Arch form

Introduction 72

The search for the ideal arch form 72 Relapse tendency after changing arch form 72 Cases where expansion may be stable 72 Variation among human arch forms 73 Summary of the issues facing the clinician 73

Practical solutions 74

The use of three arch forms 74 Recommended ratios 75 The tapered arch form 76 The square arch form 76 The ovoid arch form 76

Systemized management of arch form 77

Standardized versus customized wires 77

The use of clear templates at the start of treatment 77

Arch form control early in treatment 77

Arch form control with rectangular HANT wires 78

Arch form control with rectangular steel wires 78

Customizing - determining IAF for each patient 78

Modifications to arch form and archwire coordination 80

Posterior torque considerations 80

After maxillary expansion 80

Upper arch expansion with archwires 81

Upper arch expansion with a jockey wire 82

Asymmetries 82

Arch form during finishing and detailing - the need for settling 83

Arch form considerations during retention 83

Stock control protocol for archwires 84

Case AL A Class I case with a tapered arch form 86


During the era of standard edgewise, most orthodontists customized archwires to each patient's arch form. When the preadjusted appliance became available, there seemed to be an unwritten assumption that one arch form was appropriate, and it could be used for all cases with the preadjusted system. Time has shown that this assumption was not correct. Some customizing of the arch form for individual patients is important. In-out is built into the preadjusted appliance, which avoids the need for first-order bends. This simplifies arch form, but it does not eliminate the need to use different shapes for different individuals.

In order to properly manage arch form in a modern orthodontic practice, there needs to be a balance between efficiency (a single arch form for all patients) and accuracy (the customizing needed for case stability). In this chapter, a short literature review will be presented to support the need for this balance, followed by the description of a practical system for arch form management.

The search for the ideal arch form for the human dentition

Arch form has been discussed in dental and orthodontic publications for over a century. Many of the early attempts to explain and classify the human dental arch form involved geometric terminology such as ellipses, parabolas, and catenary curves. Ideal arch forms were described by ITawley,' Scott,2 Brader* and others. The authors have previously reviewed this early work,4 some of which was for full dentures, but feel it has little relevance to modern orthodontics. Similarly, the search for an 'ideal' arch form, suitable for eveiy patient, has been an unrealistic goal because of the wide individual variations (p. 73).

Relapse tendency after changing arch form

In I960, in a chapter on retention in Graber's text, Riedel5 reviewed previous studies on the stability of arch form. He cited numerous authors who had reported that when inter-canine and inter-molar width had been changed during orthodontic treatment, there was a strong tendency for these teeth to return to their pre-treatment position. He cited only one author who had reported the stability of a slight increase in mandibular inter-canine width after all retention had been removed for what was termed an 'adequate period'. Riedel postulated that 'arch form, particularly in the mandibular arch, cannot be permanently altered during appliance therapy.'

In 1995, De La Cruz et al6 reported on long-term changes in arch form of 45 Class I and 42 Class ll/l treated cases, a minimum of 10 years post-retention. They concluded that arch form tended to return toward the pre-treatment shape after retention and that the greater the treatment change, the greater the tendency for post-retention change. They suggested that the patient's pre-treatment arch form appeared to be the best guide for future arch form stability, but emphasized that minimizing treatment change was no guarantee of post-retention stability.

In 1998, Burke et al7 used meta-analysis to review 26 previous studies of mandibular inter-canine width. They concluded that 'regardless of patient diagnostic and treatment modalities, mandibular inter-canine width tends to expand during treatment by about 1 or 2 millimeters, and to contract post-retention to approximately the same dimension'.

The paper by Burke et al confirms the overall message from the orthodontic literature, that if arch form is changed during orthodontic treatment, in many cases there will be a tendency for relapse to the original dimensions. This is particularly true of inter-canine width. Changes in inter-molar width seem to be more stable.

