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Three-dimensional analysis of the uniqueness of the anterior dentition in orthodontically treated patients and twins
Forensic Science International 273 (2017) 80–87
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Forensic Science International journal homepage: www.elsevier.com/locate/forsciint
Three-dimensional analysis of the uniqueness of the anterior dentition in orthodontically treated patients and twins A. Francoa,b,* , G. Willemsa , P.H.C. Souzab , O.M. Tanakac , W. Coucked , P. Thevissena a
Department of Oral Health Sciences – Forensic Dentistry, KU Leuven & Dentistry, University Hospitals Leuven, Belgium Department of Dentistry – Stomatology, School of Life Sciences, Pontifícia Universidade Católica do Paraná, Brazil Department of Dentistry – Orthodontics, School of Life Sciences, Pontifícia Universidade Católica do Paraná, Brazil d Free-lance statistician, Heverlee, Belgium b c
A R T I C L E I N F O
Article history: Received 19 August 2016 Received in revised form 2 February 2017 Accepted 14 February 2017 Available online xxx Keywords: Uniqueness Human dentition Twins Orthodontic treatment Forensic odontology
A B S T R A C T
Dental uniqueness can be proven if no perfect match in pair-wise morphological comparisons of human dentitions is detected. Establishing these comparisons in a worldwide random population is practically unfeasible due to the need for a large and representative sample size. Sample stratification is an option to reduce sample size. The present study investigated the uniqueness of the human dentition in randomly selected subjects (Group 1), orthodontically treated patients (Group 2), twins (Group 3), and orthodontically treated twins (Group 4) in comparison with a threshold control sample of identical dentitions (Group 5). The samples consisted of digital cast files (DCF) obtained through extraoral 3D scanning. A total of 2.013 pair-wise morphological comparisons were performed (Group 1 n = 110, Group 2 n = 1.711, Group 3 n = 172, Group 4 n = 10, Group 5 n = 10) with Geomagic Studio1 (3D Systems1, Rock Hill, SC, USA) software package. Comparisons within groups were performed quantifying the morphological differences between DCF in Euclidean distances. Comparisons between groups were established applying One-way ANOVA. To ensure fair comparisons a post-hoc Power Analysis was performed. ROC analysis was applied to distinguish unique from non-unique dentures. Identical DCF were not detected within the experimental groups (from 1 to 4). The most similar DCF had Euclidian distance of 5.19 mm in Group 1, 2.06 mm in Group 2, 2.03 mm in Group 3, and 1.88 mm in Group 4. Groups 2 and 3 were statistically different from Group 5 (p < 0.05). Statistically significant difference between Group 4 and 5 revealed to be possible including more pair-wise comparisons in both groups. The ROC analysis revealed sensitivity rate of 80% and specificity between 66.7% and 81.6%. Evidence to sustain the uniqueness of the human dentition in random and stratified populations was observed in the present study. Further studies testing the influence of the quantity of tooth material on morphological difference between dentitions and its impact on uniqueness remain necessary. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Forensic investigations on the uniqueness of the human dentition (UHD) increased considerably in the last few years [1– 5]. Although the UHD is fundamental for forensic human dental identification and bite mark analysis, the increased prevalence of these investigations was mainly induced by the uncertainty surrounding the forensic bitemark practice [6–8]. It is estimated
* Corresponding author at: Department of Oral Health Sciences – Forensic Dentistry, KU Leuven and Dentistry, University Hospitals Leuven, Kapucijnenvoer 7, block B, 3000 Leuven, Belgium. E-mail addresses: [email protected], [email protected] (A. Franco). http://dx.doi.org/10.1016/j.forsciint.2017.02.010 0379-0738/© 2017 Elsevier B.V. All rights reserved.
that more than 14 innocents were convicted or indicted based on misinterpreted bitemark evidences [8,9]. Accordingly, the American National Academy of Science included the unproven UHD amongst the most essential topics to be revisited scientifically [10]. Several studies in the field investigated the UHD in the context of bitemarks [1,5,11,12]. However, the outcomes reported were biased potentially based on methodological aspects [13]. Random sampling was one of the issues observed in these studies [1,2,14]. Establishing a methodological investigation on the UHD with a random population requires a representative and large sample size. Sample stratification arose as an option to reduce this issue. Stratification may be applied based on the presence of specific dental identifiers or using a specific population type [13]. Using specific dental identifiers enables the selection of subjects based on their particular dental traits, e.g. on specific tooth rotations or
A. Franco et al. / Forensic Science International 273 (2017) 80–87
particular shape of dental crowns [15,16]. Evaluating a specific population type enables to filtrate subjects presenting similar dental morphology and arrangement, e.g. orthodontically treated patients and twins [11,12,14]. In practice, stratifying a sample on a specific dental identifier is extremely more difficult, than selecting individuals based on a specific population type. Applied in previous studies, sample stratification based on a specific population type did not enable to support a complete proof of the UHD due to additional methodological limitations [11,12,14– 16]. These limitations consisted of 2D image registration techniques used to compare 3D structures (human teeth); operator-depending procedures (landmarking); the lack of operator reproducibility control (intra-/inter-reliability tests); and the lack of proper data analysis (statistics) [13]. In fact, the UHD was not proved yet in the context of bitemarks impressed on human skin. These bitemarks often registers the indentations of the anterior dentition (six anterior teeth – from canine to canine). This is the reason why in the present research pair-wise superimpositions of dentitions were performed exclusively comparing the anterior dentition. The present research aims to prove the UHD three-dimensionally (3D) comparing the dental crown morphology of the anterior dentition in stratified samples of orthodontically treated patients, twins, and orthodontically treated twins in relation to a threshold sample of identical dentitions. Additionally, a sample of random patients is included to prove and express the importance of sample stratification in the investigations on the uniqueness of the human dentition. 2. Material and methods The present research was conducted after approval of the Committee of Ethics in Research (protocol number: 19575613.2.0000.0020). Three groups of dental casts were sampled and 3D digitized. Group 1 was composed by 22 dental casts (11 mandibular and 11 maxillary) of randomly selected subjects (7 males and 4 females). Group 2 consisted of 59 maxillary dental casts of orthodontically treated patients (32 males and 27 females), collected after the removal of the orthodontic brackets. Group 3 included 344 dental casts (172 mandibular and 172 maxillary) of 86 pairs of twins, 39 were monozygotic (36 males and 42 females) and 47 were dizygotic (50 males and 44 females). Group 4 comprised 20 dental casts (10 mandibular and 10 maxillary) of 5 pairs of orthodontically treated monozygotic twins (2 males and 8 females) (Table 1). All the dental casts included presented the permanent anterior teeth (from canine to canine). Dental casts with clinically visible supernumerary teeth in the anterior region, restorative or
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prosthetic dental treatment in the anterior teeth, and fixed orthodontic retainers were excluded. Specifically in Group 2, ahigh prevalence of orthodontic retainers was observed justifying the lack of analysis of mandibular dental casts. In Group 4, patients were also orthodontically treated but no orthodontic retainer was observed. In all the groups, the dental impressions were taken by the same operator (author) with alginate (Jeltrate Dustless1, Dentsply1, York, PA, USA) following the instructions of the manufacturer. These impressions were casted with plaster type IV (Durone1, Dentsply1, York, PA, USA) and digitalized using an automated motion device with angular laser scanning (XCADCAM Technology1, São Paulo, SP, Brazil) in resolution of <20 mm. The obtained digital cast files (DCF) were stored in .STL format and imported for morphometric analyses and pair-wise comparison in Geomagic Studio1 (3D Systems1, Rock Hill, SC, USA) software package (GS). To limit the comparisons to the anterior dentition, a standardized GS cropping procedure was established, placing on each DCF a cropping contour along the cemento–enamel junction of the anterior teeth based on 58 precropping points. Mean threshold values were established for the classification of two cropped DCF as identical or not. One examiner took impressions of 5 different subjects and repeated it after 7 days. The dental impressions were casted, digitized and prepared for analysis according to the procedures described previously. These DCF consisted of a reference group (Group 5). The mean threshold values were a measure of the comparative errors originating from the procedure to obtain the dental impressions, the casts, the DCF, the GS cropping procedure and the GS pair-wise morphometric comparisons. Within random (Group 1) and orthodontically treated (Group 2) patients, all possible pair-wise DCF comparisons were performed, totalizing 110 (55 per dental arch) and 1711 (only maxillary arch) comparisons, respectively. Specifically in these groups, sub-sampling was necessary to randomly select only the independent pair-wise comparisons (in which the same DCF was not repeated). This procedure was repeated 250 times combining independent comparisons. Within twins (Group 3) and orthodontically treated monozygotic twins (Group 4), the DCF were pair-wise compared with their respective twin sibling DCF, totalizing 172 (86 for the mandible and 86 for the maxilla) and 10 (5 for the mandible and 5 for the maxilla) comparisons, respectively. Additionally in Group 3 mono- and dizygotic twin pair DCF were evaluated in function of the zygosity. In the reference sample (Group 5) the DCF of each subject obtained at moment 1 was pair-wise compared with the respective DCF at moment 2, separately for the maxilla and mandible, totalizing 10 comparisons. All the pair-wise comparisons were performed with the GS automated superimposition tool.
