E HNIKH OP O ONTIKH E I EøPH H

∆∆Ô

Ô ÎΤ¤ÓÓÙÙÚ

ÚÔ

Ô ·

·ÓÓÙÙ››Û

ÛÙÙ·

·Û

ÛË

˘˜ ÙÙˆ

ˆÓÓ ‰

‰Ô

ÔÓÓÙÙÈÈÒ

ÒÓÓ Û

ÛÙÙË

ËÓÓ √

√Ú

Úı

ıÔ

Ô‰

‰Ô

ÔÓÓÙÙÈÈÎ΋

‹

ππˆ

ˆ¿

¿ÓÓÓÓË

˘˜ ™™.. ¶

¶·

·

·

·ÁÁˆ

ˆÚ

ÚÁÁ››Ô

Ô˘

˘

∂ȉÈÎfi˜ √ÚıÔ‰ÔÓÙÈÎfi˜, ÀÔ„‹ÊÈÔ˜ ¢È‰¿ÎÙˆÚ, ∂ÚÁ·ÛÙ‹ÚÈÔ √ÚıÔ‰ÔÓÙÈ΋˜, ∆Ì‹Ì· √‰ÔÓÙÈ·ÙÚÈ΋˜, ∞ÚÈÛÙÔÙ¤ÏÂÈÔ ¶·ÓÂÈÛÙ‹ÌÈÔ £ÂÛÛ·ÏÔ-ӛ΢.

TTh

hee cceen

ntteerr o

off rreessiissttaan

nccee o

off tteeeetth

h iin

n O

Orrtth

ho

od

do

on

nttiiccss

IIo

oaan

nn

niiss SS.. PPaap

paag

geeo

orrg

giio

ou

u

Orthodontist, Doctorate Degree Candidate, Department of Orthodontics, School of Dentistry, Aristotle University of Thessaloniki, Thessaloniki, Greece.

A

ABBSSTTRRAACCTT

The aim of this study is to review the literature on what concerns the center of resistance of one tooth or a group of teeth. Authors’ views about the center’s exact location often differ. This study presents the main methods used for determining the center of resistance; relevant studies and their results are also reported.

The center of resistance of single-rooted teeth is found at a point located at a distance of 33-42% of the root length, when measured from the alveolar crest. Its location may change depending on root length, direction of applied forces, quantity of surrounding bone and age; there are indications that its location is also affected by tooth morphology, type of periodontal ligament, quality of surrounding bone, tissue response to forces applied, degree of humidity of neighboring osseous structures and tooth axial inclination.

The center of resistance of a group of teeth differs depending on the number of teeth. Most research studies concern upper incisors and upper anterior teeth. However, there are conflicting views about the center’s location during palatal movement and intrusion. Furthermore, our knowledge concerning the factors affecting the center of resistance of a group of teeth is limited; this may be due to the fact that these factors cannot be easily measured when a tooth group is involved. Nevertheless, an orthodontist treats patients rather than centers of resistance and methods successfully tested in clinical practice should not be rejected, even if they might be based on theoretical centers of resistance.

K

Keeyy wwoorrddss:: Palatal tooth movement, dental intrusion, center of resistance, orthodontic movement.

¶ ¶EEPPII§§HHææHH ™ÎÔfi˜ Ù˘ ·ÚÔ‡Û·˜ ÂÚÁ·Û›·˜ Â›Ó·È Ó· Á›ÓÂÈ ÌÈ· ‚È‚ÏÈÔÁÚ·ÊÈ΋ ·Ó·ÛÎfiËÛË ÙˆÓ ·fi„ÂˆÓ Ô˘ ·ÊÔ-ÚÔ‡Ó ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÂÓfi˜ ‰ÔÓÙÈÔ‡ ‹ ÌÈ·˜ ÔÌ¿‰·˜ ‰ÔÓÙÈÒÓ. √È ·fi„ÂȘ ÙˆÓ Û˘ÁÁڷʤˆÓ ÁÈ· ÙËÓ ·ÎÚÈ‚‹ ı¤ÛË ÙÔ˘ Â›Ó·È Û˘¯Ó¿ ‰È·ÊÔÚÂÙÈΤ˜. ™ÙËÓ ÂÚÁ·Û›· ·˘Ù‹ ·ÚÔ˘ÛÈ¿˙ÔÓÙ·È ·Ú¯Èο ÔÈ Î‡ÚȘ ̤ıÔ‰ÔÈ Ô˘ ¯ÚËÛÈ-ÌÔÔÈÔ‡ÓÙ·È ÁÈ· ÙÔÓ ÚÔÛ‰ÈÔÚÈÛÌfi ÙÔ˘ Î·È ÛÙË Û˘Ó¤-¯ÂÈ· Á›ÓÂÙ·È ·Ó·ÊÔÚ¿ ÛÙȘ ÌÂϤÙ˜ Î·È ÛÙ· ·ÔÙÂϤÛÌ·-Ù¿ ÙÔ˘˜. ∆Ô Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ÌÔÓfiÚÚÈ˙ˆÓ ‰ÔÓÙÈÒÓ ‚Ú›-ÛÎÂÙ·È ·Ó¿ÌÂÛ· ÛÙÔ 33-42% ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ fiÙ·Ó Ë Ì¤ÙÚËÛË Á›ÓÂÙ·È ·fi ÙË Ê·ÙÓȷ΋ ·ÎÚÔÏÔÊ›·. ªÔÚ› Ó· ÌÂÙ·‚ÏËı› ·Ó¿ÏÔÁ· Ì ÙÔ Ì‹ÎÔ˜ Ù˘ Ú›˙·˜ ÙÔ˘ ‰ÔÓÙÈÔ‡, ÙË ‰È‡ı˘ÓÛË ÙˆÓ ÂÊ·ÚÌÔ˙fiÌÂÓˆÓ ‰˘Ó¿ÌÂ-ˆÓ, ÙËÓ ÔÛfiÙËÙ· ÙÔ˘ ÂÚÈ‚¿ÏÏÔÓÙÔ˜ ÔÛÙÔ‡ Î·È ÙËÓ ËÏÈΛ· ÂÓÒ ˘¿Ú¯Ô˘Ó ÂӉ›ÍÂȘ fiÙÈ ÂËÚ¿˙ÂÙ·È ·fi ÙË ÌÔÚÊÔÏÔÁ›· ÙÔ˘ ‰ÔÓÙÈÔ‡, ÙÔ Â›‰Ô˜ ÙÔ˘ ÂÚÈÔ‰ÔÓÙÈÎÔ‡ Û˘Ó‰¤ÛÌÔ˘, ÙËÓ ÔÈfiÙËÙ· ÙÔ˘ ÂÚÈ‚¿ÏÏÔÓÙÔ˜ ÔÛÙÔ‡, ÙËÓ ÈÛÙÈ΋ ·ÓÙ›‰Ú·ÛË ÛÙȘ ·ÛÎÔ‡ÌÂÓ˜ ‰˘Ó¿ÌÂȘ, ÙËÓ ÂʇÁÚ·ÓÛË ÙˆÓ ·Ú·Î›ÌÂÓˆÓ ÔÛÙÈÎÒÓ ‰ÔÌÒÓ Î·È ÙËÓ ·ÍÔÓÈ΋ ÎÏ›ÛË ÙÔ˘ ‰ÔÓÙÈÔ‡. ∆Ô Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÌÈ·˜ ÔÌ¿‰·˜ ‰ÔÓÙÈÒÓ ‰È·Ê¤ÚÂÈ ·Ó¿ÏÔÁ· Ì ÙÔÓ ·ÚÈıÌfi ÙˆÓ ‰ÔÓÙÈÒÓ. √È ÂÚÈÛÛfiÙÂÚ˜ ¤Ú¢Ó˜ ¤¯Ô˘Ó Á›ÓÂÈ ÁÈ· ÙÔ˘˜ ¿Óˆ ÙÔÌ›˜ Î·È ÙÔ˘˜ ¿Óˆ ÚÔÛı›Ô˘˜ À¿Ú¯Ô˘Ó fï˜ ÛÔ‚·Ú¤˜ ‰È·ÊˆÓ›Â˜ ÁÈ· ÙË ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ ÙfiÛÔ Î·Ù¿ ÙËÓ ˘ÂÚÒÈ· ÌÂٷΛÓËÛË fiÛÔ Î·È Î·Ù¿ ÙËÓ ÂÌ‚‡ıÈÛË. ∂ÈϤÔÓ ÔÈ ÁÓÒÛÂȘ Ì·˜ ÁÈ· ÙÔ˘˜ ·Ú¿ÁÔÓÙ˜ Ô˘ ÂËÚ¿˙Ô˘Ó ÙË ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ ÔÌ¿‰ˆÓ ‰ÔÓÙÈÒÓ Â›Ó·È Ôχ ÂÚÈÔÚÈṲ̂Ó˜ ›Ûˆ˜ ÂÂȉ‹ ÔÈ ·Ú¿ÁÔÓÙ˜ ·˘ÙÔ› Â›Ó·È ‰‡ÛÎÔÏÔ Ó· ÌÂÙÚËıÔ‡Ó Û ÔÌ¿‰Â˜ ‰ÔÓÙÈÒÓ. √ÚÈṲ̂ÓÔÈ fï˜ ÙÚfiÔÈ ıÂÚ·›·˜ ÛÙËÚ›˙ÔÓÙ·È ıˆÚË-ÙÈο ÛÙË ÁÓÒÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ ÔÌ¿‰ˆÓ ‰ÔÓÙÈÒÓ. ∂Âȉ‹ Ô ÔÚıÔ‰ÔÓÙÈÎfi˜ ‰ÂÓ ıÂÚ·‡ÂÈ Î¤ÓÙÚ· ·ÓÙ›ÛÙ·Û˘ ·ÏÏ¿ ·ÛıÂÓ›˜ ‰ÂÓ ı· Ú¤ÂÈ Ó· ·ÔÚÚ›ÙÂÈ

IINNTTRROODDUUCCTTIIOONN

Several free bodies behave as if their mass is concentrated at a single point. If, e.g., a free body is found in space and a force is applied at a specific point on it, then all body points will follow the same course. This point is called the mass center. However, the tooth does not behave like a free body, since the periodontal ligament and the alveolar bone restrict its movement. The point that corresponds to the mass center of a free body is the center of resistance of the tooth. The center of resistance is, therefore, the point where tooth resistance to a movement may be concentrated; in other words, when a force is applied through this point, tooth translation ensues.

Forces applied at a distance from the CR also create a moment that tends to rotate the tooth. Moment magnitude depends on force magnitude and on the distance of the force vector from the CR (Proffit and Fields, 2000).

Forces applied by the orthodontist do not usually pass through the CR (Nanda and Kuhlberg, 1997). Consequently, moments that affect and determine tooth movement do exist. When the orthodontist knows the location of a tooth’s CR, this moment or, even better, the moment / force ratio for every tooth movement may be calculated; thus, tooth movement may be controlled (Halazonetis, 1996; Yoshida et al., 2001a). If, e.g., tooth translation is to be achieved, then an opposite moment counteracting the first one or a force applied through the center of resistance should be incorporated into the system. When the moment to force ratio is between 1 and 7, the type of tooth movement is controlled tipping; when the ratio is between 8 and 10, then tooth translation is achieved; if the ratio is higher than 10, root movement (torque) is observed (Proffit and Fields, 2000). M

