Changes in the buccolingual inclination of first molars with growth in untreated subjects: A longitudinal study
To assess longitudinal changes in the buccolingual inclination of the maxillary and mandibular first molars in untreated male and female subjects. Forty-seven male and 48 female subjects whose longitudinal dental casts were available at ages 6–16 years, with normal maxillary and mandibular arch forms were included. The original casts at ages 6, 7, 8, 9, 10, 12, 14, and 16 years were digitized and standardized. Measurements were recorded as the differences in cusp heights in the vertical dimension for the mandibular and maxillary first molars using OrthoInsight software. On average, for boys from age 6 to 16 years, both maxillary and mandibular first molars uprighted with age. Maxillary molars uprighted 0.403 mm on the left and 0.418 mm on the right; mandibular molars uprighted 0.441 mm on the left and 0.589 mm on the right. Similarly, for girls from age 6 to 16, both maxillary and mandibular molars uprighted with age. Maxillary molars uprighted 0.67 mm on the left and 0.574 mm on the right; mandibular molars uprighted 0.358 mm on the left and 0.329 mm on the right. Maxillary molars erupted with buccal crown inclination at age 6 in both boys and girls and uprighted lingually with growth. At age 16, maxillary molars were not completely upright but rather maintained some buccal crown inclination. Mandibular molars erupted with lingual crown inclination at age 6 and uprighted buccally with age. At age 16, mandibular molars were not completely upright but rather maintained some lingual inclination.ABSTRACT
Objectives:
Materials and Methods:
Results:
Conclusions:
INTRODUCTION
Wilson1 was one of the first to report the lateral inclination of the grinding teeth, the lower being inclined lingually and the upper being inclined buccally. This occlusal curve on the coronal plane has been referred to as curve of Wilson. Monson2 attempted to characterize the axial inclination of human teeth by soldering 6-inch rods to plates on human skulls in order to capture the orientation of the occlusal table. Accordingly, he found that posterior teeth did not have a horizontal surface or plane either mesiodistally or buccolingually on the coronal plane. Instead, he found that the occlusal curve was tangent to a sphere with a 4-inch radius. This was referred to as the sphere (or curve) of Monson. Dempster et al.3 studied the arrangement of the roots of the teeth in 11 skulls with typical dentitions and confirmed the lingual inclination of the mandibular posterior teeth.
Dawson4 reported two reasons for the existence of the curve of Wilson, the mediolateral curve that contacts the buccal and lingual cusp tips on each side of the arch. The first is attributed to resistance on loading and the second to masticatory function. He stated that the axial alignment of almost all posterior teeth is nearly parallel with the strong inward pull of the internal pterygoid muscles. He argued that aligning both upper and lower posterior teeth with the principal direction of muscle contraction produced the greatest resistance to masticatory forces and created inclinations that form the curve of Wilson.
There is evidence to suggest that buccolingual inclination changes with time and during the course of aging. Marshall et al.5 evaluated changes in molar crown inclination with growth. They found that from ages 7.5 to 26.4 years, the maxillary first molars uprighted by 3.3° while maxillary second molars uprighted by 5.9°. In contrast, mandibular molars were found to erupt with lingual crown torque and upright with age. Mandibular first molars uprighted 5.0° and mandibular second molars uprighted 7.5°.
Buccolingual inclination is also thought to be influenced by skeletal growth patterns. Ross et al.6 looked at variations in buccolingual tooth inclination and their correlation with skeletal growth patterns in the vertical dimension. They found that the maxillary posterior teeth were buccally inclined and the mandibular posterior teeth were lingually inclined. However, they did not find a correlation between the molar buccolingual inclination and the mandibular plane angle. Janson et al.7 also explored the relationship between buccolingual inclinations of posterior teeth with horizontal and vertical growth patterns. They employed a similar methodology and utilized dental casts to measure the angle formed by the posterior occlusal plane and the occlusal surface of molars. They found that maxillary posterior teeth of subjects with a vertical growth pattern had a greater buccal inclination compared with those of subjects with a horizontal growth pattern.
The measurement of buccolingual angulation of molars by the American Board of Orthodontics employs the use of a gauge to measure vertical height differences between the buccal and lingual cusp tips to the nearest millimeter.8 The American Board of Orthodontics suggests that the difference should be within a millimeter for the maxillary and mandibular molars.
The purpose of this study was to assess longitudinal changes in the buccolingual inclination of the maxillary and mandibular first molars in untreated male and female subjects.
MATERIALS AND METHODS
The records for the subjects were obtained from the Burlington Growth Center at the University of Toronto, Ontario, Canada. They were selected based on the following criteria: (1) normal maxillary and mandibular arch forms without anterior or posterior crossbite, (2) subjects in good health with no history of orthodontic treatment, (3) no missing or extracted 1st permanent mandibular molars, and (4) longitudinal dental casts available for evaluation at ages 6–16 years. The age groups of 6, 7, 8, 9, 10, 12, 14, and 16 years were used since they had at least six subjects per age group. These criteria limited the sample to 47 male subjects and 48 female subjects.
