moments and forces delivered by transpalatal arches for ... · correctly in the fossa of the lower...

European Journal of Orthodontics 18 (1996) 131-139 O 1996 European Orthodontic Society

Moments and forces delivered by transpalatal arches for

symmetrical first molar rotation

Bengt Ingervall*, Klaus D. Honigl** and Hans-Peter Bantleon**Departments of Orthodontics, * University of Bern, Switzerland, and ** University of Vienna, Austria

SUMMARY The moments and forces delivered by round transpalatal arches of steel and ofbeta-titanium (TMA) for symmetrical derotation of molars were studied in laboratory experi-ments. Three sizes of arches were tested in two series. In the first series, the degree ofactivation was checked for symmetry in a computer-based strain-gauge measuring system.In the second series, the activation was carried out in a way simulating clinical use. Themesio-distal and transverse forces and the derotating moments at full activation and duringderotation in steps of 5 degrees were measured.

At full activation, the steel arches delivered relatively large moments which, however,decreased rapidly during deactivation. The TMA arches had a larger working range. It wasnot possible to achieve full symmetry of the moments at the two ends of the arch. Thedifference of the two moments resulted in forces acting on the two anchorage teeth in amesio-distal direction. These forces were generally small but could reach clinically relevantmagnitude. The derotation resulted in a contractive force of up to 2.7 N which has to becompensated for by expansion. The mode of activation simulating clinical use resulted inreasonably constant forces and moments. The use of a vice to hold the arch during activationwas found to be of great help and is recommended in the clinical setting. Because of thelarger working range, TMA arches are recommended if substantial derotation is needed.

Introduction

Derotation of upper molars to gain space in thedental arch and to improve a Class II molarrelationship is a simple and rewarding proced-ure. As pointed out by, among others, Stoller(1954), Andrews (1972) and Carlon (1973), arotated tooth occupies excessive space whichmay be needed in other parts of the dental arch.Upper molars are most often rotated mesic—palatally, i.e. the mesial cusp is displaced in apalatal and mesial direction but with the palatalcusp (and root) in an almost correct position(Lamons and Holmes, 1961). In the buccalview, the intermaxillary relation of rotatedupper molars is therefore more or less Class II.The palatal cusp, however, often occludescorrectly in the fossa of the lower molar.

One widely-used method for the correctionof rotated upper molars is derotation with atranspalatal arch (Carlon, 1973; Ten Hoeve,1985). A transpalatal arch is especially favour-able when the need for derotation is the sameon both sides of the dental arch. Equal and

opposite moments of rotation can then be usedwithout the creation of forces in the mesic—distal direction. Such forces are the inevitableresult of unequal moments on the two sides(Fig. 1). Mesio-distal forces are unwanted inmost cases but may be used to advantage whenthe molar on one side needs to be movedmesially and that on the opposite side distally.Molar derotation will also result in transverse(contractive) forces. This has been realized clin-ically but the magnitude of the contractive forceis unknown.

Molar derotation with a transpalatal arch isa frequent and useful clinical procedure. It wastherefore decided to study, in laboratory experi-ments, the forces and moments delivered bytranspalatal arches activated for symmetricalmolar derotation. Specifically, the forces andmoments delivered by arches of different sizesand materials and with different degrees ofactivation were evaluated. An important aspectwas to test the consistency of the forces andmoments when the arches were activated underconditions simulating clinical use.

132 B. INGERVALL ET AL.

rFigure 1 Moments and forces delivered by a transpalatalarch activated for symmetrical (A) and for asymmetrical(B) molar derotation. Note the mesio-distal forces resultingfrom unequal moments on the two sides.

