The Relationship Between the Curve of Spee ... - ResearchGate

The Relationship Between the Curve of Spee, 

Relapse, and The Alexander Discipline 

Sal Carcara, C. Brian Preston, and Ossama Jureyda 

E 

Exaggerated curves of Spee are frequently observed in dental malocclusions 

that present with deep vertical overbites. During orthodontic treatment 

such excessive curves of Spee are usually leveled and, in most instances, 

this leveling will result in a reduction of the anterior overbite. The Alexander 

Discipline provides a good example of modern straight-wire orthodontic 

techniques that purport an ability to treat abnormal variations in the depth 

of the occlusal plane. The records of 31 randomly selected patients treated 

by nonextraction with the Alexander Discipline were studied. The results 

show that the Alexander Discipline levels the curve of Spee in Class II, 

Division I deep-bite cases and that when relapse occurs, the curve of Spee 

returns to a lesser extent than was present before orthodontic treatment. 

With the Alexander Discipline, a pretreatment curve of Spee that is not 

completely level posttreatment has a slightly higher incidence and magni- 

tude of relapse than a pretreatment curve of Spee that is completely level 

posttreatment. This study indicated that, based on the pretreatment curve 

of Spee, there is no ability to predict relapse in mandibular intercanine 

width, overbite, overjet, mandibular incisor irregularity, and arch length in 

Class II, Division I deep-bite cases treated with the Alexander Discipline. 

(Semin Orthod 2001;7:90-99.) Copyright © 2001 by W.B. Saunders Company 

xaggerated curves of Spee 1,2 are frequently 

observed in dental malocclusions that 

present with deep vertical overbites. As a part of 

orthodontic treatment, such excessive curves of 

Spee are usually leveled during orthodontic 

treatment, and, in most instances, this leveling 

will, in turn, result in a reduction of, if present, 

deep anterior overbites. Clinicians who adhere 

to the Tweed I philosophy of orthodontic treatment 

use continuous arch wires that incorporate 

reverse curves of Spee to produce flat occlusal 

planes. Accordingly, arch leveling occurs mostly 

by an extrusion of the lower premolar teeth in 

conjunction with a minimal intrusion of the 

mandibular incisor teeth. In contrast to the ear- 

From the Department of Orthodontics, State University of New 

York at Buffalo, Buffizlo, NY," and Private practice, New York, NY. 

Address correspondence to C Brian Preston, BDS, Dip Orth, M 

Dent, PhD, Department of Orthodontics, School of Dental Medicine, 

Squire Hall, 3435 Main St, Buffalo, NY 14214-3008. 

Copyright Q 2001 by 14(B. Saunders Company 

1073-8746/01/0702-0006535. 00/0 

doi: 10.1053/sodo. 2001.23550 

lier approach, advocates of sectional arch orth- 

odontic mechanics z,~ treat deep curves of Spee 

by intrusion of mandibular incisors while, usu- 

ally, allowing the lower premolars to erupt into 

occlusion. 

A review of the literature reveals that there is 

disagreement among the proponents of the var- 

ious orthodontic techniques that are used to 

level deep curves of Spee. 4-s The discussion re- 

volves around which leveling technique pro- 

duces the most effective overbite correction as 

well as the most stable long-term treatment out- 

comes. Those orthodontists who primarily use 

sectional arches to produce fiat occlusal planes 

believe that leveling with continuous arch wires 

tends to extrude the posterior teeth, which, in 

most instances, will cause an increase in the 

lower facial height. They further believe that, in 

individuals with strong muscles of mastication, 

the orthodontically extruded buccal segments 

will tend to relapse after the orthodontic treat- 

ment. 4,5,9 This relapse would lead to the recur- 

rence of anterior deep bites. When a reverse 

90 Seminars in Orthodontics, Vol 7, No 2 ([une), 2001: pp 90-99

curve of Spee is placed in a continuous arch wire 

for the purpose of arch leveling, this results in 

an almost automatic tendency for the mandibu- 

lar incisors to flare labially. 1°,11 Contrary to this 

viewpoint, Ferguson a2 states that a reverse curve 

of Spee in an arch wire does not in itself cause 

the lower incisor teeth to flare unless the arch is 

allowed to act beyond the stage at which the 

occlusal plane is flat. Orthodontists who use 

Tweed's leveling technique 6,13-15 argue that the 

extrusion of premolars and molars provides a 

stable change while, on the other hand, the 

intrusion of the lower incisors often relapses to 

produce an increased overbite. 

Radiographic cephalometric studies showed 

that both the Ricketts and modified Tweed tech- 

niques can successfully correct deep dental over- 

bites. 16,a7 These studies concentrated on over- 

bite correction only and neither analyzed study 

models to evaluate how effectively the curves of 

Spee were leveled, nor did they evaluate the 

long-term stability of the results that were pro- 

duced. 

The present article reflects the findings of a 

study that was designed to evaluate the long- 

term outcomes of a representative sample of 

orthodontic patients who were treated accord- 

ing to the Alexander Discipline. Irrespective of 

the philosophy and mechanical principles of the 

orthodontic technique used, one of the primary 

objectives of orthodontic treatment is to obtain a 

level occlusal plane, is In this article, leveling will 

be defined as the process of bringing the incisal 

edges of the anterior teeth and the buccal cusp 

tips of the posterior teeth into the same horizon- 

tal plane. 19 

The anatomic definition of the anteroposte- 

rior curve of occlusion is generally accepted by 

orthodontists as describing the curve of 

Spee. 2°-94 Some studies in the orthodontic liter- 

ature propose other ways to define and measure 

the curve of Spee on orthodontic study mod- 

els. 25-27 Three-dimensional digitizers 2-~,26 have 

been used to calculate the depth of the mandib- 

ular curve of Spee mathematically. Koyama, 27 in 

a more practical approach to the problem, used 

a caliper to measure the curvature of the occlu- 

sal plane in both jaws and found the greatest 

pretreatment depth of the curvature to be lo- 

cated in the bicuspid region. 

