Development of the Curve of Spee

ORIGINAL ARTICLE

D veSt HardiStIow a

Int haractthe n hares hen, hstu devein ion froMe the Iex on th4 ( Wilcoch ts. Foma alomede decidAt 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 firstmo(PunmesligyedifmainceruasunDuint

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34lars and central incisors (mean age, 6.91 years), the curve of Spee depth increases significantly 0.0001) to a mean maximum depth of 1.32 mm. The curve of Spee then remains essentially unchangedtil eruption of the second molars (mean age, 12.38 years), when the depth increases (P 0.0001) to aan maximum depth of 2.17 mm. In the adolescent dentition (mean age, 16.21 years), the depth decreaseshtly (P 0.0009) to a mean maximum depth of 1.98 mm, and, in the adult dentition (mean age 26.98ars), the curve remains unchanged (P 0.66), with a mean maximum depth of 2.02 mm. No significantferences in curve of Spee development were found between either the right and left sides of thendibular arch or the sexes. Radiographic measurements of tooth eruption confirm that the greatestreases in the curve of Spee occur as the mandibular permanent incisors, first molars, or second molarspt above the pre-existing occlusal plane. Conclusions: On average, the curve of Spee initially developsa result of mandibular permanent first molar and incisor eruption. The curve of Spee maintains this depthtil the mandibular permanent second molars erupt above the occlusal plane, when it again deepens.ring the adolescent dentition stage, the curve depth decreases slightly and then remains relatively stableo early adulthood. (Am J Orthod Dentofacial Orthop 2008;134:344-52)

iewed in the sagittal plane, occlusal curvatureis a naturally occurring phenomenon in thehuman dentition. Found in the dentitions of

er mammals and fossil humans,1 this curvature was

termed the curve of Spee in the late 19th century, whenFerdinand Graf von Spee2,3 described it in humans.

In the sagittal view, Spee connected the anteriorsurfaces of the mandibular condyles to the occlusalsurfaces of the mandibular teeth with an arc of a circle,tangent to the surface of a cylinder lying perpendicularto the sagittal plane. He suggested that this geometricarrangement defined the most efficient pattern formaintaining maximum tooth contacts during chewingand considered it an important tenet in denture con-struction. This description became the basis for Mon-sons spherical theory4 on the ideal arrangement ofteeth in the dental arch, in which occlusal curvature isdescribed in the sagittal and frontal planes by thetangent of a sphere with a radius of approximately 4 in.Our current understanding is that, in sample popula-tions tested, occlusal curvature can be fitted to thegeometry of Spees cylinder and Monsons sphere withmuch individual variation.5-7

siting associate professor, Department of Orthodontics, College of Den-y, University of Iowa, Iowa City.

ivate practice, Fredericksburg, Va.thodontic resident, College of Dentistry, University of Oklahoma, Okla-a City.

sociate professor, Department of Anthropology, University of Iowa, Iowa.fessor, Department of Prosthodontics, College of Dentistry, University ofa, Iowa City.fessor and head, Department of Orthodontics, College of Dentistry,versity of Iowa, Iowa City.ported by the Dr George Andreasen Memorial Fund.rint requests to: Thomas E. Southard, Department of Orthodontics, College

Dentistry, University of Iowa, Iowa City, IA 52242; e-mail, [email protected], May 2006; revised and accepted, October 2006.9-5406/$34.00yright 2008 by the American Association of Orthodontists.

:10.1016/j.ajodo.2006.10.037

4evelopment of the cureven D. Marshall,a Matthew Caspersen,b Rachel R.even A. Aquilino,e and Thomas E. Southardf

a City, Iowa, Fredericksburg, Va, and Oklahoma City, Okl

roduction: Ferdinand Graf von Spee is credited with csagittal plane. This naturally occurring phenomeno

torative dentistry, yet we have little understanding of wdy was to expand our understanding by examining thea sample of untreated subjects with normal occlusthods: Records of 16 male and 17 female subjects fromamined. The depth of the curve of Spee was measureddeciduous dentition) to 26 (adult dentition) years. Theanges in the curve of Spee depth between time poinndibular teeth was measured from corresponding cephveloping curve of Spee was ascertained. Results: In theof Speenger,c Robert G. Franciscus,d

erizing human occlusal curvature viewed ins clinical importance in orthodontics andow, or why it develops. The purpose of thislopment of the curve of Spee longitudinallym the deciduous dentition to adulthood.owa Facial Growth Study were selected andeir study models at 7 time points from agesxon signed rank test was used to comparer each subject, the relative eruption of thetric radiographs, and its contribution to theuous dentition, the curve of Spee is minimal.