Cases where expansion of lower inter-canine width may be stable

In most cases, the lower inter-canine width should not be increased during treatment, because of the risk of relapse. Felton et al8 pointed out that buccal uprighting will result in lower anterior relapse in approximately 70% of cases. I lowever, the 30% of cases in which buccal uprighting will be stable will probably include:

Deep-bite cases (such as Class 11/2 cases) in which lower canines have inclined lingually in response to the palatal contour of the upper canines

As the bite is opened, the lower canines can be uprighted. The overbite corrections must remain post-treatment for this movement to be stable. In 1974, Shapiro5 reported on changes in arch length and inter-molar width in 22 non-extraction cases and 58 extraction cases after treatment and post-retention, l ie concluded that mandibular inter-canine width showed a strong tendency to return to its pre-treatment dimension in all groups, with the exception of Class II/2 cases. Expansion of inter-canine width in treated Class II/2 cases showed significantly greater stability than ('lass I or Class ll/l. Post-retention arch length reduction was also less in the Class IT/2 group. Shapiro's interesting findings could possibly be due to the fact that Class 11/2 cases normally show a deep bite, with lower canines inclined lingually in relation to the palatal surface of the upper canines. When the bite is opened, the incisal edges of the lower canines may move labially (Fig. 2.46, p. 46), but the apices of the roots of these teeth may move lingually, with the bodies of the teeth remaining in the same position.

Cases where rapid maxillary expansion is indicated in the upper arch and this expansion is maintained post-treatment

I.adner and Muhl10 have reported that the lower arch will follow this with buccal uprighting, which can be stable. The amount of this response was studied by Sandstrom et al," who observed that lower canines will upright and increase inter-canine width by an average of 1.1 mm, and molars will upright and increase inter-molar width on average 2.9 mm. This effect does not seem to produce an extensive amount of additional space in the lower arch. Haas12 reported on aggressive upper arch expansion, and found an increase in inter-cuspid width of 3-4 mm in only 'a few cases'.

Despite the overwhelming evidence on the instability of lower arch expansion, Braun et al'31'1 reported that the most popular nickel-titanium archwires sold by the major orthodontic companies expand the lower inter-canine width by 5.9 mm and the upper inter-canine width by 8.2 mm on average.

Summary of the issues facing the clinician

Research papers and clinical observations are giving clear messages:

• There are extensive variations among human arch forms.

• As a result of these variations, there does not seem to be any single arch form that can be used for all orthodontic cases.

• If the patient's original arch form is changed during treatment, there is a strong tendency (in as much as 70% of cases) for the arch form to return to its original shape after appliances are removed.

flow do the above findings affect the clinical orthodontist? Do they mean that archwires must be individually customized for each patient? Or can some form of preformed archwire system be used, which will be helpful to the orthodontist, even though some modifications may be needed?

In the following pages a systemized approach to arch form management is described and recommended.

Variation among human arch forms

Most authors have acknowledged that there is variability in the size and shape of human arch form. For example, in 1987 Felton et al8 published a study to find out whether an ideal orthodontic arch form could be identified. They examined the mandibular casts of 30 untreated normal cases (from Andrews' 120 normals study), 30 Class I non-extraction cases, and 30 Class II non-extraction cases. They found that no particular arch form predominated in any of the three samples. They stated that customizing arch forms appeared to be necessary in many cases to obtain optimum long-term stability, because of the great variability in arch form observed in the study.

It is generally accepted that the dental arch form is initially shaped by the form of the underlying bone, and then after eruption of the teeth, the shape becomes influenced by the oral musculature. Genetic and environmental differences produce great variability, which is confirmed in day-to-day clinical observation.

