Introduction

The accurate age at death estimate of unknown skeletons of adult individuals is a crucial research task in both bioarcheology and forensic anthropology, being a key feature for the determination of population demographic structures and biological profiles of individual remains [2, 3]. Current adult aging routines are traditionally based on macroscopic observations of the degenerative (“wear and tear”) changes in four skeletal regions: the pubic symphysis [4,5,6,7,8], the auricular surface [9,10,11,12], cranial sutures [13, 14], and sternal rib ends [15,16,17]. However, a plethora of other skeletal regions and methods are also used — in combination with long-standing reference methods, or independently — to estimate age at death in adults. These encompass, among others, molecular clocks in ancient proteins [18], the degeneration of the acetabulum [19, 20], amino acid racemization in dental tissues [21, 22], tooth-root translucency [23], dental attrition [24, 25], the ratio of the pulp/tooth area in canines [26], and bone histology [27, 28].

Unfortunately, most skeletal indicators are unreliable, showing weak and irregular associations with age, echoing the complexity of the aging process [29, 30]. Individual and population differences during biological senescence stem from a reticulate of factors and interactions at the genetic, sociocultural, and environmental levels [29, 31, 32]. Moreover, existing age estimation techniques often present methodological problems, such as the subjective nature of user-observation and subsequent lower reproducibility [4, 33] and the application of inappropriate sampling and statistical procedures [3, 34, 35]. Scientific organizations and individual researchers alike have been advocating for more objective, less observer-dependent, age estimation methods, with a concomitant exploration of innovative statistical approaches [3, 33, 36,37,38]. New methodologies for age estimation in skeletal remains are thus needed to address these concerns.

Bone mass decrease with age is a universal phenomenon — in individuals of both sexes from different populations, e.g., [39,40,41,42,43]. Age affects bone loss through direct and indirect mechanisms, including remodeling imbalance, secondary hyperparathyroidism, decline in the intestinal production of the active metabolite of vitamin D, and reduction in bone tissue repair [44,45,46]. Age-specific bone remodeling occurs in different skeletal regions and types of bone tissue — i.e., trabecular and cortical — at dissimilar rates, and macroscopically observable features of bone loss have long been used to develop aging standards in adults, e.g., [47,48,49,50,51,52,53,54]. Recently, bone densitometry has been used to develop and test methods for age at death estimation based on the association between bone mineral density (BMD) and age [55,56,57,58].

We have previously shown that the age-associated decrease of bone mineral density (BMD) at the proximal extremity of the femur could be considered to estimate age at death in women of Portuguese descent [1]. Published results emphasized the potential of dual-energy X-ray absorptiometry (DXA), data modeling through artificial neural networks (ANN), and a user-friendly online interface named DXAGE (http://osteomics.com/DXAGE/), to attain accurate and reproducible estimates of age at death in skeletal remains of adults. Nevertheless, DXAGE was only designed for age estimation of adult women. As such, the present study aims to provide models for age estimation of both sexes through bone densitometry at the proximal femur. Also, age-related cortical bone loss at the second metacarpal is well established in both modern and archeological samples [59,60,61,62,63,64,65] — but, except for Kimura’s (1992) method, cortical bone loss with age at the second metacarpal has not been used for age estimation in skeletal remains of adults. Accordingly, another objective of this study is to assess the potential of bone loss at the second metacarpal to estimate age at death in adult individuals. The development of an online application (DXAGE 2.0) featuring different statistical models for age estimation using BMD at the proximal femur and second metacarpal cortical index (MCI) constituted an ancillary objective.

Materials and methods

Sample

The training study base comprised 224 adults (120 females and 104 males) from the “Coimbra Identified Skeletal Collection” (CISC; Cunha and Wasterlain, [66]). Documented ages at death ranged from 20 to 96 years old (Table 1). Sampled individuals were Portuguese nationals and for the most part were non-specialized manual workers with low socioeconomic status. They were buried for at least 5 years — as a rule, after that period, the bodies were exhumed — in earth-cut shallow graves at the Conchada Municipal Cemetery (Coimbra, Portugal).

Table 1 Age and sex distribution of the study sample of the Coimbra Identified Skeletal Collection (CISC)
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Data collection

The left femur and left second metacarpal of each individual were evaluated through dual X-ray absorptiometry and conventional radiogrammetry, respectively. Individuals without gross post-depositional modifications and/or obvious disease modifications at the skeletal sites of interest were the only ones included in the sample.