MEETTHHOODDSS OOFF DDEETTEERRMMIINNIINNGG TTHHEE CCEENNTTEERR OOFF R

REESSIISSTTAANNCCEE

Many methods have been used in order to determine the center of resistance of a tooth. Several researchers applied mathematical or physical models, as well as finite EEII™™AA°°øø°°HH ∞ÚÎÂÙ¿ ÂχıÂÚ· ÛÒÌ·Ù· Û˘ÌÂÚÈʤÚÔÓÙ·È Û·Ó Ë Ì¿˙· ÙÔ˘˜ Ó· Â›Ó·È Û˘ÁÎÂÓÙڈ̤ÓË Û ¤Ó· ÛËÌ›Ô. ∂¿Ó .¯. ¤Ó· ÂχıÂÚÔ ÛÒÌ· ‚Ú›ÛÎÂÙ·È ÛÙÔ ‰È¿ÛÙËÌ· Î·È ·ÛÎËı› Â¿Óˆ ÙÔ˘ ÌÈ· ‰‡Ó·ÌË Û ¤Ó· Û˘ÁÎÂÎÚÈ̤ÓÔ ÛËÌÂ›Ô ÙfiÙ fiÏ· Ù· ÛËÌ›· ÙÔ˘ ÛÒÌ·ÙÔ˜ ı· ‰È·ÁÚ¿„Ô˘Ó Ì›· ·Ú¿Ï-ÏËÏË ÙÚԯȿ. ∆Ô ÛËÌÂ›Ô ·˘Ùfi ÔÓÔÌ¿˙ÂÙ·È Î¤ÓÙÚÔ Ù˘ Ì¿˙·˜. ∆Ô ‰fiÓÙÈ fï˜ ‰ÂÓ Û˘ÌÂÚÈʤÚÂÙ·È Û·Ó ÂχıÂÚÔ ÛÒÌ· ·ÊÔ‡ Ë Î›ÓËÛ‹ ÙÔ˘ ÂÚÈÔÚ›˙ÂÙ·È ·fi ÙÔÓ ÂÚÈÔ‰Ô-ÓÙÈÎfi Û‡Ó‰ÂÛÌÔ Î·È ÙÔ Ê·ÙÓÈ·Îfi ÔÛÙfi. ∆Ô ·ÓÙ›ÛÙÔÈ¯Ô ÛËÌÂ›Ô Ì ÙÔ Î¤ÓÙÚÔ Ì¿˙·˜ ÂÓfi˜ ÂχıÂÚÔ˘ ÛÒÌ·ÙÔ˜ Â›Ó·È ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘ ‰ÔÓÙÈÔ‡. ∂Ô̤ӈ˜ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ Â›Ó·È ÙÔ ÛËÌÂ›Ô ÛÙÔ ÔÔ›Ô ÌÔÚ› Ó· Û˘Ì˘-ÎÓˆı› Ë ·ÓÙ›ÛÙ·ÛË ÙÔ˘ ‰ÔÓÙÈÔ‡ Û ̛· ΛÓËÛË ‹ Ì ¿ÏÏ· ÏfiÁÈ· ÙÔ ÛËÌÂ›Ô ÙÔ˘ ‰ÔÓÙÈÔ‡ ·fi ÙÔ ÔÔ›Ô fiÙ·Ó ÌÈ· ‰‡Ó·-ÌË ‰È¤ÏıÂÈ ı· ÚÔηϤÛÂÈ ·Ú¿ÏÏËÏË ÌÂٷΛÓËÛË ÙÔ˘ ‰ÔÓÙÈÔ‡. √È ‰˘Ó¿ÌÂȘ Ô˘ ‰È¤Ú¯ÔÓÙ·È Û ·fiÛÙ·ÛË ·fi ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÚÔηÏÔ‡Ó ÂÈϤÔÓ Ì›· ÚÔ‹ Ë ÔÔ›· Ù›ÓÂÈ Ó· ÂÚÈÛÙÚ¤„ÂÈ ÙÔ ‰fiÓÙÈ. ∆Ô Ì¤ÁÂıÔ˜ Ù˘ ÚÔ‹˜ ÂÍ·ÚÙ¿Ù·È ·fi ÙÔ Ì¤ÁÂıÔ˜ Ù˘ ‰‡Ó·Ì˘ Î·È ÙËÓ ·fiÛÙ·ÛË ÙÔ˘ ·Ó‡-ÛÌ·ÙÔ˜ Ù˘ ‰‡Ó·Ì˘ ·fi ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘ ‰ÔÓÙÈ-Ô‡ (Proffit Î·È Fields, 2000). √È ‰˘Ó¿ÌÂȘ Ô˘ ÂÊ·ÚÌfi˙ÂÈ Ô ÔÚıÔ‰ÔÓÙÈÎfi˜ Û˘Ó‹ıˆ˜ ‰ÂÓ ‰È¤Ú¯ÔÓÙ·È ·fi ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ‰ÔÓÙÈÒÓ (Nanda Î·È Kuhlberg, 1997). ∂Ô̤ӈ˜ ı· ˘¿Ú¯Ô˘Ó ÚÔ¤˜ ÔÈ Ôԛ˜ ı· ÂËÚ¿˙Ô˘Ó Î·È ı· ηıÔÚ›˙Ô˘Ó ÙËÓ Î›ÓËÛË ÙÔ˘ ‰ÔÓÙÈÔ‡. ŸÙ·Ó Ô ÔÚıÔ‰ÔÓÙÈÎfi˜ ÁÓˆÚ›˙ÂÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›-ÛÙ·Û˘ ÙÔ˘ ‰ÔÓÙÈÔ‡ ÌÔÚ› Ó· ˘ÔÏÔÁ›ÛÂÈ ·˘Ù‹ ÙË ÚÔ‹ ‹ ηχÙÂÚ· ÙÔ ÏfiÁÔ ÚÔ‹ / ‰‡Ó·ÌË ÁÈ· οı ΛÓËÛË ÙÔ˘ ‰ÔÓÙÈÔ‡ Î·È Ó· ÂϤÁÍÂÈ ÂÔ̤ӈ˜ ÙËÓ Î›ÓËÛË ÙÔ˘ ‰ÔÓÙÈÔ‡ (Halazonetis, 1996; Yoshida Î·È Û˘Ó., 2001a). ∂¿Ó ı¤ÏÂÈ .¯. Ó· ÂÈÙ‡¯ÂÈ ·Ú¿ÏÏËÏË ÌÂٷΛÓËÛË ÙÔ˘ ‰ÔÓÙÈÔ‡ ı· Ú¤ÂÈ Ó· ÂÓۈ̷ÙÒÛÂÈ ÛÙÔ Û‡ÛÙËÌ· ÌÈ· ·ÓÙ›ıÂÙË ÚÔ‹ Ë ÔÔ›· Ó· ÂÍÔ˘‰ÂÙÂÚÒÓÂÈ ÙËÓ ÚÒÙË ‹ Ó· ÂÊ·ÚÌfiÛÂÈ Ì›· ‰‡Ó·ÌË Ô˘ Ó· ÂÚÓ¿ÂÈ ·fi ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘

Hell Orthod Rev 2005;8:41-55.

Received: 24.09.2004 - Accepted: 01.03.2005 ·˘Ù¤˜ ÙȘ ÌÂıfi‰Ô˘˜ fiÙ·Ó Ì¿ÏÈÛÙ· Â›Ó·È ‰ÔÎÈÌ·Ṳ̂Ó˜ ÛÙËÓ Î·ıËÌÂÚÈÓ‹ ÎÏÈÓÈ΋ Ú¿ÍË. § §¤¤ÍÍÂÂÈȘ˜ ÎÎÏÏÂÂÈȉ‰ÈÈ¿¿:: ÀÂÚÒÈ· ÌÂٷΛÓËÛË ÙˆÓ ‰ÔÓÙÈÒÓ, ÂÌ‚‡ıÈÛË ÙˆÓ ‰ÔÓÙÈÒÓ, ΤÓÙÚÔ ·ÓÙ›ÛÙ·Û˘, ÔÚıÔ‰ÔÓÙÈ-΋ ÌÂٷΛÓËÛË. ∂ÏÏ √ÚıÔ‰ ∂Èı 2005;8:41-55. ¶·ÚÂÏ‹ÊıË: 24.09.2004 - ŒÁÈÓ ‰ÂÎÙ‹: 01.03.2005

element models. Most of them, however, were simplified and could not satisfactorily approach the real anatomical factors they attempted to simulate (Yoshida et al., 2001a). Finite element analysis requires that the Poisson ratio be known; this depends on the modulus of elasticity. Nevertheless, the study of material mechanical properties cannot provide reliable values for the modulus of elasticity, due to the high impact of the loading process history, the specimen preparation procedure and the testing conditions on the properties per se (Fung, 1993; Reported by Gioka C, Eliades T. Orthodontic dental intrusion: indications, histological changes, biomechanical principles and possible side effects. Hell Orthod Rev 2003:6:129-46). Finite element analysis also presupposes that materials are isotropic, that is, their response to a given load is not affected by the direction of loading. However, this is not true for biological materials, such as bone (Park and Lakes, 1992; Reported by Gioka C, Eliades T. Orthodontic dental intrusion: indications, histological changes, biomechanical principles and possible side effects. Hell Orthod Rev 2003:6:129-46). In recent years, it has been attempted to incorporate the structure of the periodontium into the finite element analyses. According to Qian et al. (2001), the direction and mechanical properties of periodontal fibers do not play an important role in determining the center of resistance. In their own analyses, Schneider et al. (2002) incorporated an algorithm in order to describe bone remodeling due to mechanical stimuli; however, according to the authors, several simplifications had to take place, due to lack of data concerning materials and their morphology.

Laser - holographic or strain gauges techniques were also used for studying tooth movement. Strain gauges are electrical extensometers attached to the points of a structure the movement of which we want to measure. Each extension results in increasing the strain gauge resistance and this can be measured electrically. The disadvantage of such techniques is that even the slightest movements of the head may significantly decrease the precision of tooth movement (Nagerl et al., 1991). According to McGuiness et al. (1991), strain gauges cannot be inserted in the periodontal membrane without running the risk of damaging it.

Most recent studies use magnets and magnetic sensors for determining the center of resistance and observing tooth movement (Yoshida et al., 2001a; 2001b).

‰ÔÓÙÈÔ‡. ŸÙ·Ó Ô ÏfiÁÔ˜ Ù˘ ÚÔ‹˜ ÚÔ˜ ÙËÓ ÂÊ·ÚÌÔ˙fiÌÂ-ÓË ‰‡Ó·ÌË ‚Ú›ÛÎÂÙ·È ÌÂٷ͇ 1 Î·È 7 Ô Ù‡Ô˜ Ù˘ ÌÂٷΛ-ÓËÛ˘ ÙÔ˘ ‰ÔÓÙÈÔ‡ Ô˘ ÂÈÙ˘Á¯¿ÓÂÙ·È Â›Ó·È ÂÏÂÁ¯fiÌÂÓË ·fiÎÏÈÛË, ÌÂٷ͇ 8 Î·È 10 ·Ú¿ÏÏËÏË ÌÂٷΛÓËÛË ÂÓÒ fiÙ·Ó Â›Ó·È ÌÂÁ·Ï‡ÙÂÚÔ˜ ·fi 10 ·Ú·ÙËÚÂ›Ù·È ÌÂٷΛÓËÛË Ù˘ Ú›˙·˜ (torque) (Proffit Î·È Fields, 2000).

ª ª∂∂££√√¢¢√√ππ ∫∫∞∞££√√ƒƒπ𙙪ª√√ÀÀ ∆∆√√ÀÀ ∫∫∂∂¡¡∆∆ƒƒ√√ÀÀ ∞∞¡¡∆∆ππ™™∆∆∞∞™™∏∏™™ °È· ÙÔÓ Î·ıÔÚÈÛÌfi ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘ ‰ÔÓÙÈÔ‡ ¯ÚËÛÈÌÔÔÈ‹ıËÎ·Ó ÔÏÏÔ› ÙÚfiÔÈ. √ÚÈṲ̂ÓÔÈ ÂÚ¢ÓËÙ¤˜ ÂÊ¿ÚÌÔÛ·Ó Ì·ıËÌ·ÙÈο ‹ Ê˘ÛÈο ÌÔÓ٤Ϸ ηıÒ˜ Î·È ÌÔÓ٤Ϸ ÂÂÚ·ÛÌ¤ÓˆÓ ÛÙÔȯ›ˆÓ (finite element models). ∆· ÂÚÈÛÛfiÙÂÚ· ÌÔÓ٤Ϸ fï˜ ‹Ù·Ó ·ÏÔÔÈË-̤ӷ Î·È ‰ÂÓ ÚÔÛ¤ÁÁÈ˙·Ó ÈηÓÔÔÈËÙÈο ÙÔ˘˜ Ú·ÁÌ·ÙÈ-ÎÔ‡˜ ·Ó·ÙÔÌÈÚ·ÁÌ·ÙÈ-ÎÔ‡˜ ·Ú¿ÁÔÓÙ˜ Ô˘ ÂȯÂÈÚÔ‡Û·Ó Ó· ÂÍÔ-ÌÔÈÒÛÔ˘Ó (Yoshida Î·È Û˘Ó., 2001a). ∏ ·Ó¿Ï˘ÛË ÙˆÓ ÂÂÚ·ÛÌ¤ÓˆÓ ÛÙÔȯ›ˆÓ ÚÔ¸Ôı¤ÙÂÈ ÙË ÁÓÒÛË ÙÔ˘ ÏfiÁÔ˘ Poisson Ô ÔÔ›Ô˜ ÂÍ·ÚÙ¿Ù·È ·fi ÙÔ Ì¤ÙÚÔ ÂÏ·ÛÙÈ-ÎfiÙËÙ·˜. ∞ÍÈfiÈÛÙ˜ fï˜ ÙÈ̤˜ ÁÈ· ÙÔ Ì¤ÙÚÔ ÂÏ·ÛÙÈÎfiÙËÙ·˜ ‰ÂÓ Â›Ó·È ‰˘Ó·ÙfiÓ Ó· ÂÍ·¯ıÔ‡Ó ·fi ÙË ÌÂϤÙË ÙˆÓ Ì˯·-ÓÈÎÒÓ È‰ÈÔÙ‹ÙˆÓ ÙˆÓ ˘ÏÈÎÒÓ ÏfiÁˆ Ù˘ ÌÂÁ¿Ï˘ Â›‰Ú·Û˘ ÙÔ˘ ÈÛÙÔÚÈÎÔ‡ ÊfiÚÙÈÛ˘, Ù˘ ‰È·‰Èηۛ·˜ ‰ËÌÈÔ˘ÚÁ›·˜ ‰ÔÎÈÌ›ˆÓ Î·È ÙˆÓ Û˘ÓıËÎÒÓ ‰ÔÎÈÌ·Û›·˜ ÛÙȘ ȉÈfiÙËÙ˜ ηı’ ·˘Ù¤˜ (Fung, 1993. ∞ӷʤÚÂÙ·È ·fi ÙÔ˘˜ Gioka C, Eliades T. Orthodontic dental intrusion: indications, histological changes, biomechanical principles, possible side effects. Hell Orthod Rev 2003:6:129-46). ∏ ·Ó¿Ï˘ÛË ÂÂÚ·ÛÌ¤ÓˆÓ ÛÙÔȯ›ˆÓ ÚÔ¸Ôı¤ÙÂÈ fiÙÈ Ù· ˘ÏÈο Â›Ó·È ÈÛfiÙÚÔ· ‰ËÏ·‰‹ Ë ·ÓÙ›‰Ú·Û‹ ÙÔ˘˜ Û ¤Ó· ‰Â‰Ô̤ÓÔ ÊÔÚ-Ù›Ô ‰ÂÓ ÂËÚ¿˙ÂÙ·È ·fi ÙËÓ Î·Ù‡ı˘ÓÛË ÊfiÚÙÈÛ˘. ∏ ·Ú·‰Ô¯‹ fï˜ ·˘Ù‹ ‰ÂÓ ÈÛ¯‡ÂÈ ÁÈ· ‚ÈÔÏÔÁÈο ˘ÏÈο fiˆ˜ ÙÔ ÔÛÙfi (Park Î·È Lakes, 1992. ∞ӷʤÚÂÙ·È ·fi ÙÔ˘˜ Gioka C, Eliades T. Orthodontic dental intrusion: indications, histological changes, biomechanical principles, possible side effects. Hell Orthod Rev 2003:6:129-46). ∆· ÙÂÏÂ˘Ù·›· ¯ÚfiÓÈ· ¤ÁÈÓ ÚÔÛ¿ıÂÈ· Ó· ÂÓۈ̷وı› Ë ‰ÔÌ‹ ÙÔ˘ ÂÚÈÔ‰ÔÓÙ›Ô˘ ÛÙȘ ·Ó·Ï‡ÛÂȘ ÂÂÚ·ÛÌ¤ÓˆÓ ÛÙÔȯ›ˆÓ. ™‡Ìʈӷ Ì ÙÔ˘˜ Qian Î·È Û˘Ó. (2001) Ë ‰È‡ı˘ÓÛË Î·È ÔÈ Ì˯·ÓÈΤ˜ ȉÈfiÙËÙ˜ ÙˆÓ ÈÓÒÓ ÙÔ˘ ÂÚÈÚÚÈ˙›Ô˘ ‰ÂÓ ¤¯Ô˘Ó ÛËÌ·ÓÙÈÎfi ÚfiÏÔ ÛÙÔÓ Î·ıÔÚÈÛÌfi ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘. √È Schneider Î·È Û˘Ó. (2002) ÂÓÛˆÌ¿ÙˆÛ·Ó ÛÙȘ ·Ó·Ï‡-ÛÂȘ ÙÔ˘˜ ¤Ó·Ó ·ÏÁfiÚÈıÌÔ ÁÈ· Ó· ÂÚÈÁÚ¿„Ô˘Ó ÙËÓ ·Ó·-‰È·ÌfiÚʈÛË ÙÔ˘ ÔÛÙÔ‡ ÌÂÙ¿ ·fi Ì˯·ÓÈο ÂÚÂı›ÛÌ·Ù·, ¤ÁÈÓ·Ó fï˜ Û‡Ìʈӷ Ì ÙÔ˘˜ ›‰ÈÔ˘˜ ÙÔ˘˜ Û˘ÁÁÚ·Ê›˜ ÔÚÈṲ̂Ó˜ ·ÏÔ˘ÛÙ‡ÛÂȘ ÏfiÁˆ ÂÏÏ›„ˆ˜ ÛÙÔȯ›ˆÓ ÁÈ·