Material and methods

Types of archesTwo types of round wire material were testedin the laboratory experiments, GAC prefabric-ated stainless steel transpalatal arches (GACInternational Inc., Central Islip, New York) andOrmco p-titanium (TMA) alloy (SybronCorporation, Glendora, California). The GACarches had a diameter of 0.036 inches (0.91 mm)with a loop in the middle. At the ends, the wirewas bent back on itself, which made the com-bined cross-section rectangular to fit in theprefabricated (Ormco) rectangular tubes for theattachment of the arch. The TMA arches weremade from straight wire material (diameter0.036 inches) and had no loop in the middle(Fig. 2). On fabrication in the laboratory, thewire was bent back on itself at the ends to fitin the same rectangular tubes as the GACarches.

Size and shape of the archesIn order to standardize the size and shape ofthe arches, metal templates were made. For thispurpose, upper dental casts were measured in aseries of 103 14-year-old randomly-selectedSwiss children. The intermolar distance acrossthe palate was measured along the palatal sur-face and the median value and the upper andlower percentiles calculated. In addition theheight of the palatal vault was measured. Fromthese measurements, three sizes of metal tem-plates with an intermolar distance (and an arch

Figure 2 Transpalatal arches: (top) GAC prefabricatedstainless steel and (bottom) (5-titanium.

length) of 49, 51 and 53 mm, and with differentcurvatures were made. The templates wereequipped with rectangular tubes for the attach-ment of the arches and were used to form thearches (Fig. 3).

ActivationThe passive state of the first series of arches(five of each size) was checked in a measuringmachine which had been custom-made to meas-ure forces and moments during simulated treat-ment with fixed appliances. Adjustments weremade until the vertical forces were <0.10N(1N = 1O2 g), the horizontal forces were<0.15N and the moments <0.15 mNm (1mNm=102 gmm). In order to avoid unduedistortion during activation, the arch wires werefastened in a vice and the bent-back end of thearch was gripped with pliers and twisted relative

Figure 3 Template used to form the palatal arch.

TRANSPALATAL ARCHES FOR FIRST MOLAR ROTATION 133

to the main arch. The degree of twist waschecked by fastening the bent-back part of thearch in the vice and reading the deviation ofthe other end of the arch on millimetre paper(Fig. 4). To explore the forces and moments atdiffering degrees of activation, this was variedbetween 5-15 mm, which refers to the deviationof the free end of the arch when the other endwas fastened in the vice (see Fig. 4).

The activation of the second series of archeswas undertaken in a way simulating clinical use.The arch was placed in the clutches of themeasuring machine and adjusted to be reason-ably passive. This was carried out without accessto measuring data, which were collected afterthe arch was believed to be passive followingthe final adjustment. The activation was per-formed in the vice and checked with millimetrepaper as for the first series. A trial activationwas performed and the activation was checkedagain and adjusted when necessary. Five archesof each size and type were adjusted and activ-ated by examiner 1 and five by examiner 2.

Measuring systemThe mesio-distal and transverse forces as wellas the moments of rotation delivered by theactivated arches were measured with a com-puter-based strain-gauge system (Fig. 5). In themeasuring machine, the two ends of the arch

"' i

10 r

L.U * 1

J • • -

7

', j

!

Figure 4 Check of degree of activation with one end ofthe palatal arch fastened in a vice.

wire were inserted into rectangular tubesfastened to the movable clutches of the devicewhich were sensored by strain-gauges. With thefully activated arch the rectangular tubes werepositioned vertically. Deactivation was donemanually by unlocking the clutches and thenlocking them again in steps of five degrees asread from a scale connected to the clutches(Fig. 6). The forces and moments were meas-ured at full activation of the arch and duringstepwise deactivation. The distance between theclutches could be adjusted automatically bycontinuous recording by the computer of theforces delivered. This possibility was used afterfull deactivation of the moments in order toeliminate the transverse contractive forceresulting from the derotation.

Measuring procedure

First seriesIn this series, the degree of activation was

checked with the scale of degrees to have thesame magnitude on both sides (symmetricalactivation). When necessary, adjustments weremade until the activation was the same on bothsides. The check was made with the clutchesunlocked. These were thereafter locked in thestarting (vertical) position.

