propose a novel alternative to subjective scoring: a single, objective descriptor of vertebral cortical roughness—the mean orthogonal deviation of each vertebral endplate from an ideal ellipse (DS)—calculated automatically for C7–S1 on routine multi-detector CT scans. DS increases progressively from the mid-thoracic to the lumbar spine and correlates moderately to strongly with chronological age, particularly at L3–L5, where r values reach 0.49–0.60 in women and 0.40–0.60 in men. When DS values from all 19 vertebrae were entered into multivariable models, classical multiple regression accounted for 40% of the age variance in men and 47% in women (SEE ≈ 11–12 years). Non-parametric algorithms improved precision: a random forest ensemble reduced the male SEE to 8.49 years, whereas a k-nearest neighbors model lowered the female SEE to 10.8 years (R² = 0.448 on the hold-out set). Thus, the automated DS metric provides age estimates comparable to those generated by more complex pipelines. These findings indicate that a simple, reproducible measure of cortical roughness obtainable from routine clinical images can serve as an alternative indicator of skeletal aging.

4.2. How DS Compares with Conventional Vertebral Scores

The standard error of the estimate (SEE) achieved by the present DS models compares favorably with most vertebral-based aging studies published to date. Using a 20% hold-out set, the best female model (k-nearest neighbors) reached an SEE of 10.8 years, whereas the best male model (random forest) yielded 8.49 years; traditional multiple linear regression of the same predictors performed less well (≈12 years in females and 11 years in males). These figures place our automated method near the forefront of CT-derived vertebral methods while requiring neither deep-learning architectures nor specialized hardware.

When set against classical osteophyte or surface score approaches, the DS metric offers a clear precision advantage. Regional osteophyte-based models derived from Japanese autopsy CTs [21] and Thai dry vertebrae [19] typically report SEE values of ~10–11 years, while inspection-style indices such as Watanabe’s [17] whole-column score and Zangpo’s [26] 3-D surface-deformation metric cluster between 11 and 13 years (

Table 5. Overview of vertebral-based adult age estimation methods: cohorts, imaging modalities, modeling approaches, and reported accuracy.

