Development of the curve of Spee

ORIGINAL ARTICLE

Development of the curve of Spee Steven D. Marshall,a Matthew Caspersen,b Rachel R. Hardinger,c Robert G. Franciscus,d Steven A. Aquilino,e and Thomas E. Southardf Iowa City, Iowa, Fredericksburg, Va, and Oklahoma City, Okla Introduction: Ferdinand Graf von Spee is credited with characterizing human occlusal curvature viewed in the sagittal plane. This naturally occurring phenomenon has clinical importance in orthodontics and restorative dentistry, yet we have little understanding of when, how, or why it develops. The purpose of this study was to expand our understanding by examining the development of the curve of Spee longitudinally in a sample of untreated subjects with normal occlusion from the deciduous dentition to adulthood. Methods: Records of 16 male and 17 female subjects from the Iowa Facial Growth Study were selected and examined. The depth of the curve of Spee was measured on their study models at 7 time points from ages 4 (deciduous dentition) to 26 (adult dentition) years. The Wilcoxon signed rank test was used to compare changes in the curve of Spee depth between time points. For each subject, the relative eruption of the mandibular teeth was measured from corresponding cephalometric radiographs, and its contribution to the developing curve of Spee was ascertained. Results: In the deciduous dentition, the curve of Spee is minimal. At mean ages of 4.05 and 5.27 years, the average curve of Spee depths are 0.24 and 0.25 mm, respectively. With change to the transitional dentition, corresponding to the eruption of the mandibular permanent first molars and central incisors (mean age, 6.91 years), the curve of Spee depth increases significantly (P ⬍ 0.0001) to a mean maximum depth of 1.32 mm. The curve of Spee then remains essentially unchanged until eruption of the second molars (mean age, 12.38 years), when the depth increases (P ⬍ 0.0001) to a mean maximum depth of 2.17 mm. In the adolescent dentition (mean age, 16.21 years), the depth decreases slightly (P ⫽ 0.0009) to a mean maximum depth of 1.98 mm, and, in the adult dentition (mean age 26.98 years), the curve remains unchanged (P ⫽ 0.66), with a mean maximum depth of 2.02 mm. No significant differences in curve of Spee development were found between either the right and left sides of the mandibular arch or the sexes. Radiographic measurements of tooth eruption confirm that the greatest increases in the curve of Spee occur as the mandibular permanent incisors, first molars, or second molars erupt above the pre-existing occlusal plane. Conclusions: On average, the curve of Spee initially develops as a result of mandibular permanent first molar and incisor eruption. The curve of Spee maintains this depth until the mandibular permanent second molars erupt above the occlusal plane, when it again deepens. During the adolescent dentition stage, the curve depth decreases slightly and then remains relatively stable into early adulthood. (Am J Orthod Dentofacial Orthop 2008;134:344-52)

V

iewed in the sagittal plane, occlusal curvature is a naturally occurring phenomenon in the human dentition. Found in the dentitions of other mammals and fossil humans,1 this curvature was a

Visiting associate professor, Department of Orthodontics, College of Dentistry, University of Iowa, Iowa City. b Private practice, Fredericksburg, Va. c Orthodontic resident, College of Dentistry, University of Oklahoma, Oklahoma City. d Associate professor, Department of Anthropology, University of Iowa, Iowa City. e Professor, Department of Prosthodontics, College of Dentistry, University of Iowa, Iowa City. f Professor and head, Department of Orthodontics, College of Dentistry, University of Iowa, Iowa City. Supported by the Dr George Andreasen Memorial Fund. Reprint requests to: Thomas E. Southard, Department of Orthodontics, College of Dentistry, University of Iowa, Iowa City, IA 52242; e-mail, tom-southard@ uiowa.edu. Submitted, May 2006; revised and accepted, October 2006. 0889-5406/$34.00 Copyright © 2008 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2006.10.037

