Introduction

Age is one of the four major biological profile characteristics used to establish individual identification, with a growing essential role in the forensics [1].

The challenge of age estimation is higher in adults than in children since dental and skeletal growth is settled, and there is an increase in complexity as degenerative processes appear in adulthood [2, 3]. The most used indicators of chronological age achievement rely on skeletal and dental evaluations, considering the influence of environmental factors [4,5,6], ethnic and sexual variability [7], and a secular trend [8,9,10]. For age estimation, the Forensic Anthropology Society of Europe preconizes a radiograph of clavicle-sternal fusion, a dental study with pulp chamber methods, and a physical examination, including hormonal dosage for women. There is broad consensus that tooth assessment, relying on the dental age-related phenomena, is more predictable than the other two [11]. While comparing the radiation doses of the radiographs advocated for forensic proposals with natural and civilizing radiation exposures, it is accepted that the health risk of damage is diminutive. Exposure must respect the legislation of each country, recognizing the disparities between countries concerning purposes other than medical reasons. It is seen as a social and individual benefit in the majority, while radiation is taken for legal procedures. The imaging procedure must be performed under informed consent, including the purpose and examination type. On edge, images could be acquired from archives.

Dental age prediction in adults can rely on several methods, namely Gustafson’s parameters [12], dentinal translucency [13,14,15,16,17,18,19,20,21,22], and cementum annulations [23, 24]. Recent developments in biochemistry have allowed exact age estimation [5, 6]. However, these techniques require extraction of teeth and, usually, tooth sectioning/processing, which may not be feasible in living adults or in certain jurisdictions that prohibit tissue collection from human remains.

In 1925, Bodecker was the first author to recognize a correlation of dentine apposition with chronological age [25]. Secondary dentine apposition and pulp chamber narrowing since adulthood are well-recognized age indicators [11, 26]. After tooth full eruption, the apical closure is essential to begin secondary dentine secretion [26]. In the meantime, the pulp area decreases [27]. In 2004, Cameriere et al. introduced the pulp/tooth area ratio (PTAR) technique, measuring whole pulp and tooth areas and applying concrete age estimation statistical analysis, considering linear regression models [28]. This method, measuring the upper right canines in orthopantomograms (OPGs), has obtained high levels of accuracy in age prediction and included the effect of population affinity and culture on statistical formulation [28, 29]. It led to a simple and objective age estimation metric method, recommended for adults and individuals nearly to adulthood without third molars [26, 30]. Yet, some authors have claimed that PTAR models must be population-specific [31,32,33,34]. Later, in 2013, Cameriere et al. developed a model using peri-apical digital X-rays of both upper lateral and central incisors. The total variance explained by the model developed was the following: (a) 51.3% in lower lateral incisors, (b) 56.5% in lower central incisors, (c) 80.3% in upper central incisors, and (d) 81.6% in upper lateral incisors. The developed models were not tested in independent samples [27].

Furthermore, the study was carried out in peri-apical X-rays from skulls, which may not reproduce entirely the actual context and allow only visualization of a few teeth. This can be troublesome if the tooth the investigator was planning to assess cannot be evaluated (because it has a root canal treatment, for example) [28] and might require further radiographs to be performed. Recently, doubts have arisen about the ethics of these procedures [35], and it is a good practice to perform as few radiographs as possible [36]. Thus, an obvious advantage is using an orthopantomogram, which allows for multiple age estimation techniques. The study aimed to contribute to age estimation using the pulp/tooth area ratio in incisors assessed in orthopantomograms.

Materials and methods

This research studied 801 patients’ OPGs. An Ethical statement was issued by the Ethical Commission of the Health Sciences of FMDUP (14/2022).

The selected individuals were European with Portuguese nationality and place of birth in Portugal. The presence of systemic and dental disorders was adopted as exclusion criteria. The teeth elected were the upper central incisors due to their favorable anatomy and because they house little environmental changes over a lifetime. Regarding teeth selection, only sound teeth were considered. The dental exclusion criteria were as follows: the presence of fillings, endodontic treatments, wear, fractures, impaction, extrusion, artifacts, developmental abnormalities, periodontal disease, peri-apical lesions, root resorption, open apex, multi roots, multi canals, pulp calcification, orthodontic treatment, moderate and severe superimposition, and rotation.

The analysis and selection of OPGs have considered the quality of the image, including the resolution features and absence of magnificence, noise, or artifacts. OPGs were classified into a wide range of groups by age, from 18 to 78 years old. Four hundred sixty-six belonged to female and 335 to male patients. The mean (M) chronological age (CA) of the participants was 37.01 years old (standard deviation (SD) = 15.10 years old). The median (Mdn) was 34.0 years old (interquartile range (IQR) = 24.0 years old). The patient distribution by age group and sex can be observed below (Table 1).