Reference	Population and Sample Size	Vertebral Region and Imaging/Data	Age Indicators and Modelling Approach	Reported Performance †	Key Contribution/Remarks
Adams et al., 2024 [22]	240 medico-legal cases (120 males and 120 females; 18–101 y)	Lower T-spine and upper L-spine; digital radiographs	3-phase degenerative score of T11–L3 → Bayesian transition analysis	Bin-1 → <36 y, Bin-3 → >47 y (90% CI); no sex effect	Practical radiographic protocol for fleshed remains; usable when skeletal sampling impossible.
Cardoso & Ríos 2011 [18]	104 documented skeletons (47 males and 57 females; 9–30 y)	Cervical, thoracal, and lumbar vertebrae; dry bone	3-stage scoring of epiphyseal-ring union	Stage 0 always < 18 y; stage 3 appears ≥ 15 y	Detailed fusion timetable for adolescent vertebrae; fills gap for 10–25 y age window.
Chiba et al., 2022 [21]	250 PMCT cadavers (125 females and 125 males; 20–95 y)	T- and L-spine; post-mortem CT	Osteophyte score O (0–5) + bridge score B (0–2); regression	Best SEE ≈ 10 y using “number of vertebrae with O ≥ 2”	Demonstrates CT-based scoring viable even with partial columns.
Reference	Population and sample size	Vertebral region and imaging/data	Age indicators and modelling approach	Reported performance †	Key contribution/remarks
Etli 2023 [34]	140 Turkish CT cases (70 males and 70 females; 21–90 y)	Sacral base; abdominal–pelvic CT	Distance-to-fitted-ellipse surface roughness score (DS); sex-specific linear regression	MAE 12.5–14.8 y, RMSE 14.7–18.1 y; DS  ≥  50 y class accuracy >80%	Pilots the DS concept, showing moderate precision with sacral DS.
Garoufi et al., 2022 [28]	275 Europeans (168 Greek modern; 93 males and 75 females; 107 Danish archaeological; 56 males and 51 females; 21–82 y)	T12 superior and inferior end-plates; digital photographs	9 geometric variables → generalized additive regression	Max. R2 0.46; correct-decade hit-rate 33% (archaeol. set)	Introduces continuous 2-D shape metrics; moderate age signal, highlighted size-related sex effects.
Kaçar et al., 2017 [25]	564 living Turkish adults (279 males and 285 females; 20–84 y)	(T1–L5); 0.5 mm MDCT scans reconstructed to 3-D volume-rendered images	Vertebral osteophyte severity (0–4 scale); Linear regression for age estimation (upper/lower limits).	Significant age correlation (40–70 yrs, both sexes). Sex-specific thoracic/lumbar age formulas (p < 0.05). Inter/intra-rater reliability: 0.85/0.88.	First large CT study on living adults; shows osteophyte severity peaks in mid-thoracic region and plateaus after 70 years; detects male-biased osteophyte frequency at T9–T12; provides practical formulas for forensic age estimation.
Kawashita et al., 2024 [24]	Training: 1120 clinical CTs; 560 males and 560 females; 20–99 y; Test: 219 PMCT cadavers; 137 males and 82 females; 21–94 y	Whole spine; axial CT slices → VGG-16 regression ensemble	Deep learning regression (bagged VGG-16)	MAE = 4.36 y; SEE = 5.48 y; ICC = 0.96	First end-to-end DL model on spine; accuracy surpasses classic scores, robust to 20–90 years.
Malatong Y et al., 2022 [27]	Thai skeletal radiograph bank; 220 lumbar DR images (110 males, 110 females; 20–86 y)	L1–L5; posterior–anterior digital radiographs	Image-analysis of trabecular “black-pixel” content: total % (TP), mean % (MP), black/white ratio (BW); stepwise linear regression by sex	Best equations: male (L4) SEE 15.4 y, female (L1) SEE 13.8 y; r = 0.21–0.46	Introduces automated pixel-density metric as surrogate for bone porosity on plain films.
Nurzynska et al., 2024 [23]	166 routine axial CTs (95 males and 71 females; 20–80 y)	L-vertebral bodies; axial CT ROIs	(a) qMaZda texture features + ML regression; (b) custom CNN	Texture-ML: MAE 3.14 y, R2 0.79; CNN slightly worse	Shows grey-level texture alone can predict age within ±3 y on moderate dataset.