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termed the curve of Spee in the late 19th century, when Ferdinand Graf von Spee2,3 described it in humans. In the sagittal view, Spee connected the anterior surfaces of the mandibular condyles to the occlusal surfaces of the mandibular teeth with an arc of a circle, tangent to the surface of a cylinder lying perpendicular to the sagittal plane. He suggested that this geometric arrangement defined the most efficient pattern for maintaining maximum tooth contacts during chewing and considered it an important tenet in denture construction. This description became the basis for Monson’s spherical theory4 on the ideal arrangement of teeth in the dental arch, in which occlusal curvature is described in the sagittal and frontal planes by the tangent of a sphere with a radius of approximately 4 in. Our current understanding is that, in sample populations tested, occlusal curvature can be fitted to the geometry of Spee’s cylinder and Monson’s sphere with much individual variation.5-7

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Today in orthodontics, the curve of Spee commonly refers to the arc of a curved plane that is tangent to the incisal edges and the buccal cusp tips of the mandibular dentition viewed in the sagittal plane. In contrast, the prosthodontic specialty ignores the incisors and includes only the canine to the terminal molar as the dental arch portion of the curve. The curve then continues posteriorly to intersect the anterior surface of the condyle as originally proposed by Spee.8-10 Modern orthodontics and reconstructive dentistry differ with respect to the clinical significance of the curve of Spee. Its proper management is critical for the construction of stable complete dentures and might play a role in the success of implant-supported restorations.7 In complete denture prosthodontics, establishing a curve of Spee in harmony with the condylar guidance, incisal guidance, plane of occlusion, and prosthetic tooth cusp height is essential for developing a bilaterally balanced articulation, believed to maintain optimal denture stability.11 In the prosthodontic restoration of the natural dentition, the treatment goal is a mutually protected occlusion, whereby the posterior teeth disclude during eccentric functional movements. The curve of Spee, in conjunction with posterior cusp height, condylar inclination, and anterior guidance, plays an important role in the development of the desired occlusal scheme.10 The 4-in Monson sphere is used by some to develop an “idealized” reconstruction of the posterior dentition.12 In patients with a retrognathic mandible and steep anterior guidance, it has been suggested that the occlusal plane might be constructed with a shorter radius than the 4-in standard reported by Monson to avoid posterior interferences. The opposite is true in Class III patients, when a larger (flatter) curve, typically a 5-in radius, is more suitable.13 Andrews,14 in describing the 6 characteristics of normal occlusion, found that the curve of Spee in subjects with good occlusion ranged from flat to mild, noting that the best static intercuspation occurred when the occlusal plane was relatively flat. He proposed that flattening the occlusal plane should be a treatment goal in orthodontics. This concept, especially as applied to deep overbite patients, has been supported by others15-20 and produces variable results with regard to maintaining a level curve after treatment.21-23 Our understanding of why the curve of Spee develops is limited. Some suggest that its development probably results from a combination of factors including growth of orofacial structures, eruption of teeth, and development of the neuromuscular system. It has been suggested that the mandibular sagittal and vertical position relative to the cranium is related to the curve of

Spee, which is present in various forms in mammals.1 In humans, an increased curve of Spee is often seen in brachycephalic facial patterns24,25 and associated with short mandibular bodies.26 However, the presence of the curve of Spee based on a morphologic or cephalometric predictor has not been definitive. It has been suggested that the deciduous dentition has a curve of Spee ranging from flat to mild, whereas the adult curve of Spee is more pronounced.27 Explanations for this observation cite the differences in cusp height between the deciduous and permanent teeth and the tendency for increased occlusal wear of the deciduous teeth. However, no quantitative research supports this. Furthermore, it was reported that, once established in adolescence, the curve of Spee appears to be relatively stable.28,29 Certain cephalometric and dental factors are associated with individual variations in the curve of Spee, but they do not predict its biologic variance unequivocally. It appears that craniofacial morphology is just 1 of many factors influencing its development.6,23,26,30 Even though orthodontists must deal with the curve of Spee in virtually every patient and prosthodontists construct a curve of Spee for proper functional occlusion, an in-depth understanding of its cause and development is not found in the literature. The purpose of this study was to increase our understanding by examining the development of the curve of Spee longitudinally from the deciduous dentition to adulthood in a sample of untreated subjects with normal occlusion. MATERIAL AND METHODS

