Brief communication Correcting overestimation when determining two-dimensional occlusal area in human molars.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 145:327–332 (2011) Brief Communication: Correcting Overestimation When Determining Two-Dimensional Occlusal Area in Human Molars Christopher Schmidt,1* Stephen Ousley,2 and Molly Schmidt3 1 Department of Anthropology, University of Indianapolis, Indianapolis, IN 46227 Department of Anthropology/Archaeology, Mercyhurst College, Erie, PA 16546 3 Department of Biology, University of Indianapolis, Indianapolis, IN 46227 2 KEY WORDS dental metrics; dental morphology; robustness index ABSTRACT The robustness index (RI) is determined by multiplying dental mesiodistal and buccolingual diameters, and is used to estimate occlusal area. However, because teeth are not rectangular its calculation consistently causes overestimations. Moreover, teeth, in particular molars, are not identically shaped so overestimations vary. The current study seeks to determine the extent to which overestimations are affected by tooth shape and to improve RI’s efﬁcacy. Initially, 120 molars were sorted into six shape groups, which were determined by hypocone/hypoconulid expression. Three maxillary and three mandibular shape groups were set using the Arizona State University Dental Anthropology System. ANOVA results determined that RI overestimations, which averaged around 20%, were not the same for each shape category. Maxillary molars with large hypocones and mandib- ular molars with no hypoconulids were overestimated signiﬁcantly less than the other molar groups. Regressionbased correction formulae were generated and applied to the original sample. These formulae far more precisely estimated tooth area than RI and there were no differences in estimation based upon tooth shape. A subsequent validation study of 24 additional molars was undertaken to test the formulae on teeth not from the original sample. Overestimation/underestimation averaged 0.5% and was about the same for each of the tooth shape groups. Finally, six new correction formulae were generated using all 144 molars. The correction formulae provide, what is termed here, an adjusted robustness index (ARI), and it is recommended that ARI is used in future studies of molar occlusal area. Am J Phys Anthropol 145:327–332, 2011. V 2011 Wiley-Liss, Inc. The dental robusticity index (RI) is calculated by multiplying mesiodistal (MD) and buccolingual (BL) diameters (e.g., Goose, 1963; Wolpoff, 1971; Mayhall, 2000) and is used to approximate two-dimensional dental surface areas, usually of molars. It has been known for some time, however, that this measurement does not provide an accurate surface area estimate (i.e., Wolpoff, 1971). An obvious limitation is that the RI assumes teeth are quadrangular. Teeth are not perfect squares or rectangles, rather, they have rounded corners, and as a result their surface areas are always overestimated with the RI. Moreover, the more a tooth deviates from a quadrangular shape, the more overestimated the RI is likely to be. Although dental texture and topography, 3D geometric morphometrics, microcomputed tomography, high resolution x-ray computer tomography, and other means of 3D study are currently being pursued by researchers in bioarchaeology primatology and paleoanthropology (e.g., Boughner and Dean, 2004; Scott et al., 2005, 2006; el Zaatari, 2007; Gantt et al., 2007; Keiser et al., 2007; Olejniczak et al., 2007; Ungar, 2007; Schaefer et al., 2008; Zolnierz and Schmidt, 2008), analysts continue to study 2D dental data collected with various instruments (e.g., calipers, digitizers, and reﬂex microscopes) and in a variety of manners including standard metric comparisons, 2D geometric morphometrics, and elliptic Fourier analysis (e.g., (Hills et al., 1983; Wood and Abbott, 1983; Wood et al., 1983; Morris, 1986; Sekikawa et al., 1988; Calcagno, 1989; Keiser, 1990; Strait, 1993; Suwa et al., 1994; Peretz et al., 1997; Ferrario et al., 1999; Swindler, 2002; Bailey, 2004; Hill, 2004; Alemseged et al., 2005; Martinón-Torres et al., 2006; Gómez-Robles et al., 2007; Moggi-Cecchi and Boccone, 2007; Pilbrow, 2007; Cuozzo, 2008; Pinhasi et al., 2008), all of which necessitate improvement of the RI. We propose an adjustment to correct the RI with regression formulae that reduce RI bias. The ﬁrst step in this study was to estimate to what extent RI was biased in molars of different shapes, speciﬁcally those with large, small, and no hypocones/hypoconulids. This step was important because if the RI overestimates were all the same, it would not be imperative to develop a correction. Once differences were found, the second step was to create an adjusted index, ARI—adjusted robusticity index, via regression that was applied to the sample from which the formulae were derived, as well as to a validation sample. C 2011 V WILEY-LISS, INC. C MOLAR SHAPE Although nonpathological human molars can assume a variety of shapes, the authors were able to categorize *Correspondence to: Christopher Schmidt, Archaeology and Forensics Laboratory, University of Indianapolis, 1400 E. Hanna Avenue, Indianapolis, IN 46227. E-mail: email@example.com Received 13 August 2010; accepted 28 December 2010 DOI 10.1002/ajpa.21511 Published online 5 April 2011 in Wiley Online Library (wileyonlinelibrary.com). 