Many of these techniques were used on human cadavers, where, nevertheless, the mechanical properties of the periodontal ligament differ. For this reason, synthetic substances, such as silicone, were used as substitutes for the periodontal ligament. Unfortunately, the physical properties of these substances are not similar to those of the periodontal ligament (Vanden Bulcke et al., 1987). LLOOCCAATTIIOONN OOFF TTHHEE CCEENNTTEERR OOFF RREESSIISSTTAANNCCEE OOFF AA SSIINNGGLLEE TTOOOOTTHH

Christiansen and Burstone (1969), as well as Burstone and Pryputniewicz (1980) report that the CR lies at a point that equals 40% of the tooth root length measured from the alveolar crest in a two-dimensional model with parabolic root shape or at 33% of the tooth root length in a three-dimensional model with paraboloid of revolution root shape.

Nikolai (1974) locates the CR at a distance equal to 45% of root length in a two-dimensional model made for theoretical analysis, whereas Davidian (1971) places it at 40% and Halazonetis (1996) at 42%.

These differences are due to the different mathematical models used by the various authors. More specifically, Nikolai (1974) used two-dimensional precise models of sphenoid (triangular) roots based on the theory of periodontal membrane elasticity in combination with the equilibrium equations of a rigid tooth. Davidian (1971) developed a simple model for determining the centers of resistance and rotation, simulating the periodontal membrane with springs. Finally, Halazonetis (1996) expanded this method in order to include non-linear properties of the periodontal membrane as well as shearing stresses, even in the case of an anisotropic synthesis of the periodontium (Provatidis and Toutountzakis, 1998).)

Nagerl et al. (1991), while intruding a canine into a plastic material, supposedly substituting for the periodontal ligament, found that the center of resistance of the tooth lies at an average height of 34% (27-42%) of its root length.

Tanne et al. (1988) and Vollmer et al. (1999), using finite element models, report that the CR lies at a distance equal to 24% and 42% of the root length of an upper central incisor and canine, respectively. In a later study by Tanne et al. (1991), the upper central incisor’s CR was calculated at 34% of this distance. According to Ù· ˘ÏÈο Î·È ÙË ÌÔÚÊÔÏÔÁ›· ÙÔ˘˜.

°È· ÙË ÌÂϤÙË Ù˘ ÌÂٷΛÓËÛ˘ ÙˆÓ ‰ÔÓÙÈÒÓ ¯ÚËÛÈÌÔÔÈ‹-ıËÎ·Ó Â›Û˘ ÔÏÔÁÚ·ÊÈΤ˜ Ù¯ÓÈΤ˜ (laser- holographic techniques) ‹ Ù¯ÓÈΤ˜ strain gauges. ∆· strain gauges Â›Ó·È ËÏÂÎÙÚÈο ÂÈÌË΢ÓÛÈfiÌÂÙÚ· Ù· ÔÔ›· ÂÈÎÔÏÏÔ‡-ÓÙ·È ÛÙ· ÛËÌ›· Ù˘ ‰ÔÌ‹˜ Ô˘ ÂÈı˘Ìԇ̠ӷ ÌÂÙÚ‹ÛÔ˘-Ì ÌÈ· ÌÂÙÚ‹ÛÔ˘-ÌÂٷΛÓËÛË. ∫¿ı ÂÈÌ‹Î˘ÓÛË ¤¯ÂÈ Û·Ó ·ÔÙ¤ÏÂÛÌ· ÙËÓ ·‡ÍËÛË Ù˘ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘ strain gauge, Ô˘ ÌÔÚ› Ó· ÌÂÙÚËı› ËÏÂÎÙÚÈο. ∆Ô ÌÂÈÔÓ¤ÎÙËÌ· ·˘ÙÒÓ ÙˆÓ Ù¯ÓÈ-ÎÒÓ ‹Ù·Ó fiÙÈ ·ÎfiÌ· Î·È ÔÈ ÈÔ ÌÈÎÚ¤˜ ÌÂÙ·ÎÈÓ‹ÛÂȘ Ù˘ ÎÂÊ·Ï‹˜ ÌÔÚÔ‡Ó Ó· ÌÂÈÒÛÔ˘Ó ÛËÌ·ÓÙÈο ÙËÓ ·ÎÚ›‚ÂÈ· Ù˘ ÌÂٷΛÓËÛ˘ ÙˆÓ ‰ÔÓÙÈÒÓ (Nagerl Î·È Û˘Ó., 1991). ™‡Ìʈӷ Ì ÙÔ˘˜ McGuiness Î·È Û˘Ó. (1991) ‰ÂÓ Â›Ó·È ‰˘Ó·Ù‹ Ë ÂÈÛ·ÁˆÁ‹ ÙˆÓ strain gauges ̤۷ ÛÙËÓ ÂÚÈÔ-‰ÔÓÙÈ΋ ÌÂÌ‚Ú¿ÓË ¯ˆÚ›˜ Ó· ÚÔ·„ÂÈ ÊıÔÚ¿. ™ÙȘ ÙÂÏÂ˘Ù·›Â˜ ¤Ú¢Ó˜ ÁÈ· ÙÔÓ Î·ıÔÚÈÛÌfi ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘, Î·È ÂÓ Á¤ÓÂÈ ÙËÓ ·Ú·Ù‹ÚËÛË Ù˘ ÌÂٷΛÓËÛ˘ ÙÔ˘ ‰ÔÓÙÈÔ‡ ¯ÚËÛÈÌÔÔÈÔ‡ÓÙ·È Ì·ÁÓ‹Ù˜ Î·È Ì·ÁÓËÙÈÎÔ› ·ÈÛıËÙ‹Ú˜ (Yoshida Î·È Û˘Ó., 2001a; 2001b). ¶ÔÏϤ˜ ·fi ·˘Ù¤˜ ÙȘ Ù¯ÓÈΤ˜ ¯ÚËÛÈÌÔÔÈ‹ıËÎ·Ó Û ·ÓıÚÒÈÓ· ÙÒÌ·Ù· ÛÙ· ÔÔ›· fï˜ ÔÈ Ì˯·ÓÈΤ˜ ȉÈfiÙË-Ù˜ ÙÔ˘ ÂÚÈÔ‰ÔÓÙÈÎÔ‡ Û˘Ó‰¤ÛÌÔ˘ Â›Ó·È ‰È·ÊÔÚÂÙÈΤ˜ ÌÂÙ¿ ÙÔ ı¿Ó·ÙÔ. °È· ÙÔ ÏfiÁÔ ·˘Ùfi ¯ÚËÛÈÌÔÔÈ‹ıËÎ·Ó ˆ˜ ˘Ô-ηٿÛٷٷ ÙÔ˘ ÂÚÈÔ‰ÔÓÙÈÎÔ‡ Û˘Ó‰¤ÛÌÔ˘ Û˘ÓıÂÙÈΤ˜ Ô˘Û›Â˜, fiˆ˜ Ë ÛÈÏÈÎfiÓË. ¢˘ÛÙ˘¯Ò˜ fï˜ ÔÈ Ô˘Û›Â˜ ·˘Ù¤˜ ‰ÂÓ ¤¯Ô˘Ó Ê˘ÛÈΤ˜ ȉÈfiÙËÙ˜ ·ÚfiÌÔȘ Ì ·˘Ù¤˜ ÙÔ˘ ÂÚÈÔ‰ÔÓÙÈÎÔ‡ Û˘Ó‰¤ÛÌÔ˘ (Vanden Bulcke Î·È Û˘Ó., 1987). £ £∂∂™™∏∏ ∆∆√√ÀÀ ∫∫∂∂¡¡∆∆ƒƒ√√ÀÀ ∞∞¡¡∆∆ππ™™∆∆∞∞™™∏∏™™ ∂∂¡¡√√™™ ¢¢√√¡¡∆∆ππ√√ÀÀ √È Christiansen Î·È Burstone (1969) ηıÒ˜ Î·È ÔÈ Burstone Î·È Pryputniewicz (1980) ·Ó·Ê¤ÚÔ˘Ó fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ‚Ú›ÛÎÂÙ·È Û ¤Ó· ÛËÌÂ›Ô ›ÛÔ Ì ÙÔ 40% ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ ÙÔ˘ ‰ÔÓÙÈÔ‡ ·fi ÙË Ê·ÙÓȷ΋ ·ÎÚÔ-ÏÔÊ›· Û ¤Ó· ÌÔÓÙ¤ÏÔ ‰˘Ô ‰È·ÛÙ¿ÛÂˆÓ Ì ·Ú·‚ÔÏÈÎfi Û¯‹Ì· Ú›˙·˜ ‹ ÛÙÔ 33% ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ ÙÔ˘ ‰ÔÓÙÈÔ‡ Û ¤Ó· ÙÚÈۉȿÛÙ·ÙÔ ÌÔÓÙ¤ÏÔ Ì ڛ˙· Û ۯ‹Ì· ·Ú·‚Ô-ÏÔÂȉԇ˜ ÂÎ ÂÚÈÛÙÚÔÊ‹˜ (paraboloid of revolution). √ Nikolai (1974) ηıÔÚ›˙ÂÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘ ‰ÔÓÙÈÔ‡ Û ·fiÛÙ·ÛË ›ÛË Ì ÙÔ 45% ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ Û ¤Ó· ‰ÈۉȿÛÙ·ÙÔ ÌÔÓÙ¤ÏÔ ÁÈ· ıˆÚËÙÈ΋ ·Ó¿Ï˘ÛË, Ô Davidian (1971) ÛÙÔ 40%, ÂÓÒ Ô Halazonetis (1996) ÛÙÔ 42%. √È ‰È·ÊÔÚ¤˜ ·˘Ù¤˜ ÔÊ›ÏÔÓÙ·È ÛÙ· ·ÓfiÌÔÈ· Ì·ıËÌ·ÙÈο ÌÔÓ٤Ϸ Ô˘ ¯ÚËÛÈÌÔÔ›ËÛ·Ó ÔÈ ÂÚ¢ÓËÙ¤˜. ∂ȉÈÎfiÙÂÚ· Ô

Nikolai (1974) ¯ÚËÛÈÌÔÔ›ËÛ ‰ÈۉȿÛٷٷ ·ÎÚÈ‚‹ ÌÔÓÙ¤-Ï· ÛÊËÓÔÂȉÒÓ (ÙÚÈÁˆÓÈÎÒÓ) ÚÈ˙ÒÓ Ì ‚¿ÛË ÙË ıˆڛ· Ù˘ ÂÏ·ÛÙÈÎfiÙËÙ·˜ Ù˘ ÂÚÈÔ‰ÔÓÙÈ΋˜ ÌÂÌ‚Ú¿Ó˘ ÛÂ Û˘Ó-‰˘·ÛÌfi Ì ÙȘ ÂÍÈÛÒÛÂȘ ÈÛÔÚÚÔ›·˜ ÙÔ˘ ¿Î·ÌÙÔ˘ ‰ÔÓÙÈ-Ô‡, Ô Davidian (1971) ·Ó¤Ù˘Í ¤Ó· ·Ïfi ÌÔÓÙ¤ÏÔ ÚÔÛ-‰ÈÔÚÈÛÌÔ‡ ÙˆÓ Î¤ÓÙÚˆÓ ·ÓÙ›ÛÙ·Û˘ Î·È ÂÚÈÛÙÚÔÊ‹˜ ÂÍÔ-ÌÔÈÒÓÔÓÙ·˜ ÙËÓ ÂÚÈÔ‰ÔÓÙÈ΋ ÌÂÌ‚Ú¿ÓË Ì ÂÏ·Ù‹ÚÈ·, ÂÓÒ Ô Halazonetis (1996) Â¤ÎÙÂÈÓ ·˘Ù‹ ÙË Ì¤ıÔ‰Ô ÒÛÙ ӷ Û˘ÌÂÚÈÏ¿‚ÂÈ ÌË ÁÚ·ÌÌÈΤ˜ ȉÈfiÙËÙ˜ Ù˘ ÂÚÈÔ‰ÔÓÙÈ΋˜ ÌÂÌ‚Ú¿Ó˘ ηıÒ˜ Î·È ‰È·ÙÌËÙÈΤ˜ Ù¿ÛÂȘ Î·È ÛÙËÓ ÂÚ›-ÙˆÛË ·ÓÈÛÔÙÚÔÈ΋˜ Û‡ÓıÂÛ˘ ÙÔ˘ ÂÚÈÔ‰ÔÓÙ›Ô˘ (Provatidis Î·È Toutountzakis, 1998). √È Nagerl Î·È Û˘Ó. (1991) ÂÌ‚˘ı›˙ÔÓÙ·˜ ¤Ó·Ó ΢Ófi‰ÔÓÙ· Û Ï·ÛÙÈÎfi ˘ÏÈÎfi ÙÔ ÔÔ›Ô ˘ÔÙ›ıÂÙ·È fiÙÈ ˘ÔηıÈÛÙ¿ ÙÔÓ ÂÚÈÔ‰ÔÓÙÈÎfi Û‡Ó‰ÂÛÌÔ ‚Ú‹Î·Ó fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›-ÛÙ·Û˘ ÙˆÓ ‰ÔÓÙÈÒÓ ‚Ú›ÛÎÂÙ·È Û ¤Ó· ̤ÛÔ ‡„Ô˜ 34% (27-42%) ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ ÙÔ˘.