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American Journal of Orthodontics and Dentofacial OrthopedicsVolume 134, Number 3

Marshall et al 345Today in orthodontics, the curve of Spee commonlyers to the arc of a curved plane that is tangent to theisal edges and the buccal cusp tips of the mandibular

ntition viewed in the sagittal plane. In contrast, thesthodontic specialty ignores the incisors and in-des only the canine to the terminal molar as the

ntal arch portion of the curve. The curve thenntinues posteriorly to intersect the anterior surface of

condyle as originally proposed by Spee.8-10Modern orthodontics and reconstructive dentistry

fer with respect to the clinical significance of therve of Spee. Its proper management is critical for thenstruction of stable complete dentures and might playole in the success of implant-supported restorations.7complete denture prosthodontics, establishing a

rve of Spee in harmony with the condylar guidance,isal guidance, plane of occlusion, and prostheticth cusp height is essential for developing a bilater-

y balanced articulation, believed to maintain optimalnture stability.11

In the prosthodontic restoration of the natural den-on, the treatment goal is a mutually protected occlu-n, whereby the posterior teeth disclude during ec-

ntric functional movements. The curve of Spee, innjunction with posterior cusp height, condylar incli-tion, and anterior guidance, plays an important role in

development of the desired occlusal scheme.10 Then Monson sphere is used by some to develop anealized reconstruction of the posterior dentition.12patients with a retrognathic mandible and steep

terior guidance, it has been suggested that the occlu-plane might be constructed with a shorter radius

n the 4-in standard reported by Monson to avoidsterior interferences. The opposite is true in Class IIItients, when a larger (flatter) curve, typically a 5-inius, is more suitable.13Andrews,14 in describing the 6 characteristics of

rmal occlusion, found that the curve of Spee inbjects with good occlusion ranged from flat to mild,ting that the best static intercuspation occurred when

occlusal plane was relatively flat. He proposed thatttening the occlusal plane should be a treatment goalorthodontics. This concept, especially as applied toep overbite patients, has been supported by oth-15-20 and produces variable results with regard tointaining a level curve after treatment.21-23Our understanding of why the curve of Spee devel-

s is limited. Some suggest that its developmentbably results from a combination of factors includ-growth of orofacial structures, eruption of teeth, and

velopment of the neuromuscular system. It has been

ggested that the mandibular sagittal and verticalsition relative to the cranium is related to the curve of

as

stuee, which is present in various forms in mammals.1humans, an increased curve of Spee is often seen inchycephalic facial patterns24,25 and associated with

ort mandibular bodies.26 However, the presence ofcurve of Spee based on a morphologic or cephalo-

tric predictor has not been definitive.It has been suggested that the deciduous dentition

s a curve of Spee ranging from flat to mild, whereasadult curve of Spee is more pronounced.27 Expla-

tions for this observation cite the differences in cuspight between the deciduous and permanent teeth and

tendency for increased occlusal wear of the decid-us teeth. However, no quantitative research supportss.Furthermore, it was reported that, once established

adolescence, the curve of Spee appears to be rela-ely stable.28,29 Certain cephalometric and dentaltors are associated with individual variations in the

rve of Spee, but they do not predict its biologicriance unequivocally. It appears that craniofacialrphology is just 1 of many factors influencing its

velopment.6,23,26,30Even though orthodontists must deal with the curve

Spee in virtually every patient and prosthodontistsnstruct a curve of Spee for proper functional occlu-n, an in-depth understanding of its cause and devel-ment is not found in the literature. The purpose ofs study was to increase our understanding by exam-ng the development of the curve of Spee longitudi-lly from the deciduous dentition to adulthood in a

ple of untreated subjects with normal occlusion.TERIAL AND METHODS

Sixteen male and 17 female subjects were selectedm the Iowa Facial Growth Study, which was startedL. Bodine Higley and Howard Meredith in 1946; 89

ys and 86 girls were enrolled. They lived in or neara City, were predominately of Northern European

scent, and had clinically acceptable Class I occlu-ns and normal facial skeletal features. At enrollment,

children were not younger than 3 years of age.edical history, height, weight, and lateral and anteriorphalograms were taken quarterly until age 5. Recordsluding lateral and anterior cephalograms, dental

sts, photographs, and anthropometric measurementsre taken biannually from ages 5 to 12. After age 12,til about age 18, all records were taken annually.cords were also taken once during early adulthoodproximate age, 26 years).The 33 subjects selected from that study for this

dy were previously identified for research purposes

having complete records into adulthood includingdy casts without distortion or abrasion. All subjects