The original casts at the respective age time points described earlier were digitized at the Burlington Growth Center with the 3Shape extraoral scanner (Copenhagen, Denmark). These digital stereolithography files were uploaded to the Ortho Insight software (Motion View, Chattanooga, Tenn). The casts from the seven time points for each patient were oriented in the same plane (x, y, and z coordinates) using the Ortho Insight software by identifying the dentition on each cast and leveling the occlusal plane. Once each cast was oriented in the same plane, the highest (most occlusal) point on each cusp (millimeters) for the mandibular casts (mesiobuccal, distobuccal, mesiolingual, and distolingual cusps) and the highest point on the cusp (millimeters) for the maxillary molars (mesiobuccal, distobuccal, and palatal cusps) were identified for each pair of mandibular and maxillary first molars.
Measurements were recorded as the differences between the highest points from each cusp in the vertical dimension. If the buccal and lingual cusps were the same height, the value was recorded as zero. If the lingual cusp was higher than the buccal cusp, a negative value was recorded, whereas if the buccal cusp was higher than the lingual cusp, a positive value was recorded for the mandibular molars. If the palatal cusp defined the occlusal plane, a positive value was recorded, whereas if the buccal cusp defined the occlusal plane, a negative value was recorded for the maxillary molars. For each molar on the mandibular cast, the two buccal cusp tip heights were averaged, and the two lingual cusp tip heights were averaged for each mandibular molar. The average lingual cusp tip height (millimeters) for each molar was then subtracted from the average buccal cusp tip height for each mandibular first molar. For each maxillary first molar, the palatal cusp height was subtracted from the average buccal cusp height.
To determine the intraexaminer reliability,15 randomly chosen subjects had all time points remeasured 1 week after the initial measurements were made. A paired t-test was used for all measurements to determine whether they were within acceptable limits. To determine interexaminer reliability, another examiner used the same software to measure the same 15 subjects. A paired t-test was used to determine whether there was any statistically significant error between the examiners. The statistical significance was predetermined at P ≤ .05.
RESULTS
The intraexaminer results showed a mean difference of 0.010 mm in vertical measurements between cusp tips, with no statistical difference between two measurements and an average Pearson coefficient greater than 0.99 for the male samples. The intraexaminer results showed a mean difference of 0.008 mm in vertical measurements between cusp tips, with no statistical significance and an average Pearson coefficient greater than 0.99 for the female samples. The interexaminer results showed a mean difference of 0.011 mm in vertical measurements between cusp tips, with no statistical significance, and an average Pearson coefficient greater than 0.93.
Table 1a–d presents the mean distance (mm) between the buccal and lingual cusp tips, the range, the standard deviation (SD), and the sample size (N) for each age group in the study for the boys. The mean difference in height between mandibular buccal and lingual cusp tips in boys at age 6 was 0.955 mm on the lower left and 1.068 mm on the lower right. The mean difference in height between the maxillary buccal and palatal cusp tips in boys at age 6 was 1.044 mm on the upper left molar and 1.131 mm on the upper right molar. Figure 1a–d shows the linear regression extrapolated from the mean distance (mm) between the buccal and lingual cusp tips plotted against the age of the sample groups for boys. In boys, the difference in the vertical height between the buccal and lingual cusp decreased 0.048 mm per year for the lower left molar. For the lower right molar in boys, the difference between the vertical height between the buccal and lingual cusp decreased 0.063 mm per year. For the upper molars in boys, the difference in the vertical height between the buccal and palatal cusp decreased 0.039 mm per year for the upper right molar and 0.045 mm per year for the upper left molar.
Citation: The Angle Orthodontist 87, 5; 10.2319/120716-878.1
Table 2a–d displays the mean distance (mm) between the buccal and lingual cusp tips, the range, the standard deviation (SD), and the sample size (N) for each age group in the study for the girls. The mean difference in height between mandibular buccal and lingual cusp tips in girls at age 6 was 1.012 mm on the lower left and 1.01 mm on the lower right. The mean difference in height between maxillary buccal and palatal cusp tips in girls at age 6 was 1.428 mm on the upper left molar and 1.315 mm on the upper right molar. Figure 2a–d shows the linear regression extrapolated from the mean distance (mm) between the buccal and lingual cusp tips plotted against the age of the sample groups for girls. In girls, the difference in the vertical height between the buccal and lingual cusps decreased 0.044 mm per year for the lower left molar. For the lower right molar in girls, the difference between the vertical heights of the buccal and lingual cusps decreased 0.048 mm per year. For the upper molars in girls, the difference in the vertical height between the buccal and palatal cusps decreased 0.057 mm per year for the upper right molar and 0.083 mm per year for the upper left molar.