In a mechanical sense, the presence of a 

curve of Spee may make it possible for a denti- 

The Curve of Spee, Relapse, and the Alexander Discipline 91 

tion to resist the forces of occlusion during mas- 

tication. 2s-~-~ Although several theories have 

been proposed to explain the presence of a 

curve of Spee in natural dentitions, its role dur- 

ing normal mandibular function has been ques- 

tionedY 9,~4,35 It has been proposed that an im- 

balance between the anterior and the posterior 

components of occlusal force can cause the 

lower incisors to overerupt, the premolars to 

infraerupt, and the lower molars to be mesially 

inclined. ~6,37 According to Root 2s and Fidler et 

al, 3s when a skeletal open bite is not present, the 

curve of Spee in Class II malocclusions is deeper 

than in other malocclusions. Although an exag- 

gerated curve of Spee is often obsmwed in Class 

II, Division I relationships, it is not unique to this 

type of malocclusion. -~9 

Andrews as noted that the occlusal planes in 

120 nonorthodontically treated and ostensibly 

normal occlusions varied from being generally 

flat to having a slight curve of Spee. This finding 

led him to believe that the presence of a curve of 

Spee could be associated with postorthodontic 

treatment relapse. Andrews concluded, "even 

though not all of the orthodontic normals had 

flat planes of occlusion, I believe that a flat plane 

should be a treatment goal as a form of over- 

treatment. ''is A deep curve of Spee may make it 

almost impossible to achieve a Class I canine 

relationship ls,28 though it may also result in oc- 

clusal interferences that will manifest during 

mandibular function. -~2,$4 

To date, there are little or no data that quan- 

tify the amount of arch leveling that occurs with 

orthodontic treatment, or the long-term, pos- 

torthodontic treatment relapse of the curve of 

Spee. It is perhaps worthwhile noting that very 

little research has been undertaken to deter- 

mine the most effective, and stable, method of 

leveling a deep curve of Spee. 

Numerous studies have been performed to 

quantify the amount and type of postretention 

relapse that occurs after orthodontic treat- 

ment. 6A5-17,38,42-52 In general, these studies have 

noted posttreatment increases in overjet, over- 

bite, mandibular incisor crowding, along with 

decreases in arch length and arch width. Inves- 

tigations have also been undertaken to deter- 

mine whether untreated normal occlusions un- 

dergo the same changes that are observed in 

treated cases. 5°,51 At the same time, very little 

research has been performed to evaluate the

92 Carcara, Preston, and Jureyda 

long-term stability of leveling the curve of Spee, 

and few, if any, studies have attempted to corre- 

late the pretreatment curve of Spee with postre- 

tention changes in other aspects of the occlu- 

sion. 

The primary purpose of the present investi- 

gation was to determine the effectiveness of the 

Alexander continuous arch wire technique in 

leveling the curve of Spee in Class II, Division I 

deep bite cases. A second purpose of the study 

was to determine the long-term stability of the 

leveling of the curve of Spee achieved with the 

Alexander Discipline. A third objective of the 

research was to determine whether a relation- 

ship exists between the presence of a deep curve 

of Spee before orthodontic treatment and the 

relapse that takes place in a number of occlusal 

traits. The traits studied included the mandibu- 

lar intercanine width, overbite, overjet, mandib- 

ular incisor irregularity, and arch length. 

The sample for this retrospective study con- 

sisted of 31 patients, 22 female and 9 male, 

randomly selected from the records of orth- 

odontic patients treated in the private practice 

of Dr. R.G. "Wick" Alexander, in Arlington, 

Texas. The average age of the patients at the 

start of treatment was 12 years and 6 months. 

The average treatment time for the sample was 2 

years and 1 month whereas the average time 

from T1 to T2 record taking was 2 years and 5 

months. Each case was treated by nonextraction 

and met specific criteria for inclusion in the 

study. These selection criteria included the pres- 

ence of a Class II skeletal (ANB > 4 °) and at 

least a half-cusp Class II molar relationship, an 

overbite of 50% or greater as measured from the 

initial (T1) study models, and a curve of Spee 

measuring 2 mm or more. 37 Only cases with 

complete records were selected for this study. 

These records consisted of dental casts taken 

pretreatment (T1), post-treatment (T2), and 

postretention (T3). The posttreatment (T2) 

records were taken 2 months after debonding at 

a mean age of 14 years and 11 months. The final 

(T3) records were taken at an average of 7 years 

and 5 months after the removal of the fixed 

retainer, which was at an average of 11 years and 

5 months after the debonding of the patient. All 

31 patients were treated by a single operator, Dr. 

R.G. "Wick" Alexander, who used a fully pread- 

justed fixed orthodontic appliance with a 0.018" 

slot size according to the Alexander Discipline. 

Dr. Alexander's patients were selected for this 

study because he is the recognized authority for 

this technique, a goal of his treatment is to level 

any curve of Spee that is present in the mandib- 

ular arch, and complete long-term records were 

available for the present study. 

The Alexander technique was also selected 

for this study, over other preadjusted appliance 

techniques, because of its unique prescription, 

and its biomechanical principles that assist with 

mandibular incisor control during arch leveling. 