328 C. SCHMIDT ET AL. Fig. 1. Maxillary (above) and mandibular (below) molars with increasingly larger hypocones and hypoconulids, respectively, from left to right. Mesial is up. molar shapes based upon the presence and expression of the hypocone and hypoconulid in maxillary and mandibular molars, respectively. Hypocones and hypoconulids are the most variable cusps in terms of size and shape, although all cusps can affect overall tooth morphology. The hypocone is the distolingual cusp of maxillary molars, and it is isolated from the other cusps by the lingual groove and oblique ridge. When the hypocone is absent, maxillary molars take on a triangular shape. By contrast, when the hypocone is large, maxillary molars take on a rhomboidal appearance. The hypoconulid is the most distal cusp on mandibular molars, bordered by the distolingual and distobuccal grooves. Mandibular molars with no hypoconulid have a squarish occlusal outline. If the hypoconulid is strongly expressed the outline is more oblong (Fig. 1). However, using geometric terms to describe occlusal outline was imprecise for setting up the molar shape groups used herein. The following section provides details on how the groups were deﬁned. MATERIALS AND METHODS One hundred and twenty healthy molars (60 upper and 60 lower) were sorted into six groups based upon hypocone/hypoconulid expression. There were three maxillary (no, small, and large hypocone) and three mandibular groups (no, small, and large hypoconulid), each of which corresponded with particular hypocone/hypoconulid scores using the Arizona State University Dental Anthropology System (Scott and Turner, 1997). Maxillary molars with no hypocone had an ASUDAS score of 0 or 1. Those with a small hypocone scored a 2 or 3, and those with a large hypocone scored a 4 or 5. The mandibular molars with no hypoconulid scored a 0 or 1, those Abbreviations ARI BL MD RI adjusted robustness index buccolingual mesiodistal robustness index American Journal of Physical Anthropology with a small hypoconulid scored a 2 or 3, and those with large hypoconulids scored a 4 or 5. The sample included adult molars from osteological collections representing Amerindian and Euroamerican groups, the former being archeological and the latter being both archeological and recent. The teeth were either lightly or unworn. The sample excluded teeth with anything more than minor dentin exposure, teeth with extra cusps like Carabelli’s trait or protostylids, and teeth with pathological conditions that affect shape (e.g., fusion, occlusal hypoplasia, amelogenesis imperfecta, etc.). Most of the teeth came from very young adults, teens, and some children who had unerupted but completely formed adult molar crowns. There were 20 molars per group; each was photographed with a mounted Sony Mavica digital camera in macro mode. A bubble level was placed on the camera body to ensure that it was level and parallel to the occlusal plane of each tooth. Great care was taken to make sure that the widest margins in both the mesiodistal and buccolingual planes were visible before the picture was taken. This was accomplished by marking the greatest curvature of the mesial, distal, buccal, and lingual surfaces with a dot. Once all of the dots were visible, the occlusal surface was considered parallel to the camera lens. Also in the image was a scale graduated in millimeters placed at the level of the tooth’s widest diameter (see Wood and Abbott, 1983; Wood et al., 1983; Morris, 1986; Sekikawa et al., 1988; Suwa et al., 1994; Peretz et al., 1997; Bailey, 2004; Martinón-Torres et al., 2006; Bailey and Wood, 2007; Moggi-Cecchi and Boccone, 2007; Pilbrow, 2007; and Gómez-Robles et al., 2007 for similar approaches to collecting 2D images). The digital images were processed with ScionImage software [which is based on NIH’s Image J (www.scion corp.com)]. The scale in each image was used to calibrate the measurement tool in the software. A mouse-driven pointer was used to measure maximum length and width diameters that were compared to measurements taken with calipers. If the ScionImage measurements of a particular tooth differed from those taken with the calipers, CORRECTING OVERESTIMATION IN MOLAR AREA 329 TABLE 1. Initial study: Summary of molar data for actual area, the robusticity index (RI), and the RI overestimation as a percentage of actual area Group 1 2 3 4 Actual area RI RI overestimation (%) Mean SD 80.7 11.0 101.5 15.7 25.5 