√È Tanne Î·È Û˘Ó. (1988) Î·È ÔÈ Vollmer Î·È Û˘Ó. (1999) ¯ÚËÛÈÌÔÔÈÒÓÙ·˜ ÌÔÓ٤Ϸ ÂÂÚ·ÛÌ¤ÓˆÓ ÛÙÔȯ›ˆÓ (finite elements models) ·Ó·Ê¤ÚÔ˘Ó fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›-ÛÙ·Û˘ ‚Ú›ÛÎÂÙ·È Û ·fiÛÙ·ÛË ›ÛË Ì 24% Î·È 42% ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ ÙÔ˘ ÎÂÓÙÚÈÎÔ‡ ¿Óˆ ÙÔ̤· Î·È Î˘Ófi‰ÔÓÙ· ·ÓÙ›ÛÙÔȯ·. ™Â Ì›· ÌÂÙ·ÁÂÓ¤ÛÙÂÚË ÌÂϤÙË ÙˆÓ Tanne Î·È Û˘Ó. (1991) ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘ ÎÂÓÙÚÈÎÔ‡ ¿Óˆ ÙÔ̤· ˘ÔÏÔÁ›ÛÙËΠÛÙÔ 34%. ∆· ‰È·ÊÔÚÂÙÈο ·˘Ù¿ ·Ô-ÙÂϤÛÌ·Ù· Â›Ó·È Â‡ÎÔÏÔ Ó· ÚÔ·„Ô˘Ó Û‡Ìʈӷ Ì ÙÔ˘˜ Provatidis Î·È Toutountzakis (1998) Â¿Ó ÂËÚ·ÛÙ› Ì›· ·fi ÙȘ ·ÎfiÏÔ˘ı˜ Ù¤ÛÛÂÚȘ ·Ú·Ì¤ÙÚÔ˘˜: ·) ∆Ô Ì¤ÁÂıÔ˜ ÙÔ˘ ÌÔÓÙ¤ÏÔ˘ Á‡Úˆ ·fi ÙÔ ÂͤٷÛË ‰fiÓÙÈ ‚) ∆Ô Â›‰Ô˜ ÙˆÓ ÔÚÈ·ÎÒÓ Û˘ÓıËÎÒÓ. Á) √ ‚·ıÌfi˜ ÂÎϤÙ˘ÓÛ˘ ÙÔ˘ ϤÁÌ·ÙÔ˜ ÙˆÓ ÂÂÚ·Ṳ̂-ÓˆÓ ÛÙÔȯ›ˆÓ Ô˘ ··ÈÙÂ›Ù·È ÁÈ· ÙË Ï‹„Ë ·ÍÈfiÈÛÙˆÓ ·ÔÙÂÏÂÛÌ¿ÙˆÓ. ∞Ú·È¿ ϤÁÌ·Ù· Ô‰ËÁÔ‡Ó Û ·Ó·ÎÚÈ-‚‹ ·ÔÙÂϤÛÌ·Ù·. ‰) √È ÙÈ̤˜ ÙˆÓ Ì˯·ÓÈÎÒÓ È‰ÈÔÙ‹ÙˆÓ ÙˆÓ ˘ÏÈÎÒÓ. √È Poppe Î·È Û˘Ó. (2002) ‚Ú‹Î·Ó fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ÌÔÓfiÚÚÈ˙ˆÓ ‰ÔÓÙÈÒÓ ‚Ú›ÛÎÂÙ·È Û ·fiÛÙ·ÛË ›ÛË Ì ÙÔ 42% ÙÔ˘ ‡„Ô˘˜ ÙÔ˘ Ê·ÙÓÈ·ÎÔ‡ ÂÙ¿ÏÔ˘.

√È Yoshida Î·È Û˘Ó. (2001a) ·Ó·Ê¤ÚÔ˘Ó fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘ ÎÂÓÙÚÈÎÔ‡ ¿Óˆ ÙÔ̤· ηٿ ÙË ‰È¿ÚÎÂÈ· Ù˘ ˘ÂÚÒÈ·˜ ÌÂٷΛÓËÛ‹˜ ÙÔ˘ ‚Ú›ÛÎÂÙ·È Û ·fiÛÙ·ÛË ›ÛË ÂÚ›Ô˘ Ì ٷ 2/3 ÙÔ˘ ˘ÂÚÒÈÔ˘ ‡„Ô˘˜ fiÙ·Ó ·˘Ùfi ÌÂÙÚȤ-Ù·È ·fi ÙÔ ·ÎÚÔÚÚ›˙Èfi ÙÔ˘ ¤ˆ˜ ÙË Ê·ÙÓȷ΋ ·ÎÚÔÏÔÊ›· Î·È ÂÔ̤ӈ˜ ÂÍ·ÚÙ¿Ù·È ·fi ÙÔ Â›Â‰Ô ÙÔ˘ ÔÛÙÔ‡ Ô˘ ‚Ú›ÛÎÂÙ·È ˘ÂÚÒÈ·. √È Pedersen Î·È Û˘Ó. (1991) ÈÛ¯˘Ú›˙ÔÓÙ·È fiÙÈ, Û ¿ÙÔÌÔ

Provatidis and Toutountzakis (1998), these different results are easily derived, if one of the following parameters is affected:

a) The size of the model surrounding the examined tooth.

b) The type of terminal conditions.

c) The degree of refinement of the finite element mesh that is required for reliable results. Coarse meshes lead to inaccurate results.

d) The values of material mechanical properties.

Poppe et al. (2002) found that the CR of single-rooted teeth lies at a distance equal to 42% of the alveolar plate height.

Yoshida et al. (2001a) report that the CR of a maxillary central incisor during its palatal movement depends on the palatal osseous level and lies at a distance approximately equal to 2/3 of the palatal height, when the latter is measured from the tooth apex to the alveolar crest.

Pedersen et al. (1991) claim that, in a 20-year old individual with normal root length, the CR of lower premolars lies at 40% of their root length.

Consequently, most studies locate the CR of a single-rooted tooth at 33-42% of its root length from the alveolar tip (crest). In a tooth with a 10-mm root, such as the upper central incisor, this difference is less than 1 mm (0.9 mm). However, force systems with less than 1mm precision are not easy to create in a clinical situation. Practically, this means that forces applied on the tooth will always create a moment.

Furthermore, tooth movement following force application may be distinguished in two phases: primary, due to tooth movement within the periodontal membrane and secondary, which follows and is due to bone remodeling (bone apposition and resorption) (Burstone et al., 1982). However, the center of resistance may not be the same during these two phases of tooth movement (Halazonetis, 1996). As a consequence, tooth movement may differ from the one initially planned. Nevertheless, exact CR location also depends on other factors, such as root length and osseous height around the tooth. The effect of root length is greater than that of bone height. The center of resistance in a canine may be located at 45% of its root length, whereas in a smaller tooth with a 12-mm root may lie at 35% of this distance (Schneider et al., 2002). When root resorption is observed, the CR is displaced toward the tooth crown, due to the

decreased root length as well as the change of root shape (Schneider et al., 2002). Yoshida et al. (2001a) report that, when palatal forces are applied, the CR of an upper central incisor mainly depends on the height of the palatal osseous plate and minimally on that of the labial plate. The center of resistance also depends on the direction of loading. According to Nagerl et al. (1991), CR location ranges from 27% to 42% of root length, depending on the direction of the applied force. Halazonetis (1996) claims that this change is smaller (4%) in a two-dimensional tooth-periodontium model with anisotropic periodontal ligament.

Vander Bulcke et al. (1986) report that precise CR location may vary depending on tooth morphology, type of periodontal ligament, quality of surrounding bone, tissue response to applied forces, degree of humidity of neighboring osseous structures and tooth axial inclination without, however, mentioning any experimental evidence.

According to Stoeckli and Teuscher (1985), the CR of any unit can only be determined precisely from the clinical situation occurring after force application, as it depends on many factors.

Clinical results, when single-rooted teeth are moved distally, sometimes confirm the theoretical models, but sometimes they do not. Bourauel and Drescher (1994) report that experimental and clinical results following distal movement of maxillary canines were highly consistent. On the contrary, Vollmer et al. (1999) claim that tooth translation is difficult to achieve, because there are tuberosities and cavities on the tooth root affecting stress and strain distribution and, consequently, tooth movement.

Finally, the CR of multi-rooted teeth lies near the root furcation (Moyers, 1988; Bassigny, 1983). Pedersen et al. (1991) claim that CR location in mandibular molars depends on tooth geometry, root length, osseous level and age.

It becomes clear that there are different views concerning CR location. The main reasons are the different methodologies used by authors and the different values of parameters defining CR location (e.g. root length, root shape, force direction, alveolar plate height, etc.). No method is perfect and all of them have advantages and disadvantages, as presented at the beginning of this paper. It is also difficult to standardize all factors affecting CR location, on the one hand, because there are ËÏÈΛ·˜ 20 ÂÙÒÓ Î·È ÌÂ Ê˘ÛÈÔÏÔÁÈÎfi Ì‹ÎÔ˜ Ú›˙·˜, ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ Î¿Ùˆ ÚÔÁÔÌÊ›ˆÓ ‚Ú›ÛÎÂÙ·È ÛÙÔ 40% ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ ™˘ÓÂÒ˜, ÔÈ ÂÚÈÛÛfiÙÂÚ˜ ¤Ú¢Ó˜ ÙÔÔıÂÙÔ‡Ó ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘ ÌÔÓfiÚÚÈ˙Ô˘ ‰ÔÓÙÈÔ‡ ÛÙÔ 33-42% ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ ·fi ÙË Ê·ÙÓȷ΋ ·Ú˘Ê‹ (·ÎÚÔÏÔÊ›·). ™Â ¤Ó· ‰fiÓÙÈ Ì‹ÎÔ˘˜ Ú›˙·˜ 10 mm fiˆ˜ Â›Ó·È Ô ÎÂÓÙÚÈÎfi˜ ¿Óˆ ÙÔ̤·˜ Ë ‰È·ÊÔÚ¿ ·˘Ù‹ Â›Ó·È ÌÈÎÚfiÙÂÚË ÙÔ˘ 1 mm (0,9 mm). ŒÓ· Û‡ÛÙËÌ·, fï˜, ‰˘Ó¿ÌÂˆÓ Ì ·ÎÚ›‚ÂÈ· ÌÈÎÚfiÙÂÚË ÙÔ˘ 1 mm Â›Ó·È ‰‡ÛÎÔÏÔ Ó· ηٷÛ΢·ÛÙ› ÛÙËÓ Î·ıËÌÂÚÈÓ‹ ÎÏÈÓÈ΋ Ú¿ÍË. ¶Ú·ÎÙÈο ·˘Ùfi ÛËÌ·›ÓÂÈ fiÙÈ ÔÈ ‰˘Ó¿ÌÂȘ Ô˘ ÂÊ·ÚÌfi˙ÔÓÙ·È ÛÙÔ ‰fiÓÙÈ ı· ¤¯Ô˘Ó ۯ‰fiÓ ¿ÓÙ· Ì›· ÚÔ‹. ∂ÈϤÔÓ, Ë Î›ÓËÛË ÙÔ˘ ‰ÔÓÙÈÔ‡ ÌÂÙ¿ ÙËÓ ÂÊ·ÚÌÔÁ‹ οÔÈ·˜ ‰‡Ó·Ì˘ ÌÔÚ› Ó· ‰È·ÎÚÈı› Û ‰‡Ô Ê¿ÛÂȘ: ÙËÓ ÚˆÙÔÁÂÓ‹ Ë ÔÔ›· ÔÊ›ÏÂÙ·È ÛÙËÓ ÌÂٷΛÓËÛË ÙÔ˘ ‰ÔÓÙÈ-Ô‡ ̤۷ ÛÙËÓ ÂÚÈÔ‰ÔÓÙÈ΋ ÌÂÌ‚Ú¿ÓË Î·È ÙË ‰Â˘ÙÂÚÔÁÂÓ‹ Ë ÔÔ›· ·ÎÔÏÔ˘ı› Î·È ÔÊ›ÏÂÙ·È ÛÙËÓ Â·Ó·‰È·ÌfiÚʈÛË ÙÔ˘ ÔÛÙÔ‡ (ÂÓ·fiıÂÛË Î·È ·ÔÚÚfiÊËÛË) (Burstone Î·È Û˘Ó., 1982). ∆Ô Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ‰ÔÓÙÈÒÓ fï˜ ÂÓ‰¤¯ÂÙ·È Ó· ÌË Û˘Ì›ÙÂÈ ÛÙȘ ‰‡Ô Ê¿ÛÂȘ˜ Ù˘ ΛÓËÛ˘ ÙÔ˘ ‰ÔÓÙÈÔ‡ (Halazonetis, 1996). ∫·Ù¿ Û˘Ó¤ÂÈ· Ë Î›ÓËÛË ÙÔ˘ ‰ÔÓÙÈÔ‡ ÌÔÚ› Ó· Â›Ó·È ‰È·ÊÔÚÂÙÈ΋ ·fi ·˘Ù‹ Ô˘ ¤¯ÂÈ Û¯Â‰È·ÛÙ›. ∏ ·ÎÚÈ‚‹˜ ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘, fï˜, ÂÍ·ÚÙ¿Ù·È Î·È ·fi ¿ÏÏÔ˘˜ ·Ú¿ÁÔÓÙ˜, fiˆ˜ ÙÔ Ì‹ÎÔ˜ Ù˘ Ú›˙·˜ ÙÔ˘ ‰ÔÓÙÈÔ‡ Î·È ÙÔ ‡„Ô˜ ÙÔ˘ ÔÛÙÔ‡ Ô˘ ÂÚÈ‚¿ÏÏÂÈ ÙÔ ‰fiÓÙÈ. ªÂÁ·Ï‡ÙÂÚË Â›‰Ú·ÛË ¤¯ÂÈ ÙÔ Ì‹ÎÔ˜ Ù˘ Ú›˙·˜ ·fi ÙÔ ‡„Ô˜ ÙÔ˘ ÔÛÙÔ‡. ™Â ¤Ó·Ó ΢Ófi‰ÔÓÙ· ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÌÔÚ› Ó· ‚Ú›ÛÎÂÙ·È ÛÙÔ 45% ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ ÙÔ˘ ‰ÔÓÙÈÔ‡ ÂÓÒ Û ¤Ó· ÌÈÎÚfiÙÂÚÔ ‰fiÓÙÈ Ì ‡„Ô˜ Ú›˙·˜ 12 mm ÛÙÔ 35% ÙÔ˘ Ì‹ÎÔ˘˜ (Schneider Î·È Û˘Ó., 2002). ŸÙ·Ó ·Ú·ÙËÚÂ›Ù·È ·ÔÚÚfiÊËÛË Ù˘ Ú›˙·˜ ÂÓfi˜ ‰ÔÓÙÈÔ‡ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÌÂÙ·ÙÔ›˙ÂÙ·È ÚÔ˜ ÙË Ì‡ÏË ÙÔ˘ ‰ÔÓÙÈ-Ô‡ fi¯È ÌfiÓÔ ÂÍ·ÈÙ›·˜ Ù˘ Ì›ˆÛ˘ ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ ·ÏÏ¿ Î·È Ù˘ ·ÏÏ·Á‹˜ ÙÔ˘ Û¯‹Ì·Ùfi˜ Ù˘ (Schneider Î·È Û˘Ó., 2002). √È Yoshida Î·È Û˘Ó. (2001a) ·Ó·Ê¤ÚÔ˘Ó fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙÔ˘ ÎÂÓÙÚÈÎÔ‡ ¿Óˆ ÙÔ̤· fiÙ·Ó ÂÊ·Ú-Ìfi˙ÔÓÙ·È ˘ÂÚÒȘ ‰˘Ó¿ÌÂȘ ÂÍ·ÚÙ¿Ù·È Î˘Ú›ˆ˜ ·fi ÙÔ ‡„Ô˜ ÙÔ˘ ˘ÂÚÒÈÔ˘ ÂÙ¿ÏÔ˘ Î·È ÂÏ¿¯ÈÛÙ· ·fi ÙÔ ‡„Ô˜ ÙÔ˘ ¯ÂÈÏÈÎÔ‡ ÔÛÙÈÎÔ‡ ÂÙ¿ÏÔ˘.