The unique features of the prescription include 

a -5 ° torque built into the mandibular incisor 

bracket base to maintain the lower incisors up- 

right over the basal bone. In addition, a -6 ° 

distal tip is incorporated into the mandibular 

first molar buccal tube to facilitate molar up- 

righting, 1 and to create arch length to help re- 

duce lower incisor flaring. The early use of rect- 

angular wire, as is required in this system, makes 

it easier, than is the case with some other orth- 

odontic techniques, to control the position of 

the lower incisors from the outset of treatment. 

After the initial leveling phase of treatment 

the upper and lower first arch wires are replaced 

with "working arch wires" constructed from 

0.016 × 0.022 inches or 0.017 X 0.025 inches 

stainless steel. The maxillary arch wire has an 

accentuated curve of Spee, and the mandibular 

arch wire has a reverse curve of Spee, placed into 

it to facilitate arch leveling. Other than the ini- 

tial arch wires, all remaining arch wires include 

omega loops placed 1 to 2 mm anterior to the 

first or second molar tubes. These omega loops 

allow all of the arch wires, after the initial arch 

wires, to be actively tied back with 0.014-inch 

stainless steel ligatures. The finishing arch wires 

in both arches are constructed from 0.017 X 

0.025 inch stainless steel wires. The upper and 

lower arch wires are bent to incorporate an ac- 

centuated or a reverse curve of Spee respec- 

tively. A goal of the Alexander technique is to 

have the 0.017 × 0.025 inch stainless steel fin- 

ishing arch wire placed in both arches as early as 

possible during treatment. The early placement 

of this relatively heavy lower arch wire makes it 

possible for the curve of Spee to be flat during 

most of the active treatment. Each stainless steel 

arch wire is heat-treated before insertion to in- 

crease the stiffness of the wire. 5S At the end of 

treatment the bands are removed and retention 

appliances are inserted. In all of the 31 patients

selected for this study the mandibular canine-to- 

canine fixed retainer was removed after the 

third molars were either extracted or had 

erupted normally into occlusion. This occurred 

at a mean time of 3 years and 4 months after 

appliance removal. At the time of the removal of 

the fixed retainer, selective interproximal strip- 

ping was performed on each patient to decrease 

the tendency for relapse of lower incisor crow& 

ing. 42 

Three sets of study casts (T1, T2, and T3) 

were collected for each of the 31 randomly se- 

lected patients. The 93 sets of study models were 

each assigned a random number that made it 

possible for a single investigator to measure each 

set in a random blind fashion. The curve of Spee 

in this study was measured in the mandibular 

buccal occlusion between the center of the in- 

cisal edge of the central incisor anteriorly and 

the distobuccal cusp tip of the first molar poste- 

riorly. 27 By using a standard palatometer (GPM, 

Switzerland), the depth of the curve of Spee was 

measured on each side of the mandibular arch 

as being the vertical distance from the buccal 

cusp tip of the most infraoccluded premolar, to 

the occlusal plane previously described. 97 

The curves of Spee were measured on both 

the left, and the right, sides of each of the 93 

mandibular models included in this study. The 

resulting sets of 93 left and 93 right measure- 

ments were compared statistically by means of a 

paired t test. The results indicated that there 

were no significant statistical differences (P > 

.05) between these pairs of measurements, curve 

of Spee on the right side versus curve of Spee on 

the left side, for each of the 31 patients at T1, 

T2, and T3. The average of the right and left 

cmwes of Spee for each patient at the three 

different time intervals was therefore used for 

further definitive statistical analysis and compar- 

ison. 

The following measurements were made by a 

single operator in a random blind fashion and 

directly on study casts for each patient at three 

time intervals (T1, T2, T3): mandibular interca- 

nine width, 46 overbite, 46 overjet, 46 mandibular 

incisor irregularity index, 4:~ and mandibular 

arch length. 44 

To test whether the curve of Spee remained 

unchanged from T1 to T2, and from T2 to T3, 

paired t tests were calculated. To compare the 

incidence of relapse (T2-T3) of the curve of 

The Crave of Spee, Relapse, and the Alexander Discipline 93 

Spee in the patients that were completely level at 

T2 with those that were not completely level at 

T2, a two-sample t test was calculated to compare 

the proportion of relapse occurrence. To com- 

pare the magnitude of relapse (T2-T3) of the 

curve of Spee in the patients that were com- 

pletely level at T2 with those that were not com- 

pletely level at T2, two independent samples' t 

test was calculated. 

The treatment effects (T1 vs. T2) and relapse 

(T2 vs. T3) of five variables (mandibular inter- 

canine width, overbite, overjet, mandibular inci- 

sor irregularity, and arch length), were calcu- 

lated with paired t tests. A Pearson correlation 

coefficient and regression analysis was then per- 

formed to determine the predictive power of the 

pretreatment curve of Spee (T1) on the relapse 

of the five variables studied (T2-T3). 

The mean pretreatment (T1) curve of Spee 

for the 31 patients included in this stud}, was 

2.41 mm with a standard deviation of -+ 0.48 mm 

and a range of 2.00 to 3.75 mm. The mean 

posttreatment (T2) curve of Spee for this sample 

was 0.11 mm with a standard deviation of _+ 0.19 

mm and a range of 0.00 to 0.50 mm. The differ- 

ences between the pretreatment (T1) and post- 

treatment (T2) curves of Spee were highly 

statistically significant (P < .0001). It was con- 

eluded that in this sample of patients a mean- 

ingful degree of arch leveling was achieved with 

the Alexander Discipline. 