5.0 Mean SD 89.8 9.9 110.5 11.8 23.1 4.7 Mean SD 105.7 12.2 125.3 14.2 18.6 2.9 Mean SD 94.3 9.4 106.8 12.6 13.1 3.5 Fig. 2. Box plot of difference between the robustness index (RI) and the actual area. 5 Mean SD 101.4 9.4 118.2 11.6 16.5 3.4 6 Total Mean SD 109.7 8.1 130.6 10.3 19.1 4.2 Mean N SD 97.0 120 14.0 115.5 120 16.3 19.3 120 5.7 The groups are: 1: maxillary without hypocone; 2: maxillary with small hypocone; 3: maxillary with large hypocone; 4: mandibular without hypoconulid; 5: mandibular with small hypoconulid; 6: mandibular with large hypoconulid. N 5 20 for each group. Mean and SD values for Actual Area and RI are in mm2. that tooth was excluded. Once fully calibrated, the occlusal outline was traced three times and the two-dimensional occlusal area was calculated using the software. The three areas were averaged for each tooth. The area computed with ScionImage was termed the ‘‘Actual Area’’ and mean values were calculated for each tooth shape. Linear regression was used to calculate correction formulae, resulting in an adjusted RI (ARI). The formulae were derived for each tooth shape using actual area as the dependent variable and RI as the independent variable. Tooth shape-based overestimations of uncorrected RI and ARI were each compared using one-way ANOVAs with a Tukey’s Post Hoc test and an a of 0.05. All statistics were computed with SPSS 16. RESULTS Table 1 summarizes the comparative data. The RI overestimates the occlusal area of every molar, on average, by about 20%. Upper molars are overestimated by an average of 22.4%; mandibular molars are overestimated by an average of 16.2%. The greatest overestimations, by about 25%, were for maxillary molars with no hypocone, which have a triangular appearance. Maxillary molars with a small hypocone were overestimated by an average of 23%, and maxillary molars with a large hypocone were overestimated by 18.6%. In mandibular molars without a hypoconulid, the RI overestimated the actual area by 13.2%, those with a small hypoconulid were overestimated by almost 17%, and those with a large hypoconulid were overestimated by 19%. Analysis of variance tests of mean RI values revealed statistically signiﬁcant differences in the percentages of overestimation (df 5 5, F 5 3,334.18, sig 5 0.000). Speciﬁcally, maxillary molars with a large hypocone were different from those with a small or no hypocone. A tooth with a large hypocone is squarer and produces smaller overestimates than the other teeth that are more triangular. For the lower molars, a statistically signiﬁcant difference was found between those with no hypoconulid and those with a small or large hypoconulid. Again, it was the more square-shaped teeth (those with no hypoconulid) that were different from the rest, which had larger hypoconulids and more elongate or oblong occlusal outlines (Fig. 2 for box plots of RI overestimations). Based on the ANOVA results, six linear regression formulae were calculated, three for the maxillary and three for the mandibular molars. Correcting the RI values reduced the average overestimation to zero with a range of 20.5% to 0.3%. This improvement was substantial, but was generated by applying the regression formulae to the same set of teeth from which the formulae were derived. Therefore, a validation sample of 24 additional teeth, with four teeth for each of the six tooth shape groups, was analyzed. Again, the RI overestimation averaged 20%. After correction with the regression formulae, the RI overestimation improved to an average of about 0.5%, with a range from 21.1% to 2.9% (Table 2). ANOVA tests were run on the corrected overestimations to see if they differed signiﬁcantly based upon shape. No statistically signiﬁcant differences in mean bias were present, meaning that all of the teeth were corrected to about the same extent (df 5 5, F 5 2.07, sig. 5 0.117). For the creation of the ﬁnal correction formulae, the original and the validation samples were combined (total N 5 144). Figures 3 and 4 illustrate the linear relationships between the actual areas, the RI index values and the ARI values, respectively, using the combined samples. American Journal of Physical Anthropology 330 C. SCHMIDT ET AL. TABLE 2. Validation study: Summary data for actual area, the adjusted robusticity index (ARI), and the ARI overestimation Group 1 Actual area ARI ARI estimation (%) Mean SD 75.9 14.1 77.9 13.1 2.9 2.3 Mean SD 90.9 1.4 92.7 11.8 1.9 2.3 3 Mean SD 102.0 13.6 102.2 11.6 0.4 3.1 4 Mean SD 104.5 11.2 104.2 10.8 20.2 0.5 5 Mean SD 101.4 9.8 100.4 8.4 20.8 1.5 Mean SD 106.3 1.3 105.1 1.6 21.1 2.6 97.0 24 14.0 115.5 24 16.3 2 6 Total Mean N SD Fig. 3. Linear relationship between the actual area and robustness index (RI). Notice the overestimation of the robustness index values and the dispersal of points. Values are in mm2. Reference line is y 5 x. 0.5 24 2.5 The groups are: 1: maxillary without