Fractal dimension, lacunarity, and cortical thickness in the mandible: Analyzing differences between healthy men and women with cone-beam computed tomography

Morphological and morphometric differences between male and female individuals are evident in anatomical, biological, and physiological analyses of bone,1 which are conducted for forensic and other purposes. The mandible is one of the most reliable structures for determining sex in humans.2, 3 The mandibular bone is usually analyzed according to standard morphometric measurements, such as mandibular ramus height and width, body length, and symphyseal height.4, 5 However, little is known about the microstructural differences that show substantial differences between sexes besides pathologic conditions. Generally, the bone microarchitecture of the mandible is assessed to diagnose and monitor diseases, such as osteoporosis and other metabolic alterations,6 and the bone microarchitecture can be used to distinguish male from female individuals in these conditions.

Most studies have used X-ray imaging exams to assess bone microarchitecture.7 Conventional radiography, although it has good clinical applicability, has some limitations, mainly related to its 2-dimensionality and overlapping structures. Cone-beam computed tomography (CBCT) offers some advantages over these limitations, since it has excellent resolution, allows the assessment of multiple images, and provides a 3-dimensional reconstruction of the bones.8

Fractal dimension (FD) and lacunarity (Lac), which are assessed based on radiographs and other imaging techniques, are regarded as important research tools in bone investigation. These parameters relate to bone irregularity (meaning irregular patterns with self-similarity at different scales) and “gappiness” (from the Latin word lacuna, referring to gap or hole variability), respectively.9, 10 Several studies have used FD and Lac to assess the differences between groups of individuals with different diseases and conditions.6, 11, 12 Briefly, FD measures how the bone fills a metric space, and Lac measures the distribution of gaps in the bone.10 In addition to these parameters, quantitative methods can also be used to assess the bone microarchitecture, usually by calculating the bone volume fraction (BV/TV), which corresponds to the bone volume in a given area (i.e., the volume of mineralized bone per volume unit in the sample).13, 14, 15

In sex differentiation, age should also be considered, since structural alterations in both cortical and trabecular bone are associated with aging.6, 10 Sex determination, which can be done through bone texture analysis using X-ray images, is of great interest. Therefore, the present study aimed to measure the trabecular parameters of FD, Lac, and BV/TV, together with the cortical thickness, in the mandibles of healthy adults from 20 to 60 years of age to determine their sex.

Two previously calibrated examiners with expertise in CBCT interpretation assessed the cortical bone thickness separately. To determine intra-examiner agreement, 20% of the sample was randomly reassessed. Statistical significance (P<0.05) was observed for the intraclass correlation coefficients (ICCs), which showed moderate to strong agreement (0.52–0.90, with the only 2 ICC values under 0.6 being for the lower central and lateral incisors, at the buccal and lingual walls, respectively).

In total, 116 CBCT exams of healthy individuals were analyzed, from 57 men and 59 women, ranging from 20 to 60 years old, who were divided into subgroups according to sex and age (Table 1). As there was no significant difference in age between men and women (P=0.23, Table 2), all following comparisons (trabecular analysis of FD, Lac, and BV/TV; cortical linear measurements) were considered to compare all male subjects versus all female subjects.

Table 1
Sample distribution in relation to sex and age groups

• Click for larger image

Table 2
Comparison between men and women regarding age, texture analysis, and cortical thickness

• Click for larger image

Comparisons between the sexes for each parameter are shown in Table 2. The values for FD, Lac, and BV/TV were significantly different between men and women. Regarding the analysis in grayscale (without binarization), men revealed higher FD and lower Lac values than women. The values for bone volume through binarization were higher in women. Significant differences were also found between the sexes in terms of cortical thickness linear measurements. In men, the lingual wall in the central and lateral incisor areas and the buccal wall in the canine area were thicker than in women (Table 2).

A statistically significant and positive correlation was found between age and all linear measurements of the cortical bone in the central incisor area. A correlation was also identified between age and the cortical thickness in the basal part of the mandible in the 3 analyzed areas. Although these correlations were statistically significant and positive (i.e., the direction of association between the variables was such as one increased, so did the other), they were not strong, with correlation coefficients less than 0.4 (Table 3).

