Preformed

arch wires: Reliability

Gary Alan Engel, Encino, Cal&

of fit

A.B., MS.*

R

ecently orthodontic supply companies have made available various preformed arch wires. In some cases these wires have fit patients ’ arches adequately but in other instances the arch wires have not corresponded to patients’ arch dimensions. Several reasons for these inconsistent results merit discussion. Some preformed arch wires are based upon an arch type? which is a one-parameter curve. As a result, the general dimensions of all of these arch wires are always the same; only the over-all size is different. It has been shown recently1 that, while one-parameter curve arches provide excellent fits to the arches of some patients there are numerous cases (approximately 40 to 50%) in which the fit is poor. Thus, it would seem reasonable to assume that, without adjustment, the arches preformed to these dimensions are not useful in at least half of all orthodontic cases. Tlhe effectiveness of two-parameter catenary curves (TPCC)$ was also tested in the same study. It was shown that these arches resulted in an adequate fit to all patient arches. Frequently, one-paramater curve arch forms provided better fits than the two-parameter catenary curve arches. However, the TPCC arches always provided an adequate or acceptable fit. The success of the TPCC curves can be attributed to the fact that, as the parameters vary, the two-parameter catenary curve yields more flexibility in arch form. Arches of various sizes and dimensions can be generated. Therefore, given an adequate number of different two-parameter arch wires, a reasonable fit to any patient could be obtained. In this regard, the purpose of the present study was to determine the number and dimensions of preformed archwires necessary to best fit the majority of patient arches. Methods

and materials

Initially, a sample of 100 orthodontically treated cases from a private practices was analyzed. Models of lower arches made immediately upon completion of active orthodontic treatment were measured in order to obtain data for a series of catenary curves which ,would describe all arches in the sample. Four variables are required to describe uniquely a specific two-parameter catenary curve. These four variables are concerned with arch width and height, tooth mass, or general arch shape. In order to make curves corresponding to all combinations of high, *Research Director, The Foundation ?Brader, Bonwill-Hawley. SRocky Mountain Data Systems. $R. M. Rick&s, Pacific Palisades, 0002.9416/79/110497+08$00.80/0

0

of Orthbdontic

Research

Calif.

1979 The C. V. Mosby

Co

497

Fig. 1. Four measurements significant multiple correlation

pertinent to lower coefficients.

Table

initial

1. Measurements

Arch

No.

for

nine

NM

44.49 44.49 44.49 48.71 48.71 48.71 40.28 40.28 40.28

Measurements were performed WM = Width at molars. HM = Height at molars. WC = Width at canines. HC = Height at canines.

(mm.) 37.78 35.22 32.69 38.49 35.94 33.40 37.06 34.51 31.97

separately

dimensions

which

were

found

to have

highiy

arches

LVM (mm.)

I 2 3 4 5 6 7 8 9

arch

WC (mm.)

HC (mm.)

30.65 30.26 29.88 31.75 31.36 30.98 29.56 29.17 28.78

11.65 9.89 8.14 11.65 9.89 8.14 11.65 9.89 8.14

by two individuals.

medium, or low values of each variable, the total number of different arch types required to fit all possible arches reasonably well is 34, or eighty-one different preformed arch wires. This is truly an unmanageable number for any potential manufacturer. However, a study plan was developed that circumvents this problem. A statistical evaluation was completed in order to find correlation coefficients and multiple linear regression relationships among variables. The object was to find two variables which were highly correlated with two others. Thus, if the actual values of the first two variables were known, the correct values for the other two variables could be estimated with a high degree of accuracy. In this study, four such variables were found. It was determined that only 32, or nine arches, were necessary to define a wide range of two-parameter catenary curves which fit nearly all actual patient arches. Once these initial nine arches were found, they were compared with ninety other patient arches. * Selection of these three different samples was based on the following: *Thirty selected at random from ideal lower arches (recommended);

R. M. Ricketts’

thirty

tracings

practice (treated); thirty RMDS computerized of nontreated lower arches (original).

recommended

Volume ‘76 Number

Preformed

5

arch

wires

499

3

Y=T

298

-o.I4+,064) ie

6

\/ y=‘l

u

(e-0.0t3e0.08)

y,1.62 2

7

(&l6+,$16)

u yz 233

(,01~,0~7)

Fig. 2. Nine arches with their sample of 100 patients.

two-parameter

catenary

equations

which

best

represent

the arches

of the

Table! II. Number of casesbest fit by each preformed arch wire Arch Sample I. Actual patient posttreatment lower arches (30) 2. RMDS computerized initial lower arches (30) 3. RMDS suggested final lower arches (30) Total (90)

wire No.