hypocone; 2: maxillary with small hypocone; 3: maxillary with large hypocone; 4: mandibular without hypoconulid; 5: mandibular with small hypoconulid; 6: mandibular with large hypoconulid. N 5 4 for each group. Mean and SD values for actual area and ARI are in mm2. Presented here are the ﬁnal correction formulae: Maxilla: Formula 1: No hypocone (ASU 0–1): (0.685)(MD)(BL) 1 11.25 Formula 2: Small hypocone (ASU 2–3): (0.785)(MD)(BL) 1 3.13 Formula 3: Large hypocone (ASU 4–5): (0.840)(MD)(BL) 1 0.47 Mandible: Formula 4: No hypoconulid (ASU 0–1): (0.722)(MD)(BL) 1 17.21 Formula 5: Small hypoconulid (ASU 2–3): (0.775)(MD)(BL) 1 9.84 Formula 6: large hypoconulid (ASU 4–5): (0.710)(MD)(BL) 1 16.99 It is hoped that these formulae are of value to dental researchers who are able to score tooth shape. However, when mining data from earlier studies it may not be possible to determine original tooth shape. Therefore, two additional formulae are provided, one for all maxillary molars and one for all mandibular molars. These formulae also are capable of producing a very low bias, although they are not as precise as using the shape speciﬁc formulae above. American Journal of Physical Anthropology Fig. 4. Linear relationship between the actual area and the adjusted robustness index (ARI). Notice the similarity in the estimations for each point and the narrower distribution of points when compared to Fig. 3. Values are in mm2. Reference line is y 5 x. Formula 7: (0.861)(MD)(BL) Formula 8: (0.698)(MD)(BL) ‘All maxillary 2 4.653 ‘All mandibular 1 19.061 teeth’ formula: teeth’ formula: DISCUSSION Improving the precision with which tooth area is determined should bolster all efforts directed toward an understanding of dental size. For example, it will help to clarify how molars have reduced in size throughout much of the Holocene (e.g., Frayer, 1978; Calcagno, 1989). Hill (2004) found that maxillary molars reduced in size from about 5,000 to 1,000 years ago using standard diameters. However, these measurements do not usually include the hypocone. Currently, a study is CORRECTING OVERESTIMATION IN MOLAR AREA underway to score occlusal outlines among the teeth studied by Hill so that the ARI can be used to see if the reduction is actually greater than so far detected. In primatology, the ARI should signiﬁcantly improve our understanding of tooth size in relation to diet and body size. Primate teeth vary signiﬁcantly in shape (e.g., Swindler, 2002), yet studies do not always take that shape into account. Applying the ARI to studies that use tooth size as an indicator of dimorphism and diet or those that seek to understand dental development and size differences between wild and captive primates should be able to ascertain more precise molar area estimates (e.g., Schuman and Brace, 1954; Swindler et al., 1963; Swindler and Orlasky, 1974; Swindler et al., 1998; Hlusko and Mahaney, 2003, 2007; Cuozzo and Yamashita, 2006; Hlusko et al., 2007). In paleoanthropology, researchers use dental metrics in a variety of ways, including species determination and documenting sexual dimorphism. ARI will beneﬁt these pursuits because more realistic occlusal area values will be produced, which should allow researchers to easily revisit studies regarding the relationship of tooth size to body size (e.g., McHenry, 1988). Finally, the ARI formulae provided here should help to correct RI in those instances where researchers are studying populations whose occlusal outlines are similar to those used in this study, i.e., are not dominated by extra cusps and odd shapes. Thus, most human populations, past and present, should be suitable candidates for our ARI formulae. However, for those populations, human or otherwise, whose teeth commonly have extra cusps or have shapes that are markedly dissimilar to those described here, researchers are encouraged to develop population/species-speciﬁc correction formulae. CONCLUSION The standard robusticity index signiﬁcantly overestimates tooth area and those overestimates vary according to tooth shape. Our regression-based correction formulae produce an adjusted RI, or ARI, that remove the RI bias. Although the validation study was small, it clearly indicated a marked improvement in occlusal area estimates when using the ARI. Moreover, the ARIs had mean inaccuracies that did not differ statistically based upon tooth shape. Thus, the correction formulae should provide superior molar area estimates than what is currently provided by the robusticity index alone. This improved method will facilitate more accurate odontometric studies in several realms of dental anthropology. LITERATURE CITED Alemseged Z, Wynn JG, Kimbel WH, Reed D, Geraads D, Bobe R. 2005. First hominin from the Basal Member of the Hadar Formation. Dikika, Ethiopia and its geological context. J Hum Evol 49:499–514. Bailey SE. 2004. 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