Sixteen male and 17 female subjects were selected from the Iowa Facial Growth Study, which was started by L. Bodine Higley and Howard Meredith in 1946; 89 boys and 86 girls were enrolled. They lived in or near Iowa City, were predominately of Northern European descent, and had clinically acceptable Class I occlusions and normal facial skeletal features. At enrollment, the children were not younger than 3 years of age. Medical history, height, weight, and lateral and anterior cephalograms were taken quarterly until age 5. Records including lateral and anterior cephalograms, dental casts, photographs, and anthropometric measurements were taken biannually from ages 5 to 12. After age 12, until about age 18, all records were taken annually. Records were also taken once during early adulthood (approximate age, 26 years). The 33 subjects selected from that study for this study were previously identified for research purposes as having complete records into adulthood including study casts without distortion or abrasion. All subjects

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American Journal of Orthodontics and Dentofacial Orthopedics September 2008

Fig 1. Measurement of the maximum depth of the curve of Spee.

had tooth eruption timing and eruption patterns within normal ranges. The maximum depth of the curve of Spee was measured as the maximum of the perpendicular distances between the buccal cusp tips of the mandibular teeth and a measurement plane described by the central incisors and the distal cusp tip of the most posterior tooth in the mandibular arch (Fig 1). A digital caliper (model CD, 4-in CS, Mitutoyo, Aurora, Ill) was mounted on a standard surveying table (Fig 2). Dental casts were leveled to a plane defined by the distobuccal cusps of the right and left most posterior tooth and the most central point on the more erupted central incisor. Permanent incisors used as a tripod landmark were erupted with more than half of their clinical crown on a cast and had greater or equal eruption height than the adjacent deciduous lateral incisors. Measurements of the curve of Spee were taken on the left and right sides to within 0.01 mm. The right and left maximum depths were recorded and averaged to arrive at the average maximum depth for each subject at each time point. In this article, we use “depth” to mean the maximum depth of the curve of Spee. Study casts selected for the time points for each subject were chosen from each subject’s longitudinal study casts based on tooth eruption. T1: the study cast for each subject available between ages 3.5 and 5 years, earlier in age, by at least 6 months, than the study cast of full deciduous dentition chosen for T2; 30 subjects had models. T2: the study cast of the oldest age for which the deciduous second molars and incisors still served as the terminal reference points for the measurement plane; 33 subjects had models. T3: the study cast of the youngest age for which the permanent first molars and incisors were the measurement plane references; 33 subjects had models. T4: the study cast of the oldest age for which the

Fig 2. Apparatus used to measure the maximum depth of the curve of Spee: a digital caliper vertically mounted on a surveyor. The end of the digital caliper is enlarged (inset) to show the modification of the caliper piston to allow point contact with the study cast.

permanent first molars still served as the terminal (posterior) reference points for the measurement plane; 33 subjects had models. T5: the study cast of the youngest age for which the permanent second molars were the terminal reference points for the measurement plane; 33 subjects had models. T6: the study cast of the subject with fully erupted adolescent dentition nearest in age to 16 years; 24 subjects had models. T7: the study cast of the subject nearest in age to 26 years; 23 subjects had models. Detailed statistics for the subjects from T1 to T7 are given in Table I. To ascertain reliability, duplicate measurements were made of right maximum depth, left maximum depth, and average maximum depth in 7 subjects (4 female, 3 male) for a total of 33 paired observations (trials 1 and 2). There were no paired measurements for T1; 7 paired measurements for T2, T3, and T6; and 6

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Table I.

Descriptive statistics for the subjects’ ages at each time point

Statistic All subjects Number Mean SD Median Minimum Maximum Female subjects only Number Mean SD Median Minimum Maximum Male subjects only Number Mean SD Median Minimum Maximum