The mean treatment-induced reduction in 

the curve of Spee was 2.30 mm with a standard 

deviation of _+ 0.47 mm. The range of reduction 

of the depth of the curve of Spee from T1 to T2 

was 1.50 to 3.75 mm. This corresponds to a 

95.43% average reduction in the curve of Spee 

during treatment. Twenty-two of the 31 patients 

studied (approximately 71%) were completely 

(100%) level after treatment (T2), whereas 9 

patients (approximately 29%) had a residual 

curve of Spee at the end of the orthodontic 

treatment. 

The mean posttreatment (T2) curve of Spee 

for the 31 patients treated with the Alexander 

Discipline was 0.11 mm with a standard devia- 

tion of -+ 0.19 mm and a range of 0.00 to 0.50 

mm. The mean postretention (T3) curve of 

Spee for this sample was 0.48 mm with a stan- 

dard deviation of + 0.50 mm and a range of 0.00 

to 1.75 mm. The mean increase in the curve of 

Spee from T2 to T3 was 0.37 mm with a standard


deviation of + 0.40 mm and a range of 0.13 to 

1.25 mm. The differences between the posttreat- 

ment (T2) and postretention (T3) curves of 

Spee, though small, were statistically significant 

(P < .0001). 

The posttreatment (T2) curve of Spee data 

for the sample (N = 31) revealed two subpopu- 

lations. Twenty-two patients at T2 had curves of 

Spee that were completely leveled whereas nine 

patients had residual curves of Spee at this time. 

A comparison of the occurrence of relapse in 

the curves of Spee in these two subpopulations 

was calculated by using a two-sample t test. The 

results of this test revealed that there was a sta- 

tistically significant difference (P < .05) in the 

occurrence of relapse of the curve of Spee in 

these two subpopulations. A statistically greater 

occurrence of relapse (88.9% vs. 50%, P < .05) 

was seen between those patients that were com- 

pletely leveled at T2 and those that were not 

A comparison of the magnitude of relapse in 

the curve of Spee that takes place in these two 

groups between posttreatment and postreten- 

tion was calculated by using two independent 

samples' t test. The results of this test revealed a 

statistically significant difference (P < .0001) in 

the amount of relapse of the curve of Spee in 

these two subpopulations (P < .0001). Eleven of 

22 patients that were completely level at T2 sub- 

sequently relapsed an average of 0.28 mm at T3, 

which is equal to a relapse of 11.68% of the T1 

curve of Spee. By comparison, eight of the nine 

cases that were not completely leveled at T2 

relapsed an average of 0.39 mm at T3, which is 

equal to 22.46% of the T1 curve of Spee. 

The overall mean period of the time that 

elapsed from taking the initial records (T1) to 

taking the final records (T3) was 14 years and 4 

months with a range of 7 to 28 years, 8 months. 

Over this period (T1-T3) the overall effect on 

the curve of Spee was an average reduction of 

-1.93 mm, which represents a mean 80.62% 

reduction in the original depth of this curve. 

The means and standard deviations for each 

of the five variables measured on the study casts 

(mandibular intercanine width, overbite, over- 

jet, mandibular incisor irregularity, and arch 

length) at T1, T2, and T3 are reported in Table 

1. The means and standard deviations for treat- 

ment changes (T2-T1), posttreatment changes 

(T3-T2), and overall changes (TI-T3) are 

shown in Table 2. 

Mandibular Intercanine Width 

A total of 77.5% of the cases showed statistically 

significant increases in the mandibular interca- 

nine width during treatment (~ = +1.37 mm, 

P = .0002). The same 24 cases (77.5%) in which 

intercanine widths were increased during treat- 

merit showed a marginally significant postreten- 

tion reduction (9` = -0.62 ram, P = .0505) in 

their intercanine widths. It should be noted that 

when the mandibular fixed cuspid-to-cuspid re- 

tainer was removed, interproximal enamel re- 

duction was performed. 

Overbite 

In all 31 patients, the overbite was reduced sig- 

nificantly during treatment (9` = - 2.67 mm, P < 

.0001). In 74% of the cases the overbite in- 

creased significantly postretention (9, = +0.75 

mm, P < .0001). The posttreatment mean over- 

bite was 2.09 mm, and the postretention mean 

overbite was 2.84 mm. 

Overjet 

In all 31 cases the overjet was reduced signifi- 

cantly during treatment (9` = -4.09 mm, P < 

.0001). In 87.1% of the cases the overjet in- 

creased significantly postretention (9` = + 1.09 

Table 1. Pretreatment (T1), Posttreatment (T2), and Postretention (T3) Model Measurements 

Pretreatment (T1) Posttreatment (T2) Postretention (T3) 

Measure (mm) Mean SD Mean SD Mean SD 

Mandibular width intercanine 25.75 2.1 26.11 1.4 25.5 2.36 

Overbite 4.76 0.95 2.09 0.65 2.84 0.85 

Overjet 6.27 2.97 2.18 0.56 3.27 0.93 

Mandibular incisor irregularity 3.97 3.35 0.31 0.46 1.28 1.35 

Arch length 62.22 4.64 64.01 3.17 61.85 3.41 

Abbreviation: SD, standard deviation.