∆Ô Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÂÍ·ÚÙ¿Ù·È Â›Û˘ ·fi ÙË ‰È‡ı˘ÓÛË Ù˘ ÊfiÚÙÈÛ˘ (loading). ™‡Ìʈӷ Ì ÙÔÓ Nagerl Î·È Û˘Ó. (1991) Ë ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ ÌÂÙ·‚¿ÏÏÂÙ·È ·fi ÙÔ 27-42% ÙÔ˘ Ì‹ÎÔ˘˜ Ù˘ Ú›˙·˜ ·Ó¿ÏÔÁ· Ì ÙË ‰È‡ı˘Ó-ÛË Ù˘ ÂÊ·ÚÌÔ˙fiÌÂÓ˘ ‰‡Ó·Ì˘. √ Halazonetis (1996) ÛÂ

¤Ó· ‰ÈۉȿÛÙ·ÙÔ ÌÔÓÙ¤ÏÔ ‰ÔÓÙÈÔ‡ – ÂÚÈÔ‰ÔÓÙ›Ô˘ Ì ·ÓÈ-ÛfiÙÚÔÔ ÂÚÈÔ‰ÔÓÙÈÎfi Û‡Ó‰ÂÛÌÔ ÈÛ¯˘Ú›˙ÂÙ·È fiÙÈ Ë ÌÂÙ·-‚ÔÏ‹ ·˘Ù‹ Â›Ó·È ÌÈÎÚfiÙÂÚË (4%).

√È Vander Bulcke Î·È Û˘Ó. (1986) ·Ó·Ê¤ÚÔ˘Ó fiÙÈ Ë ·ÎÚÈ-‚‹˜ ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ ÌÔÚ› Ó· ÌÂÙ·‚ÏËı› ·Ó¿ÏÔÁ· Ì ÙË ÌÔÚÊÔÏÔÁ›· ÙÔ˘ ‰ÔÓÙÈÔ‡, ÙÔ Â›‰Ô˜ ÙÔ˘ ÂÚÈÔ‰ÔÓÙÈÎÔ‡ Û˘Ó‰¤ÛÌÔ˘, ÙËÓ ÔÈfiÙËÙ· ÙÔ˘ ÂÚÈ‚¿ÏÏÔ-ÓÙÔ˜ ÔÛÙÔ‡, ÙËÓ ÈÛÙÈ΋ ·ÓÙ›‰Ú·ÛË ÛÙȘ ·ÛÎÔ‡ÌÂÓ˜ ‰˘Ó¿-ÌÂȘ, ÙËÓ ÂʇÁÚ·ÓÛË ÙˆÓ ·Ú·Î›ÌÂÓˆÓ ÔÛÙÈÎÒÓ ‰ÔÌÒÓ Î·È ÙËÓ ·ÍÔÓÈ΋ ÎÏ›ÛË ÙÔ˘ ‰ÔÓÙÈÔ‡ ¯ˆÚ›˜ fï˜ Ó· ·Ó·Ê¤-ÚÔ˘Ó ÂÈÚ·Ì·ÙÈο ‰Â‰Ô̤ӷ Ô˘ Ó· ÙÔ ÛÙËÚ›˙Ô˘Ó. ™‡Ìʈӷ Ì ÙÔ˘˜ Stoeckli Î·È Teuscher (1985) ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÔÔÈ·Û‰‹ÔÙ ÌÔÓ¿‰·˜, ÂÂȉ‹ ÂÍ·ÚÙ¿Ù·È ·fi ÔÏÏÔ‡˜ ·Ú¿ÁÔÓÙ˜, ‰ÂÓ ÌÔÚ› Ó· ÂÓÙÔÈÛÙ› Ì ·ÎÚ›-‚ÂÈ· ·Ú¿ ÌfiÓÔ ·fi ÙËÓ ÎÏÈÓÈ΋ ÂÈÎfiÓ· ÌÂÙ¿ ÙËÓ ÂÊ·ÚÌÔ-Á‹ Ù˘ ‰‡Ó·Ì˘.

∆· ÎÏÈÓÈο ·ÔÙÂϤÛÌ·Ù· fiÙ·Ó ÂȯÂÈÚÂ›Ù·È ÌÂٷΛÓËÛË ÚÔ˜ Ù· ¿ˆ ÙˆÓ ÌÔÓfiÚÚÈ˙ˆÓ ‰ÔÓÙÈÒÓ ¿ÏϘ ÊÔÚ¤˜ ÂÈ-‚‚·ÈÒÓÔ˘Ó Ù· ıˆÚËÙÈο ÌÔÓ٤Ϸ Î·È ¿ÏϘ fi¯È. √È Bourauel Î·È Drescher (1994) ·Ó·Ê¤ÚÔ˘Ó fiÙÈ ÁÈ· ÙËÓ ¿ˆ ÌÂٷΛÓËÛË ÙÔ˘ ¿Óˆ ΢Ófi‰ÔÓÙ· Ù· ÂÈÚ·Ì·ÙÈο Î·È ÎÏÈÓÈ-ο ·ÔÙÂϤÛÌ·Ù· ·ÓÙÈÛÙÔÈ¯Ô‡Û·Ó Û ÌÂÁ¿ÏÔ ‚·ıÌfi. ∞ÓÙ›-ıÂÙ· ÔÈ Vollmer Î·È Û˘Ó. (1999) ÈÛ¯˘Ú›˙ÔÓÙ·È fiÙÈ Â›Ó·È ‰‡ÛÎÔÏÔ Ó· ÂÈÙ¢¯ı› ·Ú¿ÏÏËÏË ÌÂٷΛÓËÛË ÙÔ˘ ‰ÔÓÙÈ-Ô‡ ÂÂȉ‹ Ë Ú›˙· ÙÔ˘ ·ÚÔ˘ÛÈ¿˙ÂÈ ÂÍÔÁÎÒÌ·Ù· Î·È ÎÔÈÏfi-ÙËÙ˜ ÔÈ Ôԛ˜ ÂËÚ¿˙Ô˘Ó ÙËÓ Î·Ù·ÓÔÌ‹ ÙˆÓ Ù¿ÛÂˆÓ Î·È ÙˆÓ ȤÛÂˆÓ Î·È ÂÔ̤ӈ˜ ÙËÓ Î›ÓËÛË ÙÔ˘ ‰ÔÓÙÈÔ‡. ∆¤ÏÔ˜, ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ‰ÔÓÙÈÒÓ Ì ÔÏϤ˜ Ú›˙˜ (multirooted teeth) ‚Ú›ÛÎÂÙ·È ÎÔÓÙ¿ ÛÙËÓ ¤ÓˆÛË ÙˆÓ ÚÈ˙ÒÓ (Moyers, 1988; Bassigny, 1983). √È Pedersen Î·È Û˘Ó. (1991) ˘ÔÛÙËÚ›˙Ô˘Ó fiÙÈ Ë ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›-ÛÙ·Û˘ ÙÔ˘ οو ÁÔÌÊ›Ô˘ ÂÍ·ÚÙ¿Ù·È ·fi ÙË ÁˆÌÂÙÚ›· ÙÔ˘ ‰ÔÓÙÈÔ‡, ÙÔ Ì‹ÎÔ˜ Ù˘ Ú›˙·˜, ÙÔ Â›Â‰Ô ÙÔ˘ ÔÛÙÔ‡ Î·È ÙËÓ ËÏÈΛ· ÙÔ˘ ·ÙfiÌÔ˘. ∂›Ó·È Ê·ÓÂÚfi fiÙÈ ÔÈ Û˘ÁÁÚ·Ê›˜ ‰ÂÓ Û˘ÌʈÓÔ‡Ó ÛÙÔÓ Î·ıÔÚÈÛÌfi ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘. √È ÏfiÁÔÈ Â›Ó·È Î˘Ú›ˆ˜ Ë ‰È·ÊÔÚÂÙÈ΋ ÌÂıÔ‰ÔÏÔÁ›· Ô˘ ·ÎÔÏÔ˘ıÔ‡Ó ÔÈ ÂÚ¢ÓË-Ù¤˜ ηıÒ˜ Î·È ÔÈ ‰È·ÊÔÚÂÙÈΤ˜ ÙÈ̤˜ ÙˆÓ ·Ú·Ì¤ÙÚˆÓ Ô˘ ηıÔÚ›˙Ô˘Ó ÙËÓ ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ (.¯. ÙÔ Ì‹ÎÔ˜ Ù˘ Ú›˙·˜, ÙÔ Û¯‹Ì· Ù˘, Ë ‰È‡ı˘ÓÛË ÙˆÓ ‰˘Ó¿ÌÂ-ˆÓ, ÙÔ ‡„Ô˜ ÙÔ˘ Ê·ÙÓÈ·ÎÔ‡ ÂÙ¿ÏÔ˘ Î.Ï..). ∫·Ì›· ̤ıÔ-‰Ô˜ ‰ÂÓ Â›Ó·È Ù¤ÏÂÈ·, fiϘ ·ÚÔ˘ÛÈ¿˙Ô˘Ó ÔÚÈṲ̂ӷ ÌÂÈÔ-ÓÂÎÙ‹Ì·Ù· Î·È ÏÂÔÌÂÈÔ-ÓÂÎÙ‹Ì·Ù· Ù· ÔÔ›· ·Ó·Ï‡ÔÓÙ·È ÛÙËÓ ·Ú¯‹ ÙÔ˘ ¿ÚıÚÔ˘. ∂›Ó·È ‰‡ÛÎÔÏÔ Â›Û˘ Ó· Ù˘ÔÔÈË-ıÔ‡Ó fiÏÔÈ ÔÈ ·Ú¿ÁÔÓÙ˜ Ô˘ ÂËÚ¿˙Ô˘Ó ÙË ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ ·ÊÂÓfi˜ ÌÂÓ ÂÂȉ‹ Â›Ó·È ÔÏÏÔ›,

·ÊÂ-many factors involved and, on the other hand, because some of them may not have been or cannot yet be investigated, such as the quality of bone surrounding a tooth. For all the above reasons, it is difficult to design future research. New research is needed in order to identify factors that may affect CR location, such as type of periodontal ligament, bone quality, tooth inclination, etc. Research must be performed on living organisms, whenever possible, in order to avoid simplifications involving bone and periodontium. Such research is now feasible (Yoshida et al., 2001a; 2001b).

LLOOCCAATTIIOONN OOFF TTHHEE CCEENNTTEERR OOFF RREESSIISSTTAANNCCEE OOFF AA GGRROOUUPP O

OFF TTEEEETTHH

During orthodontic treatment it is often necessary to move a group of teeth in a specific direction. The orthodontist should know the center of resistance of this tooth group in order to effectively achieve such movement.