12345678

713020026 914031310 10 2 2 26 4 9

0 6

0 5

5 6

5 8

2 5

9

None

0

9 8 4

6

u

Some orthodontists expand lower arches routinely during the course of treatment, while others prefer to treat lower arches to a computer-determined goal. Also, there are many orthodontists who believe that the original untreated arch form should not be violated during treatment. These practitioners would never expand the lower arch at the canines or molars. Ideally, the nine preformed arch wires should fit patients regardless of tlhe mechanical philosophy preferred by the orthodontist. The three samples of thirty cases used in this study present these three different treatment philosophies. Comparision of the ninety sample arches to the nine statistically constructed arches revealed that a few of the nine arches did not fit many of the test cases. As a result, the nine arches were modified slightly by smoothing the curves to reflect more accurately the observed shapes of actual arches. Next, another set of ninety cases (thirty treated, thirty recommended, thirty original) was compared to the nine modified arch forms. The capability of the arch forms to fit these cases was then analyzed. Finally, a series of thirty upper arch models taken immediately upon completion of

AM.

:.

L)i-NILIlL

.November

Fig. 3. Teeth program.

repositioned

on the presumed

initial

arch

determined

by a basic

diagnostic

1919

computer

Ricketts Lower Arches best

0 sum

Fig. 4. Results arches mm.

to within

1 2 of distances

3

fitting

4 from

arch

type

5 6 7 6 9 teeth to best fitting

10 11 72 archwires (mm)

of analysis on thirty cases from patients of R.M. Ricketts. Ail cases fit one of the nine a sum of 12 mm. (or 1 mm. distance from each tooth), and most fit to within a sum of 6

active treatment* was compared to the nine arch forms in order to determine whether the arch forms derived from lower arches were useful for upper arches as well. Results

and discussion

Fourteen measurements pertaining to lower arch dimensions were taken from lower arch models of 100 orthodontically treated cases. Of these measurements, four are of prime interest: width and height of the arch at the distal edge of the canines and width and height of the arch at the distal edge of the molars (Fig. 1). It was found that highly significant multiple correlation coefficients existed among the four variables. Using the *From

the practice

of R.M.

Rickerts.

Volume ‘76 Number 5

Preformed

1

2

3 best

4 5 fitting

6 arch

arch

wires

501

type

!/N/l 10 sum

of

distances

from

teeth

to

best

fitting

Fig. 5. Results of analysis on thirty RMDS computer-recommended one of the nine arches to within a sum of 12 mm. (or 1 mm. distance within 6 mm.

11

12

archwires

ideal arches. Again, all cases fit from each tooth), and most fit to

techniques of stepwise multiple linear regression, it was determined that height at the molars (HM) in millimeters could be predicted accurately by the formula HM = 13.1 + 0.17 :X width at the molars (WM) + 1.45 x height at canines (HC). The multiple carrelation coefficient (R) is 0.82 and the standard error of estimate (SE) is 1.33 mm. This means that HM can be predicted to within 1.33 mm. or less approximately two thirds of the time if WM and HC are known. It was also found that width at canines (WC) = 16.5 ,t 0.26 x WM + 0.22 x HC. Multiple R = 0.53 and SE = 1.34 mm. These results indicate that, given WM and HC, we can predict WC and HM with a high degree of accuracy. Therefore, the nine arches could be chosen by taking all possible combinations of large, medium, and small WM measurements and large, medium, and small HC values and, in each case, assuming the predicted values of WC and HM using the foregoing equations. This technique was attempted. Medium values for WM and HC were assumed to be the means for the 100 initial sample cases. The large and small values taken were - 1.5 standard deviations and + 1.5 standard deviations from the norms, respectively. Table I lists the values of WM, HM, WC, and HC assumed for the nine arches. Next these nine arches, with the molar and canine measurements described above, were drawn and compared with the three additional samples of thirty cases each described in the previous section. The number of cases best fitting each arch in each sample, plus the number of cases which fit none of the arches, are shown in Table II. Accuracy of fit was determined by visual inspection by trained technicians. It can be seen from this table that about 25 percent of the cases did not fit any of the nine arches well. Thus, it was decided that some of the nine arches should be modified slightly to fit more of the sample cases. These modifications were done empirically. The resultant nine arches and their twoparameter catenary equations are shown in Fig. 2. A.n additional set of ninety cases (as described above) was used to test the effectiveness Iof this new set of nine arches. A computer program was written to examine each of

02

Am. J. Orthai. November 19-S’

Engel

1

0

2

1

3 best

Fig. 6. Results distance

of anaiysis

as previously from

each

from teeth curve to best

on thirty

stated: tooth),

6 arch

7

8

9

Actual Lower

Pre-treatment Arches

type

23456789

sum of distances along catenary

results

4 5 fitting

lower

all cases and

most

arches fit one

of original arch fitting archwire of patients

of the

fit to within

nine

before arches

realigned

any orthodonQc to within

a sum

treatment.