Table 2. Treatment, Posttreatment, and Total Changes in Model Measurements 

Treatment Changes Postt~atment Total Changes 

(T2- T1) Changes (T3- T2) (T3- T1) 

Measure (mm) Mean SD Mean SD Mean 5~ 

Mandibular intercanine width 1.37 1.85 -0.62 1.69 0.75 2.38 

Overbite - 2.67 1.05 0.75 0.89 - 1.92 1.06 

Overjet -4.09 2.96 1.09 0.84 -3.00 2.93 

Mandibular incisor irregularity - 3.66 3.25 0.98 1.19 - 2.69 2.94 

Arch length 1.79 4.57 -2.16 2.11 -0.37 4.42 

Abbreviation: SD, standard deviation. 

mm, P < .0001). The posttreatment mean over- 

jet was 2.18 mm and the postretention mean 

overjet was 3.27 mm. 

Irregularity Index 

The mean pretreatment incisor irregularity was 

3.97 mm; 54.5% of cases had minimal irregular- 

ity 52 before treatment (6.5 mm). 

Treatment produced a significant decrease in 

the incisor irregularity (z~ = -3.66 mm, P < 

.0001). Incisor irregularity increased signifi- 

cantly posttreatment (:~ = +0.98 ram, P < 

.0001). However, 90% of cases at T3 had mini- 

mal incisor irregularity, and 10% had moderate 

irregularity. All 31 cases showed a net improve- 

ment in incisor irregularity from T1 to T3. 

Arch Length 

A total of 64.5% of the cases showed a slightly 

significant increase in arch length because of 

treatment (:~ = +1.79 mm, P = .04) whereas 

87.1% of the cases showed a significant decrease 

in arch length postretention (g: = -2.16, P < 

.0001). 

The Pearson correlation coefficient was cal- 

culated by comparing the T1 curve of Spee with 

the posttreatment changes (T3-T2) observed 

for each of five variables (mandibular interca- 

nine distance, overbite, overjet, mandibular in- 

cisor irregularity, and arch length) and revealed 

no statistical correlation (P > .05). Follow-up 

regression analyses revealed no ability to predict 

relapse in any of the five factors mentioned ear- 

lier based on the T1 curve of Spee (P > .05). 

Discussion 

The important contribution that leveling the 

curve of Spee makes toward the success of orth- 

odontic treatment has been well documented in 

the literature. 18,19,25-2s,~9,34,4° There is, however, 

no general agreement as to the most appropri- 

ate biomechanical principles that should be 

used to accomplish stable long-term arch level- 

ing. Two important studies have been per- 

formed to compare the use of sectional versus 

continuous arch leveling mechanics in the treat- 

ment of deep-bite cases. 16,17 Dake and Sinclair 1~ 

in a comparison of Ricketts' and Schudy's treat- 

ments of adolescent Class II deep-bite low-angle 

nonextraction cases, concluded that both oper- 

ators' techniques were effective in overbite cor- 

rection, and that these changes remained stable 

after an average posttreatment period of 4 years 

and 6 months. 

Weiland et al, 17 in a study of 50 adult low- 

angle deep-bite cases, concluded that in adult 

patients the Burstone 4-~' segmental arch tech- 

nique is superior to conventional continuous 

arch wire techniques when arch leveling by inci- 

sor intrusion is indicated. The earlier-men- 

tioned studies 16,~7 compared the effectiveness of 

overbite correction as measured on cephalomet- 

ric radiographs. Neither study used study models 

to measure the curve of Spee nor to measure the 

effectiveness or long-term stability of leveling the 

curve of Spee. The present study was prompted 

by the recognition of a need for a long-term 

study-model analysis of the effectiveness and sta- 

bility of leveling the curve of Spee. 

Findings reported in the literature dealing 

with the stability of orthodontic treatment are 

often contradictory, in large part, because of the 

fact that investigators group malocclusions that 

require different treatment strategies together. 

Further, the orthodontic records that are used 

in outcomes studies often belong to patients 

who were treated by both experienced and inex- 

perienced operators. It is also an unfortunate 

fact that detailed outcomes goals are not regu-


lady established for orthodontic patients before 

the start of their treatment. Lastly, assessments 

of relapse are often qualitative and do not allow 

for quantitative comparison. By defining strict 

guidelines for the selection of cases treated by a 

single experienced operator with clearly defined 

goals, the present study attempted to overcome 

at least some of the earlier shortcomings. 

The effectiveness of arch leveling achieved 

with the Alexander Discipline was determined 

by comparing T1 and T2 curve of Spee data by 

using a paired t test. Results of the paired t test 

indicated a statistically significant change (P < 

.0001) in the curve of Spee during treatment. It 

was concluded that the Alexander Discipline is 

an effective preadjusted continuous arch wire 

technique for leveling a curve of Spee in Class II, 

Division I nonextraction deep-bite cases in 

which the initial curve of Spee was in the range 

of 2 to 4 mm. Seventy-one percent of the cases 

studied were leveled completely, whereas 29% 

had a slight residual curve of Spee at T2. For the 

latter cases the mean curve of Spee remaining at 

the end of treatment was 0.11 mm. A residual 

curve of Spee of 0.11 mm is probably clinically 

insignificant based on the qualitative observa- 

tions of the posttreatment study models. The T2 

models all exhibited Class I molar and canine 

relationships with properly finished buccal oc- 

clusions, and normal overjets and overbites. 18 

A question that cannot be answered by this 

study is how the curve of Spee was leveled. Sev- 

eral investigators 4,5,9,1°,u,16,~7 have reported on 

the negative effects of continuous arch wire me- 

chanics. These effects include a flaring of the 

lower incisors, an extrusion of the mandibular 

molars, and an opening of the occlusal mandib- 

ular plane. Some features of the Alexander Dis- 

cipline, including the -5 ° of torque in the lower 

incisors and the -6 ° of distal tip in the mandib- 

ular molars, are specific and probably unique 

among the preadjusted appliance prescriptions. 