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American Journal of Orthodontics and Dentofacial OrthopedicsSeptember 2008

346 Marshall et ald tooth eruption timing and eruption patterns withinrmal ranges.The maximum depth of the curve of Spee was

asured as the maximum of the perpendicular dis-ces between the buccal cusp tips of the mandibularth and a measurement plane described by the centralisors and the distal cusp tip of the most posteriorth in the mandibular arch (Fig 1). A digital caliperodel CD, 4-in CS, Mitutoyo, Aurora, Ill) wasunted on a standard surveying table (Fig 2). Dental

sts were leveled to a plane defined by the distobuccalsps of the right and left most posterior tooth and thest central point on the more erupted central incisor.

rmanent incisors used as a tripod landmark werepted with more than half of their clinical crown onast and had greater or equal eruption height than thejacent deciduous lateral incisors.

Measurements of the curve of Spee were taken onleft and right sides to within 0.01 mm. The right and

t maximum depths were recorded and averaged toive at the average maximum depth for each subject atch time point. In this article, we use depth to mean

maximum depth of the curve of Spee. Study castsected for the time points for each subject wereosen from each subjects longitudinal study castssed on tooth eruption.

T1: the study cast for each subject available be-een ages 3.5 and 5 years, earlier in age, by at least 6nths, than the study cast of full deciduous dentition

osen for T2; 30 subjects had models.T2: the study cast of the oldest age for which the

ciduous second molars and incisors still served as theminal reference points for the measurement plane; 33bjects had models.

T3: the study cast of the youngest age for which thermanent first molars and incisors were the measure-

1. Measurement of the maximum depth of therve of Spee.nt plane references; 33 subjects had models.T4: the study cast of the oldest age for which the

(trT1rmanent first molars still served as the terminalsterior) reference points for the measurement plane;subjects had models.T5: the study cast of the youngest age for which the

rmanent second molars were the terminal referenceints for the measurement plane; 33 subjects haddels.T6: the study cast of the subject with fully erupted

olescent dentition nearest in age to 16 years; 24bjects had models.

T7: the study cast of the subject nearest in age to 26ars; 23 subjects had models.

Detailed statistics for the subjects from T1 to T7 areen in Table I.To ascertain reliability, duplicate measurements

re made of right maximum depth, left maximumpth, and average maximum depth in 7 subjects (4

ale, 3 male) for a total of 33 paired observations

2. Apparatus used to measure the maximum depththe curve of Spee: a digital caliper vertically mounteda surveyor. The end of the digital caliper is enlargedset) to show the modification of the caliper piston tow point contact with the study cast.ials 1 and 2). There were no paired measurements for; 7 paired measurements for T2, T3, and T6; and 6

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Marshall et al 347ired measurements for T6 and T7. Two subjects hadaired observations; and the remaining 5 subjects hadaired observations.Intraclass correlations were used to measure the

ationship between the 2 trials. The intraclass corre-ion is typically used in situations such as this, where itof interest to obtain a measure of intrarater agreement

quantitative outcomes.31,32 Perfect agreement corre-onds to an intraclass correlation coefficient of 1. Anraclass correlation of 0 indicates complete lack ofreement between the duplicate measures. Statisticalts were used to test the null hypothesis that theraclass correlation coefficient, P, was equal to 0ainst the 2-sided alternative hypothesis that P was notual to 0. The intraclass correlation coefficient forasurement of average maximum depth, right maxi-m depth, and left maximum depth was 0.999 with a

value 0.0001.At each time point, descriptive statistics were ob-

ned for age and for left, right, and average maximumpth of the curve of Spee; this was done for allbjects and separately for the sexes. The Wilcoxonned rank test was used to compare changes inximum depth between 2 adjacent time points. Inse instances, the Wilcoxon signed rank test for

ired data was used to test the null hypothesis thatdian change between adjacent time points was equal0. Adjustment for multiple comparisons was made

ble I. Descriptive statistics for the subjects ages at eactistic T1 T2 T

subjectsumber 30 33 33ean 4.05 5.27 6.

D 0.39 0.5 0.edian 4 5 7inimum 3.6 4.6 6aximum 5.1 6 8.ale subjects onlyumber 16 17 17ean 4.17 5.27 7.

D 0.4 0.49 0.edian 4 5 7inimum 3.6 4.6 6aximum 5.1 6 8.

le subjects onlyumber 14 16 16ean 3.91 5.26 6.

D 0.34 0.53 0.edian 3.95 5 7inimum 3.6 4.6 6aximum 4.9 6 8using the standard Bonferroni method with anerall 0.05 level of type I error.33

syvediographic measurements and analysis

Based on preliminary findings, our attention waswn to the increase in the curve of Spee specificallythe time of eruption of the mandibular permanentisors, first molars, and second molars. Tracings ofmandible were made for each of the 33 subjects by

ing lateral cephalograms at T2 and T3, and T4 and. At T2, the distobuccal cusps of the deciduousond molars (right and left), mandibular permanentt molars (right and left), and the incisal tips of the

ciduous central incisors were identified. At T3, the samelar landmarks plus the incisal tip of the permanenttral incisors were identified. At T4 and T5, thetobuccal cusps of the mandibular permanent firstlars, mandibular permanent second molars (right

d left), and the incisal tip of the permanent centralisors were identified. For T2, a line was constructedgent to the deciduous central incisor tip and thetobuccal cusp tip of the deciduous second molarerage of right and left molars). For T4, a line was

nstructed tangent to the permanent central incisor tipd the distobuccal cusp tip of the permanent firstlar (average of right and left molars). For each

bject, the T2 tracing was superimposed on the T3cing, and the T4 tracing was superimposed on the T5cing according to the American Board of Orthodon-s standards by using the best fit on the mandibular

e pointT4 T5 T6 T7

33 33 24 2311.11 12.38 16.21 26.981.24 1.34 0.41 1.36

11 12 16 26.67 10.6 16 25.1

13 16 17 30.1

17 17 14 1111.02 12.18 16.14 27.81.36 1.07 0.36 1.42

11 12 16 27.97 11 16 25.4

13 14 17 30.1

16 16 10 1211.2 12.59 16.3 26.231.15 1.59 0.48 0.75

11 12.3 16 26.558 10.6 16 25.1

13 16 17 27.5T5sec

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348 Marshall et alconstructed line was measured (Fig 3). The rela-ely small amount of time between the points allowedcurate superimposition. Corrections for radiographiclargement of linear measurements were made forch subject at each time point as previously reported

the Iowa Facial Growth Study.34

SULTS

Table II gives the descriptive statistics for theerage maximum curve of Spee depth for T1 through. Figure 4 is a plot of these data. In the deciduousntition, approximately a year before change to thensitional dentition (mean age, 4.05 years) and imme-

3. Sample mandibular superimposition for a sub-t. Solid line is the cephalometric tracing at T2. Dottede is the cephalometric tracing at T3. Line A representsT2 reference plane between the mandibular decid-

us second molars and central incisors used for castasurements. Vertical bars B, C, and D representasurements made with the digital caliper and cor-ted for radiographic magnification as described intext. To calculate the relative eruption of the man-ular permanent first molars and permanent incisorsative to the mandibular deciduous second molarstween T2 and T3, the amount of eruption at C wasbtracted from that measured at B and D. The samealysis was carried out between T4 and T5 to measurerelative eruption of the mandibular second molars.tely before change to the transitional dentition (meane, 5.27 years), the curve of Spee is minimal and does

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mot change significantly (P 0.84), with mean depths0.24 0.29 mm and 0.25 0.34 mm, respectively.ith change to the transitional dentition, correspondingthe eruption of the mandibular permanent first molarsd central incisors (mean age, 6.91 years), the curve ofee increases significantly (P 0.0001) to a meanpth of 1.32 0.77 mm. Just before the eruption of

mandibular permanent second molars (mean age,.11 years), the curve remains unchanged (P 1.0),th a mean depth of 1.31 0.58 mm. Just after theption of the mandibular permanent second molarsean age, 12.38 years), the curve increases (P 0.0001)a mean depth of 2.17 0.75 mm. In the adolescentntition (mean age, 16.21 years), the curve decreasesghtly (P 0.0009) to a mean depth of 1.98 0.67