Osteodensitometry (also identified as bone densitometry) was attained with a Hologic QDR 4500C Elite densitometer (available issued formulae should be used to convert BMD values measured on a densitometer from other manufacturers, e.g., GE Healthcare or Nordland). Femora were placed anteroposteriorly, aligning the diaphysis to the densitometer’s central axis, on a low-density cardboard box, on top of 10 cm of rice (see [1, 68]). Regarding osteodensitometry, the proximal extremity of the femur is usually separated into distinctive regions of interest (ROI): total hip, trochanteric and intertrochanteric/proximal diaphysis regions, femoral neck, and Ward’s area. The total hip area of the femur (also identified in the medical literature as the total proximal femur region) stems from the aggregate of three specific parts: trochanteric region, intertrochanteric/proximal diaphysis regions, and neck (Fig. 1) [67]. In this study, bone area (cm2), bone mineral content (BMC, g), and bone mineral density (BMD, g/cm2) were determined through a semi-automatic procedure in three of the ROI: femoral neck, Ward’s area, and total hip. BMD at these sites was used to construct the models for the prediction of age at death.

Fig. 1
figure 1

Densitometry report featuring, among others, bone mineral density values, T-scores and Z-scores at the femoral neck, Ward’s area, and total hip

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Conventional radiogrammetry was employed to determine the cortical index (MCI) at the mid-diaphysis of the second metacarpal, according to [69]:

$$MCI=\frac{\mathrm{Diaphysis}\;\mathrm{total}\;\mathrm{width}-\mathrm{Medullary}\;\mathrm{width}}{\mathrm{Diaphysis}\;\mathrm{tota}\;\mathrm{lwidth}}$$

Radiographs were acquired in a Senographe DS digital radiographic device (GE Healthcare; focal length 50 cm, Kv 27–30 and mAseg 14–20, according to the features of each individual metacarpal), and all measurements were accomplished through the Centricity DICOM Viewer 3.1.1 software.

The data that sustain the results of this study are attainable from the corresponding author upon reasonable request.

Statistical analysis

Descriptive statistics, namely group means, standard deviation, and 95% confidence intervals for the mean, were assessed. Conventional least squares regression analysis [70] and an adapted General Regression Neural Network [71] were employed to assign the different variables (i.e., BMD Total, BMD Neck, BMD Ward, and MCI) toward a model of age at death estimation.

The plainest arrangement of regression (i.e., single linear regression) presupposes a linear association between two variables that can be denoted by the ensuing equation:

$$Y=\alpha +\beta X+\epsilon$$

in which X indicates the independent variable, Y the dependent variable, α the value of Y when X corresponds to zero, β the slope in Y with X, and ϵ features the non-systematic error in Y [38, 72]. The model assumes that Y shows statistical uncertainty, and errors present a normal distribution around the real values with constant variance, whereas X is error-exempted or virtually error-exempted [73]. Predictive variables selection was performed with a stepwise approach, and collinear attributes, if any, were removed from the final models.

A general regression neural network (GRNN) was also used to model BMD and MCI variables as predictors of age at death. This ANN aims to simulate the associative memory, comprising distinct layers: input, pattern, summation, and output [71, 74]. The input layer matches the BMD and MCI vectors to predict age, while in the pattern layer, the input is equated with additional instances stored at the network’s memory. Each instance, or pattern, present in the network is operated in the same way as an artificial neuron initiated by a radial basis function. The layers summation and output provide a regression surface and an assessment of age at death employing the pondered average of memory stockpiled examples. The activation values of the radial basis function linked to the artificial neurons support the factors of ponderation. Considering a matrix of predictors X and an outcome variable Y, the estimate of the network Y(X)’ can be depicted as follows:

$$Y(X)=\frac{{\sum }_{i=1}^{n}{Y}^{i}{e}^{-\frac{{D}_{i}^{2}}{{2\sigma }^{2}}}}{{\sum }_{i=1}^{n}{e}^{-\frac{{D}_{i}^{2}}{{2\sigma }^{2}}}}$$

in which \({D}_{i}^{2}\) is the distance between the vector of the input layer and the ith example pre-deposited in the pattern layer’s memory, and \({\sigma }^{2}\) is a smoothing parameter controlling the projected density and regulating the information volume surrounding the artificial neurons.