Table 1 Subject distribution per sampled group stratified on dental arch, zygosity and sex. Dental arch
Group
Zygosity
Male (n)
Female (n)
Subjects (n)
DCF (n)
Maxillary
1 2 3 3 4 5
n/a n/a Monozygotic Dizygotic Monozygotic n/a
7 32 36 50 2 2
4 27 42 44 8 3
11 59 78 94 10 5
11 59 78 94 10 10
Mandibular
1 3 3 4 5
n/a Monozygotic Dizygotic Monozygotic n/a
7 36 50 2 2
4 42 44 8 3
11 78 94 10 5
11 78 94 10 10
DCF: digital cast files; Group 1: randomly selected subjects; Group 2: orthodontically treated patients; Group 3: twins; Group 4: orthodontically treated twins; Group 5: threshold; n/a: not applicable.
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For each pair-wise DCF comparison, GS calculated the observed morphological differences in dental crown morphology of the anterior dentitions. The differences were expressed in millimeters for each of the following quantification values: the maximum positive deviation (max.+); the maximum negative deviation (max.); the average deviation (ave.); and the standard deviation (SD). The four quantification values were statistically combined and converted in a single value, comprehending the Euclidean distance from origin (zero) obtained with the formula: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Distance ¼ Maxþ2 þ Max2 þ Average2 þ Standard deviation . This procedure enabled to rank the distance values; to verify if distance values were equal; and to detect distance values equal to zero. UHD was assessed in the four studied Groups (Groups from 1 to 4) comparing their Euclidean distances with the distances obtained in the reference (Group 5). One-way ANOVA [17] with log-transformed distances, was applied for the comparisons, separately for maxilla and mandible. Considering the multiple comparisons between groups, a correction for simultaneous hypothesis testing was applied according to Tukey’s range test [18]. UHD was considered when the mean Euclidean distance of any studied Group was statistically significant higher than the reference Group. In the lack of statistically significant differences sampling quality control was assured performing a post-hoc Power Analysis with a desired effect of 80%. Quality control for the comparative approach was assured for maxillary and mandibular DCF performing a ROC analysis. In this analysis Group 5 was confronted with all the other groups exploring its threshold potential for classifying non-equal dentitions as non-equal (sensitivity) and equal dentitions as equal (specificity). Confidence intervals for the ROC-curve and for the Area Under the Curve (AUC) were obtained by means of bootstrapping. ROC analyses were also performed systematically including less quantification values. The statistical tests were performed with significance rate of 5% using S+1 8.0 (Tibco1, Palo Alto, California, USA) software package. 3. Results The most similar maxillary DCF within each Group had Euclidian distances of 5.24 (random patients – Group 1), 1.87 (orthodontically treated patients – Group 2), 2.03 mm (twins – Group 3), 1.88 mm (orthodontically treated twins – Group 4), and 0.66 mm (reference – Group 5) (Figs. 1 and 2, Table 2). For the mandibular DCF, these distances were 5.19 (Group 1), 1.29 mm (Group 3), 1.66 mm (Group 4), and 1.03 mm (Group 5) (Figs. 1 and 3, Table 2). No equal or zero Euclidian distances were observed.
Table 2 Quantification values and Euclidian distance obtained from the most similar detected pair-wise DCF comparison per Group and per dental arch. Dental arch
Group
Max.+
Max.
Ave.
SD
Distance
Maxillary
1 2 3 4 5
3.20 1.11 1.41 1.33 0.49
4.09 1.45 1.43 1.29 0.45
0.01 0.03 0.01 0.11 0.01
0.77 0.44 0.35 0.32 0.07
5.24 1.87 2.03 1.88 0.66
Mandibular
1 3 4 5
3.96 0.88 0.83 0.84
3.16 0.90 1.41 0.59
0.35 0.03 0.02 0.01
1.10 0.29 0.28 0.11
5.19 1.29 1.66 1.03
DCF: digital cast files; DCF: digital cast files; Group 1: randomly selected subjects; Group 2: orthodontically treated patients; Group 3: twins; Group 4: orthodontically treated twins; Group 5: threshold; Max.+: maximum positive deviation; Max.: maximum negative deviation; Ave.: average deviation; SD: standard deviation.
Significant statistical differences (p < 0.05) were obtained for the maxillary DCF comparisons between Groups 1 and 5, 2 and 5, and 3 and 5 (Fig. 2, Table 3). The mandibular DCF comparisons were statistically different when comparing Groups 1 and 5, 2 and 5, and 3 (considering only dizygotic twins) and 5 (p < 0.05) (Fig. 3, Table 3). No significant statistical differences were observed comparing the mandibular DCF of monozygotic twins of Group 3 with Group 5, and comparing maxillary and mandibular DCF of Groups 4 and 5 (p > 0.05) (Table 3). Post hoc power analysis demonstrated that in order to obtain significant statistical differences between mandibular DCF of Groups 3 (monozygotic twins) and 5, the inclusion of 17 pair-wise comparisons in both groups would be necessary. Between Groups 4 and 5, 11 and 56 additional pair-wise comparisons would be necessary for the maxillary and mandibular DCF comparisons, respectively (Table 3). According to the ROC analysis, the Euclidean distances combining the four quantification values (max.+, max., ave., and SD) revealed a sensitivity of 80% and a specificity of 81.6% with an accuracy of 83% for Group 5 when compared to Groups 1, 2, 3 and 4 for maxillary DCF (Fig. 4). For the mandibular DCF sensitivity reached 80% and specificity 66.7%, with an accuracy of 81% (Fig. 5). These outcomes were not modified combining less quantification values. 4. Discussion UHD is a term used commonly in forensic dentistry, especially in the fields of human identification and bitemark analysis [19]. Despite that, this term is often misinterpreted. When the comparison between ante-mortem (AM) and post-mortem (PM) dental data (human identification); and between suspect dentition and bite pattern (bitemark) is considered a match, it only indicates that the compared forensic evidences are identical. Those evidences are unique only when it is guaranteed that they cannot be detected in another person in the world. In human identifications, the probability of considering the human dentition as unique is considerably higher compared to bitemark analysis. It is justified by the larger number of teeth and dental evidences (dental treatment, morphology and pathology) available for analysis. However, the UHD was investigated mainly in the context of bitemarks in the present study. Thus, the samples studied were stratified on the number of teeth (six per dental arch), the dental part (tooth crowns), and the type of population (orthodontically treated patients and twins). In these groups, besides general morphological information, dental shape, size, angulation and mutual tooth position were considered. This information was registered in life-size 3D DCF, enabling to capture all dental characteristics used in bitemark practice [20]. Similar to most of the studies investigating the UHD, the present study analyzed the six anterior teeth [13], which are the teeth most commonly involved in bitemarks [21]. Opposite to all studies included in a related systematic review [13], currently the entire dental crown morphology was considered instead of only their incisal edges, because in bitemarks the exact amount of tooth surface that contacts and impresses the human skin may vary from case to case. The initial analysis within each group enabled to rank the Euclidian distance values in order to screen the most similar pairs of DCF in the sample. The smallest distances resulted below 5.24 mm for the maxilla and below 5.19 mm for the mandible (Table 2). This analysis also revealed no equal Euclidean distance values between the pair-wise comparisons. However, equal Euclidian distances only indicated that the combined quantification of all morphological differences calculated by GS between two pair-wise DCF comparisons were equal. Theoretically, zero is the
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Fig. 1. Clinical pair-wise comparisons of DCF (morphometric outcomes provided by GS) with the lowest Euclidean distance from the maxillary and mandibular dental arches detected in Groups 1 (randomly selected subjects) 2 (orthodontically treated patients), 3 (twins) and 4 (orthodontically treated monozygotic twins). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Reference and target DCF are represented in mono-colored blue, while comparison outcomes are represented multi-colored. In the last, the color coded system ranges from red (max.+) to dark blue (max.), in which greenish tones corresponds to morphological differences close to zero. Although no statistically significant difference was calculated (p > 0.05) between Group 4 and 5 (threshold), clinically clear signs of morphological differences (reddish areas) were observed. The chromatic representation of the morphometric differences between DCF were translated in single values in the present study using the forqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 mula:Distance ¼ Maxþ2 þ Max2 þ Average2 þ Standard deviation . As expected, the maximum and minimum deviation values could jeopardize the Euclidean distance values (formula outcome). In order to avoid this limitation, sub-sampling was performed in Group 2 to exclude the repeated DCF in the sample. More important, the different set ups were tested systematically reducing the number of quantification values in the formula. The use of 4 quantification values yielded the best distinctive power to classify equal and non-equal DCF in the present study.
Fig. 2. Euclidean distances calculated on the combination of the four quantification values (Max.+, Max., Ave., SD) for maxillary DCF in the experimental (G1, G2, G3 and G4) and reference (G5) groups. DCF: digital cast files; G1: random patients (Group 1); G2: Orthodontically treated patients (Group 2); G3M: monozygotic twins (Group 3); G3D: dizygotic twins (Group 3); G4: orthodontically treated monozygotic twins (Group 4); G5: control group used as threshold (Group 5); Max.+: maximum positive deviation; Max.: maximum negative deviation; Ave.: average deviation; SD: standard deviation; p-values from ANOVA test comparing groups may be consulted in Table 3.