Second seriesAfter activation, the arch was inserted in the

measuring machine and the measurements weremade in the starting position and during de-activation. Thus, for the second series of archesno check was made in the machine for similarityof activation on the two sides because thiswould not have been possible in clinical use.

Results

If the moments on both sides are the same, themesio-distal force will be zero. If this is not thecase, the force on one side will be in the mesialand that on the other side in the distal direction,and of equal size. As the direction of the mesio-distal force is of no importance in this study,the tables give the absolute value of the mesio-distal force as the mean of the values measuredat the two ends of the arch wire. The transverseforce may be expansive or contractive. Thetables give the mean of the values measured atthe two ends of the arch whereby a contractiveforce is designated with a minus sign. Themoments on the two sides are in the opposite


Figure S Measuring machine used to record the moments and forces delivered by the transpalatal arches.

Figure 6 Scales for the determination of the degree of deactivation.

direction and should ideally be of the samemagnitude (zero difference).

The results of the measurements of the firstseries of arches are given in Table 1. The mesio-distal force was, for all three arch sizes, relatedto the size of the moments and decreased withthe decrease of the moment during deactivation(Table 1). In other words, it was more difficultto balance the moments on the two sides whenthese were large. The median transverse force

was, for all three sizes of the GAC arch, slightlyexpansive at full activation (10-12 mm) butbecame increasingly contractive during deac-tivation and was for all three arch sizes ofsimilar magnitude at full deactivation. The con-tractive force could be eliminated by decreasingthe distance between the two ends of the arch.This was done as the final step of a meas-uring procedure after full deactivation of themoments.


The highest moments were produced by the49 mm arch activated 10 mm whereas the51 mm (activated 10 mm) and the 53 mm arch(activated 12 mm) gave rise to moments ofsimilar size (Table 1). In contrast to the twolargest arch sizes, the 49 mm arch delivereduseful moments even after 15 degrees of de-activation. In spite of the precautions taken toachieve the same magnitude of activation at thetwo ends of the arch, moments of dissimilarmagnitude were always recorded. The differ-ences were largest for the smallest arch.

When the 51 mm GAC arch was activatedonly 5 mm, considerably smaller forces andmoments were delivered compared with 10 mmactivation of the same arch. With 5 mm activa-tion, useful moments were only produced up to

5 degrees of deactivation. In this case, too, allarches showed a contractive force after fulldeactivation.

The moments delivered by a 51 mm TMAarch activated 15 mm were only about half ofthose with a similar-sized GAC arch activated10 mm (Table 1). With a TMA arch, it waspossible to achieve useful moments up to 15degrees of deactivation. The difference betweenthe moments on the two sides at full activationwas also considerably smaller for the TMA archthan for the GAC arch. The contractive forceproduced by the TMA at full deactivation wasthe some as that of the GAC arch.

The forces and moments delivered by theGAC arches of the second series are given inTable 2. This series offered the opportunity to

Table 1 Median of mesio-distal and transverse forces (in N) and moments of rotation (in mNm) deliveredby five transpalatal arches after controlled symmetrical activation for molar rotation (first series).

Degree ofdeactivation

GAC 49 mmactivation 10 mm05

1015fullGAC 51 mmactivation 10 mm05



fullTMA 51 mmactivation 15 mm05

1015full

Mesio-distalforce

0.190.220.160.13

0.160.080.09

0.090.040.03 .