The

of 12 mm.

(or 1 mm.

same

6 mm.

Table III. Cumulative totals for ninety lower arches and thirty upper arches, number of cases best fit by each arch wire

Quantity of cases

I

23

35

I

5

25

5

11

the nine catenary curves, taking the sum of the distances from each tooth to the curve and then choosing the curve with the minimum sum as the best fitting of the nine catenary curves. For the untreated sample, the teeth had to be repositioned along the presumed initial arch (Fig. 3) which was found by a basic diagnostic computer program.* Once the teeth were realigned along this arch, the sums of the distances to the nine catenary curves were calculated and the best fitting of the nine arch forms was found. The results of this aanlysis are found in Figs. 4 to 6. It can be seen that, in all cases, at least one of the nine arches in Fig. 2 fits the observed arch to within a sum of 12 mm. (or 1 mm. error per tooth), and most observed arches can be fit within a sum of 6 mm. (0.5 mm. error per tooth). This statistic is thought to be significantly superior to the results that would be obtained from any nine different one-parameter preformed arch wires.? It is certain that these nine arches are better than nine catenary arch forms found earlier in the study. Next, the arch forms were translated into arch wires by feeding the catenary equations *Rocky Mountain Data Sysrems tBrader, Bonwill-Hawley.

Volume 76 Number

Preformed

5

Fig. 7. INine arch achieveId by using into nine

ideal

wires corresponding the RMDS computer

arch

wires

by drawing

to the nine lower arches which program to interpret the catenary the dentition,

brackets,

and arch

arch wires

503

best fit the sample. This was equations of the nine arches wires.

a computer program* which draws the dentition, brackets, and ideal arch wires from catenary curves (Fig. 7). The result of this effort is the exact specifications for nine types of arch wires which could be prefabricated and then used without modification in the vast majority of orthodontic cases. Finally, thirty treated upper arches were compared to the nine arch forms derived above. The results are shown in Fig. 8. It is seen that 97 percent of the cases fit at least one arch form to within 1.O mm. average distance from each tooth. It will also be noted that some of the arch forms which fit many patients ’ upper arches are not the same arch forms which fi.t most patients ’ lower arches. Table III presents a cumulative tally of the number of arches that are best fit by each preformed arch wire based on the data of Figs. 3, 4, 5, and 7. It is seen that preformed arch wires 2, 3, and 6 would be used in orthodontic treatment far more often than the others. Future study involving nonorthodontic normal arches may be indicated to reconfirm the usefulness of the two-parameter catenary curve.

to

Summary and conclusions The preformed arch wires currently available are unsuitable for many orthodontic cases, since these arch wires do not take into account all the variations in the size and dimensions of the human arch. In this study, nine theoretical arch wires were derived, based upon two-parameter curves. Tests were conducted which demonstrated that arch wires preformed to these nine sets of dimensions would correspond with a reasonable degree o’f accuracy to a large section of the orthodontic population. *Rocky

Mountain

Data Systems.

564

Am. .i. Ortilou.

Engel

Navvmber

Actual Upper best

0 sum

1

2

of distances

3

fitting

4

from

arch

5

teeth

6

1919

Treated Arches

type

7

to best

8

9 fitting

10

11

12

archwire

13

14

15

16

(mm)

Fig. 8. Results of analysis which compared upper arches of thirty treated patients to the nine arch forms shown in Fig. 2. Almost all (97 percent) of the cases fit at least one arch form to within 1 mm. per tooth.

REFERENCES I. White, Larry W.: Individuaiized ideal arches. .I. Clin. Orthod.12: 779-787, 1978. 2. Brader, Allen C.: Dental arch form related with intraoral forces: PR = C, AM. J. QRTHOII 1972. 3. Chuck, George C.: Ideal arch form, Angle Orthod. 4:312-327, 1934. 16661

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