. In the adult dentition (mean age, 26.98 years), therve does not change (P 0.66), with a mean depth2.02 0.78 mm. No significant differences in curveSpee change were found between the right and leftes or between the sexes. Descriptive statistics forferences between curve depths of adjacent timeints are shown in Table III.Radiographic (lateral cephalometric) measurements

mparing tooth eruption during the greatest increasescurve of Spee depth (mean ages 5.27-6.91 and

.11-12.38 years) indicate that eruption of the teethfining the termini of the curve (permanent incisors,st molars, or second molars) places them significantlyove the occlusal plane, thus increasing the depth of

occlusal curve (Fig 3 and Table IV). On averagetween T2 and T3, the mandibular permanent incisorspted 3.33 1.51 mm, and the mandibular perma-

nt first molars erupted 3.35 .94 mm above theciduous second molar-deciduous incisor occlusalne established at T2, whereas, during the sameerval, the mandibular deciduous second molarspted only 1.03 0.79 mm relative to the occlusalne established at T2. On average between T4 and, the mandibular second molars erupted 3.08 0.85

above the permanent first molar-permanent centralisor occlusal plane established at T4, whereas the

rmanent first molars, deciduous second molars/sec-d premolars, first premolars, and central incisorspted above the same occlusal plane 1.00 0.48,1 0.53, 1.03 0.68, and 1.16 0.88 mm,pectively.

SCUSSION

The principal findings of this study are shown inure 4. The curve of Spee depth is minimal in the

ciduous dentition; its greatest increase occurs in the

rly mixed dentition as a result of permanent firstlar and central incisor eruption; it maintains this

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Marshall et al 349pth until it increases to maximum depth with eruptionthe permanent second molars and then remains

atively stable into late adolescence and early adult-od.To our knowledge, this is the first report measuringgitudinally the depth of the curve of Spee. Thesedings support the suggestions of Ash27 that the

ble II. Descriptive statistics for the average maximumtistic T1 T2 T

subjectsumber 30 33 33ean 0.24 0.25 1.

D 0.29 0.34 0.edian 0.18 0.14 1.inimum 1.31 1.44 3.aximum 0 0 0ale subjects onlyumber 16 17 17ean 0.3 0.28 1.

D 0.32 0.35 0.edian 0.31 0.15 1.inimum 1.31 1.44 3.aximum 0 0 0

le subjects onlyumber 14 16 16ean 0.18 0.23 1.

D 0.24 0.33 0.edian 0.12 0.09 1.inimum 0.7 1.24 2.aximum 0 0 0.

Fig 4. Sample mean curve of Spee average maxmaximum depth of the curve of Spee was calculdepths at each time point.ciduous dentition has a curve of Spee ranging fromt to mild and the adult curve is more pronounced.

radchese findings also support those of Carter andcNamara28 and Bishara et al29 that, once establishedadolescence, the curve of Spee appears to be rela-ely stable.The curve of Spee can be modeled as a simple

rve, with its length defined by an arc of a circle anddepth (sharpness or flatness) determined by the

of Spee depthT4 T5 T6 T7

33 33 24 231.31 2.17 1.98 2.02

0.58 0.75 0.67 0.781.25 2.32 2.15 2.152.4 3.73 3.27 3.330.21 0.52 0.8 0.47

17 17 14 111.37 2.3 2.12 1.96

0.48 0.71 0.7 0.791.25 2.33 2.27 2.152.24 3.73 3.27 3.330.63 0.54 0.95 0.86

16 16 10 121.24 2.03 1.8 2.08

0.67 0.79 0.61 0.811.24 2.24 1.82 2.052.4 3.02 2.68 3.240.21 0.52 0.8 0.47

depth from T1 to T7. Each subjects means the average of the left and right maximumThMintiv

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166508103ius of the same circle. In this sample, we measuredange in curve depth during a change in arc length as

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350 Marshall et alesult of permanent first and second molar eruptions.s possible to have an increase in the depth of a simplerve by increasing the arc length alone (circle radiuschanged). Therefore, the documented change in maxi-m depth in our sample might be due to a change in

rve shape, a change in curve length, or both.A plausible explanation for the development of the

rve of Spee is that mandibular permanent teeth eruptfore their maxillary antagonists. This means that, inge measure, the curve of Spee develops as a dentalt skeletal) event. In other words, on average, erup-

n of the mandibular permanent first molars precedesmaxillary permanent first molars by 1 to 2 months,

d the mandibular permanent central incisors precedemaxillary permanent central incisors by 12 months.