0.060.05

0.070.050.020.03

Transverseforce

0.53-0.21-0.61-1.07-1.28

0.25-0.22-0.88-1 .16

0.69-0 .26-0.81-1 .05

-0.06-0 .46-0 .43

0.37-0 .16-0.47-0 .80-1.11

Momentright

51.1032.9318.094.58

32.4019.087.65

41.5825.21

8.87

14.922.83

20.2513.199.143.04

Momentleft

38.3420.1410.07

1.27

36.8122.019.53

33.2821.00

6.66

14.782.43

18.4313.758.101.41

Median differencemomentsright-left

6.6510.807.923.64

4.126.502.82

3.651.734.00

2.211.65

1.072.581.041.10

Mean ofmomentsright-left

43.6828.4714.134.55

38.3219.467.61

38.8422.75

6.19

14.043.26

19.6513.698.622.56

Distance fordeactivationof horizontalforce (mm)

-1 .10

-1 .10

-1 .70

-0 .70

-2 .70


Table 2. Median of mesio-distal and transverse forces (in N) and moments of rotation (in mNm) deliveredby 10 transpalatal arches after symmetrical activation for molar rotation (second series).

Median difference Mean ofDegree of Mesio-distal Transverse Moment Moment moments momentsdeactivation force force right left right-left right-left


GAC 49 mmactivation 7 mmPassive05

10fullGAC 51 mmactivation 10 mmPassive05

10fullGAC 53 mmactivation 10 mmPassive

05

10full

0.060.190.100.08

0.020.210.160.12

0.060.140.090.13

0.160.130.240.680.96

0.060.510.170.610.96

0.040.150.550.840.90

-0 .6532.0215.622.42

-0 .0439.8023.4111.91

0.1829.7817.006.30

1.4030.2716.194.45

0.1835.0722.42

9.19

-0.2127.6115.893.49

6.664.994.82

7.796.044.45

5.493.705.20

31.9817.304.29

37.4922.9610.74

29.5116.664.70

-0 .85

-1.20

-1.40

GAC = GAC prefabricated stainless steel transpalatal arch.

check the forces and moments when the archeswere judged by the examiner to be passive. Themedian forces and moments with the 'passive'arches were, small. This was also the case forthe maximum forces measured with individualarches (Table 4). The maximum moments ofindividual 'passive' arches were, however, rela-tively large (8.28 mNm for the 49 mm arch and6.95 mNm for the 53 mm arch, Table 4).

The median mesio-distal forces exerted bythe activated arches were relatively small andtended, like those of the first series, to decreaseduring deactivation (Table 2). Individualmesio-distal forces could, however, be relativelylarge (0.57 N with the 51 mm arch, Table 4).At full activation (0 degrees of deactivation) allsizes of arches showed small median expansiveforces but for individual arches the transverseforce varied between expansive and contractive(Table 4). At full deactivation, however, allarches of all three sizes delivered contractiveforces which were of the same median size. Themode of activation of the GAC arches of thesecond series resulted, for all three arch sizes,in fairly similar median moments which rapidlydecreased during deactivation.

The TMA arches of the second series alsodelivered small median forces when judged tobe passive but with a variation up to 0.54 Nmesio-distal and 1.36 N expansive force (Tables3 and 4). The median 'passive' moments fromthe 49 mm TMA arch were greater than thosefrom the 'passive' GAC arch of the same size.Individual TMA arches could show largemoments when believed to be passive, with anextreme value of 22.59 mNm for one 49 mmarch. The second largest 'passive' moment fora TMA arch was 7.43 mNm.

The mesio-distal forces exerted by the activ-ated TMA arches were small, with a maximumvalue of 0.39 N, and generally decreased duringdeactivation. The transverse forces at full activa-tion were varying (expansive or contractive). Atfull deactivation, however, all arches delivereda contractive force. During deactivation thetransverse forces were generally of the samemagnitude as those of the GAC arches. At fulldeactivation, however, the median contractiveforces of the 49 mm and of the 53 mm archeswere double those of the GAC arches.

The moments delivered by the TMA archesat full activation were of the same magnitude


Table 3. Median of mesio-distal and transverse forces (in N) and moments of rotation (in mNm) deliveredby 10 transpalatal arches after symmetrical activation for molar rotation (second series).