Nojima ratios (Japanese patients)

Table 4.1

Practice sample

Englisch Weltsprache

Nojima ratios (Caucasian patients)


] Tapered 44%


] Ovoid 38%


] Square 18%

Practice sample


The use of three arch forms

Table 4.1

Nojima ratios (Japanese patients)

Arch forms were first classified as tapered, square, and ovoid by Chuck15 in 1932. Numerous authors and clinicians have used this classification over the years, and eventually orthodontic manufacturers began producing arch forms based on this classification (also referred to as narrow, normal, and broad). Such a three arch form approach allows for greater individualization than the single arch form approach, especially in the early archwire stages. If one classifies the arch forms in the Felton et al8 study into tapered, square, and ovoid, the ratios of these shapes in the Andrews', Class I, and Class II samples are approximately as shown in Table 4.1.

In an unpublished study in one of the authors' practices, the lower arches of 200 consecutive cases (predominantly Caucasian) were evaluated with tapered, ovoid, and square transparent templates. The results (Fig. 4.1) were that approximately 50% of the lower arch forms were tapered, 8% were square, and 42% were ovoid. This is quite similar to the Felton results.

Nojima et alK> used tapered, square, and ovoid templates to evaluate the arch forms of Class I, Class II, and Class III cases in both Japanese and Caucasian samples (Figs 4.2 & 4.3). The Caucasian sample showed 44% tapered arch forms, 18% square arch forms, and 38% ovoid arch forms. However, Nojima et al included an equal proportion of Class III cases (of which 44% have square arches) in both samples, and a typical Caucasian caseload would contain fewer Class III cases. Hence the ratios of 50% tapered, 8% square, and 42% ovoid are a more probable reflection of a predominantly Caucasian practice. Global differences are clearly significant, and it is interesting that the Japanese sample showed ratios of 12% tapered, 46% square, and 42% ovoid. This shows the opposite ratio of square to tapered arch forms, compared with the Caucasian sample.

Nojima ratios (Caucasian patients)

Recommended ratios

It has been noted (p. 72) that two categories of cases do show post-treatment stability after minor lower arch buccal uprighting. These are palatal expansion cases and deep-bite cases. Thus the recommended ratios (Fig. 4.4) of 45% tapered, 10% square, and 45% ovoid (p. 84) seem practical for a predominantly Caucasian practice.

The three shapes - tapered, square, and ovoid - used by the authors early in treatment are shown below (Figs 4.5-7). Later in treatment an individual arch form (IAF) is used for each patient (p. 78).

Recommended ratios

Tapered 45% ] Ovoid 45% Square 10%

Recommended ratios

Narrow Tapered Arch

Fig. 4.7 Ovoid

Fig. 4.5 Tapered

Fig. 4.6 Square

Fig. 4.7 Ovoid

^ The tapered arch form o

This arch form has the narrowest inter-canine width and is useful early in treatment for patients with narrow, tapered arch forms (Case AL, p. 86). It is particularly important to use this form for patients with narrow arch forms, and especially in cases with gingival recession in the canine and premolar regions (most frequently seen in adult cases). The tapered arch form is often used in combination with inverted canine brackets for these patients.

Cases undergoing single arch treatment often require the use of the tapered arch form. In this way, no expansion of the treated arch occurs, relative to the untreated arch. The posterior part of this arch form can easily be modified to match the inter-molar width of the patient.

The square arch form

This arch form is indicated from the start of treatment in cases with broad arch forms (Case CW, p. 152). It is also helpful, at least in the first part of treatment, for cases that require buccal uprighting of the lower posterior segments and expansion of the upper arch. After overexpansion has been achieved, it may be beneficial to change to the ovoid arch form in the later stages of treatment. The square arch form is useful to maintain expansion in upper arches after rapid maxillary expansion (p. 80).

The ovoid arch form

Over the past 15 years, this has been the authors' preferred arch form for most of their cases,17 for example, Case JN, p. 120. The combined use of this arch form with appropriate finishing, settling, and retention procedures (p. 289) has resulted in a majority of cases with good stability, and minimal amounts of post-treatment relapse. However, the recent research (above) indicates that a greater number of tapered arch forms should also be used. When superimposed, the three shapes vary mainly in inter-canine and inter-first-premolar width, giving a range of approximately 6 mm (Figs 4.8 & 9) in this area.