These unique features, along with biomechani- 

cal principles such as the use of heat-treated 

arch wires with omega stops tied back to the 

molar tubes, could play a role in preventing the 

untoward side effects seen with some other 

straight-wire techniques. 

The long-term stability of arch leveling 

achieved with the Alexander Discipline was de- 

termined by comparing the T2 and T3 curve of 

Spee data by using a paired t test. A statistically 

significant change (P < .0001) was seen in the 

curves of Spee after the removal of the mandib- 

ular retention appliances. The curves of Spee 

increased fi'om a mean of 0.11 mm posttreat- 

ment to a mean of 0.48 mm postretention. In 

other words, the curve of Spee relapsed on av- 

erage 0.37 mm over a period of 7 years and 5 

months after the fixed lingual canine-to-canine 

mandibular retainer was removed. Although the 

relapse in the curve of Spee may be statistically 

significant, it has been explained, in a clinical 

sense, by several investigators as being a normal 

physiologic process. 18,27,~x,~2 It was concluded 

that the Alexander Discipline efficiently "over 

treats" Class II, Division I deep-bite malocclu- 

sions so that when the relapse occurs the curve 

of Spee returns to a lesser extent than was ini- 

tially present. The overall long-term (T1-T3) 

effect of orthodontic treatment with the Alex- 

ander Discipline is an average of 80.62% reduc- 

tion in the pretreatment curve of Spee. Twelve 

of the 31 cases studied remained 100% level over 

a time span of 5 to 25 years after the conclusion 

of orthodontic treatment. This study shows that 

in this sample the observed relapse of the curve 

of Spee (:~ = 0.48 mm) was minimal and that it 

occurred slowly over an extended period of 

time. The effects of this degree of relapse of the 

curve of Spee are probably clinically insignifi- 

cant with regard to proper mandibular function, 

esthetics, and occlusion. 

The results of a two-sample t test used to 

compare the proportion of relapse that took 

place revealed a significant difference in the 

incidence of relapse that occurred in the 22 

cases that were completely leveled at the end of 

treatment (T2) and the 9 cases that were not 

(P < .05). In addition, the results of the two 

independent samples' t tests also revealed a sig- 

nificant difference in the magnitude of relapse 

that occurred in the 22 cases that were com- 

pletely leveled and the 9 cases that were not (P < 

.0001). Half of the 22 cases that were completely 

leveled at the end of treatment showed some 

relapse at T3. The amount of this relapse was 

11.68% of the original curve of Spee (T1) or 

0.28 mm. In contrast, eight of nine (88.9%) of 

the cases that were not completely leveled at T2 

relapsed, and the amount of relapse was 22.46% 

(0.39 mm) of the original curve of Spee. It was 

concluded that in those cases treated with the 

Alexander Discipline that were not completely

leveled posttreatment, there is a slightly higher 

incidence and magnitude of relapse than in 

those cases that were completely leveled. 

To establish whether significant treatment 

and posttreatment changes had taken place in 

mandibular intercanine width, overbite, overjet, 

mandibular incisor irregularity, and arch length, 

preliminary statistical analyses were performed. 

Paired t tests were calculated to compare the 

pretreatment and posttreatment data and the 

posttreatment and postretention data. 

For each of the five variables measured from 

the study casts, statistically significant changes 

occurred during treatment with the Alexander 

Discipline (P < .05). An evaluation of the effects 

of treatment on these five variables was not the 

primary goal of this research project. The find- 

ings did, however, detect that in association with 

the treatment there was a general decrease in 

overbite, overjet, and incisor irregularity, and an 

increase in mandibular intercanine width and 

arch length. With one exception, arch length, 

these results are similar to those reported by 

Elms et al. 46 The increase in the arch length 

during orthodontic treatment that was observed 

in the present study was not statistically signifi- 

cant in the Elms et a146 study. In the present 

study, four of the five variables (overbite, overjet, 

incisor irregularity, and arch length) showed sta- 

tistically significant (P < .05) posttreatment 

changes. In the present study, the mandibular 

intercanine width showed marginally significant 

(P = .0505) posttreatment changes. Although it 

was not a major goal of this study to investigate 

the relapse of mandibular occlusal traits, signif- 

icant posttreatment changes were detected for 

all five variables studied. Although these results 

are similar to those found by Elms et al, 46 the 

posttreatment changes noted for overbite, over- 

jet, and the irregularity index were marginally 

greater in the present study than are those re- 

ported by Elms et al. 46 

Most of the posttreatment changes noted in 

the mandibular intercanine width and arch 

length were small and probably reflect normal 

physiologic changes that occur with increasing 

age, as reported in the literature. 44,5°,51 It must, 

however, not be overlooked that overexpansion 

of the intercanine arch width in the mandible is 

a potential source of relapse after orthodontic 

treatment. Although a statistically significant 

posttreatment increase in incisor irregularity was 


observed, it is a fact that 90% of the cases at T3 

had minimal incisor irregularity ( .05). 

Follow-up regression analyses revealed no ability 

to predict relapse in mandibular intercanine 

width, overbite, overjet, mandibular incisor ir- 

regularity, and arch length based on the depth 

of the pretreatment curve of Spee. It should be 

noted that in each of these cases, interproximal 

enamel reduction was performed on the man- 

dibular anterior teeth. The variable with the 

highest correlation was overjet r = -0.268), yet 

only 7.2% of the variability seen in the overjet 

change can be accounted for by the pretreat- 

ment curve of Spee (r 2 = 0.072). It is possible 

that if a sample with larger pretreatment curves 

of Spee were studied, a positive correlation 

could be seen between the larger pretreatment 

curves of Spee, and the relapse in other aspects 

of the occlusion posttreatment.


