Force

Force is an act that when applied upon an object can change the object’s state from not moving to moving and also can accelerate or decelerate moving object. Force is a vector not a scalar. This means that in order to define a force, it is important to define/describe its magnitude and direction as well as its sense. Direction is described with reference to coordinate system, in other words vertical, horizontal (medio-lateral) or front to back for example. One may call each axis, X, Y or Z for example. Sense is described in terms of right or left (In the horizontal axis), front or back (In the antero-posterior), up or down (In the vertical axis) for example. Forces may be added (if applied in the same direction and sense) or counteract each other (if applied in the same axis but in different senses/directions).

Moment and the Concept of Moment to Force Ratio

The concept of moment to force ratio was first introduced by Tanne et al., in 1988 to define different types of tooth movement and changes of center of rotation according to changes of the moment to force ratio [1]. In short, the concept was described as follows. In order to move tooth bodily, a force must be applied to the center of mass or center of resistance of that body. In the case of teeth, the center of resistance is located somewhere in the root(s) and it is not practical to apply forces to the teeth roots.

When a force is applied to the tooth crown, usually it creates a moment (tendency for the tooth to rotate around the center of resistance) as the point of application of the force is away from the center of resistance (usually is located in the tooth root somewhere between the alveolar bone crest and tooth root apex). The produced moment is the resultant of multiplication of the magnitude of the force times the perpendicular distance from the line of action (not the point of application) of the force to the center of resistance (Fig. 5.1).

Fig. (5.1))
Moment is created when a force is applied to a body (tooth in this example) away from the center of resistance. Moment = Force (100 gm) ^* perpendicular distance from the force line of action (dashed horizontal line) to the center of resistance (10 mm) = 1000 g mm.In order to move a tooth bodily without applying forces to the tooth center of resistance directly that is located in the tooth root, it is important to prevent or counter act the initial moment occurred due to the applied force to the teeth crowns. To do so, a counter moment is required to negate the initial moment due to the force. The ratio between the applied moment and the force is called moment to force ratio and this ratio determines the resultant tooth movement (uncontrolled tipping, controlled tipping, bodily or root movement [torque]). These types of tooth movements are explained in detail below. In short, if we assume that the force will move the tooth crown tip in one direction, the counter moment would tend to move the root apex in the same direction or at least prevent the apex from movement in the opposite direction to where the tooth crown is moving.

Possible Orthodontic Teeth Movement using Clear Aligners

Initially when clear aligners were introduced, they were introduced to solve minimum crowded teeth (1-2 mm of arch length deficiency); minimum (1-2 mm) dental spacing cases or relapsed cases.

Although many practitioners would argue that simple crowded or spacing cases can be easily corrected using routine removable or fixed orthodontic appliances, challenges as mentioned above with regular fixed appliances are cleaning, diet restriction and bracket positioning errors. Also, regular/tra-ditional removable orthodontic appliances have their own limitations which include bulkiness of the acrylic base, one point contact of the active components (wires/clasps) with the teeth which makes it difficult to control tooth movement or achieving controlled tipping or bodily movement according to the treatment goals.

In this regard, clear aligners may provide better control of tooth movement compared to traditional removable orthodontic appliances and also, when treatment planning is well-designed, difficult tooth movement including but not limited to bodily movement can be achieved.

Types of Orthodontic Tooth Movements

There are four common types of orthodontic tooth movements with regards to crown cusp tip/incisal edge -root apex relationship. There are four common types of tooth movement with regards to general body axes (vertical [intrusion/extr-usion], horizontal [buccal/lingual] and anteroposterior [proclination/retro-clination]) and with regards to the tooth own axis (rotational tooth movement).

1. Types of Orthodontic Tooth Movements with Regards to Crown Tip-root Apex Relationship

1. Uncontrolled Tipping Where the tooth crown moves in one direction, while the root apex of the same tooth moves in the opposite direction (Fig. 5.2). Normally, this type of tooth movement is produced by removable appliances using round wires, or even fixed appliances when round wires are used as the main tooth guided tooth movement. The moment to force ratio in this type of tooth movement is less than 8. Main problem with this type of tooth movement occurs when the crown moves (>1 mm) as the involved tooth root apex moves into cortical plates of bone or even out of the alveolar bone, which is usually associated with severe root resorption and/or periodontal bone defects [2^–4]. An example of these problems can be seen in (Fig. 5.3).

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