T1

T2

T3

T4

T5

T6

T7

30 4.05 0.39 4 3.6 5.1

33 5.27 0.5 5 4.6 6

33 6.91 0.65 7 6 8.1

33 11.11 1.24 11 7 13

33 12.38 1.34 12 10.6 16

24 16.21 0.41 16 16 17

23 26.98 1.36 26.6 25.1 30.1

16 4.17 0.4 4 3.6 5.1

17 5.27 0.49 5 4.6 6

17 7.08 0.69 7 6 8.1

17 11.02 1.36 11 7 13

17 12.18 1.07 12 11 14

14 16.14 0.36 16 16 17

11 27.8 1.42 27.9 25.4 30.1

14 3.91 0.34 3.95 3.6 4.9

16 5.26 0.53 5 4.6 6

16 6.73 0.57 7 6 8

16 11.2 1.15 11 8 13

16 12.59 1.59 12.3 10.6 16

10 16.3 0.48 16 16 17

12 26.23 0.75 26.55 25.1 27.5

paired measurements for T6 and T7. Two subjects had 4 paired observations; and the remaining 5 subjects had 5 paired observations. Intraclass correlations were used to measure the relationship between the 2 trials. The intraclass correlation is typically used in situations such as this, where it is of interest to obtain a measure of intrarater agreement for quantitative outcomes.31,32 Perfect agreement corresponds to an intraclass correlation coefficient of 1. An intraclass correlation of 0 indicates complete lack of agreement between the duplicate measures. Statistical tests were used to test the null hypothesis that the intraclass correlation coefficient, P, was equal to 0 against the 2-sided alternative hypothesis that P was not equal to 0. The intraclass correlation coefficient for measurement of average maximum depth, right maximum depth, and left maximum depth was 0.999 with a P value ⬍0.0001. At each time point, descriptive statistics were obtained for age and for left, right, and average maximum depth of the curve of Spee; this was done for all subjects and separately for the sexes. The Wilcoxon signed rank test was used to compare changes in maximum depth between 2 adjacent time points. In these instances, the Wilcoxon signed rank test for paired data was used to test the null hypothesis that median change between adjacent time points was equal to 0. Adjustment for multiple comparisons was made by using the standard Bonferroni method with an overall 0.05 level of type I error.33

Radiographic measurements and analysis

Based on preliminary findings, our attention was drawn to the increase in the curve of Spee specifically at the time of eruption of the mandibular permanent incisors, first molars, and second molars. Tracings of the mandible were made for each of the 33 subjects by using lateral cephalograms at T2 and T3, and T4 and T5. At T2, the distobuccal cusps of the deciduous second molars (right and left), mandibular permanent first molars (right and left), and the incisal tips of the deciduous central incisors were identified. At T3, the same molar landmarks plus the incisal tip of the permanent central incisors were identified. At T4 and T5, the distobuccal cusps of the mandibular permanent first molars, mandibular permanent second molars (right and left), and the incisal tip of the permanent central incisors were identified. For T2, a line was constructed tangent to the deciduous central incisor tip and the distobuccal cusp tip of the deciduous second molar (average of right and left molars). For T4, a line was constructed tangent to the permanent central incisor tip and the distobuccal cusp tip of the permanent first molar (average of right and left molars). For each subject, the T2 tracing was superimposed on the T3 tracing, and the T4 tracing was superimposed on the T5 tracing according to the American Board of Orthodontics standards by using the best fit on the mandibular symphysis and canal. With the digital caliper, the vertical change in the tooth landmarks compared with

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Fig 3. Sample mandibular superimposition for a subject. Solid line is the cephalometric tracing at T2. Dotted line is the cephalometric tracing at T3. Line A represents the T2 reference plane between the mandibular deciduous second molars and central incisors used for cast measurements. Vertical bars B, C, and D represent measurements made with the digital caliper and corrected for radiographic magnification as described in the text. To calculate the relative eruption of the mandibular permanent first molars and permanent incisors relative to the mandibular deciduous second molars between T2 and T3, the amount of eruption at C was subtracted from that measured at B and D. The same analysis was carried out between T4 and T5 to measure the relative eruption of the mandibular second molars.

the constructed line was measured (Fig 3). The relatively small amount of time between the points allowed accurate superimposition. Corrections for radiographic enlargement of linear measurements were made for each subject at each time point as previously reported for the Iowa Facial Growth Study.34 RESULTS