rthermore, the mean age of emergence of the man-ular second molars is 6 months before the maxillaryond molars.35,36 This differential timing could permit

opposed mandibular permanent first molar and incisorption beyond the established mandibular occlusalne, especially if deciduous second molars are in a flushminal plane relationship or the maxillary deciduousond molars have small distolingual cusps. Later, man-ular second molar eruption could likewise be relatively

opposed. The result of both events would be deepening

ble III. Wilcoxon signed rank test results for differencintsoch difference Sample size Mean difference SD

30 0.02 0.2533 1.07 0.7333 0.01 0.7133 0.86 0.6524 0.35 0.4521 0.11 0.57

e null hypothesis is that the median change between adjacent time p

ble IV. Measurement (mm) of vertical eruption for seleasurement plane constructed at T2 and T4e point Teeth measured

Mandibular permanent first molarsMandibular deciduous second molarsMandibular permanent central incisorsMandibular permanent second molarsMandibular permanent first molarsMandibular deciduous second molars or permane

second premolarsMandibular permanent first premolarsMandibular permanent central incisorsthe curve. Of course, this dental event (mandibularrmanent molars erupting before maxillary molars)

weuld simply be a way of providing an evolutionary kickrt to curve of Spee development.In addition to the possible contribution of eruptioning, craniofacial variation and its affects on biome-

anics might also influence the curve of Spee.37 Thentitions of most mammals have a curve of Spee, andre is an association between the forward tilt of thendibular posterior teeth and the orientation of thesseter muscle in many mammals.1,38 Farella et al6orted that condylar height (relative to the occlusalne) and anteroposterior position of the mandiblelative to the cranial base) are associated with curveSpee depth. Based on our results, the finding of

rella et al could be simply explained by the fact that,patients with small mandibles, the mandibular per-nent incisors could keep erupting (curve of Speereasing) until they contact the palate. Although ourults point to a strong eruption (dental) influence onrve of Spee development, we agree that other cranio-ial factors probably play a role; we are currentlyestigating the impact of these factors.We found no statistically significant differences

tween the depth of the curve of Spee and the left andht sides of the arches. This result contrasts with theults of Farella et al,6 who found that left-side curves

average maximum depth between 2 sequential time

difference Minimum Maximum Wilcoxon P value

0.0 1.0 0.5 0.83881.1 3.1 0.5 0.00010.2 1.4 1.9 10.8 1.9 0.9 0.00010.3 0.7 1.3 0.00090.1 1.3 0.7 0.6636

0.

eeth at T3 and T5 compared with the curve of Spee

Mean (SD) Median Minimum/maximum

3.35 (1.26) 3.09 0.91/5.761.03 (0.79) 1.21 0.05/2.853.33 (0.91) 3.57 0.34/4.663.08 (0.85) 3.00 1.70/5.201.00 (0.43) 0.93 0.00/2.101.01 (0.58) 0.90 0.14/2.30

1.03 (0.68) 0.90 0.00/2.801.16 (0.88) 1.00 0.00/4.00ma

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Marshall et al 351veral studies have compared treatment techniques toal with exaggerated curves of Spee and the stabilitythose treatments.21,24,39-41 Our findings provide in-ht into the magnitude of the curve of Spee duringvelopment. These results give orthodontists a guide-e about the normal curve of Spee depth at the end ofatment or after the patient has settled in retention.rthermore, since our findings indicate that the great-

increase in the curve of Spee occurs with theption of the mandibular second molars, we believet this underscores the importance of including theond molars in orthodontic treatment.

NCLUSIONS

The occlusal plane in the deciduous dentition isrelatively flat.The largest increase in the maximum depth of thecurve of Spee occurs during, and results specificallyfrom, the differential eruption of the mandibularpermanent first molars and incisors relative to thedeciduous second molars.The curve of Spee maintains this depth until themandibular permanent second molars erupt abovethe occlusal plane, when it again deepens.During the adolescent dentition stage, the curvedecreases slightly and then remains relatively stableinto early adulthood.There are no significant differences in maximumdepth of the curve of Spee between either theright and left sides of the mandibular arch or thesexes.

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352 Marshall et al

Development of the curve of SpeeMATERIAL AND METHODSRadiographic measurements and analysis

RESULTSDISCUSSIONCONCLUSIONSREFERENCES

Development of the Curve of Spee

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