Introduction

Asymmetric occlusions are very common in the typical orthodontic patient. A unilateral crossbite can result in improper coordination of upper and lower arches. Subdivision patients present a asymmetric sagittal molar relationships in which the patient exhibits Class II on one side and Class III on the other, or Class I on one side and Class II or III on the other. Correction of these asymmetric occlusions is one of the most challenging subjects in the field of orthodontics, particularly in subdivision patients that we commonly see. There are many possibilities in correction of asymmetries, such as functional appliances in growing patients, asymmetric extraction or asymmetric mechanics in adult patients, or orthognathic surgery for severe skeletal asymmetries. In recent years, TADs have been used as the new treatment modality for asymmetry correction. However, some patients opt out of such demanding procedures, or discrepancies are relatively small or dental origin so that problems of asymmetric occlusion could be solved by orthodontics means only. Differential diagnosis regarding the nature and amount of asymmetry is the most important criteria in deciding the treatment modality; however, it is beyond the scope of this chapter.

In the case that the dental origin is identified as the cause of asymmetry, asymmetric activation of lingual arch can produce a unique force system that can correct the asymmetries that labial arches cannot. With continuous archwire in the labial brackets, all the teeth are connected from the most posterior end on one side to the other end. This makes it seem as though every tooth would be under the control of a continuous full archwire; this begs the question of why one would need to connect the bilateral molars directly across the dental arch by a lingual arch. The continuous full archwire can hardly control the posterior molar position of the dental arch due to inherent limitations that are distal flexibility and adjacent anchorage problem, necessitating the bilateral molars to be connected directly across the dental arch by a lingual arch (Burstone and Choy 2015).

Asymmetric tooth movement is very difficult. Suppose there are some ideas suggested for asymmetric movement of posterior teeth. The lingual archwire is fabricated so that it is passively fitted to the final position of a tooth. For example, to expand lower right first molar the lingual arch is made with step out bend (Δ) on the right side only for unilateral expansion (Figure 12.2.1a), or the lingual arch is bilaterally activated with same amount (Δ); however, the left side loop was incorporated in order to reduce the force/deflection rate so that lower force is produced on left side (Figure 12.2.1b). These efforts of so‐called “shape‐driven concept” or “differential force system” are in fact in vain because it does not obey the Newton’s first law; in other words, there are always equal and opposite forces, so that magnitude of left and right expansive forces should be equal and opposite to each other. No matter how cleverly we design the appliances we cannot overcome the Law of nature and this is why asymmetric tooth movement is very difficult to produce. Asymmetric application of lingual arch is no exception because it should also follow Newton’s law. However, distribution of stress in the PDL is modified so that asymmetric tooth movement is produced.

Color Code of the Wire and Force System

When the wire, or especially the lingual arch, is engaged into the attachments, it is not possible to tell if the wire is passive or active unless the lingual arch is removed from the attachments. For better understanding the state of the wires in the figure, the wires are depicted in two colors. The green‐colored wire means there is no internal stress in the wire so that the wire is passive and thus, no force system is produced. The orange‐colored wire means internal stress exists in the wire. The wire is elastically bent, which produces a certain force system that therefore entails some kind of tooth movement.

The force system is depicted in different colors in the figure. The red‐colored arrows represent the force system acting on the tooth. It is the deactivation force system because, as it is in the name, it is the force system produced during deactivation of the appliance. The blue‐colored arrows are the force system acting on the appliance. It is called the activation force system because it is the force system applied to activate the appliance by orthodontist’s hand. The gray‐colored arrows are undefined or incorrect force system. The yellow colored arrows are replaced equivalent force system (Burstone and Choy 2015).

Shape‐driven Concept

There are two basic concepts used in application of active lingual arches – a shape driven, and a force‐driven concept. The shape‐driven concept of an appliance means the wire is permanently deformed into certain shape so that it is passive to the final position of the teeth. The wire is elastically bent during the insertion of the wire into the attachments and it moves the teeth as the wire deactivates. One of the most typical appliances made from shape shape‐driven concept is the ideal archwire and a wire with reversed shape. The ideal‐shaped archwire made from super elastic wire is elastically bent and engaged into crowded tooth. As the wire deactivates, and sequential changing of the wire by increasing stiffness, misaligned teeth eventually follow the shape of an ideal archwire. Perhaps you will end up with ideally aligned dentition by this procedure. A mandibular arch showing deep curve of Spee is treated with a wire with reverse curve of Spee, so‐called compensation curve with an anticipation of a reverse shape of the wire will flatten the occlusal plane in a straight line. The appliance designed based on this shape‐driven concept may work properly in some cases; however, it does not always produce the correct force system – especially in asymmetric applications as we have discussed in Figure 12.2.1. This chapter will focus on delineating active application of lingual arch particularly in asymmetric applications for posterior crossbite and sagittal asymmetric molar relationship (Burstone 1989).

Force‐driven Concept and Definition of Shapes

As a response to the shape‐driven concept, the force‐driven concept is developed to deliver correct force system. In the force‐driven concept only the force system is considered, rather than the shape of the appliance. The appliance designed by force‐driven concept has two characteristics. First, the initial force system including magnitude and Moment/Force (M/F) ratio is correct. Second, the Force/Deflection (F/D) rate is reduced and the appliance is over activated to maintain initial correct force system hence, it moves the teeth rapidly without round tripping; therefore, a force‐driven appliance eliminates unnecessary tooth movement.

To obtain the correct shape, computers with beam theory and iterative method is required, but we will use the same principle to obtain the correct shape at clinically acceptable level (Burstone and Koenig 1981).

Unilateral Expansion

Designing Valid Force System

Suppose that we would like to expand the lower right molar only. The first step is to design a valid force diagram that is in equilibrium. Being in equilibrium means all the forces and moments acting on an object sum to zero. At first glance, a single force only acting on the right molar by differential forces would be the best choice, but in fact is an invalid choice because it is not in equilibrium, as seen in Figure 12.2.2a. Only force diagrams that satisfy the equilibrium are valid and any others are not applicable. Some valid possibilities are using differential moments between left and right molar.

First method is applying bilateral equal and opposite forces obliquely so that the line of action passes near the crown on the right side and the center of resistance on the left side (red arrows in Figure 12.2.2

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