Table II gives the descriptive statistics for the average maximum curve of Spee depth for T1 through T7. Figure 4 is a plot of these data. In the deciduous dentition, approximately a year before change to the transitional dentition (mean age, 4.05 years) and immediately before change to the transitional dentition (mean age, 5.27 years), the curve of Spee is minimal and does


not change significantly (P ⫽ 0.84), with mean depths of 0.24 ⫾ 0.29 mm and 0.25 ⫾ 0.34 mm, respectively. With change to the transitional dentition, corresponding to the eruption of the mandibular permanent first molars and central incisors (mean age, 6.91 years), the curve of Spee increases significantly (P ⬍ 0.0001) to a mean depth of 1.32 ⫾ 0.77 mm. Just before the eruption of the mandibular permanent second molars (mean age, 11.11 years), the curve remains unchanged (P ⫽ 1.0), with a mean depth of 1.31 ⫾ 0.58 mm. Just after the eruption of the mandibular permanent second molars (mean age, 12.38 years), the curve increases (P ⬍ 0.0001) to a mean depth of 2.17 ⫾ 0.75 mm. In the adolescent dentition (mean age, 16.21 years), the curve decreases slightly (P ⫽ 0.0009) to a mean depth of 1.98 ⫾ 0.67 mm. In the adult dentition (mean age, 26.98 years), the curve does not change (P ⫽ 0.66), with a mean depth of 2.02 ⫾ 0.78 mm. No significant differences in curve of Spee change were found between the right and left sides or between the sexes. Descriptive statistics for differences between curve depths of adjacent time points are shown in Table III. Radiographic (lateral cephalometric) measurements comparing tooth eruption during the greatest increases in curve of Spee depth (mean ages 5.27-6.91 and 11.11-12.38 years) indicate that eruption of the teeth defining the termini of the curve (permanent incisors, first molars, or second molars) places them significantly above the occlusal plane, thus increasing the depth of the occlusal curve (Fig 3 and Table IV). On average between T2 and T3, the mandibular permanent incisors erupted 3.33 ⫾ 1.51 mm, and the mandibular permanent first molars erupted 3.35 ⫾ .94 mm above the deciduous second molar-deciduous incisor occlusal plane established at T2, whereas, during the same interval, the mandibular deciduous second molars erupted only 1.03 ⫾ 0.79 mm relative to the occlusal plane established at T2. On average between T4 and T5, the mandibular second molars erupted 3.08 ⫾ 0.85 mm above the permanent first molar-permanent central incisor occlusal plane established at T4, whereas the permanent first molars, deciduous second molars/second premolars, first premolars, and central incisors erupted above the same occlusal plane 1.00 ⫾ 0.48, 1.01 ⫾ 0.53, 1.03 ⫾ 0.68, and 1.16 ⫾ 0.88 mm, respectively. DISCUSSION

The principal findings of this study are shown in Figure 4. The curve of Spee depth is minimal in the deciduous dentition; its greatest increase occurs in the early mixed dentition as a result of permanent first molar and central incisor eruption; it maintains this

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Table II.

Descriptive statistics for the average maximum curve of Spee depth

Statistic All subjects Number Mean SD Median Minimum Maximum Female subjects only Number Mean SD Median Minimum Maximum Male subjects only Number Mean SD Median Minimum Maximum