Fig. 4.10 Clear templates may be used at the start of treatment to assess whether the patient's lower arch has a tapered, square or ovoid form.

Brader Arch Form

Fig. 4.8 Upper arch form Fig 4.9 Lower arch form superimpositions. superimposition.

Fig. 4.10 Clear templates may be used at the start of treatment to assess whether the patient's lower arch has a tapered, square or ovoid form.



Standardized versus customized wires

It is not practical to customize every wire for every patient in a modern orthodontic practice, and it is not necessary if the system described below is used.

Multistrand .015 or round HANT .016 wires are used early in treatment as the initial leveling and aligning archwires, and these exert light forces. Their form is often temporarily distorted, due to tying into malaligned teeth. They can be expected to have little influence on arch form for the short periods that they are used. It is therefore reasonable to use a standard ovoid arch form for these early wires.

As the teeth align, and the treatment progresses into heavier HANT and then steel wires, archwires gradually have more effect on arch form. This is because of their greater tensile strength and the fact that they are used for a longer period of time. It is therefore beneficial, later in treatment, to customize wires to an arch form suitable for each individual patient.

The use of clear templates at the start of treatment

Clear templates can be used to assess the patient's lower model at the start of treatment, to determine whether the lower arch has a tapered, square, or ovoid form (Fig. 4.10). Often there will only be an approximate fit at this stage, but it is useful to have an early indication.

Fig. 4.8 Upper arch form Fig 4.9 Lower arch form superimpositions. superimposition.

Arch form control early in treatment

It is recommended that all round wires be stocked in ovoid form only (p. 84). This helps to limit inventory. The opening wires will normally be .015 or .0175 multistrand, .016 HANT, or sometimes .014 steel. These may all be used in ovoid form, with no customizing.

As leveling and aligning progress into heavier round wires (pp 111 & 112), there will be a need to customize some wires. Consequently, the ovoid .016, .018, and .020 round steel wires should be adapted as necessary for individuals with a tapered or square form at the start of treatment, as previously determined using the clear templates. Archwire adaptation will obviously not be needed at this stage for individuals with an ovoid starting arch form.

Arch form control with rectangular HANT wires

The manufactured shape of rectangular IIANT wires cannot be customized. It is therefore necessary to stock them in tapered, square, and ovoid form, because (like the heavier round wires) they should be used in the approximate form for the patient, as determined using the clear templates.

Rectangular HANT wires may be in place for several months, and they do influence the patient's arch form, especially in the important canine region. If not used in the appropriate tapered, square, or ovoid shape, they can cause undesirable changes in the patient's starting arch form.

Customizing steel rectangular wires -determining the IAF for each patient

After the rectangular HANT wires have served their purpose, a .019/.025 stainless steel archwire can be individualized for each patient, based on the form of the lower dentition. An upper form can then be made which is coordinated with the lower, and .3 mm wider in all areas. The following procedure (Fig. 4.11 A-F) is used:

• After the rectangular HANT stage (Fig. 4.11 A), a wax template is molded over the lower arch to record the indentations of the brackets (Fig. 4.1 IB).

Arch form control with rectangular steel wires

Rectangular steel .019/ .025 working wires have a major influence on arch form. They therefore need to be customized to each patient's individual arch form (IAF). It is straightforward and quick to adapt working wires to the IAF, and shaping can be delegated and then finally checked by the orthodontist. Concerning stock control of .019/.025 steel wires (p. 84), there are three possibilities:

1. To stock ovoid shape only, and modify as necessary.

2. To stock ovoid and tapered shapes, which will reduce the amount of wire modification needed. This is a good option if the caseload includes mainly children, where the square arch form is seldom used.

3. To stock ovoid, square, and tapered shapes, and thus minimize the amount of wire adaptation needed, while accepting higher inventory levels. When stocking all three shapes, there will always be a need to customize some wires, because the IAF for many patients will not exactly match the shape of the manufactured wires in the basic tapered, square, or ovoid forms.