Degree ofdeactivation

TMA 49 mmactivation 13 mmPassive05

1015fullTMA 51 mmactivation 15 mmPassive05

1015fullTMA 53 mmactivation 15 mmPassive05

1015full

Mesio-distalforce

0.080.120.100.090.07

0.030.170.100.090.16

0.030.150.140.090.06

Transverseforce

0.29-0 .17-0 .37-0 .62-1 .38-1 .83

0.130.580.11

-0 .28-0 .73-1 .37

0.100.04

-0 .49-0 .87-1 .52-1 .80

Momentright

1.0132.8224.5115.786.97

0.0832.1723.8116.178.59

-0 .4429.2921.4313.044.16

Momentleft

3.6831.5122.4715.027.02

0.1831.0222.7515.284.97

-0 .2925.9617.1610.273.17

Median differencemomentsright-left

3.933.832.492.37

5.704.093.325.35

6.025.863.682.33

Mean ofmoments'right-left

33.7524.9016.417.03

31.0523.9016.327.25

26.3119.3112.234.19


-2 .15

-1 .70

-2 .50

TMA = (5-titanium transpalatal arch.

Table 4 Maximum values of mesio-distal and minimum and maximum values of transverse forces (in N) andof moments (in mNm) delivered by 10 'passive' transpalatal arches and after symmetrical activation for molarrotation (second series).

Arch andactivation

GAC 49 mm passiveactivation 7 mmGAC 51 mm passiveactivation 10 mmGAC 53 mm passiveactivation 10 mmTMA 49 mm passiveactivation 13 mmTMA 51 mm passiveactivation 15 mmTMA 53 mm passiveactivation 15 mm

Mesio-distal forcemax

0.130.530.060.570.190.310.540.390.220.290.080.25

-0 .11-1 .51-0 .36-0 .52-0 .27-0 .88-0 .16-0 .38-0 .40-0 .49-0 .23-0 .72

Transversemin

0.451.410.081.150.180.631.361.350.380.890.410.64

forcemax

-1 .6823.16

-0 .5429.91

-1 .1323.04

-1 .4729.91

-3 .1323.66

-2 .9320.04

Momentmin

3.3243.04

0.4247.76

6.9532.984.43

40.486.05

42.120.82

31.95

rightmax

-0 .7523.02

-0.3824.60

-3.3125.91

-0 .4227.40

1.6923.52

-2 .1221.56

Moment leftmin max

8.2840.53

1.6352.05

2.5539.9222.5938.696.18

37.791.90

31.97

as those from the GAC arches but theydecreased considerably more slowly duringdeactivation (Fig. 7). Thus, useful momentswere still delivered by the TMA arches at 15degrees of deactivation.

Discussion

In spite of the precautions taken in the firstseries of arches to achieve the same degree ofactivation at the two ends of the arch, different


Moment (mNm)

40 - r

-•'. GAC 51 mm - activation 10 mm

""• TMA 49 mm - activation 13 mm

- '•• J GAC 49 mm - activation 7 mm

• TMA 51 mm - activation 15 mm

- r T GAC 53 mm - activation 10 mm

- TMA 53 mm - activation 15 mm

10° 15°

Deactivation

Figure 7 Moments delivered by GAC prefabricated stainless steel (GAC) and (3-titanium (TMA) arches of the secondseries at varying degrees of deactivation.

moments were always obtained. The degree ofactivation was checked in the measuringmachine and adjusted until the same on bothsides. In most cases, many adjustments werenecessary. This is probably one of the reasonsfor the dissimilarity of moments measured.

The frequent adjustments had work-hardenedthe wire to a different degree on the two sidesand thereby changed the limit of elasticity. Thiseffect was most marked in the steel arches andat higher degrees of activation.