T1

T2

T3

T4

T5

T6

T7

30 ⫺0.24 0.29 ⫺0.18 ⫺1.31 0

33 ⫺0.25 0.34 ⫺0.14 ⫺1.44 0

33 ⫺1.32 0.77 ⫺1.33 ⫺3.45 0

33 ⫺1.31 0.58 ⫺1.25 ⫺2.4 ⫺0.21

33 ⫺2.17 0.75 ⫺2.32 ⫺3.73 ⫺0.52

24 ⫺1.98 0.67 ⫺2.15 ⫺3.27 ⫺0.8

23 ⫺2.02 0.78 ⫺2.15 ⫺3.33 ⫺0.47

16 ⫺0.3 0.32 ⫺0.31 ⫺1.31 0

17 ⫺0.28 0.35 ⫺0.15 ⫺1.44 0

17 ⫺1.47 0.86 ⫺1.47 ⫺3.45 0

17 ⫺1.37 0.48 ⫺1.25 ⫺2.24 ⫺0.63

17 ⫺2.3 0.71 ⫺2.33 ⫺3.73 ⫺0.54

14 ⫺2.12 0.7 ⫺2.27 ⫺3.27 ⫺0.95

11 ⫺1.96 0.79 ⫺2.15 ⫺3.33 ⫺0.86

14 ⫺0.18 0.24 ⫺0.12 ⫺0.7 0

16 ⫺0.23 0.33 ⫺0.09 ⫺1.24 0

16 ⫺1.16 0.65 ⫺1.08 ⫺2.1 ⫺0.03

16 ⫺1.24 0.67 ⫺1.24 ⫺2.4 ⫺0.21

16 ⫺2.03 0.79 ⫺2.24 ⫺3.02 ⫺0.52

10 ⫺1.8 0.61 ⫺1.82 ⫺2.68 ⫺0.8

12 ⫺2.08 0.81 ⫺2.05 ⫺3.24 ⫺0.47

Fig 4. Sample mean curve of Spee average maximum depth from T1 to T7. Each subject’s mean maximum depth of the curve of Spee was calculated as the average of the left and right maximum depths at each time point.

depth until it increases to maximum depth with eruption of the permanent second molars and then remains relatively stable into late adolescence and early adulthood. To our knowledge, this is the first report measuring longitudinally the depth of the curve of Spee. These findings support the suggestions of Ash27 that the deciduous dentition has a curve of Spee ranging from flat to mild and the adult curve is more pronounced.

These findings also support those of Carter and McNamara28 and Bishara et al29 that, once established in adolescence, the curve of Spee appears to be relatively stable. The curve of Spee can be modeled as a simple curve, with its length defined by an arc of a circle and its depth (sharpness or flatness) determined by the radius of the same circle. In this sample, we measured change in curve depth during a change in arc length as

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Table III.


Wilcoxon signed rank test results for differences in average maximum depth between 2 sequential time

points Epoch difference 2-1 3-2 4-3 5-4 6-5 7-6

Sample size

Mean difference

SD

Median difference

Minimum

Maximum

Wilcoxon P value

30 33 33 33 24 21

⫺0.02 ⫺1.07 0.01 ⫺0.86 0.35 ⫺0.11

0.25 0.73 0.71 0.65 0.45 0.57

0.0 ⫺1.1 ⫺0.2 ⫺0.8 0.3 0.1

⫺1.0 ⫺3.1 ⫺1.4 ⫺1.9 ⫺0.7 ⫺1.3

0.5 0.5 1.9 0.9 1.3 0.7

0.8388 ⬍0.0001 1 ⬍0.0001 0.0009 0.6636

The null hypothesis is that the median change between adjacent time points ⫽ 0.

Table IV. Measurement (mm) of vertical eruption for selected teeth at T3 and T5 compared with the curve of Spee measurement plane constructed at T2 and T4 Time point T3

T5

Teeth measured

Mean (SD)

Median

Minimum/maximum

Mandibular permanent first molars Mandibular deciduous second molars Mandibular permanent central incisors Mandibular permanent second molars Mandibular permanent first molars Mandibular deciduous second molars or permanent second premolars Mandibular permanent first premolars Mandibular permanent central incisors

3.35 (1.26) 1.03 (0.79) 3.33 (0.91) 3.08 (0.85) 1.00 (0.43) 1.01 (0.58)

3.09 1.21 3.57 3.00 0.93 0.90

0.91/5.76 0.05/2.85 0.34/4.66 1.70/5.20 0.00/2.10 0.14/2.30

1.03 (0.68) 1.16 (0.88)