• The .019/.025 stainless steel archwire is bent to the indentations in the wax bite (Fig. 4.1 ID).

• The wire is then compared with the starting lower model, or a Xerox copy of the model, to ensure that it closely resembles the overall starting shape.

• The wire is then checked for symmetry on a template.

• Finally, a Xerox copy of the wire is made and stored in the patient notes. This is the patient's IAF. Lower rectangular steel wires are then used in the IAF shape and uppers in a form which is 3 mm wider. Archwire coordination is important throughout treatment, especially with the heavier round wires and the .019/.025 rectangular stainless steel wires. The upper wire should superimpose approximately 3 mm outside of the lower wire. This is representative of the overlap of the upper teeth relative to the lower teeth, and provides for correct archwire coordination in the majority of cases (Fig. 4.1 IF).

Fig. 4.11B A wax template is softened in warm water and molded over the lower arch to record indentations of the brackets.

Fig. 4.11 A The lower rectangular HANT wire has been removed.

Fig. 4.11B A wax template is softened in warm water and molded over the lower arch to record indentations of the brackets.

Fig. 4.11D The .019/.025 rectangular steel wire is bent to the indentations.

Fig. 4.11F After the patient's IAF has been determined for the lower archwire, an upper wire can be created which should superimpose approximately 3 mm outside of the lower wire.

Fig. 4.11C The wax template viewed from the labial.

Fig. 4.11E The steel rectangular wire is checked for symmetry on a template, and then a Xerox copy can be made and used as the patient's IAF for the lower arch.


There are some cases that will require arch form modification from the normal IAF and the usual upper/lower archwire coordination.

Modification due to posterior torque considerations

The additional buccal root torque in the upper molar brackets tends to narrow the upper arch, and the progressive buccal crown torque in the lower posterior brackets tends to upright the lower molar teeth and widen the lower arch (Fig. 4.12). The combined effect of these appliance features can be a tendency towards molar crossbite in some cases. When this is observed, the posterior segment of the upper archwire can be widened to 5 mm wider than the lower archwire in the molar regions.

Modification after maxillary expansion

After the upper arch has been expanded with a rapid maxillary expander or a quadhelix (Fig. 4.13A), two things can occur. First, the lower arch tends to upright buccally, and second, the upper arch tends to relapse (Fig. 4.1313). To manage these effects, the lower arch can be widened by using a wider arch form (usually one size wider - for example from tapered to ovoid) and the upper arch expansion can be held with a correspondingly wider arch form.

During torque correction

Before torque correction

During torque correction

Fig. 4.12 During correction of molar torque, there is a tendency for a buccal crossbite to develop. If this is observed, it is necessary to widen the posterior segment of the upper archwire.

Fig. 4.13 After upper arch expansion (A), it is often necessary to widen the upper arch form and narrow the lower arch form (B) to counteract unwanted molar changes.

Upper arch expansion with archwires

In some cases, arch form coordination requires special attention, due to one arch (usually the upper arch) being slightly smaller than the other arch. The rectangular .019/.025 steel wires can be used to help correct this condition and achieve some arch expansion (p. 108), or to maintain expansion previously obtained by use of a quadhelix or by rapid maxillary expansion. This may be done by expanding the 1AF arch form in the molar regions, or by use of the square arch form for a limited period.

There is a correct technique for archwire expansion. If the wire is bent to expand its width (Fig. 4.14), it is important to make sure it is not overexpanded and thus distorted from the arch form. When the ends of the expanded wire are held, and pressed back towards the chosen arch form (IAF), the wire should match that shape (Fig. 4.15). If overexpanded or incorrectly expanded (Figs 4.16 & 4.17), it will not match the chosen arch form (IAF) when the ends are pressed towards it, and this will cause problems due to narrowing or widening of the inter-canine width.