Although this study has shown the clinical 

effectiveness of using continuous arch wire me- 

chanics to level the curve of Spee, it must be 

kept in mind that not every straight-wire appli- 

ance has the unique prescription that is part of 

the Mexander Discipline, namely the -5 ° 

torque in the mandibular incisor and the -6 ° 

distal tip built into the molar tubes. These 

unique appliance features may play a large role 

in allowing for an effective, and controlled, man- 

dibular arch leveling as shown in this study. In 

addition, the mechanical principles of actively 

tying back a heat-treated curved arch wire may 

contribute to the success of the arch leveling 

achieved with the Alexander Discipline. It is un- 

wise to assume that every straight-wire appliance, 

using continuous arch wire mechanics to level 

the curve of Spee, will be as successful as the one 

studied here. Furthermore, this study investi- 

gated the cases of not only an experienced cli- 

nician but also the authority on the Alexander 

Discipline. 

Because only study models were evaluated, 

this investigation was unable to ascertain the 

exact process by which the curve of Spee is lev- 

eled with the continuous arch wire mechanics of 

the Alexander Discipline. Also, the exact process 

by which the slight relapse of the curve of Spee, 

noted in this study, occurred was not ascer- 

tained. A comprehensive cephalometric ap- 

praisal of the mechanism of arch leveling and 

relapse of the curve of Spee in this sample has 

been undertaken by Bernstein. 54 Additionally, 

study model and cephalometric investigations of 

the curve of Spee leveling process by using inci- 

sor intrusion mechanics should also be per- 

formed. If the sample of such a study is carefully 

matched to the present one, valid comparisons 

could be made to ultimately determine the most 

effective biomechanics necessary to level the 

curve of Spee and to maintain it level in the long 

term. 

Conclusions 

1. The Alexander Discipline is an effective con- 

tinuous arch wire technique for leveling the 

curve of Spee in Class II Division I deep-bite 

cases treated by nonextraction in which the 

initial curve of Spee is 2 to 4 mm. 

2. The Alexander Discipline efficiently over- 

treats a pretreatment curve of Spee of 2 to 4 

mm in Class II Division I deep-bite cases 

such that when relapse occurs, the curve of 

Spee returns to a lesser extent than was 

present before orthodontic treatment. 

3. Postretention changes in overbite, overjet, 

and irregularity index were small and 

showed net improvement. 

4. With the Alexander Discipline, a pretreat- 

ment curve of Spee of 2 to 4 mm that is not 

completely level posttreatment has a slightly 

higher incidence and magnitude of relapse 

than a pretreatment curve of Spee that is 

completely level posttreatment. 

5. There is no ability to predict relapse in man- 

dibular intercanine width, overbite, overjet, 

mandibular incisor irregularity, and arch 

length in Class II Division I deep-bite cases 

treated with the Alexander Discipline based 

on the pretreatment curve of Spee. 

References 

1. Tweed CH. Clinical orthodontics. St. Louis: CV Mosby, 

1966, pp 84-180. 

2. Ricketts RM. Bioprogressive therapy as an answer to 

orthodontic needs. Part I. AmJ Orthod 1969;70:241-268. 

3. Ricketts RM. Facial and denture changes during orth- 

odontic treatment as analyzed from the temperoman- 

dibular joint. Am J Orthod 1955;41:163-167. 

4. Wylie WL. Overbite and vertical facial dimensions in 

terms of muscle balance. Angle Orthod 1944;14:13-17. 

5. Bench RW, Gugino CF, Hilgers ~. Bioprogressive ther- 

apy. Part 2. J Clin Orthod 1977;11:661-682. 

6. Merritt J. A cephalometric study of the treatment and 

retention of deep overbite cases [master's thesis]. Hous- 

ton, TX: University of Texas, 1964. 

7. Schudy FF. The association of anatomical entities as 

applied to clinical orthodontics. Angle Orthod 1966;36: 

190-203. 

8. Graber TM. Orthodontics: Principles and practice. Phil- 

adelphia: W.B. Saunders, 1969. 

9. Otto RE, AnholmJM, Engel GA. A comparative analysis 

of intrusion of incisor teeth achieved in adults and chil- 

dren according to facial types. AmJ Orthod 1980;77:437- 

446. 

10. Berman MS. Straight wire myths-BJO Interview. Br J 

Orthod 1988;151:57-61. 

11. Woods M. A reassessment of space requirements for 

lower arch leveling. J Clin Orthod 1986;20:770-778. 

12. FergusonJW. Lower incisor torque-the effects of rectan- 

gular archwires with a reverse curve of Spee. BrJ Orthod 

1990;17:311-315. 

13. Schudy FF. Cant of the occlusal plane and axial inclina- 

tion of teeth. Angle Orthod 1963;23:69-82. 

14. Schudy FF. Vertical growth versus antero-posterior 

growth as related to function. Angle Orthod 1964;34: 

756-793. 

15. Lett RL. Overbite correction and relapse as analyzed by

some cephalometric and treatment related variables 

[master's thesis]. Minneapolis, MN: University of Min- 

nesota, 1969. 

16. Dake ML, Sinclair PM. A comparison of the Ricketts and 

Tweed-type arch leveling techniques. AmJ Orthod 1989; 

95:72-78. 

17. Weiland FJ, Bartleon HP, Droschl H. Evaluation of con- 

tinuous arch and segmented arch leveling techniques in 

adult patients: A clinical study. Am J Orthod 1996;110: 

647-652. 

