The Basics

In space closure the objective is simple: to bring together opposing teeth or segments of teeth by applying a force between them. This force is usually applied on the bracket attached to the crown of the teeth (Fig. 6-1) and is occlusal and buccal to the center of resistance (C_RES) of the units experiencing the force. This generates moments (moment due to force, or M_F), which cause tipping and rotation of the teeth in the direction of the applied force. The clinical observation of the amount of tipping and rotation will depend on the amount of space closure. A greater amount of space closure will yield greater degrees of side effects. The amount of space requiring correction can vary depending on the severity. Less than 2-mm of spacing can be categorized as minor, greater than 2-mm but less than 4-mm is moderate, while anything greater than 4-mm is severe. Large spaces need good anchorage control over the desired tooth movement (i.e., effectively managing the unwanted moments [causing tipping and rotation] created during space closure).

With efficient mechanical appliances and sound application of the fundamentals learned in Chapter 4, almost any desired tooth movement can be obtained. In a nutshell, the nature of tooth movement can be controlled by applying a counteracting moment (M_C) to the M_F. In Figure 6-1, the tipping showed can be controlled by this M_C. The easiest way to generate this M_C is to place a straight wire in the tipped brackets (Fig. 6-2). This ratio of moment to force (M_C/F ratio) at the orthodontic bracket can bring about various types of tooth movement. However, the type of tooth movement seen during space closure also depends on the tooth and the objectives of the overall treatment. For example, canines and molars usually need to be translated while the anterior teeth or incisors can do well with simple tipping. Root movement is frequently required for final alignment of the roots, especially during finishing. All these movements require different M_C/F ratios as we will see in the next section.

Moment to Force (M/F) Ratio

The M/F ratio is a good way to describe or predict the quality of tooth movement. In the literature it has been stated that an M/F ratio of 5 : 1 is required for tipping, of 7 : 1 is required for controlled tipping, of 10 : 1 is required for translation, and of 12 : 1 is required for root correction. However, these ratios cannot be applied universally for all teeth and in all situations. For example, for translation the ratio of 10 : 1 applies for a single rooted tooth where the distance of the bracket or the point of force application is 10-mm from the C_RES of the tooth and the amount of force applied is 100 g. A more general way of defining M/F ratio for tooth movement should follow a qualitative approach, not a quantitative approach. High, moderate, and low M/F ratios can do this aptly.

As seen in Chapter 4 and in Figure 6-1, a single force applied at the bracket of a tooth will produce uncontrolled tipping with the center of rotation (C_ROT) slightly apical to the C_RES. Now if a counterbalancing moment (M_C) is applied and is high enough, it can perhaps negate the M_F. (Note: In Figure 6-2, the M_C is generated when the opposite ends and corners of the bracket contact the wire placed in the slot.) This will result in translation. A further increase will cause root movement into the space. At these relatively high M/F ratios, stresses reportedly distribute more evenly through the entire root with minimal changes in the mechanical properties during activation; this reduces injuries to teeth and surrounding tissues. A moderate M_C will only partially oppose the M_F, leading to controlled tipping with the apex remaining stationary. It is apparent from this discussion that regulating the M_C/F (or M_C/M_F) ratio is key in producing different types of tooth movement for space closure.

However, it is important to mention that the nature of tooth movement can also be regulated by varying the point of force application (see Chapter 4 for a detailed discussion on this).

Anchorage

As discussed, space closure involves the gradual closure of space between two teeth or two segments of teeth when one or both move toward each other. Depending on the needs of the patient, one set of teeth or one tooth can be classified as the active unit while the other is classified as the passive or reactive unit. These two units have completely different roles during tooth movement. The active unit undergoes the majority of the movement while the passive unit resists any kind of movement and provides the resistance necessary to facilitate the movement of the active unit, thereby serving as an anchorage. Therefore anchorage can be defined as the resistance offered by the passive unit toward any type of unwanted movement when the active unit is undergoing the desired movement. The set of teeth that offers this anchorage or resistance is also called the “anchorage unit.” The anchorage setup for different situations can be broadly classified into four types (Fig. 6-3):

One of the easiest ways to generate Group A anchorage is by creating a high M/F ratio. In rare situations anchorage might even go beyond absolute anchorage and you might notice a net “anchorage gain.” For example, during en masse retraction of the anterior teeth, the incisors and the molar both can move distally. This sometimes occurs when skeletal anchorage is used to reinforce anchorage.

Segmental Mechanics

The basic premise of this concept is that all teeth in the upper or lower arch are not connected to each other by a continuous wire but are divided into discrete groups or segments. This segmentation is done on the basis of the role the teeth serve in space closure (i.e., which group of teeth is supposed to move and which is not). The groups are consolidated into segments: active and passive (for anchorage). Force is then applied between these segments to close the extraction space. Since the segments are not connected by a straight wire (i.e., the teeth are not moving on a wire), this is also referred to as “frictionless mechanics.” Closure of space is usually done by loops (potential energy–loaded springs) constructed from regular orthodontic archwires. All closing loops have specific mechanical properties (i.e., response to mechanical forces). Clinicians need to know these properties in order to use them optimally to move teeth or groups of teeth in predetermined directions. In the next section we will elaborate on these properties.

The main mechanical loop properties are the M/F ratio, load and deflection ratios, and the vertical force created. Among these, the M/F ratio can be considered the most significant because it is related to the type of tooth movement.

Concept of Differential Moments

Typically, for severe space closure scenarios a high M/F ratio loop is desirable, while minor spaces can be dealt with loops expressing a low M/F ratio. This is because with more space, teeth have a tendency to show more tipping. Therefore a high M/F ratio will ensure that they remain upright through the space closure.

For example, during incisor retraction the high M/F ratio for the posterior teeth will encourage anchorage preservation as it resists any tipping into the extraction space. In fact, a large posterior moment can cause distal crown movement, thereby opening up more extraction space. On the other hand, the low M/F ratio for the incisors encourages tipping. Simply described, methods using differential M/F ratios may be represented mathematically by the inequality M_Cp/F ≠ M_Ca/F and M_Cp/F ≫ M_Ca/F (here, a indicates anterior and p indicates posterior).

The application of such unequal moments must also comply with the laws of equilibrium discussed in Chapter 4. Because the moments created at each end of the loop or spring are unequal, the total force system must have additional effects. Vertical forces (intrusive and extrusive) are therefore also acting on the two segments. The magnitude of the vertical force depends on the difference between the two moments and the distance between the two segments.

In contemporary orthodontics, many closing loop shapes are being used, such as vertical or teardrop loops, T-loops, L-loops, Gjessing springs, and others.^1–6 These loop types can be further modified by adding a coil, altering the height, tipping the vertical legs (to increase the M_C), and so on.

Optimizing Loops for Space Closure: How Loop Design Affects the M/F Ratios

Researchers and clinicians have tried to design and refine loop geometry to obtain the highest M/F ratios possible, with the primary objective of reinforcing anchorage. Mechanical properties of closing loops depend on many factors, such as loop height, width, shape, and position; wire material; cross-sectional dimensions; and so on.^4,5,7–9 Let’s look into some of these factors in detail.

Segmental Mechanics for Space Closure