How Use Archwire Stoplock
Fig. 4.14 It is important to use a correct technique for archwire expansion.

Fig. 4.15 After correct expansion, if the ends of the archwire are pressed towards the ideal arch, the expanded arch will show correct form.

Fig. 4.16 Incorrect expansion. Fig. 4.17 Incorrect expansion.
Expansion Arch

Fig. 4.18 Occlusal view of a 'jockey arch' in place. This may be of .019/.025 rectangular steel wire or of heavier round steel wire.

Fig. 4.19 Occlusal view of an asymmetrical lower arch.


* Upper arch expansion with a jockey wire

> There are limits to the expansion force which can be delivered n by one .019/.025 rectangular wire during routine treatment. If

-p necessary, particularly near the end of treatment, a little more

O expansion force can be achieved by using a 'jockey arch' (Case

MS, pp 238 & 239). This is merely a second archwire, also expanded, tied in place over the normal archwire (Fig. 4.18). The jockey arch may be of .0I9/.025 rectangular steel, or of heavier round steel wire. If the upper first molars carry headgear tubes, it can be convenient to end the jockey archwire in those tubes.

It is helpful if the normal .019/.025 wire has buccal root torque in the molar region (Fig. 5.30, p. 108) to attempt bodily movement of molars and avoid tipping. It is important to have adequate bone width to achieve upper molar expansion (Fig. 10.15, p. 290).


In cases where it is clear that the patient has an arch asymmetry, and there are many such cases, the archwires later in the treatment may be modified to assist correction of the asymmetry (Figs 4.19-21).

Fig. 4.18 Occlusal view of a 'jockey arch' in place. This may be of .019/.025 rectangular steel wire or of heavier round steel wire.

Fig. 4.19 Occlusal view of an asymmetrical lower arch.

Occlusal View Coordinated Archwires

Ovoid arch form

Shape of modified arch wire

Ovoid arch form

Ovoid arch form

Shape of modified arch wire

Fig. 4.21 Modification of the lower archwire to counteract and correct the dental asymmetry in Figure 4.19.

Ovoid arch form

Fig. 4.20 Asymmetry of the lower arch in Figure 4.19, compared with the ovoid lower arch form.


There are important arch form considerations during the closing stages of any treatment. A careful protocol allows the arch form to settle in the later stages of treatment. A settling phase is required in almost every case. The following steps are recommended:

• Patients should not progress directly from rectangular wires to retainers without a phase of settling in lighter wires. The authors prefer a full .014 stainless steel or .016 nickel-titanium lower archwire, and an upper .014 stainless steel sectional wire, to include only the upper incisors, in combination with light triangular elastics, near (he completion of treatment. The patient is checked at 2-weekly intervals for approximately 6 weeks (Case IN, p. 124, and Case MOT, p. 274). During this period, vertical tooth settling occurs and the upper and lower arch forms are also allowed to settle, so that a balance between the tongue and perioral musculature can re-establish.

• During this settling phase, teeth adjacent to extraction sites should be lightly tied together, to prevent space opening.

• If the maxillary arch has been expanded earlier in the treatment, the expansion needs to be held during the settling phase. An upper removable acrylic plate may be used for this (Fig. 10.22, p. 295).

In Class 11 treatments (where overjet relapse may occur during settling), a full .014 upper archwire is necessary, bent back behind the molars (Case DO, p. 210). This may slow the settling, but it is needed to hold the corrected overjet. Some second-order bends can be placed in this wire to encourage proper settling.


There is a constant tendency for lower incisor relapse in the majority of cases. I.ower bonded retainers from canine to canine (p. 307) are recommended to minimize this tendency. In first premolar extraction cases, the bonded retainer may be extended onto the second premolars. Typically, a patient in retention will have a lower bonded retainer and an upper acrylic removable retainer. The lower premolars and molars are thus free to narrow, relative to the fully retained upper arch (Fig. 4.22). It may be necessary to modify or leave out (he upper acrylic retainer for 2 to 4 weeks, to let the upper premolars and molars adjust to lower arch changes (Fig. 4.23). A new acrylic retainer can then be made. If a vacuum-formed upper retainer is used, it may be modified for 2 to 4 weeks and then re-made.