The activation of the second series of archeswas undertaken in a way simulating clinical use.It was encouraging to note that it was possibleto adjust the arches to a passive state with onlysmall forces and moments remaining when thearches were believed to be passive. The smallest'passive' forces were generally obtained with thesteel arches while some TMA arches could exertrelatively large forces and moments whenbelieved to be passive. Our results agree withthose of Jager et al. (1992), who were unable

to eliminate all forces and moments from trans-palatal arches when adjusting for passivity. Incontrast to our findings, however, they recordedsmaller residual forces and moments with TMAthan with steel arches.

It was also encouraging that the differencesbetween the moments and the variation betweenthe arches (not shown in the tables) were notlarger in the second than in the first series ofarches. This means that a reasonable consist-ency of forces and moments is obtainable inclinical use. The use of a vice was found to beof great help in the activation of the archessince the arch can be held securely in the viceduring activation, which can also be checked ina satisfactory way. The use of a vice in theclinical setting is, therefore, recommended.

The difference of the moments on the twosides resulted in mesio-distal forces which weregenerally low. In individual cases, however,these forces reached levels capable of movingthe molars in a mesio-distal direction. As such

TRANSPALATAL ARCHES FORV FIRST MOLAR ROTATION 139

unwanted forces are found under the optimalconditions of laboratory experiments, they cer-tainly also occur in the clinic. Unfortunately,they seem to be unavoidable as the force systemis very sensitive. Because of the long lever arm,small differences in activation on the two sideswill result in unequal moments.

A consistent rinding for all arches was thelarge moments delivered at full activation. Theoptimal moment for molar derotation isunknown but moments in the range of 30 mNmhave been suggested (Melsen and Burstone,1990). The optimal moment is dependent onfactors which are largely unknown, such as thesize of the roots and the character and conditionof the tooth-supporting tissues. A way to obtainsmaller moments would be less activation of thearches. However, with steel arches this wouldresult in only a small working range. Anexample is the 51 mm GAC arch activated only5 mm, which delivered a moment of 14 mNmbut only 3 mNm after 5 degrees of deactivation(Table 1). Because of their large working range,TMA arches are much better in this respect.The use of TMA arches is recommended, atleast in cases with a large need of derotation.An objection to the use of TMA arches couldbe breakage during fabrication and activationdue to brittleness. We did not find this to be agreat problem and although occasional break-age of TMA arches occurred, this also arosewith steel arches.

All arches delivered a contractive force ofdeactivation. The size of the contractive forcevaried but it was sufficiently large to be clinicallyrelevant. The decrease of the transverse distancenecessary to eliminate the contractive force was

small. The amount of tooth movement to obtainthis equals at most 1.5 mm per side. We there-fore suggest that expansion to compensate forthe contractive force be carried out after derota-tion is completed. A clinical check of the toothpositions can then indicate how much expan-sion, if any, is needed.

Address for correspondence

Prof. B. IngervallKlinik fur KieferorthopadieFreiburgstrasse 7CH-3010 BernSwitzerland

References

Andrews L F 1972 The six keys to normal occlusion.American Journal of Orthodontics 62: 296-309

Carlon J A 1973 Die Rotation des ersten Oberkiefermolaren.Informationen aus Orthodontie und Kieferorthopadie2: 137-162

Jager A, Planert J, Modler H, Gripp L 1992 In-vitro-Studiezur Anwendung von Palatinalbdgen bei der Kontrolleder Position oberer Molaren. Fortschritte derKieferorthopadie 53: 230-238

Lamons F F, Holmes C W 1961 The problem of the rotatedmaxillary first permanent molar. American Journal ofOrthodontics 40: 259-271

Melsen B, Burstone Ch J 1990 The transpalatal arch andthe lower lingual arch. Their use as active and passiveappliance. In Melsen B, Burstone Ch, Introduction tobiomechanics, Syllabus University of Aarhus

Stoller A E 1954 The normal position of the maxillary firstpermanent molar. American Journal of Orthodontics40: 259-271

Ten Hoeve A 1985 Palatal bar and lip bumper in nonextrac-tion treatment. Journal of Clinical Orthodontics 19:272-291

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