Table 1 Patients’ age and sex distribution included in the study (n, %)
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The PTAR measurements of both upper central incisors were performed without prior knowledge of the individual CA.

The OPGs were obtained in JPEG format and numbered from one to 801. Image J® software version 1.8.0 (open-source Java®-based image processing program developed by the National Institutes of Health and the Laboratory of Optical and Computational Instrumentation, LOCI, University of Wisconsin, USA) was used for semi-automatic area measurements. We have acquired area measurements using the “freehand selections” mode of Image J software to manually draw the pulp and tooth anatomical outlines (Fig. 1). About image optimization, the most adopted tool for the edition was the inversion, and the most used adjustment tools were contrast and brightness. Smoothing and sharpening processing tools were also very useful. Then, the pixel amount of each pulp and tooth area drawn was converted into areas automatically by the software, which performs the area calculation. Data were registered in Microsoft Excel®.

Fig. 1
figure 1

Manual tooth and pulp delineation, considering tooth laterality, using Image J®

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Statistical analysis was performed using the Statistical Package for Social Sciences program (SPSS), version 27.0. Reproducibility and repeatability were assessed using the Cronbach alpha coefficient by evaluating the agreement of the upper right central incisor (tooth 11) measurements in 30 randomly selected digital OPGs. The same OPG was examined three times for tooth and pulp measurements by the same observer (SMM), 2 days apart between each observation and by another (IMC). Normality was tested, resorting to the Kolmogorov-Smirnov test. As seen above, descriptive analysis has been performed for the continuous variable, resorting to M, SD, maximum (Max), minimum (Min) limits, Mdn, and IQR.

PTAR measurements were used for age estimation using Cameriere’s regression model [27]:

$$\text{Age}=78.55-3.86\cdot\text{g}-313.45\cdot\text{RA1sup}$$

where g is the sex [0, female and 1, male], and RA1sup stands for the PTAR of the upper central incisor.

The used model total variance (R2) is 0.803, and the standard estimate error (SE) is 7.03 years. As both upper central incisors were measured, we estimated age using 11(EA11) and 21(EA21).

The Pearson chi-square test was used to check possible associations between categorical variables. Spearman’s rho was used to analyze possible correlations. Estimated age (EA) using Cameriere’s equation was compared with CA. Resorting to linear regression, an age estimation model for the Portuguese population was developed. Then, the population sample was divided into six age groups (≤ 29, 30–39, 40–49, 50–59, 60–69, and 70–79 years old). Using a paired-sample t-test, EA with Cameriere’s method and the developed model were compared with CA in each group. The statistical significance level was set at 5%.

Results

The Cronbach’s alpha values were 0.996 for inter-agreement and 0.991 for intra-agreement, both relatively high.

The Kolmogorov-Smirnov normality test showed a skewed distribution (p < 0.05). The M and Mdn of EA, using tooth 11, were 44.23 (SD = 7.27) and 44.45 years (IQR = 8.83), respectively. Using tooth 21, the M and Mdn of EA were 42.82 (SD = 7.73) and 43.14 years (IQR = 9.0), respectively (Table 2).

Table 2 Descriptive analysis of estimated age using PTAR method, considering both upper central incisors (in years)
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CA did not display a statistically significant association with the PTAR (p = 0.423). Yet, this link was present when we divided the sample by age groups (p < 0.001). As for the correlation between CA and EA, a moderate direct correlation was found using tooth 11 (r = 0.679) and slightly higher with tooth 21 (r = 0.706) (Table 3). This correlation was statistically significant (p < 0.001 for both).

Table 3 Spearman’s rho correlation test between CA and EA
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Wilcoxon Signed Rank test was employed to compare CA and EA within groups and the total sample (Table 4). There were statistically significant differences in both cases (p < 0.001). The Z-score showed a slightly better relationship while using tooth 21.

Table 4 Wilcoxon signed rank test results comparing CA and EA
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Using linear regression, a model for estimating age was developed. We observed sex and teeth laterality as possible confounding variables, and the variable sex was excluded, as it presented a low correlation value (r = 0.018) with CA. Conversely, a moderate negative correlation was found between CA and PTAR, using tooth 11 (r =  − 0.672) and tooth 21 (r =  − 0.687). The variables PTAR 11 and PTAR 21 were strongly correlated (r = 0.876). Yet, as the correlation did not pose an absolute contraindication and could increase the robustness of the prediction, they were both kept.

The assumptions for the model were checked, starting with the multicollinearity analysis. As mentioned, the independent variables presented a correlation with the dependent variable greater than 0.3 (r =  − 0.672 and r =  − 0.687). The tolerance (t = 0.233) and variance inflation factor (VIF = 4) were more significant than 0.1 and less than 10, respectively. Thus, the assumption of multicollinearity was not violated. The assumptions regarding outliers, normality, linearity, homoskedasticity, and independence of residuals were also verified. The model explained 49.3% (R2 = 0.493) of the variance of age, showing a statistical significance of the built model (p < 0.001). The PTAR 21 variable showed the most significant contribution to the developed equation. All variables presented statistical significance (p < 0.001) (Table 5).

