E HNIKH OP O ONTIKH E I EøPH H

Transcription

1 Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÔÓÙÈÒÓ ÛÙËÓ ÚıÔ ÔÓÙÈÎ πˆ ÓÓË. apple ÁˆÚÁ Ô È ÈÎfi ÚıÔ ÔÓÙÈÎfi, ÀappleÔ ÊÈÔ È ÎÙˆÚ, ÚÁ ÛÙ ÚÈÔ ÚıÔ ÔÓÙÈÎ, Ì Ì ÔÓÙÈ ÙÚÈÎ, ÚÈÛÙÔÙ ÏÂÈÔ ÓÂappleÈÛÙ ÌÈÔ ÂÛÛ ÏÔ- Ó ÎË. The center of resistance of teeth in Orthodontics Ioannis S. Papageorgiou Orthodontist, Doctorate Degree Candidate, Department of Orthodontics, School of Dentistry, Aristotle University of Thessaloniki, Thessaloniki, Greece. EPI HæH ÎÔapplefi ÙË apple ÚÔ Û ÂÚÁ Û Â Ó È Ó Á ÓÂÈ ÌÈ È ÏÈÔÁÚ ÊÈÎ Ó ÛÎfiappleËÛË ÙˆÓ applefi ÂˆÓ appleô ÊÔ- ÚÔ Ó ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÂÓfi ÔÓÙÈÔ ÌÈ ÔÌ ÔÓÙÈÒÓ. È applefi ÂÈ ÙˆÓ Û ÁÁÚ Ê ˆÓ ÁÈ ÙËÓ ÎÚÈ ı ÛË ÙÔ Â Ó È Û Ó È ÊÔÚÂÙÈÎ. ÙËÓ ÂÚÁ Û Ù apple ÚÔ ÛÈ ÔÓÙ È Ú ÈÎ ÔÈ Î ÚÈÂ Ì ıô ÔÈ appleô ÚËÛÈ- ÌÔappleÔÈÔ ÓÙ È ÁÈ ÙÔÓ appleúôû ÈÔÚÈÛÌfi ÙÔ Î È ÛÙË Û Ó - ÂÈ Á ÓÂÙ È Ó ÊÔÚ ÛÙÈ ÌÂÏ ÙÂ Î È ÛÙ appleôùâï ÛÌ - Ù ÙÔ. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÌÔÓfiÚÚÈ ˆÓ ÔÓÙÈÒÓ Ú - ÛÎÂÙ È Ó ÌÂÛ ÛÙÔ 33-42% ÙÔ Ì ÎÔ ÙË Ú fiù Ó Ë Ì ÙÚËÛË Á ÓÂÙ È applefi ÙË Ê ÙÓÈ Î ÎÚÔÏÔÊ. ªappleÔÚÂ Ó ÌÂÙ ÏËıÂ Ó ÏÔÁ Ì ÙÔ Ì ÎÔ ÙË Ú ÙÔ ÔÓÙÈÔ, ÙË È ı ÓÛË ÙˆÓ ÂÊ ÚÌÔ fiìâóˆó Ó ÌÂ- ˆÓ, ÙËÓ appleôûfiùëù ÙÔ appleâúè ÏÏÔÓÙÔ ÔÛÙÔ Î È ÙËÓ ËÏÈÎ ÂÓÒ apple Ú Ô Ó ÂÓ Â ÍÂÈ fiùè ÂappleËÚ ÂÙ È applefi ÙË ÌÔÚÊÔÏÔÁ ÙÔ ÔÓÙÈÔ, ÙÔ Â Ô ÙÔ appleâúèô ÔÓÙÈÎÔ Û Ó ÛÌÔ, ÙËÓ appleôèfiùëù ÙÔ appleâúè ÏÏÔÓÙÔ ÔÛÙÔ, ÙËÓ ÈÛÙÈÎ ÓÙ Ú ÛË ÛÙÈ ÛÎÔ ÌÂÓÂ Ó ÌÂÈ, ÙËÓ ÂÊ ÁÚ ÓÛË ÙˆÓ apple Ú Î ÌÂÓˆÓ ÔÛÙÈÎÒÓ ÔÌÒÓ Î È ÙËÓ ÍÔÓÈÎ ÎÏ ÛË ÙÔ ÔÓÙÈÔ. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÌÈ ÔÌ ÔÓÙÈÒÓ È Ê ÚÂÈ Ó ÏÔÁ Ì ÙÔÓ ÚÈıÌfi ÙˆÓ ÔÓÙÈÒÓ. È appleâúèûûfiùâúâ Ú ÓÂ Ô Ó Á ÓÂÈ ÁÈ ÙÔ Óˆ ÙÔÌÂ Î È ÙÔ Óˆ appleúôûı Ô Àapple Ú Ô Ó fiìˆ ÛÔ Ú È ÊˆÓ Â ÁÈ ÙË ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙfiÛÔ Î Ù ÙËÓ appleâúòè ÌÂÙ Î ÓËÛË fiûô Î È Î Ù ÙËÓ ÂÌ ıèûë. appleèappleï ÔÓ ÔÈ ÁÓÒÛÂÈ Ì ÁÈ ÙÔ apple Ú ÁÔÓÙ appleô ÂappleËÚÂ Ô Ó ÙË ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÔÌ ˆÓ ÔÓÙÈÒÓ Â Ó È appleôï appleâúèôúèûì Ó ۈ ÂappleÂÈ ÔÈ apple Ú ÁÔÓÙ ÙÔ Â Ó È ÛÎÔÏÔ Ó ÌÂÙÚËıÔ Ó Û ÔÌ Â ÔÓÙÈÒÓ. ÚÈÛÌ ÓÔÈ fiìˆ ÙÚfiappleÔÈ ıâú appleâ ÛÙËÚ ÔÓÙ È ıâˆúë- ÙÈÎ ÛÙË ÁÓÒÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÔÌ ˆÓ ÔÓÙÈÒÓ. appleâè Ô ÔÚıÔ ÔÓÙÈÎfi ÂÓ ıâú appleâ ÂÈ Î ÓÙÚ ÓÙ ÛÙ ÛË ÏÏ ÛıÂÓ ÂÓ ı appleú appleâè Ó appleôúú appleùâè ABSTRACT 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. Key words: Palatal tooth movement, dental intrusion, center of resistance, orthodontic movement. E HNIKH OP O ONTIKH E I EøPH H 2005 ñ TOMO 8 ñ TEYXO 1 43

2 HELLENIC ORTHODONTIC REVIEW Ù ÙÈ ÌÂıfi Ô fiù Ó Ì ÏÈÛÙ Â Ó È ÔÎÈÌ ÛÌ Ó ÛÙËÓ Î ıëìâúèó ÎÏÈÓÈÎ appleú ÍË. ÍÂÈ ÎÏÂÈ È : ÀappleÂÚÒÈ ÌÂÙ Î ÓËÛË ÙˆÓ ÔÓÙÈÒÓ, ÂÌ ıèûë ÙˆÓ ÔÓÙÈÒÓ, Î ÓÙÚÔ ÓÙ ÛÙ ÛË, ÔÚıÔ ÔÓÙÈ- Î ÌÂÙ Î ÓËÛË. ÏÏ ÚıÔ appleèı 2005;8: ÚÂÏ ÊıË: ŒÁÈÓ ÂÎÙ : EI A ø H ÚÎÂÙ ÂÏ ıâú ÛÒÌ Ù Û ÌappleÂÚÈÊ ÚÔÓÙ È Û Ó Ë Ì ÙÔ Ó Â Ó È Û ÁÎÂÓÙÚˆÌ ÓË ÛÂ Ó ÛËÌ Ô. Ó apple.. Ó ÂÏ ıâúô ÛÒÌ Ú ÛÎÂÙ È ÛÙÔ È ÛÙËÌ Î È ÛÎËı Âapple Óˆ ÙÔ ÌÈ Ó ÌË ÛÂ Ó Û ÁÎÂÎÚÈÌ ÓÔ ÛËÌÂ Ô ÙfiÙ fiï Ù ÛËÌ ÙÔ ÛÒÌ ÙÔ ı È ÁÚ Ô Ó Ì apple Ú Ï- ÏËÏË ÙÚÔ È. Ô ÛËÌÂ Ô Ùfi ÔÓÔÌ ÂÙ È Î ÓÙÚÔ ÙË Ì. Ô fióùè fiìˆ ÂÓ Û ÌappleÂÚÈÊ ÚÂÙ È Û Ó ÂÏ ıâúô ÛÒÌ ÊÔ Ë Î ÓËÛ ÙÔ appleâúèôú ÂÙ È applefi ÙÔÓ appleâúèô Ô- ÓÙÈÎfi Û Ó ÂÛÌÔ Î È ÙÔ Ê ÙÓÈ Îfi ÔÛÙfi. Ô ÓÙ ÛÙÔÈ Ô ÛËÌÂ Ô Ì ÙÔ Î ÓÙÚÔ Ì ÂÓfi ÂÏ ıâúô ÛÒÌ ÙÔ Â Ó È ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ ÔÓÙÈÔ. appleôì Óˆ ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË Â Ó È ÙÔ ÛËÌÂ Ô ÛÙÔ ÔappleÔ Ô ÌappleÔÚÂ Ó Û Ìapple - ÎÓˆıÂ Ë ÓÙ ÛÙ ÛË ÙÔ ÔÓÙÈÔ ÛÂ Ì Î ÓËÛË Ì ÏÏ ÏfiÁÈ ÙÔ ÛËÌÂ Ô ÙÔ ÔÓÙÈÔ applefi ÙÔ ÔappleÔ Ô fiù Ó ÌÈ Ó - ÌË È ÏıÂÈ ı appleúôî Ï ÛÂÈ apple Ú ÏÏËÏË ÌÂÙ Î ÓËÛË ÙÔ ÔÓÙÈÔ. È Ó ÌÂÈ appleô È Ú ÔÓÙ È Û applefiûù ÛË applefi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË appleúôî ÏÔ Ó ÂappleÈappleÏ ÔÓ Ì ÚÔapple Ë ÔappleÔ Ù ÓÂÈ Ó appleâúèûùú ÂÈ ÙÔ fióùè. Ô Ì ÁÂıÔ ÙË ÚÔapple ÂÍ ÚÙ Ù È applefi ÙÔ Ì ÁÂıÔ ÙË Ó ÌË Î È ÙËÓ applefiûù ÛË ÙÔ Ó - ÛÌ ÙÔ ÙË Ó ÌË applefi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ ÔÓÙÈ- Ô (Proffit Î È Fields, 2000). È Ó ÌÂÈ appleô ÂÊ ÚÌfi ÂÈ Ô ÔÚıÔ ÔÓÙÈÎfi Û Ó ıˆ ÂÓ È Ú ÔÓÙ È applefi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÔÓÙÈÒÓ (Nanda Î È Kuhlberg, 1997). appleôì Óˆ ı apple Ú Ô Ó ÚÔapple ÔÈ ÔappleÔ Â ı ÂappleËÚÂ Ô Ó Î È ı Î ıôú Ô Ó ÙËÓ Î ÓËÛË ÙÔ ÔÓÙÈÔ. ŸÙ Ó Ô ÔÚıÔ ÔÓÙÈÎfi ÁÓˆÚ ÂÈ ÙÔ Î ÓÙÚÔ ÓÙ - ÛÙ ÛË ÙÔ ÔÓÙÈÔ ÌappleÔÚÂ Ó appleôïôá ÛÂÈ Ù ÙË ÚÔapple Î Ï ÙÂÚ ÙÔ ÏfiÁÔ ÚÔapple / Ó ÌË ÁÈ Î ıâ Î ÓËÛË ÙÔ ÔÓÙÈÔ Î È Ó ÂÏ ÁÍÂÈ ÂappleÔÌ Óˆ ÙËÓ Î ÓËÛË ÙÔ ÔÓÙÈÔ (Halazonetis, 1996; Yoshida Î È Û Ó., 2001a). Ó ı ÏÂÈ apple.. Ó ÂappleÈÙ ÂÈ apple Ú ÏÏËÏË ÌÂÙ Î ÓËÛË ÙÔ ÔÓÙÈÔ ı appleú appleâè Ó ÂÓÛˆÌ ÙÒÛÂÈ ÛÙÔ Û ÛÙËÌ ÌÈ ÓÙ ıâùë ÚÔapple Ë ÔappleÔ Ó ÂÍÔ ÂÙÂÚÒÓÂÈ ÙËÓ appleúòùë Ó ÂÊ ÚÌfiÛÂÈ Ì Ó ÌË appleô Ó appleâúó ÂÈ applefi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ Hell Orthod Rev 2005;8: Received: Accepted: INTRODUCTION 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). METHODS OF DETERMINING THE CENTER OF RESISTANCE 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 44 HELLENIC ORTHODONTIC REVIEW 2005 ñ VOLUME 8 ñ ISSUE 1

3 ÔÓÙÈÔ. ŸÙ Ó Ô ÏfiÁÔ ÙË ÚÔapple appleúô ÙËÓ ÂÊ ÚÌÔ fiìâ- ÓË Ó ÌË Ú ÛÎÂÙ È ÌÂÙ Í 1 Î È 7 Ô Ù appleô ÙË ÌÂÙ Î - ÓËÛË ÙÔ ÔÓÙÈÔ appleô ÂappleÈÙ Á ÓÂÙ È Â Ó È ÂÏÂÁ fiìâóë applefiîïèûë, ÌÂÙ Í 8 Î È 10 apple Ú ÏÏËÏË ÌÂÙ Î ÓËÛË ÂÓÒ fiù Ó Â Ó È ÌÂÁ Ï ÙÂÚÔ applefi 10 apple Ú ÙËÚÂ Ù È ÌÂÙ Î ÓËÛË ÙË Ú (torque) (Proffit Î È Fields, 2000). ª π ƒπ ª À À ƒ À π È ÙÔÓ Î ıôúèûìfi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ ÔÓÙÈÔ ÚËÛÈÌÔappleÔÈ ıëî Ó appleôïïô ÙÚfiappleÔÈ. ÚÈÛÌ ÓÔÈ ÂÚ ÓËÙ ÂÊ ÚÌÔÛ Ó Ì ıëì ÙÈÎ Ê ÛÈÎ ÌÔÓÙ Ï Î ıò Î È ÌÔÓÙ Ï appleâappleâú ÛÌ ÓˆÓ ÛÙÔÈ Â ˆÓ (finite element models). appleâúèûûfiùâú ÌÔÓÙ Ï fiìˆ Ù Ó appleïôappleôèë- Ì Ó Î È ÂÓ appleúôû ÁÁÈ Ó ÈÎ ÓÔappleÔÈËÙÈÎ ÙÔ appleú ÁÌ ÙÈ- ÎÔ Ó ÙÔÌÈÎÔ apple Ú ÁÔÓÙ appleô ÂappleÈ ÂÈÚÔ Û Ó Ó ÂÍÔ- ÌÔÈÒÛÔ Ó (Yoshida Î È Û Ó., 2001a). Ó Ï ÛË ÙˆÓ appleâappleâú ÛÌ ÓˆÓ ÛÙÔÈ Â ˆÓ appleúô appleôı ÙÂÈ ÙË ÁÓÒÛË ÙÔ ÏfiÁÔ Poisson Ô ÔappleÔ Ô ÂÍ ÚÙ Ù È applefi ÙÔ Ì ÙÚÔ ÂÏ ÛÙÈ- ÎfiÙËÙ. ÍÈfiappleÈÛÙ fiìˆ ÙÈÌ ÁÈ ÙÔ Ì ÙÚÔ ÂÏ ÛÙÈÎfiÙËÙ ÂÓ Â Ó È Ó ÙfiÓ Ó ÂÍ ıô Ó applefi ÙË ÌÂÏ ÙË ÙˆÓ ÌË - ÓÈÎÒÓ È ÈÔÙ ÙˆÓ ÙˆÓ ÏÈÎÒÓ ÏfiÁˆ ÙË ÌÂÁ ÏË Âapple Ú ÛË ÙÔ ÈÛÙÔÚÈÎÔ ÊfiÚÙÈÛË, ÙË È ÈÎ Û ËÌÈÔ ÚÁ ÔÎÈÌ ˆÓ Î È ÙˆÓ Û ÓıËÎÒÓ ÔÎÈÌ Û ÛÙÈ È ÈfiÙËÙ Πı Ù (Fung, Ó Ê ÚÂÙ È applefi 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 appleâappleâú ÛÌ ÓˆÓ ÛÙÔÈ Â ˆÓ appleúô appleôı ÙÂÈ fiùè Ù ÏÈÎ Â Ó È ÈÛfiÙÚÔapple ËÏ Ë ÓÙ Ú Û ÙÔ ÛÂ Ó Â ÔÌ ÓÔ ÊÔÚ- Ù Ô ÂÓ ÂappleËÚ ÂÙ È applefi ÙËÓ Î Ù ı ÓÛË ÊfiÚÙÈÛË. apple Ú Ô fiìˆ Ù ÂÓ ÈÛ ÂÈ ÁÈ ÈÔÏÔÁÈÎ ÏÈÎ fiappleˆ ÙÔ ÔÛÙfi (Park Î È Lakes, Ó Ê ÚÂÙ È applefi ÙÔ Gioka C, Eliades T. Orthodontic dental intrusion: indications, histological changes, biomechanical principles, possible side effects. Hell Orthod Rev 2003:6:129-46). ÙÂÏ ٠ÚfiÓÈ ÁÈÓ appleúôûapple ıâè Ó ÂÓÛˆÌ ÙˆıÂ Ë ÔÌ ÙÔ appleâúèô ÔÓÙ Ô ÛÙÈ Ó Ï ÛÂÈ appleâappleâú ÛÌ ÓˆÓ ÛÙÔÈ Â ˆÓ. ÌÊˆÓ Ì ÙÔ Qian Î È Û Ó. (2001) Ë È ı ÓÛË Î È ÔÈ ÌË ÓÈÎ È ÈfiÙËÙÂ ÙˆÓ ÈÓÒÓ ÙÔ appleâúèúúè Ô ÂÓ Ô Ó ÛËÌ ÓÙÈÎfi ÚfiÏÔ ÛÙÔÓ Î ıôúèûìfi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË. È Schneider Î È Û Ó. (2002) ÂÓÛˆÌ ÙˆÛ Ó ÛÙÈ Ó Ï - ÛÂÈ ÙÔ Ó Ó ÏÁfiÚÈıÌÔ ÁÈ Ó appleâúèáú Ô Ó ÙËÓ Ó - È ÌfiÚʈÛË ÙÔ ÔÛÙÔ ÌÂÙ applefi ÌË ÓÈÎ ÂÚÂı ÛÌ Ù, ÁÈÓ Ó fiìˆ Û ÌÊˆÓ Ì ÙÔ ÈÔ ÙÔ Û ÁÁÚ Ê ÔÚÈÛÌ Ó appleïô ÛÙ ÛÂÈ ÏfiÁˆ ÂÏÏ ˆ ÛÙÔÈ Â ˆÓ ÁÈ 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). E HNIKH OP O ONTIKH E I EøPH H 2005 ñ TOMO 8 ñ TEYXO 1 45

4 HELLENIC ORTHODONTIC REVIEW Ù ÏÈÎ Î È ÙË ÌÔÚÊÔÏÔÁ ÙÔ. È ÙË ÌÂÏ ÙË ÙË ÌÂÙ Î ÓËÛË ÙˆÓ ÔÓÙÈÒÓ ÚËÛÈÌÔappleÔÈ - ıëî Ó Âapple ÛË ÔÏÔÁÚ ÊÈÎ Ù ÓÈÎ (laser- holographic techniques) Ù ÓÈÎ strain gauges. strain gauges Â Ó È ËÏÂÎÙÚÈÎ ÂappleÈÌËÎ ÓÛÈfiÌÂÙÚ Ù ÔappleÔ ÂappleÈÎÔÏÏÔ - ÓÙ È ÛÙ ÛËÌ ÙË ÔÌ appleô ÂappleÈı ÌÔ ÌÂ Ó ÌÂÙÚ ÛÔ - Ì ÌÈ ÌÂÙ Î ÓËÛË. ıâ ÂappleÈÌ Î ÓÛË ÂÈ Û Ó appleôù ÏÂÛÌ ÙËÓ ÍËÛË ÙË ÓÙ ÛÙ ÛË ÙÔ strain gauge, appleô ÌappleÔÚÂ Ó ÌÂÙÚËı ËÏÂÎÙÚÈÎ. Ô ÌÂÈÔÓ ÎÙËÌ ÙÒÓ ÙˆÓ Ù ÓÈ- ÎÒÓ Ù Ó fiùè ÎfiÌ Î È ÔÈ appleèô ÌÈÎÚ ÌÂÙ ÎÈÓ ÛÂÈ ÙË ÎÂÊ Ï ÌappleÔÚÔ Ó Ó ÌÂÈÒÛÔ Ó ÛËÌ ÓÙÈÎ ÙËÓ ÎÚ ÂÈ ÙË ÌÂÙ Î ÓËÛË ÙˆÓ ÔÓÙÈÒÓ (Nagerl Î È Û Ó., 1991). ÌÊˆÓ Ì ÙÔ McGuiness Î È Û Ó. (1991) ÂÓ Â Ó È Ó Ù Ë ÂÈÛ ÁˆÁ ÙˆÓ strain gauges Ì Û ÛÙËÓ appleâúèô- ÔÓÙÈÎ ÌÂÌ Ú ÓË ˆÚ Ó appleúôî ÂÈ ÊıÔÚ. ÙÈ ÙÂÏ ٠ Ú Ó ÁÈ ÙÔÓ Î ıôúèûìfi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË, Î È ÂÓ Á ÓÂÈ ÙËÓ apple Ú Ù ÚËÛË ÙË ÌÂÙ Î ÓËÛË ÙÔ ÔÓÙÈÔ ÚËÛÈÌÔappleÔÈÔ ÓÙ È Ì ÁÓ ÙÂ Î È Ì ÁÓËÙÈÎÔ ÈÛıËÙ Ú (Yoshida Î È Û Ó., 2001a; 2001b). ÔÏÏ applefi Ù ÙÈ Ù ÓÈÎ ÚËÛÈÌÔappleÔÈ ıëî Ó Û ÓıÚÒappleÈÓ appleùòì Ù ÛÙ ÔappleÔ fiìˆ ÔÈ ÌË ÓÈÎ È ÈfiÙË- Ù ÙÔ appleâúèô ÔÓÙÈÎÔ Û Ó ÛÌÔ Â Ó È È ÊÔÚÂÙÈÎ ÌÂÙ ÙÔ ı Ó ÙÔ. È ÙÔ ÏfiÁÔ Ùfi ÚËÛÈÌÔappleÔÈ ıëî Ó ˆ appleô- Î Ù ÛÙ Ù ÙÔ appleâúèô ÔÓÙÈÎÔ Û Ó ÛÌÔ Û ÓıÂÙÈÎ Ô Û Â, fiappleˆ Ë ÛÈÏÈÎfiÓË. ÛÙ Ò fiìˆ ÔÈ Ô Û Â Ù ÂÓ Ô Ó Ê ÛÈÎ È ÈfiÙËÙ apple ÚfiÌÔÈ Ì ٠ÙÔ appleâúèô ÔÓÙÈÎÔ Û Ó ÛÌÔ (Vanden Bulcke Î È Û Ó., 1987). À ƒ À π π À È Christiansen Î È Burstone (1969) Î ıò Î È ÔÈ Burstone Î È Pryputniewicz (1980) Ó Ê ÚÔ Ó fiùè ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË Ú ÛÎÂÙ È ÛÂ Ó ÛËÌÂ Ô ÛÔ Ì ÙÔ 40% ÙÔ Ì ÎÔ ÙË Ú ÙÔ ÔÓÙÈÔ applefi ÙË Ê ÙÓÈ Î ÎÚÔ- ÏÔÊ ÛÂ Ó ÌÔÓÙ ÏÔ Ô È ÛÙ ÛÂˆÓ Ì apple Ú ÔÏÈÎfi Û Ì Ú ÛÙÔ 33% ÙÔ Ì ÎÔ ÙË Ú ÙÔ ÔÓÙÈÔ ÛÂ Ó ÙÚÈÛ È ÛÙ ÙÔ ÌÔÓÙ ÏÔ ÌÂ Ú ÛÂ Û Ì apple Ú Ô- ÏÔÂÈ Ô ÂÎ appleâúèûùúôê (paraboloid of revolution). Nikolai (1974) Î ıôú ÂÈ ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ ÔÓÙÈÔ Û applefiûù ÛË ÛË Ì ÙÔ 45% ÙÔ Ì ÎÔ ÙË Ú ÛÂ Ó ÈÛ È ÛÙ ÙÔ ÌÔÓÙ ÏÔ ÁÈ ıâˆúëùèî 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 ÙÈÎ ÌÔÓÙ Ï appleô ÚËÛÈÌÔappleÔ ËÛ Ó ÔÈ ÂÚ ÓËÙ. È ÈÎfiÙÂÚ Ô 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). LOCATION OF THE CENTER OF RESISTANCE OF A SINGLE TOOTH 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 46 HELLENIC ORTHODONTIC REVIEW 2005 ñ VOLUME 8 ñ ISSUE 1