Praneatpolgrang et al., 2019 [19]	400 Thai skeletons (262 males and 138 females, 22–97 y)	C2–L5; dry bone	Length-based osteophyte score (modified Snodgrass/Watanabe)	Lumbar female: r = 0.80; SEE ≈ 10–11 y (author-reported)	Provides full sex-/region-specific equations for tropical Southeast-Asian population.
Ramadan et al., 2017 [29]	123 clinical CTs (61 males and 62 females, 10–64 y)	Last thoracic (T12); MDCT axial slices	15 linear dimensions; stepwise multiple regression	Sex-classification 88.6%; age r ≤ 0.40, SEE not reported	Shows T12 size grows with age but correlation too weak for precise aging; useful primarily for sexing.
Rizos et al., 2024 [30]	219 documented Greeks (121 males and 98 females; 19–99 y)	64 skeletal traits incl. vertebral osteophytes; macroscopic scoring	Deep randomized neural network ensembles	MAE ≈ 6 y in >50 y group; poor (<10%) correct-decade in <50 y	Independent test questions “universal” accuracy. claims; stresses population-specific training.
Reference	Population and sample size	Vertebral region and imaging/data	Age indicators and modelling approach	Reported performance †	Key contribution/remarks
Schanandore et al., 2024 [31]	North-American medical CT archive; 319 scans (149 males and 170 females; 10–89 y)	T12–L5; clinical CT (0.6–1.3 mm slices); 3-D surface models in Mimics®	Six-point semi-quantitative osteophyte score on superior and inferior margins of each level (0–2); single and multiple linear regressions, 6-fold CV ×100	Best models (L1–L5 mean or multi-level totals): RMSE ≈ 8.4 y, R2 0.85; 73–77% of cases ± 10 y; ICC 0.80–0.95	First to subdivide each margin; demonstrates lumbar (esp. L4) dominance; high accuracy with simple scores.
Sluis et al., 2022 [13]	88 19th-c. Dutch skeletons (40 males and 48 females; 19–90 y)	Full spine; dry bone	Mean osteophyte stage by three published methods	Correct age bin assignment 73–76%	External validation of three scoring schemes; supplies Dutch-specific regressions.
Snodgrass 2004 [15]	384 Terry Collection cases (192 males and 192 females; 20–80 y)	T- and L-spine; dry bone	5-stage osteophyte scale; sex comparison	Greater variability in female; recommends wider CI	Found broadly parallel aging curves; underscores need for sex-specific intervals.
Suwanlikhid et al., 2018 [33]	250 Thai dry vertebral columns (125 males and 125 females; 22–89 y)	L1–L5 macroporosity, cortical roughness, osteophytes; naked-eye scoring	Multiple linear regressions per surface	Best: L1-inferior surface R2 0.41, SEE 11.7 y	Simple portable method; advocates combining three degenerative traits for tropical skeletal sets.
Thomsen et al., 2015  [16]	80 cadaver pairs (39 males and 41 females; 19–96 y)	L2 and iliac crest; μCT 3-D	Trabecular BV/TV, Tb.Th, SMI etc. vs. age	No explicit SEE; shows linear BV/TV decline (r ≈ −0.8)	Highlights microstructural trajectories; useful explanatory context for imaging biomarkers.
Watanabe & Terazawa 2006 [17]	225 Japanese autopsy cases (138 males and 87 females; 20–88 y)	Whole column; direct inspection and palpation	0–3 height-based scores averaged to “osteophyte index”; sex-specific regression	SEE 12.6 y (M)/11.9 y (F); r ≈ 0.70	Classic benchmark for simple inspection-based ageing in East Asian population.
Zangpo et al., 2023 [26]	200 Japanese PMCT cases (126 males/74 females, 25–99 y)	L4 body; 3-D PMCT surface mesh vs. convex-hull volumes	VR = mesh/hull; VD = (hull–mesh)/mesh; simple regressions	SEE 11.9 y (M)/12.5 y (F); ρ = ±0.76	First to quantify age from global 3-D surface bulging/concavity rather than marginal osteophytes.
Zangpo et al., 2024 [32]	200 Japanese PMCT cases (same cohort as 2023 study)	L4 body; max Hausdorff-distance (maxHD) between mesh and smoothed template	maxHD vs. age; sex-specific linear regression	SEE 12.5 y (M)/13.1 y (F); ρ ≈ 0.74	Confirms 3-D surface-deformation signal with an intuitive shape-difference metric (HD).

