Draft:Center of Resistance of a Tooth

The Center of resistance of a tooth is a point within the root that is physically equivalent to the Center of mass of a free body. It is a biomechanical concept in orthodontics that allows for the execution of physical analyses, particularly concerning the definition of tooth movements and the vectors acting upon them. Unlike a free body, a tooth in its position in the jaw is not a free body but a restrained body. The difference between the position of the Center of mass of a tooth, if it were a free body removed from the dental arch, and the position of the Center of Resistance of that same tooth in the mouth is a few millimeters. The Center of Resistance of the tooth is located in the root, while the Center of mass is approximately at the junction of the tooth's crown and root. Therefore, as a force, the restraint itself shifts the Center of mass of the tooth toward the root by a few millimeters.

Center of Mass: When a vector acts on a mass, the type of movement that develops in the mass depends on the relationship between the location of the force vector (or the resultant of multiple vectors acting simultaneously on the tooth) and the Center of mass. If the vector or resultant passes precisely through the Center of mass, the resulting movement is translation, where all body points move equally in the direction of the vector. If the vector or resultant does not pass through the Center of mass, rotation (rotational movement) occurs around the Center of mass, which remains in place. An additional force that can be applied to a mass is a couple (two equal forces acting in opposite directions in different planes so that they do not cancel each other out). Regardless of where the couple is applied on the free body, the resulting movement will always be rotational around the Center of mass, similar to applying a vector to a free body that does not pass through its Center of mass.

Tooth's Center of Resistance: Applying a vector that does not pass through the tooth's Center of Resistance or a couple to the tooth, regardless of where it is applied, will cause the tooth to rotate around its Center of Resistance. The possibility of applying a single vector that passes through the Center of Resistance for translation is not feasible, as the precise location of the Center of Resistance within the tooth space is elusive and not precisely known according to the physics requirements.

To summarize this part, one can say that only two physical forces or vectors can be applied to a tooth, tipping and a couple, which causes the same outcome: rotation of the tooth around its Center of Resistance.

The first to define this point and give it the name "Center of Resistance of a tooth" was Dr. G.D. Fish in 1917. According to his definition, the Center of Resistance of a tooth is located at a point within the tooth root, positioned between the apex (tip of the root) and the gingival margin, such that when a force is applied along a line passing through this point, neither tipping nor rotation (torque) of the tooth occurs relative to its long axis. This definition proves that it is not a purely physical definition where all data is known, and the location of the point is unequivocal, but rather a definition of an estimated location within a specific space of the tooth, all due to the restraint of the tooth by living tissues.

Compared to a free body, in which the Center of Mass, as long as the body has not undergone a significant change, constitutes a fixed and clear point in space, the position of the Center of Resistance of a tooth in a restrained body is elusive. The reason for this is that the means of restraint of the tooth, namely the alveolar bone and periodontal ligament, are living entities that constantly change their physical properties, thereby altering the strength of the tooth's retention in its place. The change in physical properties, such as the periodontal ligament's viscosity and the alveolar bone's strength as restraining tissues, is especially notable during orthodontic treatment. During such treatment, the biological turnover of these tissues, due to the application of forces on the teeth, constantly alters their physical properties. This restraint by these two tissues is called the natural (biological) restraint of the teeth. Since the location of the Center of Resistance of a tooth depends on active, living tissues, over time, as a result of normal processes (maturation and aging) or pathological processes (e.g., periodontal diseases and alveolar bone loss) occurring around the teeth, such as gum recession or alveolar bone resorption, the Center of Resistance of the tooth moves toward the apex of the tooth.

Additional changes in the position of the Center of Resistance of the tooth occur when the nature of the tooth as a naturally restrained body is altered. For instance, partial restoration of the tooth with amalgam or composite fillings or crowning the tooth with a metallic material can change the location of the tooth's Center of Resistance. The new Center of Resistance will shift to a different point, albeit within a relatively small range along the root.

As long as the tooth remains free and no external restraint is added, the variability in the position of the tooth's Center of Resistance within the root, which depends only on the metabolism of the restraining tissues, is minimal. However, when a fixed orthodontic appliance is attached to the tooth, such as metal or ceramic brackets, which are connected by orthodontic metal archwires that link the entire arch or part of it, to move the teeth from place to place to improve the appearance andb or function of the dental arches, the level of restraint of the teeth is significantly increased. Any increase in the degree of tooth restraint necessarily alters the position of the Center of Resistance accordingly: increasing restraint shifts the Center of Resistance of the tooth towards the crown, even to the crown itself. The new position of the Center of Resistance depends on the physical properties of the metallic archwires (e.g., the materials they are made from, such as stainless steel or nickel-titanium, and the size of their cross-section, which strengthens as the cross-sectional area increases). Conversely, releasing the restraint, for example, by removing the metal archwire from the brackets or detaching the brackets from the teeth, "returns" the Center of Resistance of the tooth to its primary position within the root.

The strength of the restraint from the fixed appliance, which moves the Center of Resistance of the tooth from its position in the root to, for example, the bracket center, naturally changes the physical system acting on the tooth. When subjected to a tipping vector or a couple, the tooth can rotate around the new position of the Center of Resistance, now located at the crown.

When a vector is applied while only the natural restraint is active, and the Center of Resistance is located in the root, at about half the length of an incisor or canine, the vector will cause the tooth to rotate around its Center of Resistance, so that the tip of the crown and the apex move equally in opposite directions. This tipping movement changes the inclination of the tooth. However, when the Center of Resistance of the tooth is located at the bracket itself, which is bonded to the crown, a tipping vector or couple applied to the tooth will cause rotation around an axis located at the bracket center. In this scenario, the apex moves much more than the crown tip in the opposite direction. In all dimensions, this movement also alters the tooth's inclination, but the axis of rotation is at the crown, at the bracket center, rather than at about the Center of the tooth. Such an inclination change in orthodontics is referred to as torque. Combining these movements, one after the other, and so on, first, rotation around the Center of Resistance when positioned in the root, followed by rotation when the Center of Resistance moves to the bracket center, and so forth, produces the orthodontic translational movement. This combination of movements is referred to in orthodontics as "Walking," which is immensely important in the profession. It should be emphasized that the 'Walking' movement can only be achieved during treatment with fixed appliances that can change the location of the Center of Resistance. No removable appliance, including Clear Aligners, can ever produce such a movement.

The concepts related to biological restraint and artificial restraint, as well as information about their properties concerning orthodontic treatment, such as the ability to move the Center of Resistance of a tooth from the root to the crown and vice versa, and that control over the Center of Resistance location, enables the movement of teeth, alone or in combination with other movements, in all directions and possible movements, were 'developed' by Dr. Naphtali Brezniak, MD. DMD, MsD, ABO, an orthodontic specialist, in 2024.