1

1.. CCeenntteerr ooff rreessiissttaannccee ooff aanntteerriioorr mmaaxxiillllaarryy tteeeetthh C

CRR llooccaattiioonn dduurriinngg iinnttrruussiioonn

Anterior tooth intrusion is often the goal in patients with gummy smile or short upper lip or in patients with increased mandibular plane angle (Burstone, 1977). Dermaut and Vanden Bulcke (1986) used brackets and the Begg technique to study dental intrusion in dry skulls. The CR of the four upper incisors is distal to the upper laterals, whereas the CR of the six upper anterior teeth is distal to the canines. However, moments and independent tooth movements are observed, especially when the system includes two teeth and to a lesser extent when all six anterior teeth are included. For this reason, it is impossible to find the CR of the two central incisors using this technique (Dermaut and Vanden Bulcke, 1986). Toutountzakis and Mavreas (1989), in order to manage these movements in clinical practice, recommend that incisors be tied together with a figure-eight stainless steel ligature.

Vanden Bulcke et al. (1986) used the same method, but intruded teeth within a metal splint. The center of resistance of upper central incisors during intrusion lies on a line parallel to the mid-sagittal plane on a point situated at the distal half of the canines, whereas the CR of all four maxillary incisors is located on a line

Ù¤ÚÔ˘ ‰Â ÂÂȉ‹ οÔÈÔÈ Èı·ÓfiÓ Ó· ÌËÓ ¤¯Ô˘Ó ÂÚ¢ÓËı› ‹ Ó· ÌËÓ ÌÔÚÔ‡Ó Ó· ÂÚ¢ÓËıÔ‡Ó ·ÎfiÌ· fiˆ˜ .¯. Ë ÔÈ-fiÙËÙ· ÙÔ˘ ÔÛÙÔ‡ Ô˘ ÂÚÈ‚¿ÏÏÂÈ ÙÔ ‰fiÓÙÈ. °È· fiÏÔ˘˜ ·˘ÙÔ‡˜ ÙÔ˘˜ ÏfiÁÔ˘˜ Ô Û¯Â‰È·ÛÌfi˜ ÙˆÓ ÌÂÏÏÔÓÙÈÎÒÓ ÂÚ¢-ÓÒÓ Â›Ó·È ·ÚÎÂÙ¿ ‰‡ÛÎÔÏÔ˜. ÃÚÂÈ¿˙ÔÓÙ·È Ó¤Â˜ ÂÚ¢ÓËÙÈΤ˜ ÚÔÛ¿ıÂȘ ÁÈ· ÙÔ˘˜ ·Ú¿ÁÔÓÙ˜ Ô˘ Èı·ÓfiÓ Ó· ÂËÚÂ-¿˙Ô˘Ó ÙË ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ fiˆ˜ ÙÔ Â›‰Ô˜ ÙÔ˘ ÂÚÈÔ‰ÔÓÙÈÎÔ‡ Û˘Ó‰¤ÛÌÔ˘, Ë ÔÈfiÙËÙ· ÙÔ˘ ÔÛÙÔ‡, Ë ÎÏ›ÛË ÙÔ˘ ‰ÔÓÙÈÔ‡ Î.Ï.. √È ¤Ú¢Ó˜ Ú¤ÂÈ Ó· Á›ÓÔÓÙ·È Û ˙ÒÓÙ˜ ÔÚÁ·ÓÈÛÌÔ‡˜, fiÙ·Ó ·˘Ùfi Â›Ó·È ‰˘Ó·Ùfi, ÁÈ· Ó· ·Ô-ʇÁÔÓÙ·È ÔÈ ·ÏÔ˘ÛÙ‡ÛÂȘ ÔÈ Ôԛ˜ Û¯ÂÙ›˙ÔÓÙ·È Ì ÙÔ ÔÛÙfi Î·È ÙÔ ÂÚÈÔ‰fiÓÙÈÔ. √È ¤Ú¢Ó˜ ·˘Ù¤˜ Â›Ó·È ϤÔÓ ‰˘Ó·Ù¤˜ (Yoshida Î·È Û˘Ó., 2001a; 2001b). £ £∂∂™™∏∏ ∆∆√√ÀÀ ∫∫∂∂¡¡∆∆ƒƒ√√ÀÀ ∞∞¡¡∆∆ππ™™∆∆∞∞™™∏∏™™ √√ªª∞∞¢¢øø¡¡ ¢¢√√¡¡∆∆ππøø¡¡ ∫·Ù¿ ÙË ‰È¿ÚÎÂÈ· Ù˘ ÔÚıÔ‰ÔÓÙÈ΋˜ ıÂÚ·›·˜ ÔÏϤ˜ ÊÔÚ¤˜ Â›Ó·È ··Ú·›ÙËÙË Ë ÌÂٷΛÓËÛË Ì›·˜ ÔÌ¿‰·˜ ‰ÔÓÙÈÒÓ ÚÔ˜ ÌÈ· ÔÚÈṲ̂ÓË Î·Ù‡ı˘ÓÛË. √ ÔÚıÔ‰ÔÓÙÈÎfi˜ ÁÈ· Ó· Ú·ÁÌ·ÙÔÔÈ‹ÛÂÈ ·ÔÙÂÏÂÛÌ·ÙÈο ·˘Ù¤˜ ÙȘ ÎÈÓ‹ÛÂȘ Ú¤ÂÈ Ó· ÁÓˆÚ›˙ÂÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ Ù˘ ÔÌ¿‰·˜ ÙˆÓ ‰ÔÓÙÈÒÓ. 1 1.. ££¤¤ÛÛËË ÙÙÔÔ˘˘ ÎΤ¤ÓÓÙÙÚÚÔÔ˘˘ ··ÓÓÙÙ››ÛÛÙÙ··ÛÛˢ˜ ÙÙˆˆÓÓ ¿¿ÓÓˆˆ ÚÚÔÔÛÛıı››ˆˆÓÓ £ £¤¤ÛÛËË ÙÙÔÔ˘˘ ÎΤ¤ÓÓÙÙÚÚÔÔ˘˘ ··ÓÓÙÙ››ÛÛÙÙ··ÛÛˢ˜ Îη·ÙÙ¿¿ ÙÙËËÓÓ ÂÂÌÌ‚‚‡‡ııÈÈÛÛËË ∏ ÂÌ‚‡ıÈÛË ÙˆÓ ÚÔÛı›ˆÓ ‰ÔÓÙÈÒÓ ÂȉÈÒÎÂÙ·È Û˘¯Ó¿ Û ·ÛıÂÓ›˜ Ì ԢÏÈÎfi ¯·ÌfiÁÂÏÔ ‹ ÎÔÓÙfi ¿Óˆ ¯Â›ÏÔ˜ ‹ Û ·ÛıÂÓ›˜ Ì ·˘ÍË̤ÓË ÁˆÓ›· ÙÔ˘ ÂÈ¤‰Ô˘ Ù˘ οو ÁÓ¿-ıÔ˘ (Burstone, 1977).

√È Dermaut Î·È Vanden Bulcke (1986) ¯ÚËÛÈÌÔÔ›ËÛ·Ó Ù· ¿ÁÎÈÛÙÚ· Î·È ÙËÓ Ù¯ÓÈ΋ Begg ÁÈ· Ó· ÌÂÏÂÙ‹ÛÔ˘Ó ÙËÓ ÂÌ‚‡ıÈÛË ÙˆÓ ‰ÔÓÙÈÒÓ Û ÍËÚ¿ ÎÚ·Ó›·. ∆Ô Î¤ÓÙÚÔ ·ÓÙ›-ÛÙ·Û˘ ÙˆÓ ÙÂÛÛ¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ ‚Ú›ÛÎÂÙ·È Î·Ù¿ ÚÔ-Û¤ÁÁÈÛË ¿ˆ ÙˆÓ ¿Óˆ Ï·Á›ˆÓ ÂÓÒ ÙÔ Î¤ÓÙÚÔ ÙˆÓ ¤ÍÈ ¿Óˆ ÚÔÛı›ˆÓ ¿ˆ ÙˆÓ Î˘ÓÔ‰fiÓÙˆÓ. ¶·ÚfiÏ· ·˘Ù¿ ·Ú·ÙË-ÚÔ‡ÓÙ·È ÚÔ¤˜ Î·È ·ÓÂÍ¿ÚÙËÙ˜ ÌÂÙ·ÎÈÓ‹ÛÂȘ ‰ÔÓÙÈÒÓ È‰›ˆ˜ fiÙ·Ó ÙÔ Û‡ÛÙËÌ· ÂÚÈÏ·Ì‚¿ÓÂÈ ‰‡Ô ‰fiÓÙÈ· Î·È ÌÈÎÚfiÙÂÚ˜ fiÙ·Ó ÂÚÈÏ·Ì‚¿ÓÂÈ ¤ÍÈ ‰fiÓÙÈ·. °È· ÙÔ ÏfiÁÔ ·˘Ùfi Ì ·˘Ù‹ Ù¯ÓÈ΋ Â›Ó·È ·‰‡Ó·ÙÔ Ó· ‚ÚÂı› ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ‰‡Ô ÎÂÓÙÚÈÎÒÓ ¿Óˆ ÙÔ̤ˆÓ (Dermaut Î·È Vanden Bulcke, 1986). ™ÙËÓ ÎÏÈÓÈ΋ Ú¿ÍË ÁÈ· Ó· ·ÓÙÈÌÂÙˆÈÛÙÔ‡Ó ·˘Ù¤˜ ÔÈ ÌÂÙ·ÎÈÓ‹ÛÂȘ ÔÈ Toutountzakis Î·È Mavreas (1989) Û˘ÓÈ-ÛÙÔ‡Ó ÔÈ ÙÔÌ›˜ Ó· ‰¤ÓÔÓÙ·È ÌÂٷ͇ ÙÔ˘˜ Ì ÙË ‚Ô‹ıÂÈ· ÌÂÙ·ÏÏÈ΋˜ ÚfiÛ‰ÂÛ˘ Û ۯ‹Ì· ÔÎÙÒ.

√È Vanden Bulcke Î·È Û˘Ó. (1986) ¯ÚËÛÈÌÔÔ›ËÛ·Ó ÙËÓ

perpendicular to the occlusal plane between canines and first premolars. These two centers of resistance are at a 2-mm distance from each other (Vanden Bulcke et al., 1986). On the contrary, the CR of the six upper anterior teeth is located on a line perpendicular to the occlusal plane distal to the first premolars (Vanden Bulcke et al., 1986). The center of resistance during intrusion does not change significantly as force magnitude increases. Greenfield (1993), without referring to his sources, reports that the CR of the four upper incisors lies on the line dissecting the cemento-enamel junction at the palatal surface of the upper central incisors. In the figure of this paper, the center of resistance is shown to be distal to the lateral incisor.

Many authors, such as Shroff et al. (1995) and, Lindauer and Isaacson (1995), who use the segmented arch technique for maxillary incisor intrusion, do not mention the CR of upper incisors in their main paper, but they depict it in their figures situated distally to and above the upper lateral incisor bracket. This research is obviously based on the paper by Dermaut and Vanden Bulcke (1986), who studied intrusion using the Begg technique and brackets. However, according to these authors, their results cannot be consistently applied in clinical practice. The use of Araldite, as a substitute for the periodontal ligament, and dry skulls for studying tooth movement pose certain limitations. Furthermore, moments and independent tooth movements have been observed during intrusion. These movements of anterior teeth occur even with edgewise brackets (Vanden Bulcke et al., 1986). For this reason, Vanden Bulcke et al. (1986) used a similar method, but intruded teeth within a metal splint. However, their results differed.

Pedersen et al. (1991) report that the centers of resistance of the two maxillary central incisors and of all four incisors are located approximately 13 mm posteriorly to the upper central incisor brackets on a line that passes 3 mm in front of the canine distal surface. The CR of the six maxillary anterior teeth lies 6 mm further posteriorly (Fig. 1). LLooccaattiioonn ooff tthhee cceenntteerr ooff CCRR dduurriinngg ppaallaattaall mmoovveemmeenntt Vanden Bulcke et al. (1987) used a metal splint within which they intruded teeth in two dry skulls and examined the CR of anterior teeth during palatal movement. The center of resistance of maxillary central incisors lies approximately 3.5 mm apically to the incisor interproximal bone level; that of the four upper incisors 5