† SEE = Standard Error of the Estimate; MAE = Mean Absolute Error; RMSE = Root-Mean-Square Error; r = Pearson Correlation; ρ = Spearman Correlation.

). Using the same linear regression framework, our DS predictor produces SEE values in a comparable range (≈11–12 years). However, when DS is coupled with non-parametric algorithms—k-nearest neighbors in females and random forests in males—the SEE falls to 10.8 years and 8.49 years, respectively (Table 4). Although these errors are roughly one-third to one-half lower than the classical figures, the improvement partly reflects the greater flexibility of machine learning learners rather than an inherent superiority of DS alone. Indeed, more advanced models in earlier studies (e.g., Schanandore’s [31] semi-quantitative lumbar RMSE ≈ 8.4 years) narrow the gap, emphasizing that numerical comparisons should be interpreted with caution whenever statistical platforms differ. Nevertheless, the present results demonstrate that DS contains sufficient signal to equal or exceed the precision of most traditional vertebral indicators under like-for-like modelling, and that its accuracy can be substantially enhanced by applying readily available non-parametric methods.

4.3. DS Versus Deep Learning Pipelines

Deep learning pipelines currently set the numerical gold standard. Kawashita et al.’s [24] whole-spine bagged VGG−16 ensemble achieved an SEE of 5.5 years on a cadaver validation set, and Nurzynska et al.’s [23] texture-based CNN reported an MAE of 3.1 years. While our female SEE lies within roughly one year of the Kawashita figure, the male error remains higher. Nonetheless, the DS approach attains this level of accuracy with an interpretable single-feature paradigm, minute preprocessing, and conventional CPUs—traits that may facilitate deployment in resource-constrained forensic or clinical settings.

4.4. Population-, Sex-, and Age-Specific Patterns

Sample composition remains a critical—and often under-reported—determinant of external validity in vertebral aging research. The most accurate pipelines to date have been trained and validated almost exclusively within a single ethnic group: the bagged VGG-16 ensemble of Kawashita et al. [24] used only Japanese clinical and post-mortem CTs, while the texture analysis study of Nurzynska et al. [23] relied on Polish cardiac patients. By contrast, several osteophyte-based investigations draw on Thai dry bone [19] collections that are markedly male-skewed (≈65% male), whereas Adams et al.’s [22] radiographic series was deliberately balanced at 50% per sex. Our cohort of 176 living Eastern Turkish adults (94 males, 82 females) therefore fills a geographic gap, introducing Middle Eastern representation while maintaining a near-even sex split. The broader biogeographic coverage is valuable for future meta-analyses and may help test whether the DS roughness metric is truly ethnicity-agnostic or, like many macromorphological scores, demands population-specific calibration. Replicating the DS workflow in independent African, East Asian, and European samples—ideally with comparable sex balance—will clarify whether universal decision thresholds can be set or whether regional standardization is still required to achieve forensic-grade accuracy.

Osteophyte-based formulas typically lose traction in very old adults because osteophyte height approaches a biological ceiling after about 70 years [17,25]. By contrast, the regression scatterplots generated for our study (Figure 6 and Figure 7) reveal that lumbar DS values continue to rise across the full adult age span, with a clearly positive slope that persists even among the small cluster of octogenarians. Consistent with that visual trend, the overall Pearson correlations reported in Table 2 remain moderate for L3–L5 (≈0.40–0.60 in men and 0.49–0.60 in women), indicating that cortical roughness keeps accruing after osteophyte growth has largely stabilized. Consequently, the DS-based models do not show the marked loss of precision in seniors that is characteristic of height-limited osteophyte equations, supporting the view that surface roughness trajectories provide a more informative signal of late-life skeletal ageing.

Lumbar vertebrae consistently carry the strongest chronological signal in vertebral-aging research: for example, the Thai dry bone study of Praneatpolgrang et al. [19] reported its highest age correlations in the lumbar mean score (r = 0.76), and our own permutation importance map for males likewise places L3–L5 at the top of the ranking. In women, however, the DS metric shows a broader “thoraco-lumbar” footprint—moderate correlations extend from T8 through L5 (Table 2). This sex-specific topography may reflect biomechanical and hormonal factors: pregnancy-related shifts in lumbar lordosis, lower-thoracic rib cage expansion, and post-menopausal estrogen decline all redistribute loading and remodeling rates along the spine, potentially accelerating cortical scalloping in the mid-thorax for females while concentrating it in the lower lumbar bodies for males. A practical consequence of this anatomical breadth is workflow burden. The image preparation step of our proposed method is labor intensive, and the time required limited our sample size. Future studies could streamline the protocol by targeting only the vertebrae that show the strongest age associations in each sex (e.g., T8–L5 in women, L3–L5 in men) or by using deep learning segmentation to automate the image preparation step.

4.5. Model Diagnostics and Practical Performance

Classic vertebral age protocols rest on observer-assigned scores—for example, the five-stage Snodgrass [15] or the four-stage Watanabe [17] osteophyte scales—whose inter-observer agreement rarely exceeds an intraclass correlation coefficient of ≈ 0.85 even after calibration sessions [25]. Such subjectivity poses a reproducibility risk when multiple laboratories must defend estimates in court. By contrast, the present study uses an automated contour-fit algorithm to extract the DS roughness metric, eliminating rater bias and allowing the same result to be regenerated from the raw DICOMs at any site.