0.90 1.00

0.00/2.80 0.00/4.00

a result of permanent first and second molar eruptions. It is possible to have an increase in the depth of a simple curve by increasing the arc length alone (circle radius unchanged). Therefore, the documented change in maximum depth in our sample might be due to a change in curve shape, a change in curve length, or both. A plausible explanation for the development of the curve of Spee is that mandibular permanent teeth erupt before their maxillary antagonists. This means that, in large measure, the curve of Spee develops as a dental (not skeletal) event. In other words, on average, eruption of the mandibular permanent first molars precedes the maxillary permanent first molars by 1 to 2 months, and the mandibular permanent central incisors precede the maxillary permanent central incisors by 12 months. Furthermore, the mean age of emergence of the mandibular second molars is 6 months before the maxillary second molars.35,36 This differential timing could permit unopposed mandibular permanent first molar and incisor eruption beyond the established mandibular occlusal plane, especially if deciduous second molars are in a flush terminal plane relationship or the maxillary deciduous second molars have small distolingual cusps. Later, mandibular second molar eruption could likewise be relatively unopposed. The result of both events would be deepening in the curve. Of course, this dental event (mandibular permanent molars erupting before maxillary molars)

could simply be a way of providing an evolutionary “kick start” to curve of Spee development. In addition to the possible contribution of eruption timing, craniofacial variation and its affects on biomechanics might also influence the curve of Spee.37 The dentitions of most mammals have a curve of Spee, and there is an association between the forward tilt of the mandibular posterior teeth and the orientation of the masseter muscle in many mammals.1,38 Farella et al6 reported that condylar height (relative to the occlusal plane) and anteroposterior position of the mandible (relative to the cranial base) are associated with curve of Spee depth. Based on our results, the finding of Farella et al could be simply explained by the fact that, in patients with small mandibles, the mandibular permanent incisors could keep erupting (curve of Spee increasing) until they contact the palate. Although our results point to a strong eruption (dental) influence on curve of Spee development, we agree that other craniofacial factors probably play a role; we are currently investigating the impact of these factors. We found no statistically significant differences between the depth of the curve of Spee and the left and right sides of the arches. This result contrasts with the results of Farella et al,6 who found that left-side curves were significantly deeper in both sexes. What are the clinical implications of our findings?


Several studies have compared treatment techniques to deal with exaggerated curves of Spee and the stability of those treatments.21,24,39-41 Our findings provide insight into the magnitude of the curve of Spee during development. These results give orthodontists a guideline about the normal curve of Spee depth at the end of treatment or after the patient has settled in retention. Furthermore, since our findings indicate that the greatest increase in the curve of Spee occurs with the eruption of the mandibular second molars, we believe that this underscores the importance of including the second molars in orthodontic treatment. CONCLUSIONS

1. The occlusal plane in the deciduous dentition is relatively flat. 2. The largest increase in the maximum depth of the curve of Spee occurs during, and results specifically from, the differential eruption of the mandibular permanent first molars and incisors relative to the deciduous second molars. 3. The curve of Spee maintains this depth until the mandibular permanent second molars erupt above the occlusal plane, when it again deepens. 4. During the adolescent dentition stage, the curve decreases slightly and then remains relatively stable into early adulthood. 5. There are no significant differences in maximum depth of the curve of Spee between either the right and left sides of the mandibular arch or the sexes. REFERENCES 1. Osborn JW. Orientation of the masseter muscle and the curve of Spee in relation to crushing forces on the molar teeth of primates. Am J Phys Anthropol 1993;92:99-106. 2. Spee FG. Die verschiebungsbahn des unterkiefers am schadel. Arch Anat Physiol 1890;16:285-94. 3. Spee FG, Beidenbach MA, Hotz M, Hitchcock HP. The gliding path of the mandible along the skull. J Am Dent Assoc 1980;100:670-5. 4. Monson GS. Applied mechanics to the theory of mandibular movements. Dent Cosmos 1932;74:1039-53. 5. Ferrario VF, Sforza C, Miani A. Statistical evaluation of Monson’s sphere in the healthy permanent dentitions in man. Arch Oral Biol 1997;42:365-9. 6. Farella M, Michelotti A, Martina R. The curve of Spee and craniofacial morphology: a multiple regression analysis. Eur J Oral Sci 2002;110:277-81. 7. Xu H, Suzuki T, Muronoi M, Ooya K. An evaluation of the curve of Spee in the maxilla and mandible of human permanent healthy dentitions. J Prosthet Dent 2004;92:536-9. 8. Ramfjord SP, Ash MM. Occlusion. Philadelphia: W. B. Saunders; 1971. 9. Van Blarcom CW, editor. The glossary of prosthodontic terms. 8th ed. St. Louis: Mosby; 2005.

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