Euclidean distance value indicating that two compared DCF are equal (and proves the lack of uniqueness). However, in the performed research, measuring and operator errors need to be taken into account. The factors potentially biasing the performed pair-wise DCF comparisons were 1) the confection of dental
impressions and dental casts, 2) the 3D scanning process; 3) the 3D digital cropping; and 4) the GS comparison measure error. In this context, Group 5 was created combining and quantifying these factors to establish a threshold that enables to classify non-equal and equal DCF (separately for the mandible and the maxilla). This
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Table 3 p-Values obtained from ANOVA comparisons between Groups per dental arch. Dental arch
Comparison
Mean distances
p
Maxillary
G1 vs. G2 G1 vs. G3D G1 vs. G3M G1 vs. G4 G1 vs. G5 G2 vs. G3D G2 vs. G3M G2 vs. G4 G2 vs. G5 G3D vs. G3M G3D vs. G4 G3D vs. G5 G3M vs. G4 G3M vs. G5 G4 vs. G5
8.03 vs. 4.74 8.03 vs. 5.62 8.03 vs. 4.43 8.03 vs. 3.51 8.03 vs. 2.24 4.74 vs. 5.62 4.74 vs. 4.43 4.74 vs. 3.51 4.74 vs. 2.24 5.62 vs. 4.43 5.62 vs. 3.51 5.62 vs. 2.24 4.43 vs. 3.51 4.43 vs. 2.24 3.51 vs. 2.24
0.0888 0.4196 0.0248 0.0298 0.0001 0.5140 0.9631 0.7531 0.0001 0.0613 0.2166 0.0001 0.9302 0.0003 0.0998a
Mandibular
G1 vs. G3D G1 vs. G3M G1 vs. G4 G1 vs. G5 G3D vs. G3M G3D vs. G4 G3D vs. G5 G3M vs. G4 G3M vs. G5 G4 vs. G5
10.79 vs. 4.85 10.79 vs. 3.79 10.79 vs. 2.70 10.79 vs. 2.09 4.85 vs. 3.79 4.85 vs. 2.70 4.85 vs. 2.09 3.79 vs. 2.70 3.79 vs. 2.09 2.70 vs. 2.09
0.0066 0.0003 0.0006 0.0001 0.2148 0.1941 0.0040 0.7562 0.0723b 0.8150c
DCF: digital cast files; G1: randomly selected subjects; G2: orthodontically treated patients; G3M: monozygotic twins; G3D: dizygotic twins; G4: orthodontically treated twins; G5: threshold; p-values from ANOVA test for significance rate of 5%. a Post-hoc Power Analysis indicates that both groups need to be enlarged in 11 comparisons to reach statistically significant difference. b Post-hoc Power Analysis indicates that both groups need to be enlarged in 17 comparisons to reach statistically significant difference. c Post-hoc Power Analysis indicates that both groups need to be enlarged in 56 comparisons to reach statistically significant difference.
threshold was used as reference in the search for equal DCF in the studied Groups 1, 2, 3 and 4. Randomly selected subjects (Group 1) were included in the present study not to prove uniqueness within this population but
yet to highlight the importance of sample stratification on studies in the field. Based on that, it became more relevant to compare Group 1 with the other experimental groups (Groups 2, 3 and 4) than with the threshold group (Group 5). As observed, the mean Euclidean distances obtained in Group 1 were the highest in this study. However, the mean Euclidean distance for maxillary DCF (8.03) was only statistically different (p < 0.05) when compared to monozygotic twins (Group 3) and orthodontically treated monozygotic twins (Group 4). Yet the mean Euclidean distance for mandibular DCF (10.79) was statistically different (p < 0.05) compared to all the groups. This finding suggest that sample stratification for maxillary DCF better succeeds using samples (Group 3) and sub-samples (Group 4) of monozygotic twins, while for mandibular DCF orthodontically treated patients may be used as well. A secondary finding obtained from these outcomes suggests that UHD is more difficult to be proved within the maxillary anterior teeth, which required stronger sample stratification to reach statistically significant difference from the random population. As expected, when compared to Group 5, Group 1 revealed statistically significant differences (p < 0.05) for maxillary and mandibular DCF. However, as previously observed, proving UHD in a random population (Group 1) is less difficult than in populations stratified by the similarity in dental arrangement and morphology, such as orthodontically treated patients (Group 2) and twins (Groups 3 and 4), respectively. All the Euclidean distance values obtained from orthodontically treated patients (Group 2) revealed statistically significant difference compared to the reference Euclidean distances (Group 5) (p < 0.05). Previous studies used 2D registration techniques and landmarking procedures to report outcomes obtained from orthodontically treated patients [11,12]. Their results were contradictory. Kieser et al. [11], found no match between pairwise comparison and Sheets et al. [12] detected matches. The present study differs in set up from both previous, mainly due to the use of 3D imaging techniques combined with automated image superimposition. While 3D imaging enables the investigation of morphometric information without restricting morphological dental evidences, automated superimposition eliminates the bias
Fig. 3. Euclidean distances calculated on the combination of the four quantification values (Max.+, Max., Ave., SD) for mandibular DCF in the experimental (G1, G3 and G4) and reference (G5) group. DCF: digital cast files; G1: random patients (Group 1); G2: Orthodontically treated patients (Group 2); G3M: monozygotic twins (Group 3); G3D: dizygotic twins (Group 3); G4: orthodontically treated monozygotic twins (Group 4); G5: control group used as threshold (Group 5); Max.+: maximum positive deviation; Max.: maximum negative deviation; Ave.: average deviation; SD: standard deviation; p-values from ANOVA test comparing groups may be consulted in Table 3.
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Fig. 4. ROC curve expressing the threshold potential of Group 5 to correctly classify maxillary DCF as non-equal (sensitivity) or equal (specificity) based on the combination of the four quantification values (Max.+, Max., Ave., SD). The maximized potential prediction (grey circle) indicates that Group 5 reached sensitivity of 80% – for classifying non-equal maxillary dentitions as non-equal and specificity of 81.6% – for classifying equal maxillary dentitions as equal (specificity). The Area Under the Curve (AUC, vertical arrow) suggests classification accuracy of 83%. Analyses combining less quantification values negligibly changed the current values.
Fig. 5. ROC curve expressing the threshold potential of Group 5 to correctly classify mandibular DCF as non-equal (sensitivity) or equal (specificity) based on the combination of the four quantification values (Max.+, Max., Ave., SD). The maximized potential prediction (grey circle) indicates that Group 5 reached sensitivity of 80% – for classifying non-equal mandibular dentitions as non-equal and specificity of 66.7% – for classifying equal mandibular dentitions as equal. The Area Under the Curve (AUC, vertical arrow) suggests classification accuracy of 81%. Analyses combining less quantification values negligibly changed the current values.