From a modelling standpoint, our linear regression baseline (SEE ≈ 11–12 years) mirrors the precision of most classical regression formulas, isolating the intrinsic signal contained in DS. When we switched to shallow, non-parametric learners—random forests for men and k-nearest neighbors for women—the SEE dropped to 8.49 years and 10.8 years, respectively, demonstrating the added value of algorithmic flexibility without sacrificing interpretability. Deep learning systems such as the bagged VGG-16 ensemble of Kawashita et al. [24] push the SEE down to ≈ 5.5 years, but they do so at the cost of “black-box” decision rules and high GPU demand. The DS + shallow-ML approach occupies a transparent middle ground: it matches or modestly surpasses the SEE reported for manual osteophyte-based formulas (≈11–13 y; see Table 5) while clearly outperforming our own classical linear baseline (≈11–12 y), yet remains computationally light, fully explainable, and readily portable. Because manual scores were not applied to the present CT set, this comparison is indirect and warrants verification in a future head-to-head study.

4.6. Practical Significance of the Results

Because the method presented here is implemented with open-source code, can be readily applied to routinely acquired vertebral CT scans, and—with future development—could be deployed as a fully automated, user-friendly software, it holds practical utility across several key areas. First, in forensic anthropology practice—especially in jurisdictions that routinely employ postmortem computed tomography (PMCT) on unidentified remains [40]—analysts could automatically survey the entire vertebral column to generate an initial age estimate, thereby guiding and potentially reducing the need for subsequent, more advanced, costly, or destructive sampling procedures. Even an age range estimated with an error margin of ±8–10 years can markedly narrow the pool of potential matches. Furthermore, this method can be extended to other bones and teeth, and, by employing an ensemble approach, the error margin can be further reduced. Second, in clinical forensic contexts—such as elite sport eligibility determinations or asylum cases [41,42]—this method could be applied to living individuals for age estimation. In particular, the availability of existing trauma CT scans in medical archives would allow application of this technique without additional radiation exposure. Finally, this method could be fully automated and extended to additional skeletal elements to enhance predictive accuracy, then integrated into hospital information management systems, thereby enabling routine use by clinicians. Because it requires neither high computational power nor GPUs, this method can be readily implemented in hospital systems without imposing an undue burden.

4.7. Population and Sex Variation and Taphonomic Considerations

While the present study focused exclusively on a contemporary Turkish clinical population, the issue of population variability remains a central concern in age estimation research. Previous work has shown that skeletal aging trajectories can differ substantially across geographic and ethnic groups due to genetic, environmental, and cultural influences [15,30]. Although our dataset helps address the underrepresentation of Middle Eastern populations, external validation in diverse cohorts remains necessary to assess whether the DS metric generalizes across populations or requires region-specific calibration. With respect to sex-related differences, our results show that while lumbar roughness patterns dominate age prediction in males, females exhibit a more diffuse thoraco-lumbar pattern. This topographic difference may reflect biomechanical factors (e.g., pregnancy-induced lordosis, rib cage remodeling) or hormonal changes, especially postmenopausal bone turnover [15,43,44]. These differences are captured both in correlation profiles (Table 2) and in the variable selection paths of the sex-specific models (Section 3.4 and Section 3.5). Finally, because our sample consisted exclusively of living adults undergoing diagnostic CT scans, postmortem taphonomic alterations—such as microbial degradation, desiccation, or soil pressure—that might affect surface roughness [35,45,46] were not present in these images. While this design avoids the noise introduced by such variables, it also limits generalizability to forensic remains. Future work should replicate this pipeline on postmortem CT datasets, which may introduce new sources of surface distortion or artefacts that affect the DS score.