Table 5 Test statistics for the proposed model
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Paired-sample t-tests showed statistically significant differences between EA means, using Cameriere’s equation (EA11 and EA21) and using our model (EA3), with CA means in all age groups (Table 6).

Table 6 Mean age differences and correlations between CA and EA11, EA21, and EA3 for age groups
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Discussion

Age estimation in adults is particularly troublesome, as no developmental markers are available for these ages, and therefore, age estimation relies on senescence indicators. Yet, age-related changes and environmental factors often alter these indicators, making it virtually impossible to discriminate between older ages reasonably [11]. Our results point out that difficulty, as the statistically significative correlation between CA and EA (regardless of the model used), is lost in ages over 50 years, and all models underestimate age in all age groups. Other authors report similar difficulties in identical age groups, although using different teeth [37]. These results point out that PTAR, namely using central incisors, may not be suitable for age estimation over this age, and other methodologies should be used. Different results were obtained by Cameriere et al. [27], who successfully applied this method in individuals older than 70, suggesting that population differences may exist, and these should be considered when choosing the methodology for age estimation. Also, the selected tooth to apply the method might play an important role as most studies reporting accuracy in EA using PTAR refer to canines and lower premolars (Table 7) [28, 32, 37,38,39,40,41,42,43,44,45,46]. Another critical factor to consider is that Cameriere’s methodology was developed in apical radiographs, and forcing its use in orthopantomograms can lead to errors, as the incisors’ images are undoubtedly distorted. Yet, we have chosen to use orthopantomograms due to the possibility of selecting different methods using one radiograph alone.

Table 7 Review of the main results of articles related to PTAR method using 2D images (by year, population studied, and used teeth)
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Regarding estimating the age of the dead, an adaptation to the corpse’s state of preservation is required. Portable apical radiographs could make obtaining the best angle for the best image easier. However, other methods, such as the biochemical techniques [5, 6], Lamendin [14, 16,17,18], and Gustafson methods [12], are well established with good results.

In ages 30–49, a correlation between CA and EA was found, regardless of the model used. This is of little value, as it would be a requirement to know a person’s age before the age estimation process. Age was underestimated, and statistically significant differences between CA and EA means were determined. This was true for all age groups, suggesting that this methodology may be inadequate for age estimation in this population. Similar results were obtained by Jeevan et al. [37] found this methodology in canines useful up to age 45. On the other hand, Anastacio et al., who also studied a Portuguese population but applied the PTAR methodology on second premolars, found the methodology unreliable in all age groups [31].

As stated, there was an age overestimation until age 50, and from there on, an underestimation. This may happen because secondary dentine deposition is a finite process, and as time goes by and the pulp area diminishes, the quantity of secondary dentine deposited diminishes. Hence, the increase in tooth area is also lower. This means this method may also have an upper age use limit. This may differ in different populations and certainly with the used tooth, as explained in Table 7.

Many authors justify the selection of a specific tooth for PTAR based on technical issues, such as visibility in the X-ray, lower superimposition phenomenon, and the frequent presence of the tooth (and less damaged) [46], among others. Yet, other considerations should be made, namely the probable age frame and the population affinity. Regarding the existence of specific population formulas, other investigators also support this claim [33, 34], arguing that this approach considers the specific population correlation with secondary dentine deposition. We believe this to be true, but the choice of the tooth in which the methodology will be applied should also reflect this, as different populations for different age intervals may favor other teeth. Cameriere et al. [27] said that PTAR using incisors could be a helpful methodology in age estimation. However, if used in other teeth, the process offers better results, namely in canines [28, 39, 42] and premolars [40]. Yet, Zaher et al. [47] reported high levels of accuracy using upper incisors, supporting the idea that tooth choice matters.

The limitations of the present study include the low representativeness of older adults, which may have caused less accuracy for the older age group’s assessment. Additionally, regression equations will always overestimate the younger age group and underestimate the older age groups. In the future, the developed model should be tested in an independent sample.

Conclusions

Our results conclude that the upper incisors’ pulp/tooth area ratio, using orthopantomograms, overestimated age, and statistically significant differences between chronological and estimated age, are present. For those over 50, no correlation between pulp/tooth area ratio and chronological age was found, suggesting that this may be the upper limit of this technique in this population.

Key points

  1. 1.

    Age estimation in adults is a complex process

  2. 2.

    The pulp/tooth area ratio in incisors has been proposed as a valuable methodology for adult age estimation

  3. 3.

    In orthopantomograms, pulp/tooth area ratio analyses overestimate age

  4. 4.

    In orthopantomograms, pulp/tooth area ratio analysis does not work in people over 50