related to operator-depending procedures. Moreover, Sheets et al. [12], reported outcomes for mandibular dentitions, while in the current study maxillary dentitions were examined. Sheets et al. [12] justified the use of mandibular dentitions explaining that
“fewer matches would result in the mandibles due to the higher incidence of crowding and malalignment”. This statement supports the choice of maxillary dentitions in the current study, confirming the current sample stratification based on selecting subjects with
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most similar dental traits. Opposite to Sheets et al. [12], in the current study no match between dentitions was found, proving UHD in a stratified sample. The study of twins (Group 3) and orthodontically treated monozygotic twins (Group 4) included maxillary and mandibular dentitions. In twins (Group 3) higher mean Euclidean distances both for mono- and dizygotic twins were observed in relation to the reference group (Group 5) (Table 2). Statistically significant difference was observed from these comparisons, except for mandibular DCF of monozygotic twins (p > 0.05). Despite that, mandibular DCF of monozygotic twins slightly varied out of statistical significance (p = 0.07), presenting clear clinically visible differences (Table 1; Fig. 1). Sognnaes et al. [14] performed the only study on the UHD sampling twins. The authors used bite impressions registered in wax compared through photography (2D), probably including high inherent research bias. Similar to the current reports for twins (Group 3), Sognnaes et al. [14] did not find matches between dentitions. Oppositely in the present study, when a higher level of stratification was applied using orthodontically treated monozygotic twins (Groups 4) no statistically significant difference was observed in relation to the reference group (Group 5) (p > 0.05) both mandibular and maxillary DCF (Table 2). According to the Power Analysis outcomes, the lack of significant differences found in Groups 3 and 4 was possibly related to the unequal (Group 3) and small (Group 4) sample size compared to Group 5. Specifically, the addition of pair-wise comparisons revealed to generate statistically significant differences, indirectly suggesting UHD in Groups 3 and 4. Moreover these samples reveal clinically significant morphological differences in the pair-wise compared DCF with the lowest Euclidean distance values in the experimental sample groups (Fig. 1). Both considerations enable to conclude that UHD was observed in the present study, but a larger sample size with more equally sized groups is necessary to provide statistical significance where it was not found. Ranking the studied groups based on their mean Euclidian distance, indicated that orthodontically treated monozygotic twins (Group 4) presented the more similar DCF, followed by the monozygotic twins of Group 3, the dizygotic twins of Group 3, the orthodontically treated patients (Group 2), and the randomly selected subjects (Group 1) (Figs. 3 and 4). As expected monozygotic twins had lower mean Euclidean distance values compared to dizygotics. The literature suggests a genetic control over dental morphology [23,24]. Despite that, no statistically significant difference was observed in relation to zygosity both for maxillary and mandibular DCF. It indicates that probably the choice of dental arch does not guarantee to detect less or more equal DCF, and consequently does not positively contribute in the proposed sample stratification. In fact the current study revealed that the best sample stratification may be achieved combining the standard alignment of tooth position found in orthodontically treated patients (Group 2) and the similar dental morphology observed in twins (Group 3), resulting in subjects (Group 4) that have Euclidean distances closest to the reference threshold (Group 5). The ROC analysis was used to test Group 5 as potential reference threshold. This analysis was based on the dichotomization of the unique versus the not unique outcomes [25]. In the maxilla, sensitivity and specificity outcomes reached 80% and 81.6%, respectively, revealing a balanced power for reference threshold (Group 5) as a classifier of uniqueness. In the mandible, these outcomes reached 80% and 66.7%, respectively, suggesting an unbalanced power and indicating that Group 5 had better performance classifying unique dentitions and more deficiency for classifying non unique dentitions. However, for both maxillary and mandibular dentition the level of accuracy expressed by the
AUC reached 83% and 81%, respectively, classifying the overall threshold power of Group 5 as good [26]. This outcome did not change modifying the number of included quantification values provided by GS (max.+, ave., and SD; max., ave. and SD; and ave. and SD). It indicates that in future researches less quantification values may be tested and used. In practice it is translated in a faster data collection and analysis. Future researches should focus on overcoming the limitations found in the present study, such as sampling higher number of orthodontically treated monozygotic twins, avoiding the need for statistical power inferences. Further on the possible bias related to the manual confection of dental impressions and casts and the semi-automated digital cropping could be excluded using intraoral scanning and automated algorithms, respectively. Because the 3D technology contributed significantly to the comparative human identification process in the last decades [26], further research could focus on extrapolating the current study methodology to the field of human identification. Human dental identifications are based mainly on the comparison of AM and PM data [27]. These data may consist of dental casts (3M), computed tomography scans (3D), radiographs (2D), photographs (2D), and descriptive dental records [19]. Following the concept of the present study, 3D pair-wise comparisons between AM and PM dental casts can be performed to match or exclude victims referred for human identification. However, the comparison should be performed carefully considering that PM dental loss may have occurred, or that peri-mortem dental pathology and even AM unreceived late treatment could have been performed in the victim, resulting in explainable differences between the AM and PM dental cast. In these situations, both the AM and PM dental casts should be cropped digitally to compare only the corresponding tooth positions without explainable AM PM differences. An important outcome of present study also may be extrapolated to the field of human identification, namely the detected uniqueness of the human anterior dentition based on the morphology of its complete dental crowns. It means that the 3D comparison of maxillary and mandibular dental casts can be used reliably to support positive identifications in Court because uniqueness guarantees that the body examined PM can linked exclusively to the dental cast (from a missing person) examined AM. Oppositely to bitemark analysis, in human identifications the forensic dentists can use extended dental information from other dental structures. Further studies are necessary to investigate the uniqueness of the morphology of these structures, such as the dental roots and even pulp chamber arrangement. Apart the need for studies towards human identification, the constant need for more studies in bitemark analysis remains. The present research provided evidence for UHD based on the evaluation of the six anterior tooth crowns. However, in Forensic Dentistry is important to known exactly the level of tooth quantity in which uniqueness remains. Considering that uniqueness may be influenced by the quantity of dental material analyzed [22], future studies on UHD are necessary to mimic the exact quantity of tooth material that contacts the skin and leaves traces during the biting process. For that reason, the morphology of the human teeth must be investigated diminishing systematically the quantity of dental crown material examined to detect its influences on the UHD. The hypothesis inherent to this research set up should be that uniqueness depends on the quantity of tooth material considered. Minor probability of finding unique dentitions exists if less dental material is analyzed. Further on, “not every case is suitable for analysis” in the field of bitemarks [28]. The cases with insufficient evidence quality should be disregarded from further analysis. For that reason, training and research on bitemark analysis must be encouraged and should focus on the triage of bitemark cases suitable for investigation, based on the quality of the obtained bitemark evidence. For the cases
A. Franco et al. / Forensic Science International 273 (2017) 80–87
considered qualified for analysis, a secondary suitability test could be performed using the present research method. E.g. in cases with closed populations, the assessment of morphological differences between their dentitions would benefit the Court with scientific proof on how similar or how different two suspects may be regarding their anterior tooth morphology. Specifically, pair-wise morphometric differences between suspect dentitions could be quantified with GS software. In practice it could be performed establishing a threshold group and comparing it with each individual of the group of suspects. Only suspects with dentitions with Euclidean distances statistically highly significant different and above the threshold should be suitable for analysis. Indeed, bitemark analysis in a closed group is only allowed if the dentitions of the group members are distinguishable from each other and if those differences are detectable in the patterned injury. In further studies, these differences could be investigated in a dentition quantity level not restricted to the crown level, but reducing it to the quantity of dental material impressed in the bitemark. For that reason, thresholds should be reestablished including only the dental parts that potentially interact with the human skin during the bite process Individuals in the group of suspects with Euclidean distances higher than the threshold value established on bitemark level should be compared and only retained for analysis if their mutual Euclidean distances are statistically different. The magnitude of this difference should be established based on future research measuring the ability to observe clinical differences in the bitemark inflicted by the compared dentitions. 5. Conclusion The present research provides evidence to support the uniqueness of the human dentition considering the complete crowns of the anterior teeth of orthodontically treated patients, monozygotic twins and orthodontically treated twins. Acknowledgments The authors would like to express gratitude to the Coordination for the Improvement of Higher Education Personnel (CAPES) for funding the present research, as well to SCANCAST Dental Technology1 for enabling the digitalization of dental casts. References [1] S.A. Blackwell, R.V. Taylor, I. Gordon, C.L. Ogleby, T. Tanijiri, M. Yoshino, et al., 3D imaging and quantitative comparison of human dentitions and simulated bite marks, Int. J. Legal Med. 121 (2007) 9–17, doi:http://dx.doi.org/10.1007/ s00414-005-0058-6. [2] M. Tuceryan, F. Li, H.L. Blitzer, E.T. Parks, J.A. Platt, A framework for estimating probability of a match in forensic bite mark identification, J. Forensic Sci. 56 (2011) S83–S89, doi:http://dx.doi.org/10.1111/j.1556-4029.2010.01571.x. [3] H.D. Sheets, P.J. Bush, M.A. Bush, Patterns of variation and match rates of the anterior biting dentition: characteristics of a database of 3d-scanned dentitions, J. Forensic Sci. 58 (2013) 60–68, doi:http://dx.doi.org/10.1111/ j.1556-4029.2012.02293.x.