5 Nikolai (1974) ÚËÛÈÌÔappleÔ ËÛ ÈÛ È ÛÙ Ù ÎÚÈ ÌÔÓÙ - Ï ÛÊËÓÔÂÈ ÒÓ (ÙÚÈÁˆÓÈÎÒÓ) ÚÈ ÒÓ Ì ÛË ÙË ıâˆú ÙË ÂÏ ÛÙÈÎfiÙËÙ ÙË appleâúèô ÔÓÙÈÎ ÌÂÌ Ú ÓË ÛÂ Û Ó- ÛÌfi Ì ÙÈ ÂÍÈÛÒÛÂÈ ÈÛÔÚÚÔapple ÙÔ Î ÌappleÙÔ ÔÓÙÈ- Ô, Ô Davidian (1971) Ó appleù ÍÂ Ó appleïfi ÌÔÓÙ ÏÔ appleúôû- ÈÔÚÈÛÌÔ ÙˆÓ Î ÓÙÚˆÓ ÓÙ ÛÙ ÛË Î È appleâúèûùúôê ÂÍÔ- ÌÔÈÒÓÔÓÙ ÙËÓ appleâúèô ÔÓÙÈÎ ÌÂÌ Ú ÓË Ì ÂÏ Ù ÚÈ, ÂÓÒ Ô Halazonetis (1996) Âapple ÎÙÂÈÓ ٠ÙË Ì ıô Ô ÒÛÙÂ Ó Û ÌappleÂÚÈÏ ÂÈ ÌË ÁÚ ÌÌÈÎ È ÈfiÙËÙ ÙË appleâúèô ÔÓÙÈÎ ÌÂÌ Ú ÓË Î ıò Î È È ÙÌËÙÈÎ Ù ÛÂÈ Î È ÛÙËÓ appleâú - appleùˆûë ÓÈÛÔÙÚÔappleÈÎ Û ÓıÂÛË ÙÔ appleâúèô ÔÓÙ Ô (Provatidis Î È Toutountzakis, 1998). È Nagerl Î È Û Ó. (1991) ÂÌ ı ÔÓÙ Ó Ó Î Ófi ÔÓÙ Û appleï ÛÙÈÎfi ÏÈÎfi ÙÔ ÔappleÔ Ô appleôù ıâù È fiùè appleôî ıèûù ÙÔÓ appleâúèô ÔÓÙÈÎfi Û Ó ÂÛÌÔ Ú Î Ó fiùè ÙÔ Î ÓÙÚÔ ÓÙ - ÛÙ ÛË ÙˆÓ ÔÓÙÈÒÓ Ú ÛÎÂÙ È ÛÂ Ó Ì ÛÔ Ô 34% (27-42%) ÙÔ Ì ÎÔ ÙË Ú ÙÔ. È Tanne Î È Û Ó. (1988) Î È ÔÈ Vollmer Î È Û Ó. (1999) ÚËÛÈÌÔappleÔÈÒÓÙ ÌÔÓÙ Ï appleâappleâú ÛÌ ÓˆÓ ÛÙÔÈ Â ˆÓ (finite elements models) Ó Ê ÚÔ Ó fiùè ÙÔ Î ÓÙÚÔ ÓÙ - ÛÙ ÛË Ú ÛÎÂÙ È Û applefiûù ÛË ÛË Ì 24% Î È 42% ÙÔ Ì ÎÔ ÙË Ú ÙÔ ÎÂÓÙÚÈÎÔ Óˆ ÙÔÌ Î È Î Ófi ÔÓÙ ÓÙ ÛÙÔÈ. Â Ì ÌÂÙ ÁÂÓ ÛÙÂÚË ÌÂÏ ÙË ÙˆÓ Tanne Î È Û Ó. (1991) ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ ÎÂÓÙÚÈÎÔ Óˆ ÙÔÌ appleôïôá ÛÙËΠÛÙÔ 34%. È ÊÔÚÂÙÈÎ Ù appleô- ÙÂÏ ÛÌ Ù Â Ó È Â ÎÔÏÔ Ó appleúôî Ô Ó Û ÌÊˆÓ Ì ÙÔ Provatidis Î È Toutountzakis (1998) Â Ó ÂappleËÚ ÛÙÂ Ì applefi ÙÈ ÎfiÏÔ ıâ Ù ÛÛÂÚÈ apple Ú Ì ÙÚÔ : ) Ô Ì ÁÂıÔ ÙÔ ÌÔÓÙ ÏÔ Á Úˆ applefi ÙÔ ÂÍ Ù ÛË fióùè ) Ô Â Ô ÙˆÓ ÔÚÈ ÎÒÓ Û ÓıËÎÒÓ. Á) ıìfi ÂÎÏ appleù ÓÛË ÙÔ appleï ÁÌ ÙÔ ÙˆÓ appleâappleâú ÛÌ - ÓˆÓ ÛÙÔÈ Â ˆÓ appleô apple ÈÙÂ Ù È ÁÈ ÙË Ï Ë ÍÈfiappleÈÛÙˆÓ appleôùâïâûì ÙˆÓ. Ú È appleï ÁÌ Ù Ô ËÁÔ Ó ÛÂ Ó ÎÚÈ- appleôùâï ÛÌ Ù. ) È ÙÈÌ ÙˆÓ ÌË ÓÈÎÒÓ È ÈÔÙ ÙˆÓ ÙˆÓ ÏÈÎÒÓ. È Poppe Î È Û Ó. (2002) Ú Î Ó fiùè ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÌÔÓfiÚÚÈ ˆÓ ÔÓÙÈÒÓ Ú ÛÎÂÙ È Û applefiûù ÛË ÛË Ì ÙÔ 42% ÙÔ Ô ÙÔ Ê ÙÓÈ ÎÔ appleâù ÏÔ. È Yoshida Î È Û Ó. (2001a) Ó Ê ÚÔ Ó fiùè ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ ÎÂÓÙÚÈÎÔ Óˆ ÙÔÌ Î Ù ÙË È ÚÎÂÈ ÙË appleâúòè ÌÂÙ Î ÓËÛ ÙÔ Ú ÛÎÂÙ È Û applefiûù ÛË ÛË appleâú appleô Ì ٠2/3 ÙÔ appleâúòèô Ô fiù Ó Ùfi ÌÂÙÚÈ - Ù È applefi ÙÔ ÎÚÔÚÚ Èfi ÙÔ ˆ ÙË Ê ÙÓÈ Î ÎÚÔÏÔÊ Î È ÂappleÔÌ Óˆ ÂÍ ÚÙ Ù È applefi ÙÔ Âapple appleâ Ô ÙÔ ÔÛÙÔ appleô Ú ÛÎÂÙ È appleâúòè. 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 singlerooted 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 E HNIKH OP O ONTIKH E I EøPH H 2005 ñ TOMO 8 ñ TEYXO 1 47

6 HELLENIC ORTHODONTIC REVIEW ËÏÈÎ 20 ÂÙÒÓ Î È ÌÂ Ê ÛÈÔÏÔÁÈÎfi Ì ÎÔ Ú, ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Î Ùˆ appleúôáôìê ˆÓ Ú ÛÎÂÙ È ÛÙÔ 40% ÙÔ Ì ÎÔ ÙË Ú ÓÂappleÒ, ÔÈ appleâúèûûfiùâúâ Ú Ó ÙÔappleÔıÂÙÔ Ó ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ ÌÔÓfiÚÚÈ Ô ÔÓÙÈÔ ÛÙÔ 33-42% ÙÔ Ì ÎÔ ÙË Ú applefi ÙË Ê ÙÓÈ Î apple Ú Ê ( ÎÚÔÏÔÊ ). Â Ó fióùè Ì ÎÔ Ú 10 mm fiappleˆ Â Ó È Ô ÎÂÓÙÚÈÎfi Óˆ ÙÔÌ Ë È ÊÔÚ Ù Â Ó È ÌÈÎÚfiÙÂÚË ÙÔ 1 mm (0,9 mm). ŒÓ Û ÛÙËÌ, fiìˆ, Ó ÌÂˆÓ Ì ÎÚ ÂÈ ÌÈÎÚfiÙÂÚË ÙÔ 1 mm Â Ó È ÛÎÔÏÔ Ó Î Ù ÛΠÛÙ ÛÙËÓ Î ıëìâúèó ÎÏÈÓÈÎ appleú ÍË. Ú ÎÙÈÎ Ùfi ÛËÌ ÓÂÈ fiùè ÔÈ Ó ÌÂÈ appleô ÂÊ ÚÌfi ÔÓÙ È ÛÙÔ fióùè ı Ô Ó Û Â fió apple ÓÙ Ì ÚÔapple. appleèappleï ÔÓ, Ë Î ÓËÛË ÙÔ ÔÓÙÈÔ ÌÂÙ ÙËÓ ÂÊ ÚÌÔÁ Î appleôè Ó ÌË ÌappleÔÚÂ Ó È ÎÚÈı ÛÂ Ô Ê ÛÂÈ : ÙËÓ appleúˆùôáâó Ë ÔappleÔ ÔÊ ÏÂÙ È ÛÙËÓ ÌÂÙ Î ÓËÛË ÙÔ ÔÓÙÈ- Ô Ì Û ÛÙËÓ appleâúèô ÔÓÙÈÎ ÌÂÌ Ú ÓË Î È ÙË Â ÙÂÚÔÁÂÓ Ë ÔappleÔ ÎÔÏÔ ıâ Î È ÔÊ ÏÂÙ È ÛÙËÓ Âapple Ó È ÌfiÚʈÛË ÙÔ ÔÛÙÔ (ÂÓ applefiıâûë Î È appleôúúfiêëûë) (Burstone Î È Û Ó., 1982). Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÔÓÙÈÒÓ fiìˆ ÂÓ ÂÙ È Ó ÌË Û Ìapple appleùâè ÛÙÈ Ô Ê ÛÂÈ ÙË Î ÓËÛË ÙÔ ÔÓÙÈÔ (Halazonetis, 1996). Ù Û Ó appleâè Ë Î ÓËÛË ÙÔ ÔÓÙÈÔ ÌappleÔÚÂ Ó Â Ó È È ÊÔÚÂÙÈÎ applefi Ù appleô ÂÈ Û Â È ÛÙÂ. ÎÚÈ ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË, fiìˆ, ÂÍ ÚÙ Ù È Î È applefi ÏÏÔ apple Ú ÁÔÓÙÂ, fiappleˆ ÙÔ Ì ÎÔ ÙË Ú ÙÔ ÔÓÙÈÔ Î È ÙÔ Ô ÙÔ ÔÛÙÔ appleô appleâúè ÏÏÂÈ ÙÔ fióùè. ªÂÁ Ï ÙÂÚË Âapple Ú ÛË ÂÈ ÙÔ Ì ÎÔ ÙË Ú applefi ÙÔ Ô ÙÔ ÔÛÙÔ. Â Ó Ó Î Ófi ÔÓÙ ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÌappleÔÚÂ Ó Ú ÛÎÂÙ È ÛÙÔ 45% ÙÔ Ì ÎÔ ÙË Ú ÙÔ ÔÓÙÈÔ ÂÓÒ ÛÂ Ó ÌÈÎÚfiÙÂÚÔ fióùè ÌÂ Ô Ú 12 mm ÛÙÔ 35% ÙÔ Ì ÎÔ (Schneider Î È Û Ó., 2002). ŸÙ Ó apple Ú ÙËÚÂ Ù È appleôúúfiêëûë ÙË Ú ÂÓfi ÔÓÙÈÔ ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÌÂÙ ÙÔapple ÂÙ È appleúô ÙË Ì ÏË ÙÔ ÔÓÙÈ- Ô fi È ÌfiÓÔ ÂÍ ÈÙ ÙË Ì ˆÛË ÙÔ Ì ÎÔ ÙË Ú ÏÏ Î È ÙË ÏÏ Á ÙÔ Û Ì Ùfi ÙË (Schneider Î È Û Ó., 2002). È Yoshida Î È Û Ó. (2001a) Ó Ê ÚÔ Ó fiùè ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ ÎÂÓÙÚÈÎÔ Óˆ ÙÔÌ fiù Ó ÂÊ Ú- Ìfi ÔÓÙ È appleâúòèâ Ó ÌÂÈ ÂÍ ÚÙ Ù È Î Ú ˆ applefi ÙÔ Ô ÙÔ appleâúòèô appleâù ÏÔ Î È ÂÏ ÈÛÙ applefi ÙÔ Ô ÙÔ ÂÈÏÈÎÔ ÔÛÙÈÎÔ appleâù ÏÔ. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÂÍ ÚÙ Ù È Âapple ÛË applefi ÙË È ı ÓÛË ÙË ÊfiÚÙÈÛË (loading). ÌÊˆÓ Ì ÙÔÓ Nagerl Î È Û Ó. (1991) Ë ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÌÂÙ ÏÏÂÙ È applefi ÙÔ 27-42% ÙÔ Ì ÎÔ ÙË Ú Ó ÏÔÁ Ì ÙË È ı Ó- ÛË ÙË ÂÊ ÚÌÔ fiìâóë Ó ÌË. Halazonetis (1996) Û 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 twodimensional 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 48 HELLENIC ORTHODONTIC REVIEW 2005 ñ VOLUME 8 ñ ISSUE 1

7 Ó ÈÛ È ÛÙ ÙÔ ÌÔÓÙ ÏÔ ÔÓÙÈÔ appleâúèô ÔÓÙ Ô Ì ÓÈ- ÛfiÙÚÔappleÔ appleâúèô 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 Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÌappleÔÚÂ Ó ÌÂÙ ÏËıÂ Ó ÏÔÁ Ì ÙË ÌÔÚÊÔÏÔÁ ÙÔ ÔÓÙÈÔ, ÙÔ Â Ô ÙÔ appleâúèô ÔÓÙÈÎÔ Û Ó ÛÌÔ, ÙËÓ appleôèfiùëù ÙÔ appleâúè ÏÏÔ- ÓÙÔ ÔÛÙÔ, ÙËÓ ÈÛÙÈÎ ÓÙ Ú ÛË ÛÙÈ ÛÎÔ ÌÂÓÂ Ó - ÌÂÈ, ÙËÓ ÂÊ ÁÚ ÓÛË ÙˆÓ apple Ú Î ÌÂÓˆÓ ÔÛÙÈÎÒÓ ÔÌÒÓ Î È ÙËÓ ÍÔÓÈÎ ÎÏ ÛË ÙÔ ÔÓÙÈÔ ˆÚ fiìˆ Ó Ó Ê - ÚÔ Ó appleâèú Ì ÙÈÎ Â ÔÌ Ó appleô Ó ÙÔ ÛÙËÚ Ô Ó. ÌÊˆÓ Ì ÙÔ Stoeckli Î È Teuscher (1985) ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÔappleÔÈ Û appleôùâ ÌÔÓ, ÂappleÂÈ ÂÍ ÚÙ Ù È applefi appleôïïô apple Ú ÁÔÓÙÂ, ÂÓ ÌappleÔÚÂ Ó ÂÓÙÔappleÈÛÙ Ì ÎÚ - ÂÈ apple Ú ÌfiÓÔ applefi ÙËÓ ÎÏÈÓÈÎ ÂÈÎfiÓ ÌÂÙ ÙËÓ ÂÊ ÚÌÔ- Á ÙË Ó ÌË. ÎÏÈÓÈÎ appleôùâï ÛÌ Ù fiù Ó ÂappleÈ ÂÈÚÂ Ù È ÌÂÙ Î ÓËÛË appleúô Ù appleˆ ÙˆÓ ÌÔÓfiÚÚÈ ˆÓ ÔÓÙÈÒÓ ÏÏ ÊÔÚ ÂappleÈ-  ÈÒÓÔ Ó Ù ıâˆúëùèî ÌÔÓÙ Ï Î È ÏÏ fi È. È Bourauel Î È Drescher (1994) Ó Ê ÚÔ Ó fiùè ÁÈ ÙËÓ appleˆ ÌÂÙ Î ÓËÛË ÙÔ Óˆ Î Ófi ÔÓÙ Ù appleâèú Ì ÙÈÎ Î È ÎÏÈÓÈ- Î appleôùâï ÛÌ 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 ÂappleÈÙ ıâ apple Ú ÏÏËÏË ÌÂÙ Î ÓËÛË ÙÔ ÔÓÙÈ- Ô ÂappleÂÈ Ë Ú ÙÔ apple ÚÔ ÛÈ ÂÈ ÂÍÔÁÎÒÌ Ù Î È ÎÔÈÏfi- ÙËÙ ÔÈ ÔappleÔ Â ÂappleËÚÂ Ô Ó ÙËÓ Î Ù ÓÔÌ ÙˆÓ Ù ÛÂˆÓ Î È ÙˆÓ appleè ÛÂˆÓ Î È ÂappleÔÌ Óˆ ÙËÓ Î ÓËÛË ÙÔ ÔÓÙÈÔ. ÏÔ, ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÔÓÙÈÒÓ Ì appleôïï Ú Â (multirooted teeth) Ú ÛÎÂÙ È ÎÔÓÙ ÛÙËÓ ÓˆÛË ÙˆÓ ÚÈ ÒÓ (Moyers, 1988; Bassigny, 1983). È Pedersen Î È Û Ó. (1991) appleôûùëú Ô Ó fiùè Ë ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ - ÛÙ ÛË ÙÔ Î Ùˆ ÁÔÌÊ Ô ÂÍ ÚÙ Ù È applefi ÙË ÁˆÌÂÙÚ ÙÔ ÔÓÙÈÔ, ÙÔ Ì ÎÔ ÙË Ú, ÙÔ Âapple appleâ Ô ÙÔ ÔÛÙÔ Î È ÙËÓ ËÏÈÎ ÙÔ ÙfiÌÔ. Ó È Ê ÓÂÚfi fiùè ÔÈ Û ÁÁÚ Ê ÂÓ Û ÌʈÓÔ Ó ÛÙÔÓ Î ıôúèûìfi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË. È ÏfiÁÔÈ Â Ó È Î Ú ˆ Ë È ÊÔÚÂÙÈÎ ÌÂıÔ ÔÏÔÁ appleô ÎÔÏÔ ıô Ó ÔÈ ÂÚ ÓË- Ù Î ıò Î È ÔÈ È ÊÔÚÂÙÈÎ ÙÈÌ ÙˆÓ apple Ú Ì ÙÚˆÓ appleô Î ıôú Ô Ó ÙËÓ ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË (apple.. ÙÔ Ì ÎÔ ÙË Ú, ÙÔ Û Ì ÙË, Ë È ı ÓÛË ÙˆÓ Ó ÌÂ- ˆÓ, ÙÔ Ô ÙÔ Ê ÙÓÈ ÎÔ appleâù ÏÔ Î.