Table 3
Spearman correlation coefficient (r_s) between age and each texture parameter and cortical thickness

• Click for larger image

In the present study, men and women with a wide range of ages showed differences in terms of FD and Lac. BV/TV was also different between the sexes, as women presented higher values of trabecular volume in the anterior mandible than men. According to the literature, bone loss is mainly observed in female individuals, as has been demonstrated in several studies. Research on postmenopausal osteoporosis, usually diagnosed in the lumbar spine and proximal femur of woman >50 years of age, has revealed that an imbalance in bone formation and resorption affects trabecular bone (loss of connectivity) and cortical bone (cortical thinning and porosity).18, 19 However, some facts need to be considered when comparing those studies with the results of the present study, as follows: the difference in the ossification process (intramembranous in the mandible and endochondral in the long bones);20 differences in the turnover rates (in the jaw bones, turnover could be 10 times more active, mostly considering the masticatory behavior and the related biomechanics);21 the age of the women included in other studies (bone loss is more evident in postmenopausal woman,18, 19 while our study included young women, with an age range starting at 20 years); and finally, in general (regarding all bones at different ages, considering sexual dimorphism), androgen hormones are more related to the longitudinal growth of bones in the cortical area (mostly because of the delay in growth plate closure), whereas estrogen favors the growth of trabecular bone.22

Besides trabecular bone volume, the additional parameters evaluated in our study (FD and Lac) showed statistically significant differences in men and women from 20 to 60 years of age, implying that they might be useful parameters for sex determination when combined with conventional parameters such as bone volume and thickness. Regarding mandible thickness, both sexes presented differences in terms of cortical thickness in some areas of the anterior mandible, but not in all analyzed areas. Measuring the cortical thickness of the lingual wall in the central incisor area of the mandible seems to be a reliable method for sex determination, mainly because it is easy to access this area using CBCT.

Sex determination is very important for the forensic process of human identification. Sex is usually the second out of the 4 parameters that are addressed in biological profile assessments (population affinity, sex, age, and height) since many methods for estimating age and height rely on sex identification. There are only 2 possible results for sex determination: male or female. In contrast, the results of the other parameters are much more diverse.2, 23 Forensic anthropological analyses for sex determination can use qualitative characteristics (i.e., morphological and osteological analysis) or quantitative characteristics (i.e., osteometric analysis).2, 3 Sex determination based on the skeleton depends on the available bones and their state of preservation, and it can be particularly difficult when the bones are fragmented.

The mandible is the largest and hardest facial bone. It usually resists postmortem damage and is thus an important indicator of sexual dimorphism.2, 3, 24, 25 The mandibular bone can reveal sexual dimorphism2, 3 through standard morphometric measurements, such as the mandibular angle, ramus height, and mandibular symphysis.2, 3, 24, 25 However, little is known about the microstructural bone differences between the sexes and how those differences can be used for sex determination.

Parameters related to bone complexity could yield new insights into sexual dimorphism in addition to conventional linear measurements. FD analysis is a mathematical method for analyzing complex shapes and structural patterns. A meta-analysis26 revealed that FD assessments based on dental radiographs were unable to distinguish healthy individuals from patients with osteoporosis based on dental images. The authors concluded that a standardized FD calculation is needed. In addition to radiographs, analyses of CBCT images could be improved, including other parameters, such as bone microarchitecture. The present study calculated FD and Lac based on CBCT images to obtain data that could later be used in sex determination. FD was assessed based on grayscale CBCT images because it was considered a good option for an in vivo high-resolution assessment of the trabecular microstructure of the mandible. Gaalaas et al.27 performed a texture analysis based on CBCT images of healthy individuals, but did not find a significant difference between the sexes. In contrast, other authors,28 who assessed FD in healthy individuals, found significant differences between the sexes, similar to the present study. When comparing men and women over the age of 40, those authors found a significant difference in the area of the mandibular first premolars and condyle. When comparing individuals younger than 40, they found a significant difference in the area of the maxillary premolars and the mandibular lateral incisors.