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[4] M.A. Bush, P.J. Bush, H.D. Sheets, Similarity and match rates of the human dentition in three dimensions: relevance to bitemark analysis, Int. J. Legal Med. 125 (2011) 779–784, doi:http://dx.doi.org/10.1007/s00414-010-0507-8. [5] M.A. Bush, P.J. Bush, H.D. Sheets, Statistical evidence for the similarity of the human dentition, J. Forensic Sci. 56 (2011) 118–123, doi:http://dx.doi.org/ 10.1111/j.1556-4029.2010.01531.x. [6] I.A. Pretty, The barriers to achieving an evidence base for bitemark analysis, Forensic Sci. Int. 159 (2006) 110–120, doi:http://dx.doi.org/10.1016/j.forsciint.2006.02.033. [7] I.A. Pretty, D. Sweet, The scientific basis for human bitemark analyses – a critical review, Sci. Justice 41 (2001) 85–92, doi:http://dx.doi.org/10.1016/ S1355-0306(01)71859-X. [8] J.G. Clement, S.A. Blackwell, Is current bite mark analysis a misnomer? Forensic Sci. Int. 201 (2010) 33–37, doi:http://dx.doi.org/10.1016/j.forsciint.2010.03.006. [9] The Innocence Project, Cases Where DNA Revealed That Bite Mark Analysis Led to Wrongful Arrests and Convictions, (2007) . [10] National Research Council – Committee on Identifying the Needs of the Forensic Sciences Community, Strengthening Forensic Science in the United States: a Path Forward, (2009), doi:http://dx.doi.org/10.1016/0379-0738(86) 90074-5. [11] J.A. Kieser, V. Bernal, J. Neil Waddell, S. Raju, The uniqueness of the human anterior dentition: a geometric morphometric analysis, J. Forensic Sci. 52 (2007) 671–677, doi:http://dx.doi.org/10.1111/j.1556-4029.2007.00403.x. [12] H.D. Sheets, P.J. Bush, C. Brzozowski, L.A. Nawrocki, P. Ho, M.A. Bush, Dental shape match rates in selected and orthodontically treated populations in New York State: a two-dimensional study, J. Forensic Sci. 56 (2011) 621–626, doi: http://dx.doi.org/10.1111/j.1556-4029.2011.01731.x. [13] A. Franco, G. Willems, P.H.C. Souza, G.E. Bekkering, P. Thevissen, The uniqueness of the human dentition as forensic evidence: a systematic review on the technological methodology, Int. J. Legal Med. 129 (2015) 1277–1283, doi:http://dx.doi.org/10.1007/s00414-014-1109-7. [14] R.F. Sognnaes, R.D. Rawson, B.M. Gratt, N.B. Nguyen, Computer comparison of bitemark patterns in identical twins, J. Am. Dent. Assoc. 105 (1982) 449–451. [15] P. Nambiar, T.E. Bridges, K.A. Brown, Quantitative forensic evaluation of bite marks with the aid of a shape analysis computer program: part 1 – the development of SCIP and the similarity index, J. Forensic Odontostomatol. 13 (1995) 18–25. [16] P. Nambiar, T.E. Bridges, K.A. Brown, Quantitative forensic evaluation of bite marks with the aid of a shape analysis computer program: part 2 – “SCIP” and bite marks in skin and foodstuffs, J. Forensic Odontostomatol. 13 (1995) 26–32. [17] G. Casella, Statistical Design, Springer, New York, 2008. [18] J. Tukey, Comparing individual means in the analysis of variance, Biometrics 5 (1949) 99–114. [19] D.R. Senn, R.A. Weems, Manual of Forensic Odontology, Fifth ed., CRC Press, Boca Raton, 2013. [20] R. Johansen, C. Bowers, Digital Analysis of Bite Mark Evidence, Forensic Imaginging Institute, Indianapolis, 2000. [21] R. Dorion, Bite Mark Evidence: A Color Atlas and Text, Second ed., CRC Press, Boca Raton, 2011. [22] A. Franco, G. Willems, P.H.C. Souza, W. Coucke, P. Thevissen, Threedimensional validation of the impact of the quantity of teeth or tooth parts on the morphological difference between twin dentitions, J. Forensic Odontostomatol. 34 (2016) 27–37. [23] R. Osborne, S. Horowitz, F. De George, Genetic variation in tooth dimensions: a twin study of the permanent anterior teeth, Physiol. Res. 10 (1958) 350–356. [24] A. Lundstrom, Tooth morphology as a basis for distinguishing monozygotic and dizygotic twins, Am. J. Hum. Genet. 15 (1963) 34–43. [25] K. Hajian-Tilaki, Receiver operating characteristic (ROC) curve analysis for medical diagnostic test evaluation, Casp. J. Int. Med. 4 (2013) 627–635. [26] R. Khouli, K. Macura, P. Barker, D. Phil, M. Habba, M. Jacobs, et al., The Relationship of temporal resolution to diagnostic performance for dynamic contrast enhanced (DCE) MRI of the breast, J. Magn. Reson. Imaging 30 (2009) 999–1004. [27] A. Franco, P. Thevissen, W. Coudyzer, W. Develter, W. Van de Voorde, R. Oyen, et al., Feasibility and validation of virtual autopsy for dental identification using the Interpol dental codes, J. Forensic Legal Med. 20 (2013) 248–254. [28] R. Barsley, A. Freeman, R. Metcalf, D. Senn, F. Wright, Bitemark analysis, J. Am. Dent. Assoc. 143 (2012) 444, 446, author reply 446, 448.
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Forensic Science International journal homepage: www.elsevier.com/locate/forsciint
Three-dimensional analysis of the uniqueness of the anterior dentition in orthodontically treated patients and twins A. Francoa,b,* , G. Willemsa , P.H.C. Souzab , O.M. Tanakac , W. Coucked , P. Thevissena a
Department of Oral Health Sciences – Forensic Dentistry, KU Leuven & Dentistry, University Hospitals Leuven, Belgium Department of Dentistry – Stomatology, School of Life Sciences, Pontifícia Universidade Católica do Paraná, Brazil Department of Dentistry – Orthodontics, School of Life Sciences, Pontifícia Universidade Católica do Paraná, Brazil d Free-lance statistician, Heverlee, Belgium b c
A R T I C L E I N F O
Article history: Received 19 August 2016 Received in revised form 2 February 2017 Accepted 14 February 2017 Available online xxx Keywords: Uniqueness Human dentition Twins Orthodontic treatment Forensic odontology
A B S T R A C T
Dental uniqueness can be proven if no perfect match in pair-wise morphological comparisons of human dentitions is detected. Establishing these comparisons in a worldwide random population is practically unfeasible due to the need for a large and representative sample size. Sample stratification is an option to reduce sample size. The present study investigated the uniqueness of the human dentition in randomly selected subjects (Group 1), orthodontically treated patients (Group 2), twins (Group 3), and orthodontically treated twins (Group 4) in comparison with a threshold control sample of identical dentitions (Group 5). The samples consisted of digital cast files (DCF) obtained through extraoral 3D scanning. A total of 2.013 pair-wise morphological comparisons were performed (Group 1 n = 110, Group 2 n = 1.711, Group 3 n = 172, Group 4 n = 10, Group 5 n = 10) with Geomagic Studio1 (3D Systems1, Rock Hill, SC, USA) software package. Comparisons within groups were performed quantifying the morphological differences between DCF in Euclidean distances. Comparisons between groups were established applying One-way ANOVA. To ensure fair comparisons a post-hoc Power Analysis was performed. ROC analysis was applied to distinguish unique from non-unique dentures. Identical DCF were not detected within the experimental groups (from 1 to 4). The most similar DCF had Euclidian distance of 5.19 mm in Group 1, 2.06 mm in Group 2, 2.03 mm in Group 3, and 1.88 mm in Group 4. Groups 2 and 3 were statistically different from Group 5 (p < 0.05). Statistically significant difference between Group 4 and 5 revealed to be possible including more pair-wise comparisons in both groups. The ROC analysis revealed sensitivity rate of 80% and specificity between 66.7% and 81.6%. Evidence to sustain the uniqueness of the human dentition in random and stratified populations was observed in the present study. Further studies testing the influence of the quantity of tooth material on morphological difference between dentitions and its impact on uniqueness remain necessary. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Forensic investigations on the uniqueness of the human dentition (UHD) increased considerably in the last few years [1– 5]. Although the UHD is fundamental for forensic human dental identification and bite mark analysis, the increased prevalence of these investigations was mainly induced by the uncertainty surrounding the forensic bitemark practice [6–8]. It is estimated
* Corresponding author at: Department of Oral Health Sciences – Forensic Dentistry, KU Leuven and Dentistry, University Hospitals Leuven, Kapucijnenvoer 7, block B, 3000 Leuven, Belgium. E-mail addresses: [email protected], [email protected] (A. Franco). http://dx.doi.org/10.1016/j.forsciint.2017.02.010 0379-0738/© 2017 Elsevier B.V. All rights reserved.
that more than 14 innocents were convicted or indicted based on misinterpreted bitemark evidences [8,9]. Accordingly, the American National Academy of Science included the unproven UHD amongst the most essential topics to be revisited scientifically [10]. Several studies in the field investigated the UHD in the context of bitemarks [1,5,11,12]. However, the outcomes reported were biased potentially based on methodological aspects [13]. Random sampling was one of the issues observed in these studies [1,2,14]. Establishing a methodological investigation on the UHD with a random population requires a representative and large sample size. Sample stratification arose as an option to reduce this issue. Stratification may be applied based on the presence of specific dental identifiers or using a specific population type [13]. Using specific dental identifiers enables the selection of subjects based on their particular dental traits, e.g. on specific tooth rotations or
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particular shape of dental crowns [15,16]. Evaluating a specific population type enables to filtrate subjects presenting similar dental morphology and arrangement, e.g. orthodontically treated patients and twins [11,12,14]. In practice, stratifying a sample on a specific dental identifier is extremely more difficult, than selecting individuals based on a specific population type. Applied in previous studies, sample stratification based on a specific population type did not enable to support a complete proof of the UHD due to additional methodological limitations [11,12,14– 16]. These limitations consisted of 2D image registration techniques used to compare 3D structures (human teeth); operator-depending procedures (landmarking); the lack of operator reproducibility control (intra-/inter-reliability tests); and the lack of proper data analysis (statistics) [13]. In fact, the UHD was not proved yet in the context of bitemarks impressed on human skin. These bitemarks often registers the indentations of the anterior dentition (six anterior teeth – from canine to canine). This is the reason why in the present research pair-wise superimpositions of dentitions were performed exclusively comparing the anterior dentition. The present research aims to prove the UHD three-dimensionally (3D) comparing the dental crown morphology of the anterior dentition in stratified samples of orthodontically treated patients, twins, and orthodontically treated twins in relation to a threshold sample of identical dentitions. Additionally, a sample of random patients is included to prove and express the importance of sample stratification in the investigations on the uniqueness of the human dentition. 2. Material and methods The present research was conducted after approval of the Committee of Ethics in Research (protocol number: 19575613.2.0000.0020). Three groups of dental casts were sampled and 3D digitized. Group 1 was composed by 22 dental casts (11 mandibular and 11 maxillary) of randomly selected subjects (7 males and 4 females). Group 2 consisted of 59 maxillary dental casts of orthodontically treated patients (32 males and 27 females), collected after the removal of the orthodontic brackets. Group 3 included 344 dental casts (172 mandibular and 172 maxillary) of 86 pairs of twins, 39 were monozygotic (36 males and 42 females) and 47 were dizygotic (50 males and 44 females). Group 4 comprised 20 dental casts (10 mandibular and 10 maxillary) of 5 pairs of orthodontically treated monozygotic twins (2 males and 8 females) (Table 1). All the dental casts included presented the permanent anterior teeth (from canine to canine). Dental casts with clinically visible supernumerary teeth in the anterior region, restorative or
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prosthetic dental treatment in the anterior teeth, and fixed orthodontic retainers were excluded. Specifically in Group 2, ahigh prevalence of orthodontic retainers was observed justifying the lack of analysis of mandibular dental casts. In Group 4, patients were also orthodontically treated but no orthodontic retainer was observed. In all the groups, the dental impressions were taken by the same operator (author) with alginate (Jeltrate Dustless1, Dentsply1, York, PA, USA) following the instructions of the manufacturer. These impressions were casted with plaster type IV (Durone1, Dentsply1, York, PA, USA) and digitalized using an automated motion device with angular laser scanning (XCADCAM Technology1, São Paulo, SP, Brazil) in resolution of <20 mm. The obtained digital cast files (DCF) were stored in .STL format and imported for morphometric analyses and pair-wise comparison in Geomagic Studio1 (3D Systems1, Rock Hill, SC, USA) software package (GS). To limit the comparisons to the anterior dentition, a standardized GS cropping procedure was established, placing on each DCF a cropping contour along the cemento–enamel junction of the anterior teeth based on 58 precropping points. Mean threshold values were established for the classification of two cropped DCF as identical or not. One examiner took impressions of 5 different subjects and repeated it after 7 days. The dental impressions were casted, digitized and prepared for analysis according to the procedures described previously. These DCF consisted of a reference group (Group 5). The mean threshold values were a measure of the comparative errors originating from the procedure to obtain the dental impressions, the casts, the DCF, the GS cropping procedure and the GS pair-wise morphometric comparisons. Within random (Group 1) and orthodontically treated (Group 2) patients, all possible pair-wise DCF comparisons were performed, totalizing 110 (55 per dental arch) and 1711 (only maxillary arch) comparisons, respectively. Specifically in these groups, sub-sampling was necessary to randomly select only the independent pair-wise comparisons (in which the same DCF was not repeated). This procedure was repeated 250 times combining independent comparisons. Within twins (Group 3) and orthodontically treated monozygotic twins (Group 4), the DCF were pair-wise compared with their respective twin sibling DCF, totalizing 172 (86 for the mandible and 86 for the maxilla) and 10 (5 for the mandible and 5 for the maxilla) comparisons, respectively. Additionally in Group 3 mono- and dizygotic twin pair DCF were evaluated in function of the zygosity. In the reference sample (Group 5) the DCF of each subject obtained at moment 1 was pair-wise compared with the respective DCF at moment 2, separately for the maxilla and mandible, totalizing 10 comparisons. All the pair-wise comparisons were performed with the GS automated superimposition tool.