Ï.apple.). Ì Ì ıô- Ô ÂÓ Â Ó È Ù ÏÂÈ, fiïâ apple ÚÔ ÛÈ Ô Ó ÔÚÈÛÌ Ó ÌÂÈÔ- ÓÂÎÙ Ì Ù Î È appleïâôóâîù Ì Ù Ù ÔappleÔ Ó Ï ÔÓÙ È ÛÙËÓ Ú ÙÔ ÚıÚÔ. Ó È ÛÎÔÏÔ Âapple ÛË Ó Ù appleôappleôèëıô Ó fiïôè ÔÈ apple Ú ÁÔÓÙ appleô ÂappleËÚÂ Ô Ó ÙË ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÊÂÓfi ÌÂÓ ÂappleÂÈ Â Ó È appleôïïô, ÊÂmany 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). LOCATION OF THE CENTER OF RESISTANCE OF A GROUP OF TEETH 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. Center of resistance of anterior maxillary teeth CR location during intrusion 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 figureeight 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 E HNIKH OP O ONTIKH E I EøPH H 2005 ñ TOMO 8 ñ TEYXO 1 49

8 HELLENIC ORTHODONTIC REVIEW Ù ÚÔ Â ÂappleÂÈ Î appleôèôè appleèı ÓfiÓ Ó ÌËÓ Ô Ó ÂÚ ÓËıÂ Ó ÌËÓ ÌappleÔÚÔ Ó Ó ÂÚ ÓËıÔ Ó ÎfiÌ fiappleˆ apple.. Ë appleôèfiùëù ÙÔ ÔÛÙÔ appleô appleâúè 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 ÓËÙÈÎ appleúôûapple ıâèâ ÁÈ ÙÔ apple Ú ÁÔÓÙ appleô appleèı ÓfiÓ Ó ÂappleËÚÂ- Ô Ó ÙË ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË fiappleˆ ÙÔ Â Ô ÙÔ appleâúèô ÔÓÙÈÎÔ Û Ó ÛÌÔ, Ë appleôèfiùëù ÙÔ ÔÛÙÔ, Ë ÎÏ ÛË ÙÔ ÔÓÙÈÔ Î.Ï.apple. È Ú Ó appleú appleâè Ó Á ÓÔÓÙ È Û ÒÓÙ ÔÚÁ ÓÈÛÌÔ, fiù Ó Ùfi Â Ó È Ó Ùfi, ÁÈ Ó appleô- Ê ÁÔÓÙ È ÔÈ appleïô ÛÙ ÛÂÈ ÔÈ ÔappleÔ Â Û ÂÙ ÔÓÙ È Ì ÙÔ ÔÛÙfi Î È ÙÔ appleâúèô fióùèô. È Ú ÓÂ Ù Â Ó È appleï ÔÓ Ó Ù (Yoshida Î È Û Ó., 2001a; 2001b). À ƒ À π ª ø πø Ù ÙË È ÚÎÂÈ ÙË ÔÚıÔ ÔÓÙÈÎ ıâú appleâ appleôïï ÊÔÚ Â Ó È apple Ú ÙËÙË Ë ÌÂÙ Î ÓËÛË Ì ÔÌ ÔÓÙÈÒÓ appleúô ÌÈ ÔÚÈÛÌ ÓË Î Ù ı ÓÛË. ÔÚıÔ ÔÓÙÈÎfi ÁÈ Ó appleú ÁÌ ÙÔappleÔÈ ÛÂÈ appleôùâïâûì ÙÈÎ Ù ÙÈ ÎÈÓ ÛÂÈ appleú appleâè Ó ÁÓˆÚ ÂÈ ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙË ÔÌ ÙˆÓ ÔÓÙÈÒÓ. 1. ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ appleúôûı ˆÓ ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË Î Ù ÙËÓ ÂÌ ıèûë ÂÌ ıèûë ÙˆÓ appleúôûı ˆÓ ÔÓÙÈÒÓ ÂappleÈ ÈÒÎÂÙ È Û Ó Û ÛıÂÓ ÌÂ Ô ÏÈÎfi ÌfiÁÂÏÔ ÎÔÓÙfi Óˆ  ÏÔ Û ÛıÂÓ Ì ÍËÌ ÓË ÁˆÓ ÙÔ ÂappleÈapple Ô ÙË Î Ùˆ ÁÓ - ıô (Burstone, 1977). È Dermaut Î È Vanden Bulcke (1986) ÚËÛÈÌÔappleÔ ËÛ Ó Ù ÁÎÈÛÙÚ Î È ÙËÓ Ù ÓÈÎ Begg ÁÈ Ó ÌÂÏÂÙ ÛÔ Ó ÙËÓ ÂÌ ıèûë ÙˆÓ ÔÓÙÈÒÓ Û ÍËÚ ÎÚ Ó. Ô Î ÓÙÚÔ ÓÙ - ÛÙ ÛË ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ Ú ÛÎÂÙ È Î Ù appleúô- Û ÁÁÈÛË appleˆ ÙˆÓ Óˆ appleï Á ˆÓ ÂÓÒ ÙÔ Î ÓÙÚÔ ÙˆÓ ÍÈ Óˆ appleúôûı ˆÓ appleˆ ÙˆÓ Î ÓÔ fióùˆó. ÚfiÏ Ù apple Ú ÙË- ÚÔ ÓÙ È ÚÔapple Î È ÓÂÍ ÚÙËÙ ÌÂÙ ÎÈÓ ÛÂÈ ÔÓÙÈÒÓ È ˆ fiù Ó ÙÔ Û ÛÙËÌ appleâúèï Ì ÓÂÈ Ô fióùè Î È ÌÈÎÚfiÙÂÚ fiù Ó appleâúèï Ì ÓÂÈ ÍÈ fióùè. È ÙÔ ÏfiÁÔ Ùfi Ì ٠Ù ÓÈÎ Â Ó È Ó ÙÔ Ó ÚÂı ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Ô ÎÂÓÙÚÈÎÒÓ Óˆ ÙÔÌ ˆÓ (Dermaut Î È Vanden Bulcke, 1986). ÙËÓ ÎÏÈÓÈÎ appleú ÍË ÁÈ Ó ÓÙÈÌÂÙˆappleÈÛÙÔ Ó Ù ÔÈ ÌÂÙ ÎÈÓ ÛÂÈ ÔÈ Toutountzakis Î È Mavreas (1989) Û ÓÈ- ÛÙÔ Ó ÔÈ ÙÔÌÂ Ó ÓÔÓÙ È ÌÂÙ Í ÙÔ Ì ÙË Ô ıâè ÌÂÙ ÏÏÈÎ appleúfiû ÂÛË ÛÂ Û Ì ÔÎÙÒ. È Vanden Bulcke Î È Û Ó. (1986) ÚËÛÈÌÔappleÔ 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). Location of the center of CR during palatal movement 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 50 HELLENIC ORTHODONTIC REVIEW 2005 ñ VOLUME 8 ñ ISSUE 1