Citation: The Angle Orthodontist 87, 5; 10.2319/120716-878.1
Tables 1 and 2 and Figures 1 and 2 show a general trend of the average cuspal height (mm) differences between the buccal and lingual cusp tips decreasing from age 6 years to 16 years in both the male and female groups, indicating that the lower molars were uprighting more buccally, and the upper molars were uprighting more palatally. On average, from ages 6 to 16 years, the lower molars in boys uprighted 0.441 mm per year on the left and 0.589 mm on the right. In girls, the lower molars uprighted 0.358 mm on average on the left and 0.329 mm on average on the right.
DISCUSSION
It has been proposed that the mandibular molars erupt into the oral cavity with lingual crown torque.5 The current longitudinal study confirmed the presence of a curve of Wilson, which is illustrated by the fact that in boys at age 6 on average, the buccal cusps were more occlusal than the lingual cusps by 0.955 mm on the lower left and 1.068 mm on the lower right molars. In girls, the difference was 1.012 mm on the lower left and 1.01 mm on the lower right. Similarly, the study showed that maxillary molars erupted with buccal crown torque, which is illustrated by the fact that, in boys at age 6 on average, the lingual cusps were more occlusal than the buccal cusps in height by 1.044 mm on the upper left molar and 1.131 mm on the upper right molar. In girls, the difference was 1.428 mm on the upper left molar and 1.315 mm on the upper right molar.
The results also illustrate that the mandibular molars upright with growth over time. On average, from ages 6 to 16 years, the lower molars in boys uprighted 0.441 mm per year on the left and 0.589 mm on the right. In girls, the lower molars uprighted 0.358 mm per year on average on the left and 0.329 mm on average on the right. Similarly, it was shown that the maxillary molars upright with growth over time. On average, from ages 6 to 16 years, the upper molars in boys uprighted 0.403 mm per year on the left and 0.418 mm on the right. In girls, the maxillary molars uprighted 0.670 mm per year on average on the left and 0.574 mm on the right.
Weinstein et al.9 report that each unit of the dentition is in equilibrium with its surroundings at any instant. The surroundings can include adjacent teeth, the tongue, the buccolabial musculature, the bone, and the intervening periodontal ligament. The time it takes for the uprighting to occur can be described as the fourth dimension of the equilibrium theory that Weinstein proposed. Brodie10 and Moyers11 referred to the dimension of time as a contributor to the equilibrium of teeth. Brodie10 stated that, as the primary teeth begin to erupt and as the alveolar process is formed to accompany them, the contact is broken between the cheek and lips on one side and the tongue on the other side. Moyers11 stated that a change in muscular environment around a tooth would cause the tooth to move through the bone until it was again in balance.
The results of the current study support Marshall et al.5 that mandibular molars erupt with lingual crown torque and upright over time. It is important to note that this study illustrated that molars do not upright completely within the age groups studied. In fact, the mandibular molars maintain some lingual inclination while the maxillary molars maintain some buccal inclination.
Okeson12 explained that the curve of Wilson exists to have the most effective use of cuspal contacts while avoiding nonfunctional contacts known as balancing interferences. Nanda13 stated that a small curve of Wilson between the buccal segments allows for proper occlusal function, but that “an accentuated curve will result in balancing interferences, especially in the second molar area.”
Orthodontic philosophies have varied in their handling of the presence of an occlusal curvature and molar torque. Andrews and Andrews14 explained in their six elements philosophy that “each crown must be inclined so that the occlusal surface can interface and function optimally with the teeth in the opposing arch”. McNamara15 suggested that one of the goals of orthodontic treatment should be to flatten the occlusal plane, and level the curve of Wilson. Conversely, Dawson4 stated that when the curve of Wilson is made too flat, ease of masticatory function may be impaired. The current findings are well aligned with the American Board of Orthodontics recommendation for case finishing. When grading casts for the clinical examination, the board requires that buccolingual inclination of the posterior teeth should be assessed by a flat surface that extends between the occlusal surfaces of the right and left posterior teeth.8 When the mandibular cast is being analyzed, the straight edge should lie on the buccal cusps, while the lingual cusps should fall within 1 mm of the surface. Similarly, when analyzing the maxillary cast, the straight edge should contact the lingual cusps and the buccal cusps should be within 1 mm of the surface. Thus, it would be logical to consider maintaining some degree of a curve of Wilson after orthodontic treatment to be consistent with the physiologic needs of masticatory function and encourage stability of treatment.
CONCLUSIONS
Based on the findings from this study, the following conclusions can be made:
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Mandibular molars erupt with lingual crown torque and upright buccally with age.
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Mandibular molars do not completely upright but, rather, maintain some lingual inclination.
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Maxillary molars erupt with buccal crown torque and upright lingually with age.
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Maxillary molars do not completely upright but, rather, maintain some buccal inclination.
Linear regression of the change in vertical heights (mm) between the buccal and lingual cusp tips plotted against the age of the sample groups for boys age 6 to 16 years.
Linear regression of the change in vertical heights (mm) between the buccal and lingual cusp tips plotted against the age of the sample groups for girls age 6 to 16 years.
Contributor Notes