Table 1 Subject distribution per sampled group stratified on dental arch, zygosity and sex. Dental arch
Group
Zygosity
Male (n)
Female (n)
Subjects (n)
DCF (n)
Maxillary
1 2 3 3 4 5
n/a n/a Monozygotic Dizygotic Monozygotic n/a
7 32 36 50 2 2
4 27 42 44 8 3
11 59 78 94 10 5
11 59 78 94 10 10
Mandibular
1 3 3 4 5
n/a Monozygotic Dizygotic Monozygotic n/a
7 36 50 2 2
4 42 44 8 3
11 78 94 10 5
11 78 94 10 10
DCF: digital cast files; Group 1: randomly selected subjects; Group 2: orthodontically treated patients; Group 3: twins; Group 4: orthodontically treated twins; Group 5: threshold; n/a: not applicable.
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For each pair-wise DCF comparison, GS calculated the observed morphological differences in dental crown morphology of the anterior dentitions. The differences were expressed in millimeters for each of the following quantification values: the maximum positive deviation (max.+); the maximum negative deviation (max.); the average deviation (ave.); and the standard deviation (SD). The four quantification values were statistically combined and converted in a single value, comprehending the Euclidean distance from origin (zero) obtained with the formula: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Distance ¼ Maxþ2 þ Max2 þ Average2 þ Standard deviation . This procedure enabled to rank the distance values; to verify if distance values were equal; and to detect distance values equal to zero. UHD was assessed in the four studied Groups (Groups from 1 to 4) comparing their Euclidean distances with the distances obtained in the reference (Group 5). One-way ANOVA [17] with log-transformed distances, was applied for the comparisons, separately for maxilla and mandible. Considering the multiple comparisons between groups, a correction for simultaneous hypothesis testing was applied according to Tukey’s range test [18]. UHD was considered when the mean Euclidean distance of any studied Group was statistically significant higher than the reference Group. In the lack of statistically significant differences sampling quality control was assured performing a post-hoc Power Analysis with a desired effect of 80%. Quality control for the comparative approach was assured for maxillary and mandibular DCF performing a ROC analysis. In this analysis Group 5 was confronted with all the other groups exploring its threshold potential for classifying non-equal dentitions as non-equal (sensitivity) and equal dentitions as equal (specificity). Confidence intervals for the ROC-curve and for the Area Under the Curve (AUC) were obtained by means of bootstrapping. ROC analyses were also performed systematically including less quantification values. The statistical tests were performed with significance rate of 5% using S+1 8.0 (Tibco1, Palo Alto, California, USA) software package. 3. Results The most similar maxillary DCF within each Group had Euclidian distances of 5.24 (random patients – Group 1), 1.87 (orthodontically treated patients – Group 2), 2.03 mm (twins – Group 3), 1.88 mm (orthodontically treated twins – Group 4), and 0.66 mm (reference – Group 5) (Figs. 1 and 2, Table 2). For the mandibular DCF, these distances were 5.19 (Group 1), 1.29 mm (Group 3), 1.66 mm (Group 4), and 1.03 mm (Group 5) (Figs. 1 and 3, Table 2). No equal or zero Euclidian distances were observed.
Table 2 Quantification values and Euclidian distance obtained from the most similar detected pair-wise DCF comparison per Group and per dental arch. Dental arch
Group
Max.+
Max.
Ave.
SD
Distance
Maxillary
1 2 3 4 5
3.20 1.11 1.41 1.33 0.49
4.09 1.45 1.43 1.29 0.45
0.01 0.03 0.01 0.11 0.01
0.77 0.44 0.35 0.32 0.07
5.24 1.87 2.03 1.88 0.66
Mandibular
1 3 4 5
3.96 0.88 0.83 0.84
3.16 0.90 1.41 0.59
0.35 0.03 0.02 0.01
1.10 0.29 0.28 0.11
5.19 1.29 1.66 1.03
DCF: digital cast files; DCF: digital cast files; Group 1: randomly selected subjects; Group 2: orthodontically treated patients; Group 3: twins; Group 4: orthodontically treated twins; Group 5: threshold; Max.+: maximum positive deviation; Max.: maximum negative deviation; Ave.: average deviation; SD: standard deviation.
Significant statistical differences (p < 0.05) were obtained for the maxillary DCF comparisons between Groups 1 and 5, 2 and 5, and 3 and 5 (Fig. 2, Table 3). The mandibular DCF comparisons were statistically different when comparing Groups 1 and 5, 2 and 5, and 3 (considering only dizygotic twins) and 5 (p < 0.05) (Fig. 3, Table 3). No significant statistical differences were observed comparing the mandibular DCF of monozygotic twins of Group 3 with Group 5, and comparing maxillary and mandibular DCF of Groups 4 and 5 (p > 0.05) (Table 3). Post hoc power analysis demonstrated that in order to obtain significant statistical differences between mandibular DCF of Groups 3 (monozygotic twins) and 5, the inclusion of 17 pair-wise comparisons in both groups would be necessary. Between Groups 4 and 5, 11 and 56 additional pair-wise comparisons would be necessary for the maxillary and mandibular DCF comparisons, respectively (Table 3). According to the ROC analysis, the Euclidean distances combining the four quantification values (max.+, max., ave., and SD) revealed a sensitivity of 80% and a specificity of 81.6% with an accuracy of 83% for Group 5 when compared to Groups 1, 2, 3 and 4 for maxillary DCF (Fig. 4). For the mandibular DCF sensitivity reached 80% and specificity 66.7%, with an accuracy of 81% (Fig. 5). These outcomes were not modified combining less quantification values. 4. Discussion UHD is a term used commonly in forensic dentistry, especially in the fields of human identification and bitemark analysis [19]. Despite that, this term is often misinterpreted. When the comparison between ante-mortem (AM) and post-mortem (PM) dental data (human identification); and between suspect dentition and bite pattern (bitemark) is considered a match, it only indicates that the compared forensic evidences are identical. Those evidences are unique only when it is guaranteed that they cannot be detected in another person in the world. In human identifications, the probability of considering the human dentition as unique is considerably higher compared to bitemark analysis. It is justified by the larger number of teeth and dental evidences (dental treatment, morphology and pathology) available for analysis. However, the UHD was investigated mainly in the context of bitemarks in the present study. Thus, the samples studied were stratified on the number of teeth (six per dental arch), the dental part (tooth crowns), and the type of population (orthodontically treated patients and twins). In these groups, besides general morphological information, dental shape, size, angulation and mutual tooth position were considered. This information was registered in life-size 3D DCF, enabling to capture all dental characteristics used in bitemark practice [20]. Similar to most of the studies investigating the UHD, the present study analyzed the six anterior teeth [13], which are the teeth most commonly involved in bitemarks [21]. Opposite to all studies included in a related systematic review [13], currently the entire dental crown morphology was considered instead of only their incisal edges, because in bitemarks the exact amount of tooth surface that contacts and impresses the human skin may vary from case to case. The initial analysis within each group enabled to rank the Euclidian distance values in order to screen the most similar pairs of DCF in the sample. The smallest distances resulted below 5.24 mm for the maxilla and below 5.19 mm for the mandible (Table 2). This analysis also revealed no equal Euclidean distance values between the pair-wise comparisons. However, equal Euclidian distances only indicated that the combined quantification of all morphological differences calculated by GS between two pair-wise DCF comparisons were equal. Theoretically, zero is the
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Fig. 1. Clinical pair-wise comparisons of DCF (morphometric outcomes provided by GS) with the lowest Euclidean distance from the maxillary and mandibular dental arches detected in Groups 1 (randomly selected subjects) 2 (orthodontically treated patients), 3 (twins) and 4 (orthodontically treated monozygotic twins). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Reference and target DCF are represented in mono-colored blue, while comparison outcomes are represented multi-colored. In the last, the color coded system ranges from red (max.+) to dark blue (max.), in which greenish tones corresponds to morphological differences close to zero. Although no statistically significant difference was calculated (p > 0.05) between Group 4 and 5 (threshold), clinically clear signs of morphological differences (reddish areas) were observed. The chromatic representation of the morphometric differences between DCF were translated in single values in the present study using the forqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 mula:Distance ¼ Maxþ2 þ Max2 þ Average2 þ Standard deviation . As expected, the maximum and minimum deviation values could jeopardize the Euclidean distance values (formula outcome). In order to avoid this limitation, sub-sampling was performed in Group 2 to exclude the repeated DCF in the sample. More important, the different set ups were tested systematically reducing the number of quantification values in the formula. The use of 4 quantification values yielded the best distinctive power to classify equal and non-equal DCF in the present study.