›‰È· ̤ıÔ‰Ô Ì ÙÔ˘˜ ÚÔËÁÔ‡ÌÂÓÔ˘˜ Û˘ÁÁÚ·Ê›˜ ÂÌ‚‡ıÈ-Û·Ó fï˜ Ù· ‰fiÓÙÈ· Û ¤Ó· ÌÂÙ·ÏÏÈÎfi Ó¿ÚıËη. ∆Ô Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ‰‡Ô ÎÂÓÙÚÈÎÒÓ ¿Óˆ ÙÔ̤ˆÓ ηٿ ÙË ‰È¿Ú-ÎÂÈ· Ù˘ ÂÌ‚‡ıÈÛ˘ ‚Ú›ÛÎÂÙ·È Û ̛· ÁÚ·ÌÌ‹ ·Ú¿ÏÏËÏË Ì ÙÔ Ì¤ÛÔ Ô‚ÂÏÈ·›Ô Â›Â‰Ô ÛÙÔ ¿ˆ ‹ÌÈÛ˘ ÙˆÓ Î˘ÓÔ‰fi-ÓÙˆÓ, ÂÓÒ ÙˆÓ ÙÂÛÛ¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ Û ̛· ÁÚ·ÌÌ‹ οıÂÙË ÛÙÔ Û˘ÁÎÏÂÈÛÈ·Îfi Â›Â‰Ô ÌÂٷ͇ ÙˆÓ Î˘ÓÔ‰fi-ÓÙˆÓ Î·È ÙˆÓ ÚÒÙˆÓ ÚÔÁÔÌÊ›ˆÓ. ∆· ‰‡Ô ΤÓÙÚ· ·ÓÙ›-ÛÙ·Û˘ ‚Ú›ÛÎÔÓÙ·È Û ·fiÛÙ·ÛË ÂÚ›Ô˘ 2 mm ÙÔ ¤Ó· ·fi ÙÔ ¿ÏÏÔ (Vanden Bulcke Î·È Û˘Ó., 1986). ∞ÓÙ›ıÂÙ· ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ¤ÍÈ ¿Óˆ ÚÔÛı›ˆÓ ‚Ú›ÛÎÂÙ·È Û ̛· ÁÚ·ÌÌ‹ οıÂÙË ÛÙÔ Û˘ÁÎÏÂÈÛÈ·Îfi Â›Â‰Ô ¿ˆ ÙˆÓ ÚÒ-ÙˆÓ ÚÔÁÔÌÊ›ˆÓ (Vanden Bulcke Î·È Û˘Ó., 1986). ∆Ô Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ηٿ ÙË ‰È¿ÚÎÂÈ· Ù˘ ÂÌ‚‡ıÈÛ˘ ‰Â ÌÂÙ·‚¿ÏÏÂÙ·È ÛËÌ·ÓÙÈο Ì ÙËÓ ·‡ÍËÛË Ù˘ ¤ÓÙ·Û˘ ÙˆÓ ‰˘Ó¿ÌˆÓ. √ Greenfield (1993) ·Ó·Ê¤ÚÂÈ, ¯ˆÚ›˜ fï˜ Ó· ·Ôηχ-ÙÂÈ ÙȘ ËÁ¤˜ ÙÔ˘, fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ÙÂÛÛ¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ ‚Ú›ÛÎÂÙ·È ¿Óˆ ÛÙËÓ Â˘ı›· Ë ÔÔ›· ‰È·Ù¤-ÌÓÂÈ ÙËÓ ÔÛÙÂ˚ÓÔ-·‰·Ì·ÓÙÈÓÈ΋ ¤ÓˆÛË ÛÙË ˘ÂÚÒÈ· Ï¢-Ú¿ ÙˆÓ ¿Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔ̤ˆÓ. ∏ ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›-ÛÙ·Û˘ ÛÙÔ Û¯‹Ì· ÙÔ˘ ¿ÚıÚÔ˘ Ê·›ÓÂÙ·È Ó· ‚Ú›ÛÎÂÙ·È ¿ˆ ÙÔ˘ Ï¿ÁÈÔ˘ ÙÔ̤·. ¶ÔÏÏÔ› Û˘ÁÁÚ·Ê›˜ ÔÈ ÔÔ›ÔÈ ¯ÚËÛÈÌÔÔÈÔ‡Ó ÙÌËÌ·ÙÈΤ˜ Ù¯ÓÈΤ˜ ÁÈ· ÙËÓ ÂÌ‚‡ıÈÛË ÙˆÓ ¿Óˆ ÙÔ̤ˆÓ fiˆ˜ Ô Shroff Î·È Û˘Ó. (1995), ÔÈ Lindauer Î·È Isaacson (1995) ‰ÂÓ ·Ó·-ʤÚÔ˘Ó, Û˘ÛÙËÌ·ÙÈο, ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ¿Óˆ ÙÔ̤ˆÓ ÛÙÔ Î‡ÚÈÔ Ì¤ÚÔ˜ ÙˆÓ ¿ÚıÚˆÓ ÙÔ˘˜ ·ÏÏ¿ ÙÔ ·ÂÈ-ÎÔÓ›˙Ô˘Ó ÌfiÓÔ ÛÙ· Û¯‹Ì·Ù¿ ÙÔ˘˜ ¿ˆ Î·È ¿Óˆ ·fi ÙÔ ·Á·ÏÈÔ ÙÔ˘ Ï·Á›Ô˘ ¿Óˆ ÙÔ̤·. √È Û˘ÁÁÚ·Ê›˜ ·˘ÙÔ› ÛÙËÚ›˙ÔÓÙ·È ÚÔÊ·ÓÒ˜ ÛÙÔ ¿ÚıÚÔ ÙˆÓ Dermaut Î·È Vanden Bulcke (1986) ÔÈ ÔÔ›ÔÈ ÌÂϤÙËÛ·Ó ÙËÓ ÂÌ‚‡ıÈÛË ¯ÚËÛÈÌÔÔÈÒÓÙ·˜ Ù· ·Á·ÏÈ· Î·È ÙËÓ Ù¯ÓÈ΋ Begg. ∆· ·ÔÙÂϤÛÌ·Ù¿ ÙÔ˘˜ fï˜, Û‡Ìʈӷ Ì ÙÔ˘˜ ›‰ÈÔ˘˜ ÙÔ˘˜ Û˘ÁÁÚ·Ê›˜, ‰ÂÓ ÌÔÚÔ‡Ó Ó· ÌÂÙ·ÊÂÚıÔ‡Ó ÈÛÙ¿ ÛÙËÓ ÎÏÈÓÈ΋ Ú¿ÍË. ∏ ¯Ú‹ÛË ÙÔ˘ Araldite Û·Ó ˘ÔηٿÛÙ·ÙÔ ÙÔ˘ ÂÚÈÔ‰ÔÓÙÈÎÔ‡ Û˘Ó‰¤ÛÌÔ˘ fiˆ˜ Î·È ÙÔ˘ ÍËÚÔ‡ ÎÚ·-Ó›Ô˘ ÛÙË ÌÂϤÙË ÙˆÓ Ô‰ÔÓÙÈÎÒÓ ÌÂÙ·ÎÈÓ‹ÛÂˆÓ ¤¯Ô˘Ó ÔÚÈ-Ṳ̂ÓÔ˘˜ ÂÚÈÔÚÈÛÌÔ‡˜. ∂ÈϤÔÓ Î·Ù¿ ÙË ‰È¿ÚÎÂÈ· Ù˘ ÂÌ‚‡ıÈÛ˘ ·Ú·ÙËÚ‹ıËÎ·Ó ÚÔ¤˜ Î·È ·ÓÂÍ¿ÚÙËÙ˜ ÌÂÙ·ÎÈ-Ó‹ÛÂȘ ‰ÔÓÙÈÒÓ. √È ·ÓÂÍ¿ÚÙËÙ˜ ·˘Ù¤˜ ÌÂÙ·ÎÈÌÂÙ·ÎÈ-Ó‹ÛÂȘ ÙˆÓ ÚÔÛı›ˆÓ ‰ÔÓÙÈÒÓ Û˘Ì‚·›ÓÔ˘Ó ·ÎfiÌ· Î·È Ì ·Á·ÏÈ· edgewise (Vanden Bulcke Î·È Û˘Ó., 1986). °È· ÙÔ ÏfiÁÔ ·˘Ùfi ÔÈ Vanden Bulcke Î·È Û˘Ó. (1986) ¯ÚËÛÈÌÔÔ›ËÛ·Ó ·ÚfiÌÔÈ· ̤ıÔ‰Ô ·ÏÏ¿ ÂÌ‚‡ıÈÛ·Ó Ù· ‰fiÓÙÈ· Û ¤Ó· ÌÂÙ·ÏÏÈÎfi Ó¿ÚıËη. ∆· ·ÔÙÂϤÛÌ·Ù· fï˜ ‹Ù·Ó

‰È·ÊÔ-mm apically and of all six upper anterior teeth 7 ‰È·ÊÔ-mm apically (Vanden Bulcke et al., 1987).

These absolute values, according to the previous authors, cannot be applied in clinical practice. Differences in the anatomy of tooth, bone and periodontal ligament may shift the location of the center of resistance, which involves only the initial tooth movement. The system with the metal splint within which teeth are intruded is not used in routine clinical practice, where teeth are engaged in an archwire and tooth movements are allowed, at least to a certain degree.

Pedersen et al. (1991), measuring jaws of non-living humans following autopsy, report that the CR of the two upper central incisors and of all upper anterior teeth is found at almost the same location (6.5 mm apical to the brackets of the upper central incisors). The center of resistance of the four upper incisors lies more incisally (5 mm apical to the brackets of upper central incisors) (Fig. 1).

Melsen et al. (1990), based on a theoretical model, support the view that the CR of the six upper anterior teeth is located halfway between the midpoint of the four incisors’ center of resistance and the canines’ center of resistance.

The CR of upper anterior teeth differs from one individual to another and depends on root length and upper anterior tooth inclination. According to these authors, the CR of upper anterior teeth at the horizontal plane lies 0.72 mm distally to the maxillary canine bracket (Fig. 2). Bourauel and Drescher (1994), using a modified Burstone T loop, report that the experimental and clinical results during palatal movement of upper incisors are not highly consistent. According to these authors, the CR of upper incisors cannot yet be accurately determined.

Yoshida et al. (2001b) found that the CR of either two or four upper incisors more or less coincide at 4.3 mm apically to the palatal osseous plate, whereas the CR of the 6 upper anterior teeth lies 0.8 mm more incisally. These authors compared their study to those of Vanden Bulcke et al. (1987) and Pedersen et al. (1991) by measuring from the incisal edge of upper incisors. They report that, during retraction, the CR of the two upper central incisors seems to be located between 10.3 and 11.1 mm from the incisal edge, of the four upper incisors between 8.1 and 12.3 mm and of the six upper anterior teeth between 10.5 and 13.7 mm from the incisal edge (Vanden Bulcke et al., 1987; Pedersen et al., 1991;

ÚÂÙÈο. √È Pedersen Î·È Û˘Ó. (1991) ·Ó·Ê¤ÚÔ˘Ó fiÙÈ Ù· ΤÓÙÚ· ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ‰‡Ô ¿Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔ̤ˆÓ Î·È ÙˆÓ ÙÂÛ-Û¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ ‚Ú›ÛÎÔÓÙ·È ÂÚ›Ô˘ 13 mm ›Ûˆ ·fi Ù· ·Á·ÏÈ· ÙˆÓ ¿Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔ̤ˆÓ Û ̛· ÁÚ·ÌÌ‹ 3 mm ÌÚÔÛÙ¿ ·fi ÙËÓ ¿ˆ ÂÈÊ¿ÓÂÈ· ÙˆÓ Î˘ÓÔ‰fiÓÙˆÓ. ∆Ô Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ¤ÍÈ ¿Óˆ ÚÔÛı›ˆÓ ‚Ú›ÛÎÂÙ·È 6 mm ÈÔ ›Ûˆ (∂ÈÎ. 1). £ £¤¤ÛÛËË ÙÙÔÔ˘˘ ÎΤ¤ÓÓÙÙÚÚÔÔ˘˘ ··ÓÓÙÙ››ÛÛÙÙ··ÛÛˢ˜ Îη·ÙÙ¿¿ ÙÙËËÓÓ ˘˘ÂÂÚÚÒÒÈÈ·· ÌÌÂÂÙÙ· ·ÎΛ›--ÓÓËËÛÛËË √È Vanden Bulcke Î·È Û˘Ó. (1987) ¯ÚËÛÈÌÔÔÈÒÓÙ·˜ ¤Ó·Ó ÌÂÙ·ÏÏÈÎfi Ó¿ÚıËη ÛÙÔÓ ÔÔ›Ô ÂÌ‚‡ıÈÛ·Ó Ù· ‰fiÓÙÈ· Âͤ-Ù·Û·Ó ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ÚÔÛı›ˆÓ ‰ÔÓÙÈÒÓ Î·Ù¿ ÙË ‰È¿ÚÎÂÈ· Ù˘ ˘ÂÚÒÈ·˜ ÌÂٷΛÓËÛ˘ Û ‰‡Ô ÍËÚ¿ ÎÚ·-Ó›·. ∆Ô Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ‰‡Ô ÎÂÓÙÚÈÎÒÓ ¿Óˆ ÙÔ̤ˆÓ ‚Ú›ÛÎÂÙ·È 3,5 mm ÂÚ›Ô˘ ·ÎÚÔÚÚÈ˙Èο ·fi ÙÔ Â›Â‰Ô ÙÔ˘ ÔÛÙÔ‡ ÌÂٷ͇ ÙˆÓ ÙÔ̤ˆÓ (interproximal bone level) ÙˆÓ ÙÂÛÛ¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ 5 mm Î·È ÙˆÓ ¤ÍÈ ¿Óˆ ÚÔ-Ûı›ˆÓ 7 mm (Vanden Bulcke Î·È Û˘Ó., 1987). √È ·fiÏ˘ÙÔÈ ·˘ÙÔ› ·ÚÈıÌÔ› ‰Â ÌÔÚÔ‡Ó Ó· ÌÂÙ·ÊÂÚıÔ‡Ó Û‡Ìʈӷ Ì ÙÔ˘˜ ÚÔËÁÔ‡ÌÂÓÔ˘˜ Û˘ÁÁÚ·Ê›˜ ÛÙËÓ ÎÏÈ-ÓÈ΋ Ú¿ÍË. √È ‰È·ÊÔÚ¤˜ ÛÙËÓ ·Ó·ÙÔÌ›· ÙÔ˘ ‰ÔÓÙÈÔ‡, ÙÔ˘ ÔÛÙÔ‡ Î·È ÛÙÔ ÂÚÈÚÚ›˙ÈÔ ÌÔÚÔ‡Ó Ó· ·ÏÏ¿ÍÔ˘Ó ÙË ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ Ë ÔÔ›· ÂÈϤÔÓ ‰ÂÓ ·ÊÔÚ¿ fiÏË ÙËÓ Î›ÓËÛË ÙÔ˘ ‰ÔÓÙÈÔ‡ ·ÏÏ¿ ÌfiÓÔ ÙËÓ ·Ú¯È΋. ∆Ô Û‡ÛÙË-Ì· Ì ÙÔÓ ÌÂÙ·ÏÏÈÎfi Ó¿ÚıËη ÛÙÔÓ ÔÔ›Ô ÂÌ‚˘ı›˙ÔÓÙ·È Ù· ‰fiÓÙÈ· ‰Â ¯ÚËÛÈÌÔÔÈÂ›Ù·È ÛÙËÓ Î·ıËÌÂÚÈÓ‹ ÎÏÈÓÈ΋ Ú¿ÍË fiÔ˘ Ù· ‰fiÓÙÈ· Û˘Ó‹ıˆ˜ Û˘Ó‰¤ÔÓÙ·È Ì ÌÂÙ·ÏÏÈÎfi Û‡ÚÌ· Î·È ÂÈÙÚ¤ÔÓÙ·È Û οÔÈÔ ‚·ıÌfi ÔÈ ÌÂÙ·ÎÈÓ‹ÛÂȘ ÙˆÓ ‰ÔÓÙÈÒÓ. √È Pedersen Î·È Û˘Ó. (1991) οÓÔÓÙ·˜ ÌÂÙÚ‹ÛÂȘ Û ÁÓ¿-ıÔ˘˜ ÌË ˙ÒÓÙˆÓ ·ÓıÚÒˆÓ ÌÂÙ¿ ·fi ÓÂÎÚÔ„›· ·Ó·Ê¤-ÚÔ˘Ó fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ‰‡Ô ÎÂÓÙÚÈÎÒÓ ¿Óˆ ÙÔ̤ˆÓ Î·È ÙˆÓ ¿Óˆ ÚÔÛı›ˆÓ ‚Ú›ÛÎÂÙ·È Û¯Â‰fiÓ ÛÙËÓ ›‰È· ı¤ÛË (6,5 mm ¿Óˆ ·fi Ù· ·Á·ÏÈ· ÙˆÓ ÎÂÓÙÚÈÎÒÓ ¿Óˆ ÙÔ̤ˆÓ) ÂÓÒ ·˘Ùfi ÙˆÓ ÙÂÛÛ¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ ÈÔ ÎÔÙÈο (5 mm ¿Óˆ ·fi Ù· ·Á·ÏÈ· ÙˆÓ ÎÂÓÙÚÈÎÒÓ ¿Óˆ ÙÔ̤ˆÓ) (∂ÈÎ. 1). √È Melsen Î·È Û˘Ó. (1990) ‚·ÛÈṲ̂ÓÔÈ Û ¤Ó· ıˆÚËÙÈÎfi ÌÔÓÙ¤ÏÔ ÈÛ¯˘Ú›˙ÔÓÙ·È fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ¤ÍÈ ¿Óˆ ÚÔÛı›ˆÓ ‚Ú›ÛÎÂÙ·È ÛÙÔ Ì¤ÛÔ Ù˘ ·fiÛÙ·Û˘ (halfway) ÌÂٷ͇ ÙÔ˘ ̤ÛÔ˘ (midpoint) ÙˆÓ Î¤ÓÙÚˆÓ ÛÙ·Û˘ ÙˆÓ ÙÂÛÛ¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ Î·È ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›-ÛÙ·Û˘ ÙÔ˘ ΢Ófi‰ÔÓÙ·. ∆Ô Î¤ÓÙÚÔ ·ÓÙ›·ÓÙ›-ÛÙ·Û˘ ÙˆÓ ¿Óˆ ÚÔÛı›ˆÓ ‰È·Ê¤ÚÂÈ ·fi ¿ÙÔÌÔ Û ¿ÙÔÌÔ Î·È ÂÍ·ÚٿٷÈ