The preparation of these models was implemented with Brent’s algorithm, in combination with an arrangement of cross-validation (\(K=n-1\)) and used the entire sample. The probabilistic estimation of age at death is considered the most appropriate [75, 76]; thus, the ANN employed was adapted to produce, not only the conditional mean, but also an estimate of the a posteriori distribution. By adopting a probabilistic framework, the estimation of age at death can be mathematically expressed as follows:

$$f(y|x) =\frac{f(x|y)f(y)}{f(x)}=\frac{f(x|y)f(y)}{{\int }_{a}^{b}f\left(x|y\right)f\left(y\right)dy}$$

The third and fourth layers of the artificial neural network have to be altered to obtain f(y|x) and to allow for the assessment of f(x|y) through a kernel function of Gaussian type. The concluding age at death prediction is attained by the quantile estimation related to the a posteriori distribution.

Results

BMD shows a graded decrease with increasing age at all sites. Results by sex and age class are summarized in Table 2, Table 3 Table 4. In women, BMD Total exhibits a negative and moderate linear association with age at death (Pearson’s r =  − 0.696; p < 0.001), whereas both BMD at the neck of the femur (Pearson’s r =  − 0.743; p < 0.001) and BMD at the Ward’s area (Pearson’s r =  − 0.765; p < 0.001) present a negative and strong correlation with age (Fig. 2). Relative change between the first age class (20–29 years) and the oldest age group (80 + years) oscillates between 39.0% (BMD Total) and 56.9% (BMD Ward). Among men, BMD Total (Pearson’s r =  − 0.543; p < 0.001) and BMD Neck (Pearson’s r =  − 0.660; p < 0.001) decline moderately with age, while BMD Ward shows a strong and negative linear correlation with age (Pearson’s r =  − 0.718; p < 0.001; Fig. 3). BMD variation between the youngest and oldest age classes is lesser than in women, fluctuating between 23.1% (BMD Total) and 44.0% (BMD Ward). MCI also decreases with increasing age at death in both sexes (Table 5), with a negative and moderate linear association in the women’s group (Pearson’s r =  − 0.582; p < 0.001), and a weak, negative, correlation among men (Pearson’s r =  − 0.202; p = 0.040). Relative variation between the youngest and oldest age classes is 39.9% in women and 21.0% in men.

Table 2 Mean values of bone mineral density at the total hip (BMDTotal) according to sex and age class (CISC)
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Table 3 Mean values of bone mineral density at the femoral neck (BMDNeck) according to sex and age class (CISC)
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Table 4 Mean values of bone mineral density at Ward’s area (BMDWard) according to sex and age class (CISC)
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Fig. 2
figure 2

Strong negative association between bone mineral density at Ward’s area (g/cm.3) and age at death in females (CISC)

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Fig. 3
figure 3

Strong negative association between bone mineral density at Ward’s area (g/cm.3) and age at death in males (CISC)

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Table 5 Mean values of metacarpal cortical index (MCI) according to sex and age class (CISC)
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A conventional least squares regression analysis was conducted, and three age estimation models — tailored for each sex and also for individuals whose biological sex is not known — were generated (Table 6). Goodness-of-fit statistics for the different linear regression models used to predict adult age at death are summarized in Table 7. The mean absolute difference between the known and predicted age at death ranges from 9.39 to 13.18 years among women and 10.33 to 15.76 among men. The best linear regression models combine BMD Ward with MCI, while those that employ only the metacarpal cortical index present the poorer performance.

Table 6 Age estimation models with least squares regression
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Table 7 Statistical metrics for different linear regression models used to estimate age at death through bone mineral density (BMD Ward) and metacarpal cortical index (MCI)
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A modified general regression neural network was employed to generate different models for age estimation. A total of 15 models for each sex — and for individuals with unknown sex — were created. Measures of prediction accuracy for the age at death predicting method are summarized in Table 8. In women, the mean absolute difference between documented and projected age ranges from 8.44 to 12.58 years, while in men, the difference ranges from 10.56 and 16.18 years, contingent to the variables employed to generate the models. As a rule, models relying on BMD variables show increased accuracy: a model with BMD at the neck and BMD Ward exhibits the best performance in women, and the model that uses only BMD measured at Ward’s is superlative in men. The least efficient models include those that only use the metacarpal cortical index, followed by those that employ BMD Total in isolation.