A systematic review29 revealed that, out of 15 studies that assessed FD based on CBCT, all of them analyzed the trabecular bone, and 14 of them used the box-counting method, with values ranging from 0.91 to 2.4. Our study found a mean FD value of 1.02 in men and 0.97 in women. Although these values coincide with the intervals reported by other studies on CBCT, the use of grayscale images, without binarization, was a new approach conducted in the present study. This approach is less time-consuming since it excludes the preprocessing that is required for binarization. It can be recommended that future studies on CBCT-based FD compare the values found in this study with healthy control individuals. FD values that represent bone complexity should be considered for differentiating men and women.

Another interesting approach for assessing bone organization is measuring the Lac index, which shows how pixels and voxels are spatially organized within an image.10 Lac refers to the distribution and size of empty spaces on an image.9, 10 In this study, the Lac index was assessed using grayscale images without binarization, similar to how FD was measured. Lac was significantly different between men and women. The mean values were 0.15 and 0.12, respectively. Women presented larger void spaces in the mandibular trabecular bone than men. These results suggest that Lac can be used for sex determination. However, further studies should be carried out on other populations using the same preprocessing methods with grayscale images to ensure their reliability for sex determination.

In addition to FD and Lac, assessing the mandibular microarchitecture based on CBCT might be a good option for obtaining more data for sex determination. Nevertheless, the limitations of CBCT in analyzing the trabecular bone should be considered. Even if it has some limitations, Pauwels et al.30 stated that parameters related to the trabecular bone structure are strongly affected by voxel size. Van Dessel et al.31 demonstrated that most CBCT equipment could quantitatively assess alveolar bone quality with a level of accuracy and reliability approaching that of micro-computed tomography (CT). However, they reported that the tomography equipment used in this study (i-Cat Next Generation) overestimated bone quantity and presented a different structural pattern from the images obtained by other CBCT equipment. He et al.15 evaluated several CBCT image post-processing protocols to approximate the results obtained by CBCT images with those of micro-CT. The authors concluded that post-processing approaches can be used to increase the effectiveness of CBCT when assessing trabecular bone parameters. However, regardless of the type of processing, the CBCT images yielded significantly different results from those measured on micro-CT images.

Anthropological analyses of human remains provide information for the reconstruction of the biological profile. These analyses comprise 4 major parameters: probable geographic origin (also known as ancestry or population affinity), sex, age at the time of death, and height. Generally, in sex determination, the options are male, female, or undefined (when the results are inconclusive).23 Schimitt et al.32 stated that sex determination is more problematic when the body is skeletonized than when the body still has soft tissues. Sex determination is conducted in the paleoanthropological and criminal investigation fields, which require a high level of reliability and face biological and methodological limitations. The reliability and accuracy of sex determination of human remains depend on the available anatomical area and, most importantly, the integrity of the bones. Sex determination can be reliable, as it usually stems from observable features in the hip bones, skull, and long bones of the upper and lower limbs, if the bones are not fragmented.

It is important to develop and study methods that facilitate sex determination in different environments, with the available materials (in some cases, fragmented bones), either for research or professional purposes, at universities or by expert services. The present study presents a possible approach to sex determination through the assessment of FD, Lac, trabecular BV/TV, and cortical thickness in the mandible of healthy adults of different ages based on mandibular sections. These parameters can at least partially facilitate sex determination during the human identification process.

The major limitation of this study is that it was retrospective. Furthermore, FD was not assessed through binarization, although this is the most frequently used method in the literature. However, a simpler method, such as the one adopted in this study, would be less time-consuming and require fewer steps for image processing.

In conclusion, the mandible trabecular parameters of FD, Lac, and bone volume were different between healthy men and women from 20 to 60 years of age. Cortical thickness in the anterior mandible also revealed differences between males and females. Therefore, these parameters could be useful for sex determination based on an intact mandibular bone or its fragments.