Fig. 2. Euclidean distances calculated on the combination of the four quantification values (Max.+, Max., Ave., SD) for maxillary DCF in the experimental (G1, G2, G3 and G4) and reference (G5) groups. DCF: digital cast files; G1: random patients (Group 1); G2: Orthodontically treated patients (Group 2); G3M: monozygotic twins (Group 3); G3D: dizygotic twins (Group 3); G4: orthodontically treated monozygotic twins (Group 4); G5: control group used as threshold (Group 5); Max.+: maximum positive deviation; Max.: maximum negative deviation; Ave.: average deviation; SD: standard deviation; p-values from ANOVA test comparing groups may be consulted in Table 3.
Euclidean distance value indicating that two compared DCF are equal (and proves the lack of uniqueness). However, in the performed research, measuring and operator errors need to be taken into account. The factors potentially biasing the performed pair-wise DCF comparisons were 1) the confection of dental
impressions and dental casts, 2) the 3D scanning process; 3) the 3D digital cropping; and 4) the GS comparison measure error. In this context, Group 5 was created combining and quantifying these factors to establish a threshold that enables to classify non-equal and equal DCF (separately for the mandible and the maxilla). This
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Table 3 p-Values obtained from ANOVA comparisons between Groups per dental arch. Dental arch
Comparison
Mean distances
p
Maxillary
G1 vs. G2 G1 vs. G3D G1 vs. G3M G1 vs. G4 G1 vs. G5 G2 vs. G3D G2 vs. G3M G2 vs. G4 G2 vs. G5 G3D vs. G3M G3D vs. G4 G3D vs. G5 G3M vs. G4 G3M vs. G5 G4 vs. G5
8.03 vs. 4.74 8.03 vs. 5.62 8.03 vs. 4.43 8.03 vs. 3.51 8.03 vs. 2.24 4.74 vs. 5.62 4.74 vs. 4.43 4.74 vs. 3.51 4.74 vs. 2.24 5.62 vs. 4.43 5.62 vs. 3.51 5.62 vs. 2.24 4.43 vs. 3.51 4.43 vs. 2.24 3.51 vs. 2.24
0.0888 0.4196 0.0248 0.0298 0.0001 0.5140 0.9631 0.7531 0.0001 0.0613 0.2166 0.0001 0.9302 0.0003 0.0998a
Mandibular
G1 vs. G3D G1 vs. G3M G1 vs. G4 G1 vs. G5 G3D vs. G3M G3D vs. G4 G3D vs. G5 G3M vs. G4 G3M vs. G5 G4 vs. G5
10.79 vs. 4.85 10.79 vs. 3.79 10.79 vs. 2.70 10.79 vs. 2.09 4.85 vs. 3.79 4.85 vs. 2.70 4.85 vs. 2.09 3.79 vs. 2.70 3.79 vs. 2.09 2.70 vs. 2.09
0.0066 0.0003 0.0006 0.0001 0.2148 0.1941 0.0040 0.7562 0.0723b 0.8150c
DCF: digital cast files; G1: randomly selected subjects; G2: orthodontically treated patients; G3M: monozygotic twins; G3D: dizygotic twins; G4: orthodontically treated twins; G5: threshold; p-values from ANOVA test for significance rate of 5%. a Post-hoc Power Analysis indicates that both groups need to be enlarged in 11 comparisons to reach statistically significant difference. b Post-hoc Power Analysis indicates that both groups need to be enlarged in 17 comparisons to reach statistically significant difference. c Post-hoc Power Analysis indicates that both groups need to be enlarged in 56 comparisons to reach statistically significant difference.
threshold was used as reference in the search for equal DCF in the studied Groups 1, 2, 3 and 4. Randomly selected subjects (Group 1) were included in the present study not to prove uniqueness within this population but
yet to highlight the importance of sample stratification on studies in the field. Based on that, it became more relevant to compare Group 1 with the other experimental groups (Groups 2, 3 and 4) than with the threshold group (Group 5). As observed, the mean Euclidean distances obtained in Group 1 were the highest in this study. However, the mean Euclidean distance for maxillary DCF (8.03) was only statistically different (p < 0.05) when compared to monozygotic twins (Group 3) and orthodontically treated monozygotic twins (Group 4). Yet the mean Euclidean distance for mandibular DCF (10.79) was statistically different (p < 0.05) compared to all the groups. This finding suggest that sample stratification for maxillary DCF better succeeds using samples (Group 3) and sub-samples (Group 4) of monozygotic twins, while for mandibular DCF orthodontically treated patients may be used as well. A secondary finding obtained from these outcomes suggests that UHD is more difficult to be proved within the maxillary anterior teeth, which required stronger sample stratification to reach statistically significant difference from the random population. As expected, when compared to Group 5, Group 1 revealed statistically significant differences (p < 0.05) for maxillary and mandibular DCF. However, as previously observed, proving UHD in a random population (Group 1) is less difficult than in populations stratified by the similarity in dental arrangement and morphology, such as orthodontically treated patients (Group 2) and twins (Groups 3 and 4), respectively. All the Euclidean distance values obtained from orthodontically treated patients (Group 2) revealed statistically significant difference compared to the reference Euclidean distances (Group 5) (p < 0.05). Previous studies used 2D registration techniques and landmarking procedures to report outcomes obtained from orthodontically treated patients [11,12]. Their results were contradictory. Kieser et al. [11], found no match between pairwise comparison and Sheets et al. [12] detected matches. The present study differs in set up from both previous, mainly due to the use of 3D imaging techniques combined with automated image superimposition. While 3D imaging enables the investigation of morphometric information without restricting morphological dental evidences, automated superimposition eliminates the bias
Fig. 3. Euclidean distances calculated on the combination of the four quantification values (Max.+, Max., Ave., SD) for mandibular DCF in the experimental (G1, G3 and G4) and reference (G5) group. DCF: digital cast files; G1: random patients (Group 1); G2: Orthodontically treated patients (Group 2); G3M: monozygotic twins (Group 3); G3D: dizygotic twins (Group 3); G4: orthodontically treated monozygotic twins (Group 4); G5: control group used as threshold (Group 5); Max.+: maximum positive deviation; Max.: maximum negative deviation; Ave.: average deviation; SD: standard deviation; p-values from ANOVA test comparing groups may be consulted in Table 3.
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Fig. 4. ROC curve expressing the threshold potential of Group 5 to correctly classify maxillary DCF as non-equal (sensitivity) or equal (specificity) based on the combination of the four quantification values (Max.+, Max., Ave., SD). The maximized potential prediction (grey circle) indicates that Group 5 reached sensitivity of 80% – for classifying non-equal maxillary dentitions as non-equal and specificity of 81.6% – for classifying equal maxillary dentitions as equal (specificity). The Area Under the Curve (AUC, vertical arrow) suggests classification accuracy of 83%. Analyses combining less quantification values negligibly changed the current values.