18. Andrews LF. The six keys to normal occlusion. Am J 

Orthod 1972;9:296-309. 

19. Baldridge DW. Leveling the curve of Spee: Its effect on 

mandibular archlength. J Clin Orthod 1969;64:26-41. 

20. Spee FG. The gliding path of the mandible along the 

skull. J Am Dent Assoc 1980;100:670-675. 

21. Gysi A. The problem of articulation. Dental Cosmos 

1910;52:1-19, 148-169. 

22. Christensen C. The problem of the bite. Dental Cosmos 

1905;47:1184-1195. 

23. Orthlieb J. The curve of Spee: Understanding the sagit- 

tal organization of mandibular teeth. J Craniomandib 

Pract 1997;15:333-340. 

24. The Academy of Prosthodontics. Glossary of prosth- 

odontic terms. J Prosthet Dent 1994;71:50-112. 

25. Germane N, Staggers JA, Rubenstein L, et al. Arch 

length consideration due to the curve of Spee: A math- 

ematical model. AmJ Orthod 1992;102:251-255. 

26. Braun S, Hnat WP, Johnson BE. The curve of Spee 

revisited. Am J Orthod 1996;110:206-210. 

27. Koyama T. A comparative analysis of the curve of Spee 

(lateral aspect) before and after orthodontic treatment- 

with particular reference to overbite patients. J Nihon 

Univ Sch Dent 1979;21:25-34. 

28. Root T. Level anchorage. Monrovia, CA: Unitek Corp, 

1988. 

29. Sicher H. Oral anatomy. St. Louis: CV Mosby, 1949. 

30. Hemley S. Orthodontic theory and practice (ed. 2). New 

York: Grune and Stratton, 1953. 

31. Wheeler RC. A textbook of dental anatomy and physiol- 

ogy (ed. 2). Philadelphia: W.B. Saunders, 1950. 

32. Ash MM. Wheeler's dental anatomy, physiology and oc- 

clusion (ed. 6). Philadelphia: W.B. Saunders, 1984. 

33. OsbornJW. 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. 

34. Dawson P. Evaluation, diagnosis and treatment of occlu- 

sal problems. St. Louis: CV Mosby, 1974. 

35. Diamond M. Dental anatomy (ed. 3). NewYork: McMil- 

lan, 1952. 

36. Strang RH. A textbook of orthodontia (ed. 3). Philadel- 

phia: Lea and Feibiger, 1950. 

37. Gresham H. A manual of orthodontics. Christ Church, 

New Zealand: N.M. Peryer, 1957. 


38. Fidler BC, Artun J, Joondeph DR, et al. Long-term sta- 

bility of angle class II, Division I malocclusions with 

successful occlusal results at the end of active treatment. 

AmJ Orthod 1995;107:276-285. 

39. Braun ML, Schmidt WG. A cephalometric appraisal of 

the curve of Spee in class 1 and class II division I occlu- 

sion for males and females. Am J Orthod 1956;42:255- 

278. 

40. Hellsing E. Increased overbite and craniomandibular 

disorders-a clinical approach. AmJ Orthod 1990;98:516- 

522. 

41. McNamara JA, Seligman DA, Okeson JP. Occlusion, 

orthodontic treatment, and temporomandibular disor- 

ders: A review. J Orofac Pain 1995;9:73-90. 

42. Williams R. Eliminating lower retention. J Clin Orthod 

1985;22:342-349. 

43. Little RM. The irregularity index: A quantitative score of 

mandibular anterior teeth. Am J Orthod 1975;68:554- 

563. 

44. Bishara SE,JakobsenJR, TrederJE, et al. Changes in the 

maxillary and mandibular tooth-size-archlength rela- 

tionship from early adolescence to early adulthood. 

Am J Orthod 1989; 1:46-59. 

45. Burstone CJ. The mechanics of the segmental arch tech- 

nique. Angle Orthod 1966;36:99-120. 

46. Elms TN, Buschang PH, Alexander RG. Long-term sta- 

bility of class II division I nonextraction cervical face-bow 

therapy: I. Model analysis. Am J Orthod 1996;109:271- 

276. 

47. Glenn, G, Sinclair PM, Alexander RG. Nonextraction 

orthodontic therapy: Postreatment dental and skeletal 

stability. Am J Orthod 1987;92:321-328. 

48. Little RM, Reidel RA, Artun J. An evaluation of changes 

in mandibular anterior alignment from 10 to 20 years 

post-retention. Am J Orthod 1988;5:423-428. 

49. Puneky PJ, Sadowsky C, BeGole EA. Tooth morphology 

and lower incisor alignment many years after orthodon- 

tic therapy. AnlJ Orthod 1984;10:299-305. 

50. Sinclair PM. Little RM. Maturation of untreated normal 

occlusion. AmJ Orthod 1983;2:114-123. 

51. DeKock WH. Dental arch depth and width studied lon- 

gitudinally from 12 years of age to adulthood. Am J 

Orthod 1972;62:56-66. 

52. Little RM, Wallen TR, Reidel RA. Stability and relapse of 

mandibular anterior alignment-first premolar cases 

treated by traditional edgewise orthodontics. Am J 

Orthod 1981;80:349-364. 

53. Alexander RG. The Alexander Discipline, contemporary 

concepts and philosophies. Glendora, CA: Ormco, 1986. 

54. Bernstein: Leveling the curve of Spee with a continuous 

archwire technique-A long-term cephalometric analysis 

[master's thesis]. Buffalo, NY: University of Buffalo, 

1999.

The Relationship Between the Curve of Spee ... - ResearchGate

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?