Table 8 Statistical metrics for different artificial neural network models used to estimate age at death through bone mineral density (BMD Total, Neck, and Ward) and metacarpal cortical index (MCI)
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All models were contrived as a new online application — DXAGE 2.0, freely available at http://osteomics.com/DXAGE2/ — that enables a user-friendly and interactive routine for age estimation with BMD and MCI values. In the case of GRNN models, DXAGE 2.0 displays the most probable point estimate for age at death, as well as a credible interval featuring the lowest and highest values of age predicted (Fig. 4). The application facilitates the exclusion of any of the variables when appropriate. The least squares regression module (GLM) features a map of data points that supports measurement validation.

Fig. 4
figure 4

available at http://osteomics.com/DXAGE2/. DXAGE 2.0 displays the most probable point estimate for age at death, as well as a credible interval for the estimation

DXAGE 2.0 is freely

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Discussion

This study elaborates a previous method [1] by extending its application to adult males, introducing metacarpal cortical bone loss features to the age estimation models, and adding least squares regression analysis to the statistical models. Bone mineral density declines with age, a general pattern identified in epidemiological and anthropological samples, e.g., [39, 40, 42, 43, 68, 77,78,79,80]. Age-related cortical bone decline at the second metacarpal has been also observed in both contemporary and historical assemblages, e.g., [59, 61,62,63, 81]. Bone loss continues even during old age [41, 82], a feature that is useful for the assessment of age in older individuals.

Bone decline with age seems more evident in women and in the proximal femur — and that explains the better results found in the models designed for females and in those using BMD features instead of MCI. Before puberty, there are no consistent differences in bone mass between women and men [83, 84] with sex heterogeneity in bone morphology and mass resulting from the later onset and prolonged extent of puberty in males [85]. After the attainment of peak bone mass, age-related bone loss occurs in both sexes, independently of gonadal hormonal levels, involving both trabecular and cortical bone. Of course, sex-specific age-related variation in bone mass is expected since bone loss accelerates during perimenopausal and postmenopausal years, as estrogen withdrawal around and after menopause promotes bone remodeling [86, 87]. This acceleration in bone loss around menopause is a leading determinant of the sex differences in the age-related patterns of bone loss [88].

Age estimation models based on BMD measured at the proximal femur are more accurate than those that rely in the metacarpal cortical index, individually or in conjugation. In sharp contrast with the proximal femur, the second metacarpal diaphysis is primarily composed by cortical bone, which is subjected to a slower remodeling due to its lower surface-area-to-volume ratio [86]. Interestingly, the best model (a GRNN model) to predict age at death in females employs both a predominantly cortical (femoral neck) and a mostly trabecular (Ward’s area) ROI. In males, the best model is based upon Ward’s area only (a GRNN model). Diagenesis (namely macrostructural, microstructural, or chemical variations of the bone) can influence the densitometric analyses. Hence, a previous evaluation of the possible effect of taphonomic factors on the densitometry readings is warranted. A mounting body of evidence suggests that, even in bones showing different degrees of diagenetic change, bone mineral content is not significantly modified [89, 90]. Direct and indirect evidence (macroscopical examination, lack of bone erosion caused by soil as shown on conventional radiographs, microradiography, and an epidemiologically expected pattern of bone loss) indicate that the studied sample presents a good state of preservation [1, 68, 91].

It is important to note that DXA is a more precise technique, while the sensitivity of conventional radiogrammetry regarding bone loss is restricted, as it can only detect a bone mass reduction of more than 30–50% [92]. It was noted in a French study that the cortical index shows a significant, but poor, association with age in non-adults — in contrast, measurements of the epiphyseal-metaphyseal ratio (REM) presented a good correlation with age [65]. Notwithstanding, we have decided to maintain the models based on MCI, prioritizing applicability instead of accuracy, since, in certain circumstances, the second metacarpal may be the only bone available to estimate age at death.