Fig. 5. ROC curve expressing the threshold potential of Group 5 to correctly classify mandibular DCF as non-equal (sensitivity) or equal (specificity) based on the combination of the four quantification values (Max.+, Max., Ave., SD). The maximized potential prediction (grey circle) indicates that Group 5 reached sensitivity of 80% – for classifying non-equal mandibular dentitions as non-equal and specificity of 66.7% – for classifying equal mandibular dentitions as equal. The Area Under the Curve (AUC, vertical arrow) suggests classification accuracy of 81%. Analyses combining less quantification values negligibly changed the current values.
related to operator-depending procedures. Moreover, Sheets et al. [12], reported outcomes for mandibular dentitions, while in the current study maxillary dentitions were examined. Sheets et al. [12] justified the use of mandibular dentitions explaining that
“fewer matches would result in the mandibles due to the higher incidence of crowding and malalignment”. This statement supports the choice of maxillary dentitions in the current study, confirming the current sample stratification based on selecting subjects with
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most similar dental traits. Opposite to Sheets et al. [12], in the current study no match between dentitions was found, proving UHD in a stratified sample. The study of twins (Group 3) and orthodontically treated monozygotic twins (Group 4) included maxillary and mandibular dentitions. In twins (Group 3) higher mean Euclidean distances both for mono- and dizygotic twins were observed in relation to the reference group (Group 5) (Table 2). Statistically significant difference was observed from these comparisons, except for mandibular DCF of monozygotic twins (p > 0.05). Despite that, mandibular DCF of monozygotic twins slightly varied out of statistical significance (p = 0.07), presenting clear clinically visible differences (Table 1; Fig. 1). Sognnaes et al. [14] performed the only study on the UHD sampling twins. The authors used bite impressions registered in wax compared through photography (2D), probably including high inherent research bias. Similar to the current reports for twins (Group 3), Sognnaes et al. [14] did not find matches between dentitions. Oppositely in the present study, when a higher level of stratification was applied using orthodontically treated monozygotic twins (Groups 4) no statistically significant difference was observed in relation to the reference group (Group 5) (p > 0.05) both mandibular and maxillary DCF (Table 2). According to the Power Analysis outcomes, the lack of significant differences found in Groups 3 and 4 was possibly related to the unequal (Group 3) and small (Group 4) sample size compared to Group 5. Specifically, the addition of pair-wise comparisons revealed to generate statistically significant differences, indirectly suggesting UHD in Groups 3 and 4. Moreover these samples reveal clinically significant morphological differences in the pair-wise compared DCF with the lowest Euclidean distance values in the experimental sample groups (Fig. 1). Both considerations enable to conclude that UHD was observed in the present study, but a larger sample size with more equally sized groups is necessary to provide statistical significance where it was not found. Ranking the studied groups based on their mean Euclidian distance, indicated that orthodontically treated monozygotic twins (Group 4) presented the more similar DCF, followed by the monozygotic twins of Group 3, the dizygotic twins of Group 3, the orthodontically treated patients (Group 2), and the randomly selected subjects (Group 1) (Figs. 3 and 4). As expected monozygotic twins had lower mean Euclidean distance values compared to dizygotics. The literature suggests a genetic control over dental morphology [23,24]. Despite that, no statistically significant difference was observed in relation to zygosity both for maxillary and mandibular DCF. It indicates that probably the choice of dental arch does not guarantee to detect less or more equal DCF, and consequently does not positively contribute in the proposed sample stratification. In fact the current study revealed that the best sample stratification may be achieved combining the standard alignment of tooth position found in orthodontically treated patients (Group 2) and the similar dental morphology observed in twins (Group 3), resulting in subjects (Group 4) that have Euclidean distances closest to the reference threshold (Group 5). The ROC analysis was used to test Group 5 as potential reference threshold. This analysis was based on the dichotomization of the unique versus the not unique outcomes [25]. In the maxilla, sensitivity and specificity outcomes reached 80% and 81.6%, respectively, revealing a balanced power for reference threshold (Group 5) as a classifier of uniqueness. In the mandible, these outcomes reached 80% and 66.7%, respectively, suggesting an unbalanced power and indicating that Group 5 had better performance classifying unique dentitions and more deficiency for classifying non unique dentitions. However, for both maxillary and mandibular dentition the level of accuracy expressed by the
AUC reached 83% and 81%, respectively, classifying the overall threshold power of Group 5 as good [26]. This outcome did not change modifying the number of included quantification values provided by GS (max.+, ave., and SD; max., ave. and SD; and ave. and SD). It indicates that in future researches less quantification values may be tested and used. In practice it is translated in a faster data collection and analysis. Future researches should focus on overcoming the limitations found in the present study, such as sampling higher number of orthodontically treated monozygotic twins, avoiding the need for statistical power inferences. Further on the possible bias related to the manual confection of dental impressions and casts and the semi-automated digital cropping could be excluded using intraoral scanning and automated algorithms, respectively. Because the 3D technology contributed significantly to the comparative human identification process in the last decades [26], further research could focus on extrapolating the current study methodology to the field of human identification. Human dental identifications are based mainly on the comparison of AM and PM data [27]. These data may consist of dental casts (3M), computed tomography scans (3D), radiographs (2D), photographs (2D), and descriptive dental records [19]. Following the concept of the present study, 3D pair-wise comparisons between AM and PM dental casts can be performed to match or exclude victims referred for human identification. However, the comparison should be performed carefully considering that PM dental loss may have occurred, or that peri-mortem dental pathology and even AM unreceived late treatment could have been performed in the victim, resulting in explainable differences between the AM and PM dental cast. In these situations, both the AM and PM dental casts should be cropped digitally to compare only the corresponding tooth positions without explainable AM PM differences. An important outcome of present study also may be extrapolated to the field of human identification, namely the detected uniqueness of the human anterior dentition based on the morphology of its complete dental crowns. It means that the 3D comparison of maxillary and mandibular dental casts can be used reliably to support positive identifications in Court because uniqueness guarantees that the body examined PM can linked exclusively to the dental cast (from a missing person) examined AM. Oppositely to bitemark analysis, in human identifications the forensic dentists can use extended dental information from other dental structures. Further studies are necessary to investigate the uniqueness of the morphology of these structures, such as the dental roots and even pulp chamber arrangement. Apart the need for studies towards human identification, the constant need for more studies in bitemark analysis remains. The present research provided evidence for UHD based on the evaluation of the six anterior tooth crowns. However, in Forensic Dentistry is important to known exactly the level of tooth quantity in which uniqueness remains. Considering that uniqueness may be influenced by the quantity of dental material analyzed [22], future studies on UHD are necessary to mimic the exact quantity of tooth material that contacts the skin and leaves traces during the biting process. For that reason, the morphology of the human teeth must be investigated diminishing systematically the quantity of dental crown material examined to detect its influences on the UHD. The hypothesis inherent to this research set up should be that uniqueness depends on the quantity of tooth material considered. Minor probability of finding unique dentitions exists if less dental material is analyzed. Further on, “not every case is suitable for analysis” in the field of bitemarks [28]. The cases with insufficient evidence quality should be disregarded from further analysis. For that reason, training and research on bitemark analysis must be encouraged and should focus on the triage of bitemark cases suitable for investigation, based on the quality of the obtained bitemark evidence. For the cases
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considered qualified for analysis, a secondary suitability test could be performed using the present research method. E.g. in cases with closed populations, the assessment of morphological differences between their dentitions would benefit the Court with scientific proof on how similar or how different two suspects may be regarding their anterior tooth morphology. Specifically, pair-wise morphometric differences between suspect dentitions could be quantified with GS software. In practice it could be performed establishing a threshold group and comparing it with each individual of the group of suspects. Only suspects with dentitions with Euclidean distances statistically highly significant different and above the threshold should be suitable for analysis. Indeed, bitemark analysis in a closed group is only allowed if the dentitions of the group members are distinguishable from each other and if those differences are detectable in the patterned injury. In further studies, these differences could be investigated in a dentition quantity level not restricted to the crown level, but reducing it to the quantity of dental material impressed in the bitemark. For that reason, thresholds should be reestablished including only the dental parts that potentially interact with the human skin during the bite process Individuals in the group of suspects with Euclidean distances higher than the threshold value established on bitemark level should be compared and only retained for analysis if their mutual Euclidean distances are statistically different. The magnitude of this difference should be established based on future research measuring the ability to observe clinical differences in the bitemark inflicted by the compared dentitions. 5. Conclusion The present research provides evidence to support the uniqueness of the human dentition considering the complete crowns of the anterior teeth of orthodontically treated patients, monozygotic twins and orthodontically treated twins. Acknowledgments The authors would like to express gratitude to the Coordination for the Improvement of Higher Education Personnel (CAPES) for funding the present research, as well to SCANCAST Dental Technology1 for enabling the digitalization of dental casts. References [1] S.A. Blackwell, R.V. Taylor, I. Gordon, C.L. Ogleby, T. Tanijiri, M. Yoshino, et al., 3D imaging and quantitative comparison of human dentitions and simulated bite marks, Int. J. Legal Med. 121 (2007) 9–17, doi:http://dx.doi.org/10.1007/ s00414-005-0058-6. [2] M. Tuceryan, F. Li, H.L. Blitzer, E.T. Parks, J.A. Platt, A framework for estimating probability of a match in forensic bite mark identification, J. Forensic Sci. 56 (2011) S83–S89, doi:http://dx.doi.org/10.1111/j.1556-4029.2010.01571.x. [3] H.D. Sheets, P.J. Bush, M.A. Bush, Patterns of variation and match rates of the anterior biting dentition: characteristics of a database of 3d-scanned dentitions, J. Forensic Sci. 58 (2013) 60–68, doi:http://dx.doi.org/10.1111/ j.1556-4029.2012.02293.x.
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