4.8. Ethical and Legal Implications of Bone Surface Roughness-Based Age Estimation

Bone surface roughness—as determined by DS calculations from CT images in this study or acquired from dry skeletal remains using structured light scanning (SLS) [47]—qualifies as biometric data under the EU General Data Protection Regulation [48,49]. Therefore, when such data is to be used in forensic medical research, particularly in cases involving minors, asylum seekers, or deceased individuals, it may be necessary to obtain consent from appropriate legal guardians or next of kin before proceeding with examinations. Another ethical and legal concern relates to the probabilistic nature of adult age estimation. The DS-based pipeline, like all current adult age estimation techniques, yields a probabilistic estimate rather than a deterministic determination [50]. Even at our best standard error of the estimate (SEE ≈ 8 years), cases will inevitably fall outside the ±8-year confidence band, and misclassification may have substantial legal or humanitarian consequences (e.g., asylum eligibility, criminal liability thresholds). When age opinions are presented in court, experts therefore have an ethical obligation to (i) report the method’s quantified error margins, (ii) state that the result is an estimate rather than a factual age, and (iii) caution decision makers against using the point estimate in isolation [51].

4.9. Pathophysiological Basis of the DS Metric

The progressive increase we observe in the DS score has a clear histo-morphological foundation. With advancing age, the anterior-superior vertebral cortex is subjected to rising compressive and shear loads—especially after disc height loss [52]—causing repetitive micro-fracture [53], osteoclastic resorption, and subsequent remodeling [54]. Histological and µCT studies demonstrate a linear rise in cortical porosity [55], Haversian canal enlargement [56], and surface scalloping throughout adulthood [54], while trabecular bone volume fraction and connectivity decline in parallel [57]. These processes generate two macroscopic signatures that the DS algorithm captures: (i) outward protrusions (osteophytic ridges, ligamentous ossification) that shift boundary nodes beyond the “young/healthy” ellipse; and (ii) inward indentations (resorption pits, cortical thinning) that pull nodes inside the ellipse. The DS measure is therefore an integrated geometric read-out of both productive (osteophyte formation) and destructive (porosity-driven undermining) phases of vertebral aging. Importantly, these alterations accumulate even after osteophyte height reaches its biological ceiling [17,25], explaining why lumbar DS continues to climb in octogenarians whereas height-based scores plateau. Hence, the metric is not a black-box surrogate but a quantifiable expression of well-documented degenerative pathways, reinforcing its biological plausibility and forensic relevance.

5. Limitations

The principal limitation is the sample size relative to the model complexity. Although post hoc power for the global regression is high, the ratio of observations to predictors raises the risk of over-fitting, inflates coefficient sampling error, and limits the precision of the SEE—especially in cross-validation and external test sets (SEE 95% CI up to ±3 years). Second, the cohorts originate from a single clinical center and share similar ethnic and socio-economic backgrounds; extrapolation to other populations therefore warrants caution. These constraints should be addressed in future studies by enlarging the sample and validating the method on independent populations. Because classical osteophyte/degeneration scores were not re-assessed on the same CT sample, our comparison with “traditional” methods remains indirect; a future head-to-head study is therefore required to confirm the incremental accuracy of the DS + shallow-ML approach.

6. Conclusions

This study introduces an automated “average distance to the fitted ellipse” score (DS) descriptor of vertebral cortical roughness and demonstrates its utility for adult age estimation on routine multi-detector CT scans spanning C7–S1. DS correlates positively with chronological age across the thoraco-lumbar spine and, when entered into sex-specific machine learning models, yields SEE values of 10.8 years in females (k-nearest neighbors) and 8.49 years in males (random forest)—demonstrating comparable accuracy relative to classical multiple linear regressions (≈11–12 years) and most published osteophyte-based formulas. Because the pipeline is observer independent, light on hardware, and fully reproducible from raw DICOM data, it offers a transparent alternative to subjective scoring systems and data-hungry deep learning solutions. Nevertheless, several limitations warrant attention: the preparation of 19 vertebral images per subject is time consuming; the sample derives from a single Turkish center; and model generalizability beyond the studied ethnicity remains untested. Future work should automate the image preparation step, explore whether a reduced vertebral subset can retain accuracy, and validate the DS approach in larger, multi-ethnic cohorts.