Overall, GRNN models perform better than least squares regression models. By comparing similar models (i.e., models that feature the same variables), it is obvious that GRNN models present better goodness-of-fit statistics. For example, the mean absolute error in GRNN models ranges from 8.70 years (BMD Ward + MCI) to 12.58 years (MCI) in women, while in linear regression models, it varies from 9.39 years (BMD Ward + MCI) to 13.18 years (MCI). The difference is not impressive, but while least squares regression is a powerful and interpretable methodology, it shows some caveats — namely a detrimental effect by outliers and bias [93]. In fact, a well-recognized problem in adult age estimation — particularly when the dependent variable in linear regression is the age at death — is expressed by the “attraction of the middle,” i.e., the systematic trend towards age overestimation in younger adults and age underestimation in older persons [34, 72, 94]. This trend has been recognized in different validation studies [95], including in an earlier method based in bone mineral density values [55]. The “age mimicry,” specifically whereby age can be underestimated [94], can be magnified if the demographic composition of the reference sample does not include a large number of older individuals — and that is possibly the case for the males’ sample in this study, particularly in the older age class (80 + years) that features only seven individuals. Different statistical approaches (e.g., Bayesian statistics, transition analysis or probabilistic models) have been employed to counteract estimation bias, e.g., [36, 37, 96,97,98,99,100,101,102].

Artificial neural networks are adaptative models that emulate the architecture of the brain [103, 104] and have been used to solve a plethora of generic tasks, being appropriate for modeling multifaceted and nonlinear phenomena [105]. ANN have been occasionally exploited in bioarcheology and forensic anthropology, but have shown their usefulness in applied purposes, such as sex estimation [106,107,108,109] and age prediction [35, 37, 98]. General regression neural networks are based on the general regression theory but operate as a black-box (however see Navega and Cunha, 2020), producing highly nonlinear functions with no interpretability constrains [111]. With the GRNN implementation, age at death is not simply estimated as a point value, but rather as a likely age interval.

A significant improvement of DXAGE 2.0 stems from the type of bones used to generate models for age estimation. The femur is among the strongest skeletal elements and one of the most abundant and well-preserved bones in archeological assemblages or forensic settings. The second metacarpal is less well represented in archeological contexts but tends to be well preserved and complete when present [112, 113]. This is particularly relevant since it is not always possible to use classic aging methods due to taphonomic factors [76, 114]. The pubic symphysis, for example, is extremely fragile and often does not resist to post-depositional processes [19]. Also, in the case of comingled and/or scattered remains, or mass disasters, individuals are usually represented by a subset of bones, or fragments of bone, severely limiting age at death assessment [115]. The study of commingled remains demands a larger degree of flexibility in the assessment of demographic features, such as age at death [116].

DXAGE 2.0 enables age estimation in incomplete or fragmentary skeletal remains — providing an additional tool to reconstruct the biological profile in different mortuary contexts, such as ossuaries, secondary burials, or mass graves. For example, crania and long bones compose the bulk of skeletal remains in ossuaries from protohistoric North America, characterized by multiple ritual steps during the mortuary treatment of the dead, or collective burials from the Late Neolithic in the Iberian Peninsula [117, 118]. Furthermore, techniques based in medical imaging modalities, including DXA, are non-invasive and suitable for age assessment in fleshed or partially fleshed cadaveric remains [56,57,58, 100, 119,120,121,122,123,124]. These are frequently recovered in forensic contexts and often skeletal preparation is not feasible, practical, or culturally acceptable. A DXA analysis of the proximal femur can also be used to estimate sex in skeletal remains [125,126,127]. Hence, an isolated femur has the potential to convey essential data about the major parameters of a biological profile, viz. age at death, sex, and stature.

Final remarks

Age at death estimation techniques have increasingly relied on more objective evaluations of the aging process combined with unconventional statistical approaches. Nevertheless, age estimation in adult skeletons is still fraught with difficulties, with individual and population factors influencing remodeling and degeneration of the skeleton and biological age. Accordingly, it is necessary to use different indicators to provide a more detailed and nuanced view of skeletal aging. DXAGE 2.0 yields comparable age estimates to those obtained by conventional methods, employing alternative skeletal regions, an objective analytic procedure, and providing an easy online platform for age prediction in adult skeletal remains. The proposed models show some limitations, particularly the fact that only individuals of south European ancestry were included in the training sample. Likewise, the relatively smaller sample of older males features a potential methodological shortcoming. The addition of densitometric and radiogrammetric data from other populations, as well as from older individuals, to the current database of DXAGE 2.0 is thus desirable in future refinements.