Moving Tooth Lingually
Fig. 4.22 During retention, the upper teeth are held, but lower molars and premolars can move labio-lingually.

Fig. 4.23 The upper acrylic retainer may be omitted or modified for 2 to 4 weeks to let upper molars and premolars adjust to lower changes. A new upper removable retainer can then be made and fitted.


An example of a suitable stock system is shown below. It is possible to stock steel working wires in one, two, or three shapes, depending on the size of the practice and the desire to minimize wire modification.

Customization of archwires reduces the risk of relapse and helps to achieve good esthetics. If a broad arch form is used for an individual with a narrow facial appearance, for example, there will be a risk of relapse and an unnatural look to the smile. It is therefore desirable for the clinical orthodontist to have a system of customizing the arch form for each patient, but without having to overstock practice inventory or spend time with needless wire bending. This chapter has described a system which the authors use and recommend with confidence.

Educacion Basica Secundaria Regular



1 Hawley C A 1905 Determination of the normal arch and its application to orthodontia. Dental Cosmos 47:541-552

2 Scott J H 1957 The shape of the dental arches. Journal of Dental Research 36:996-1003

3 Brader A C 1972 Dental arch form related to intra-oral forces. American Journal of Orthodontics 61:541-561

4 McLaughlin R P, Bennett J C 1999 Arch form considerations for stability and esthetics. Revista Espana Ortodontica 29(2):46-63

5 Rledel R A 1969 In: Graber T M (ed) Current orthodontic concepts and techniques. Saunders, Philadelphia

6 De La Cruz A R, Sampson P, Little R M, Artun J, Shapiro P A 1995 Long-term changes in arch form after orthodontic treatment and retention. American Journal of Orthodontics 107:518-530

7 Burke S P, Silveira A M, Goldsmith L J, Yancey J M, Van Stewart A, Scarfe WC 1998 A meta-analysis of mandibular intercanine width in treatment and post retention. Angle Orthodontist 68(1):53-60

8 Felton M J, Sinclair P M, Jones D L, Alexander R G 1987 A computerized analysis of the shape and stability of mandibular arch form. American Journal of Orthodontics 92:478-483

9 Shapiro P A 1974 Mandibular arch form and dimension. American Journal of Orthodontics 66:58-70

10 LadnerPT, Muhl Z F 1995 Changes concurrent with orthodontic treatment when maxillary expansion is a primary goal. American Journal of Orthodontics and Dentofaclal Orthopedics 108:184-193

11 Sandstrom R A, Klapper L, Papaconstantinou S 1988 Expansion of the lower arch concurrent with rapid maxillary expansion. American Journal of Orthodontics 94:296-302

12 Haas A J 1980 Long-term posttreatment evaluation of rapid palatal expansion. Angle Orthodontist 50:189-217

13 Braun S , Hnat W P, Fender D E, Legan H L 1998 The form of the human dental arch. Angle Orthodontist 68(1):29-36

14 Braun S, Hnat W P, Leschlnksy R, Legan H L 1999 An evaluation of the shape of some popular nickel titanium alloy preformed arch wires. American Journal of Orthodontics and Dentofacial Orthopedics 116:1-12

15 Chuck G C 1934 Ideal arch form. Angle Orthodontist 4:312-327

16 Nojima K, McLaughlin R P, Isshiki Y, Sinclair P M 2001 A comparative study on Caucasian and Japanese mandibular clinical arch forms. Angle Orthodontist 71:195-200

17 Bennett J, McLaughlin R P 1993 Orthodontic treatment mechanics and the preadjusted appliance. Mosby-Wolfe, London (ISBN 0 7235 1906X)

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