Yoshida et al., 2001a). Thus, the exact location of the centers of resistance is not known, especially in the case of upper incisors and upper anterior teeth; all we know is its approximate location.

Finally, Matsui et al. (2000), in a photoelastic model, found that the CR of the four upper incisors is located at the mid-sagittal plane, 4 mm posterior to and 6 mm above the labial alveolar crest of the upper central incisors. The authors attributed this difference; with the other studies to the use of the photoelastic material and to the 6-mm space created between lateral incisor and canine.

There are many studies that are concerned with maxillary incisor palatal movement. Below, we indicatively present several studies, where different centers of resistance are used.

Park et al. (2000) claim to have achieved translation of anterior teeth with a lever arm system and lingual brackets; however, they do not mention the CR of teeth, although they design it.

Choy et al. (2002) invented the SDRS system for palatal movement of upper anterior teeth. They, too, do not mention the CR, although they design it.

Kim et al. (2004) use the C-lingual retractor for palatal movement and intrusion of upper anterior teeth. For determining the center of resistance they depend on the study by Vanden Bulcke et al. (1986).

Guray and Orhan (1997) use an anterior headgear for palatal movement of upper anterior teeth. They use the study by Melsen et al. (1990) to determine the center of resistance.

Gjessing (1992) invents the PG spring for palatal movement of upper incisors. For the center of resistance of upper anterior teeth he uses Pedersen’s definition. These studies consist of a theoretical part including the principles of the system proposed for palatal movement of anterior teeth, experimental data and a clinical case showing the action of the appliance. These systems cannot be easily compared, but they have a sound theoretical basis and their results, at least in the clinical cases shown, are excellent. Most authors use forces or forces and moments for retraction of maxillary incisors or anterior teeth and select a CR. However, it is not possible to decide whether the center of resistance has been correctly determined or not. Nevertheless, the definitions given by Pedersen et al. (1991) and Melsen et al. (1990) are quite similar.

∂∂ÈÈÎÎfifiÓÓ·· 11.. a) √ÚÈ˙fiÓÙȘ Î·È Î¿ıÂÙ˜ ‰˘Ó¿ÌÂȘ ‰ÈÂÚ¯fiÌÂÓ˜ ·fi ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ¿Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔ̤ˆÓ. b) √ÚÈ˙fiÓÙȘ Î·È Î¿ıÂÙ˜ ‰˘Ó¿-ÌÂȘ ‰ÈÂÚ¯fiÌÂÓ˜ ·fi ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ÙÂÛÛ¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ. c) √ÚÈ˙fiÓÙȘ Î·È Î¿ıÂÙ˜ ‰˘Ó¿‰˘Ó¿-ÌÂȘ ‰ÈÂÚ¯fiÌÂÓ˜ ·fi ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·-Û˘ ÙˆÓ ¤ÍÈ ¿Óˆ ÚÔÛı›ˆÓ.(Afi: Pedersen Î·È Û˘Ó. (1991), ηÙfiÈÓ ·‰Â›·˜ ÙÔ˘ Oxford University Press.)

FFiigguurree 11.. Horizontal and perpendicular forces passing through the center of resistance of upper central incisors. b) Horizontal and perpendicular forces passing through the center of resistance of the four upper incisors. c) Horizontal and perpendicular forces passing through the center of resistance of the six upper anterior teeth.(From: Pedersen et al. (1991), with permission of Oxford University Press.)

·fi ÙÔ Ì‹ÎÔ˜ ÙˆÓ ÚÈ˙ÒÓ Î·È ÙȘ ÎÏ›ÛÂȘ ÙˆÓ ¿Óˆ ÚÔ-Ûı›ˆÓ. ™‡Ìʈӷ Ì ÙÔ˘˜ ÚÔËÁÔ‡ÌÂÓÔ˘˜ Û˘ÁÁÚ·Ê›˜ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ¿Óˆ ÚÔÛı›ˆÓ ÛÙÔ ÔÚÈ˙fiÓÙÈÔ Â›-Â‰Ô ‚Ú›ÛÎÂÙ·È 0.72 mm ¿ˆ ÙÔ˘ ·ÁÎ˘Ï›Ô˘ ÙÔ˘ ¿Óˆ ΢Ófi‰ÔÓÙ· (∂ÈÎ. 2). √È Bourauel Î·È Drescher (1994) ¯ÚËÛÈÌÔÔÈÒÓÙ·˜ ÌÈ· ÙÚÔÔÔÈË̤ÓË ·Á·ÏË ∆ ÙÔ˘ Burstone ·Ó·Ê¤ÚÔ˘Ó fiÙÈ ÛÙËÓ ˘ÂÚÒÈ· ÌÂٷΛÓËÛË ÙˆÓ ¿Óˆ ÙÔ̤ˆÓ Ù· ÂÈÚ·Ì·ÙÈ-ο Î·È ÎÏÈÓÈÂÈÚ·Ì·ÙÈ-ο ·ÔÙÂϤÛÌ·Ù· ‰ÂÓ ·ÓÙÈÛÙÔÈ¯Ô‡Ó Û ÌÂÁ¿ÏÔ ‚·ıÌfi. ™‡Ìʈӷ Ì ÙÔ˘˜ ÚÔËÁÔ‡ÌÂÓÔ˘˜ Û˘ÁÁÚ·Ê›˜ Ë ı¤ÛË ÙÔ˘ ΤÓÙÚÔ˘ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ¿Óˆ ÙÔ̤ˆÓ ‰ÂÓ ¤¯ÂÈ Ï‹Úˆ˜ ·ÔÛ·ÊËÓÈÛı›. √È Yoshida Î·È Û˘Ó. (2001b) ‚Ú›ÛÎÔ˘Ó fiÙÈ ÙÔ Î¤ÓÙÚÔ ·ÓÙ›-ÛÙ·Û˘ ÙˆÓ ‰‡Ô Î·È ÙˆÓ ÙÂÛÛ¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ Û˘Ì›-ÙÔ˘Ó Ï›ÁÔ Ôχ Î·È ‚Ú›ÛÎÔÓÙ·È 4,3 mm ·ÎÚÔÚÚÈ˙Èο ÙÔ˘ ˘ÂÚÒÈÔ˘ ÂÙ¿ÏÔ˘ ÂÓÒ ·˘Ùfi ÙˆÓ 6 ÚÔÛı›ˆÓ 0,8 mm ÈÔ ÎÔÙÈο. √È ÚÔËÁÔ‡ÌÂÓÔÈ Û˘ÁÁÚ·Ê›˜ ÚÔÛ¿ıËÛ·Ó Ó· Û˘ÁÎÚ›ÓÔ˘Ó ÙȘ ÂÚÁ·Û›Â˜ ÙˆÓ Vanden Bulcke Î·È Û˘Ó. (1987), Pedersen Î·È Û˘Ó. (1991) Ì ÙË ‰È΋ ÙÔ˘˜ ÌÂÙÚÒ-ÓÙ·˜ ·fi ÙËÓ ÎÔÙÈ΋ ÂÈÊ¿ÓÂÈ· ÙˆÓ ¿Óˆ ÙÔ̤ˆÓ. ™‡Ìʈ-Ó· Ì ·˘ÙÔ‡˜ ηٿ ÙËÓ ¤ÏÍË, ÙÔ Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ‰‡Ô ¿Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔ̤ˆÓ Ê·›ÓÂÙ·È Ó· ‚Ú›ÛÎÂÙ·È ÌÂٷ͇ ÙˆÓ 10,3 Î·È 11,1 mm, ÙˆÓ ÙÂÛÛ¿ÚˆÓ ¿Óˆ ÙÔ̤ˆÓ ÌÂٷ͇ ÙˆÓ 8,1 Î·È ÙˆÓ 12,3 mm Î·È ÙˆÓ ¤ÍÈ ¿Óˆ ÚÔÛı›ˆÓ ÌÂÙ·-͇ ÙˆÓ 10,5 Î·È 13,7 mm ·fi ÙËÓ ÎÔÙÈ΋ ÂÈÊ¿ÓÂÈ· ÙˆÓ ¿Óˆ ÙÔ̤ˆÓ (Vanden Bulcke Î·È Û˘Ó., 1987; Pedersen Î·È Û˘Ó., 1991; Yoshida Î·È Û˘Ó., 2001a). ¢ÂÓ Â›Ó·È ÁÓˆÛÙ‹ ÂÔ̤ӈ˜ Ë ·ÎÚÈ‚‹˜ ı¤ÛË ÙˆÓ Î¤ÓÙÚˆÓ ·ÓÙ›ÛÙ·Û˘, ȉ›ˆ˜ ÙˆÓ ¿Óˆ ÙÔ̤ˆÓ Î·È ÙˆÓ ¿Óˆ ÚÔÛı›ˆÓ ·ÏÏ¿ Ë ÂÚÈÔ¯‹ Á‡Úˆ ·fi ÙËÓ ÔÔ›· Èı·ÓfiÓ Ó· ÂÓÙÔ›˙ÔÓÙ·È.

∆¤ÏÔ˜, ÔÈ Matsui Î·È Û˘Ó. (2000) Û ¤Ó· ʈÙÔÂÏ·ÛÙÈÎfi

not consider a definitive; center of resistance in their experimental studies, but rather the center of resistance during palatal movement or intrusion without referring to other types of tooth movement (occlusal movement etc.) (Dermaut and Vanden Bulcke, 1986; Vanden Bulcke et al., 1986; Vanden Bulcke et al., 1987; Yoshida et al., 2001b). In the conclusion section of the studies they refer to the location of the center of resistance during palatal movement or intrusion, always taking only one dimension into account.

Even researchers who investigated CR location during palatal movement or intrusion, such as Pedersen et al. (1991) did in the same skull and, Vanden Bulcke et al. (1986) and Vanden Bulcke et al. (1987) in two separate studies with similar methodology, do not report that the two centers coincide.

The center of resistance may differ depending on the direction of the applied force. The CR of a single-rooted tooth is different during palatal movement and intrusion (Nagerl et al., 1991). In certain segmented arch techniques, such as the three-piece intrusion arch, the force, although mainly intrusive, also has a palatal component that may change the theoretical center of resistance. The segmented arch technique for upper incisor intrusion offers many advantages and is often the only effective method in clinical practice. However, practical results may vary somewhat from their theoretical background.

2

2.. LLooccaattiioonn ooff tthhee cceenntteerr ooff rreessiissttaannccee ooff ootthheerr ggrroouuppss ooff tteeeetthh

Some authors determine centers of resistance based on clinical observations and not on experimental or laboratory data; therefore, their findings must be examined critically (Papadopoulos and Christou, 2000). The CR of upper incisors and first molars connected through a segmented arch lies at the point of dissection of the mid-sagittal plane and a plane parallel to the frontal plane passing through the mesiobuccal roots of maxillary first molars (Stoeckli and Teuscher, 1985). Finally, the center of resistance of the upper arch with full fixed appliances lies at the point of dissection of the mid-sagittal plane and a plane parallel to the frontal plane, passing through the roots of the two premolars and is perpendicular to the occlusal plane (Stoeckli and Teuscher, 1985).

∂∂ÈÈÎÎfifiÓÓ·· 22.. ∆Ô Î¤ÓÙÚÔ ·ÓÙ›ÛÙ·Û˘ ÙˆÓ ¿Óˆ ÚÔÛı›ˆÓ Û‡Ìʈӷ Ì ÙÔ˘˜ Melsen Î·È Û˘Ó. (1990). (∞fi: Melsen Î·È Û˘Ó. (1990), ηÙfiÈÓ ·‰Â›-·˜ ÙÔ˘ J Clin Orthod.)

FFiigguurree 22.. The center of resistance of maxillary anterior teeth according to Melsen et al. (1990). (From: Melsen Î·È Û˘Ó. (1990), with permission of J Clin Orthod.)