9 È Ì ıô Ô Ì ÙÔ appleúôëáô ÌÂÓÔ Û ÁÁÚ Ê ÂÌ ıè- Û Ó fiìˆ Ù fióùè ÛÂ Ó ÌÂÙ ÏÏÈÎfi Ó ÚıËÎ. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Ô ÎÂÓÙÚÈÎÒÓ Óˆ ÙÔÌ ˆÓ Î Ù ÙË È Ú- ÎÂÈ ÙË ÂÌ ıèûë Ú ÛÎÂÙ È ÛÂ Ì ÁÚ ÌÌ apple Ú ÏÏËÏË Ì ÙÔ Ì ÛÔ Ô ÂÏÈ Ô Âapple appleâ Ô ÛÙÔ appleˆ ÌÈÛ ÙˆÓ Î ÓÔ fi- ÓÙˆÓ, ÂÓÒ ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ ÛÂ Ì ÁÚ ÌÌ Î ıâùë ÛÙÔ Û ÁÎÏÂÈÛÈ Îfi Âapple appleâ Ô ÌÂÙ Í ÙˆÓ Î ÓÔ fi- ÓÙˆÓ Î È ÙˆÓ appleúòùˆó appleúôáôìê ˆÓ. Ô Î ÓÙÚ ÓÙ - ÛÙ ÛË Ú ÛÎÔÓÙ È Û applefiûù ÛË appleâú appleô 2 mm ÙÔ Ó applefi ÙÔ ÏÏÔ (Vanden Bulcke Î È Û Ó., 1986). ÓÙ ıâù ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÍÈ Óˆ appleúôûı ˆÓ Ú ÛÎÂÙ È ÛÂ Ì ÁÚ ÌÌ Î ıâùë ÛÙÔ Û ÁÎÏÂÈÛÈ Îfi Âapple appleâ Ô appleˆ ÙˆÓ appleúò- ÙˆÓ appleúôáôìê ˆÓ (Vanden Bulcke Î È Û Ó., 1986). Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË Î Ù ÙË È ÚÎÂÈ ÙË ÂÌ ıèûë  ÌÂÙ ÏÏÂÙ È ÛËÌ ÓÙÈÎ Ì ÙËÓ ÍËÛË ÙË ÓÙ ÛË ÙˆÓ Ó ÌˆÓ. Greenfield (1993) Ó Ê ÚÂÈ, ˆÚ fiìˆ Ó appleôî Ï - appleùâè ÙÈ appleëá ÙÔ, fiùè ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ Ú ÛÎÂÙ È apple Óˆ ÛÙËÓ Â ıâ Ë ÔappleÔ È Ù - ÌÓÂÈ ÙËÓ ÔÛÙ ÓÔ- Ì ÓÙÈÓÈÎ ÓˆÛË ÛÙË appleâúòè appleïâ - Ú ÙˆÓ Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔÌ ˆÓ. ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ - ÛÙ ÛË ÛÙÔ Û Ì ÙÔ ÚıÚÔ Ê ÓÂÙ È Ó Ú ÛÎÂÙ È appleˆ ÙÔ appleï ÁÈÔ ÙÔÌ. ÔÏÏÔ Û ÁÁÚ Ê ÔÈ ÔappleÔ ÔÈ ÚËÛÈÌÔappleÔÈÔ Ó ÙÌËÌ ÙÈÎ Ù ÓÈÎ ÁÈ ÙËÓ ÂÌ ıèûë ÙˆÓ Óˆ ÙÔÌ ˆÓ fiappleˆ Ô Shroff Î È Û Ó. (1995), ÔÈ Lindauer Î È Isaacson (1995) ÂÓ Ó - Ê ÚÔ Ó, Û ÛÙËÌ ÙÈÎ, ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ ÙÔÌ ˆÓ ÛÙÔ Î ÚÈÔ Ì ÚÔ ÙˆÓ ÚıÚˆÓ ÙÔ ÏÏ ÙÔ appleâè- ÎÔÓ Ô Ó ÌfiÓÔ ÛÙ Û Ì Ù ÙÔ appleˆ Î È apple Óˆ applefi ÙÔ ÁÎ ÏÈÔ ÙÔ appleï Á Ô Óˆ ÙÔÌ. È Û ÁÁÚ Ê ÙÔ ÛÙËÚ ÔÓÙ È appleúôê ÓÒ ÛÙÔ ÚıÚÔ ÙˆÓ Dermaut Î È Vanden Bulcke (1986) ÔÈ ÔappleÔ ÔÈ ÌÂÏ ÙËÛ Ó ÙËÓ ÂÌ ıèûë ÚËÛÈÌÔappleÔÈÒÓÙ Ù ÁÎ ÏÈ Î È ÙËÓ Ù ÓÈÎ Begg. appleôùâï ÛÌ Ù ÙÔ fiìˆ, Û ÌÊˆÓ Ì ÙÔ ÈÔ ÙÔ Û ÁÁÚ ÊÂ, ÂÓ ÌappleÔÚÔ Ó Ó ÌÂÙ ÊÂÚıÔ Ó appleèûù ÛÙËÓ ÎÏÈÓÈÎ appleú ÍË. Ú ÛË ÙÔ Araldite Û Ó appleôî Ù ÛÙ ÙÔ ÙÔ appleâúèô ÔÓÙÈÎÔ Û Ó ÛÌÔ fiappleˆ Î È ÙÔ ÍËÚÔ ÎÚ - Ó Ô ÛÙË ÌÂÏ ÙË ÙˆÓ Ô ÔÓÙÈÎÒÓ ÌÂÙ ÎÈÓ ÛÂˆÓ Ô Ó ÔÚÈ- ÛÌ ÓÔ appleâúèôúèûìô. appleèappleï ÔÓ Î Ù ÙË È ÚÎÂÈ ÙË ÂÌ ıèûë apple Ú ÙËÚ ıëî Ó ÚÔapple Î È ÓÂÍ ÚÙËÙ ÌÂÙ ÎÈ- Ó ÛÂÈ ÔÓÙÈÒÓ. È ÓÂÍ ÚÙËÙ ٠ÌÂÙ ÎÈÓ ÛÂÈ ÙˆÓ appleúôûı ˆÓ ÔÓÙÈÒÓ Û Ì ÓÔ Ó ÎfiÌ Î È Ì ÁÎ ÏÈ edgewise (Vanden Bulcke Î È Û Ó., 1986). È ÙÔ ÏfiÁÔ Ùfi ÔÈ Vanden Bulcke Î È Û Ó. (1986) ÚËÛÈÌÔappleÔ ËÛ Ó apple ÚfiÌÔÈ Ì ıô Ô ÏÏ ÂÌ ıèû Ó Ù fióùè ÛÂ Ó ÌÂÙ ÏÏÈÎfi Ó ÚıËÎ. appleôùâï ÛÌ Ù fiìˆ Ù Ó È ÊÔmm apically and of all six upper anterior teeth 7 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; E HNIKH OP O ONTIKH E I EøPH H 2005 ñ TOMO 8 ñ TEYXO 1 51

10 HELLENIC ORTHODONTIC REVIEW ÚÂÙÈÎ. È Pedersen Î È Û Ó. (1991) Ó Ê ÚÔ Ó fiùè Ù Î ÓÙÚ ÓÙ ÛÙ ÛË ÙˆÓ Ô Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔÌ ˆÓ Î È ÙˆÓ ÙÂÛ- Û ÚˆÓ Óˆ ÙÔÌ ˆÓ Ú ÛÎÔÓÙ È appleâú appleô 13 mm apple Ûˆ applefi Ù ÁÎ ÏÈ ÙˆÓ Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔÌ ˆÓ ÛÂ Ì ÁÚ ÌÌ 3 mm ÌappleÚÔÛÙ applefi ÙËÓ appleˆ ÂappleÈÊ ÓÂÈ ÙˆÓ Î ÓÔ fióùˆó. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÍÈ Óˆ appleúôûı ˆÓ Ú ÛÎÂÙ È 6 mm appleèô apple Ûˆ ( ÈÎ. 1). ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË Î Ù ÙËÓ appleâúòè ÌÂÙ Î - ÓËÛË È Vanden Bulcke Î È Û Ó. (1987) ÚËÛÈÌÔappleÔÈÒÓÙ Ó Ó ÌÂÙ ÏÏÈÎfi Ó ÚıËÎ ÛÙÔÓ ÔappleÔ Ô ÂÌ ıèû Ó Ù fióùè ÂÍ - Ù Û Ó ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ appleúôûı ˆÓ ÔÓÙÈÒÓ Î Ù ÙË È ÚÎÂÈ ÙË appleâúòè ÌÂÙ Î ÓËÛË ÛÂ Ô ÍËÚ ÎÚ - Ó. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Ô ÎÂÓÙÚÈÎÒÓ Óˆ ÙÔÌ ˆÓ Ú ÛÎÂÙ È 3,5 mm appleâú appleô ÎÚÔÚÚÈ ÈÎ applefi ÙÔ Âapple appleâ Ô ÙÔ ÔÛÙÔ ÌÂÙ Í ÙˆÓ ÙÔÌ ˆÓ (interproximal bone level) ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ 5 mm Î È ÙˆÓ ÍÈ Óˆ appleúô- Ûı ˆÓ 7 mm (Vanden Bulcke Î È Û Ó., 1987). È applefiï ÙÔÈ ÙÔ ÚÈıÌÔ Â ÌappleÔÚÔ Ó Ó ÌÂÙ ÊÂÚıÔ Ó Û ÌÊˆÓ Ì ÙÔ appleúôëáô ÌÂÓÔ Û ÁÁÚ Ê ÛÙËÓ ÎÏÈ- ÓÈÎ appleú ÍË. È È ÊÔÚ ÛÙËÓ Ó ÙÔÌ ÙÔ ÔÓÙÈÔ, ÙÔ ÔÛÙÔ Î È ÛÙÔ appleâúèúú ÈÔ ÌappleÔÚÔ Ó Ó ÏÏ ÍÔ Ó ÙË ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË Ë ÔappleÔ ÂappleÈappleÏ ÔÓ ÂÓ ÊÔÚ fiïë ÙËÓ Î ÓËÛË ÙÔ ÔÓÙÈÔ ÏÏ ÌfiÓÔ ÙËÓ Ú ÈÎ. Ô Û ÛÙË- Ì Ì ÙÔÓ ÌÂÙ ÏÏÈÎfi Ó ÚıËÎ ÛÙÔÓ ÔappleÔ Ô ÂÌ ı ÔÓÙ È Ù fióùè  ÚËÛÈÌÔappleÔÈÂ Ù È ÛÙËÓ Î ıëìâúèó ÎÏÈÓÈÎ appleú ÍË fiappleô Ù fióùè Û Ó ıˆ Û Ó ÔÓÙ È Ì ÌÂÙ ÏÏÈÎfi Û ÚÌ Î È ÂappleÈÙÚ appleôóù È Û Πappleôèô ıìfi ÔÈ ÌÂÙ ÎÈÓ ÛÂÈ ÙˆÓ ÔÓÙÈÒÓ. È Pedersen Î È Û Ó. (1991) Î ÓÔÓÙ ÌÂÙÚ ÛÂÈ Û ÁÓ - ıô ÌË ÒÓÙˆÓ ÓıÚÒappleˆÓ ÌÂÙ applefi ÓÂÎÚÔ Ó Ê - ÚÔ Ó fiùè ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Ô ÎÂÓÙÚÈÎÒÓ Óˆ ÙÔÌ ˆÓ Î È ÙˆÓ Óˆ appleúôûı ˆÓ Ú ÛÎÂÙ È Û Â fió ÛÙËÓ È ı ÛË (6,5 mm apple Óˆ applefi Ù ÁÎ ÏÈ ÙˆÓ ÎÂÓÙÚÈÎÒÓ Óˆ ÙÔÌ ˆÓ) ÂÓÒ Ùfi ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ appleèô ÎÔappleÙÈÎ (5 mm apple Óˆ applefi Ù ÁÎ ÏÈ ÙˆÓ ÎÂÓÙÚÈÎÒÓ Óˆ ÙÔÌ ˆÓ) ( ÈÎ. 1). È Melsen Î È Û Ó. (1990) ÛÈÛÌ ÓÔÈ ÛÂ Ó ıâˆúëùèîfi ÌÔÓÙ ÏÔ ÈÛ Ú ÔÓÙ È fiùè ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÍÈ Óˆ appleúôûı ˆÓ Ú ÛÎÂÙ È ÛÙÔ Ì ÛÔ ÙË applefiûù ÛË (halfway) ÌÂÙ Í ÙÔ Ì ÛÔ (midpoint) ÙˆÓ Î ÓÙÚˆÓ ÓÙ - ÛÙ ÛË ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ Î È ÙÔ Î ÓÙÚÔ ÓÙ - ÛÙ ÛË ÙÔ Î Ófi ÔÓÙ. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ appleúôûı ˆÓ È Ê ÚÂÈ applefi ÙÔÌÔ Û ÙÔÌÔ Î È ÂÍ ÚÙ Ù È 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 midsagittal 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. A review of the literature shows that most researchers do 52 HELLENIC ORTHODONTIC REVIEW 2005 ñ VOLUME 8 ñ ISSUE 1

11 ÈÎfiÓ 1. a) ÚÈ fióùèâ Î È Î ıâùâ Ó ÌÂÈ ÈÂÚ fiìâóâ applefi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔÌ ˆÓ. b) ÚÈ fióùèâ Î È Î ıâùâ Ó - ÌÂÈ ÈÂÚ fiìâóâ applefi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ. c) ÚÈ fióùèâ Î È Î ıâùâ Ó ÌÂÈ ÈÂÚ fiìâóâ applefi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ - ÛË ÙˆÓ ÍÈ Óˆ appleúôûı ˆÓ. (Aapplefi: Pedersen Î È Û Ó. (1991), Î ÙfiappleÈÓ Â ÙÔ Oxford University Press.) Figure 1. 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.) E HNIKH OP O ONTIKH E I EøPH H 2005 ñ TOMO 8 ñ TEYXO 1 53

12 HELLENIC ORTHODONTIC REVIEW applefi ÙÔ Ì ÎÔ ÙˆÓ ÚÈ ÒÓ Î È ÙÈ ÎÏ ÛÂÈ ÙˆÓ Óˆ appleúô- Ûı ˆÓ. ÌÊˆÓ Ì ÙÔ appleúôëáô ÌÂÓÔ Û ÁÁÚ Ê ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ appleúôûı ˆÓ ÛÙÔ ÔÚÈ fióùèô Âapple - appleâ Ô Ú ÛÎÂÙ È 0.72 mm appleˆ ÙÔ ÁÎ Ï Ô ÙÔ Óˆ Î Ófi ÔÓÙ ( ÈÎ. 2). È Bourauel Î È Drescher (1994) ÚËÛÈÌÔappleÔÈÒÓÙ ÌÈ ÙÚÔappleÔappleÔÈËÌ ÓË ÁÎ ÏË ÙÔ Burstone Ó Ê ÚÔ Ó fiùè ÛÙËÓ appleâúòè ÌÂÙ Î ÓËÛË ÙˆÓ Óˆ ÙÔÌ ˆÓ Ù appleâèú Ì ÙÈ- Î Î È ÎÏÈÓÈÎ appleôùâï ÛÌ Ù ÂÓ ÓÙÈÛÙÔÈ Ô Ó Û ÌÂÁ ÏÔ ıìfi. ÌÊˆÓ Ì ÙÔ appleúôëáô ÌÂÓÔ Û ÁÁÚ ÊÂ Ë ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ ÙÔÌ ˆÓ ÂÓ ÂÈ appleï Úˆ appleôû ÊËÓÈÛıÂ. È Yoshida Î È Û Ó. (2001b) Ú ÛÎÔ Ó fiùè ÙÔ Î ÓÙÚÔ ÓÙ - ÛÙ ÛË ÙˆÓ Ô Î È ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ Û Ìapple - appleùô Ó Ï ÁÔ appleôï Î È Ú ÛÎÔÓÙ È 4,3 mm ÎÚÔÚÚÈ ÈÎ ÙÔ appleâúòèô appleâù ÏÔ ÂÓÒ Ùfi ÙˆÓ 6 appleúôûı ˆÓ 0,8 mm appleèô ÎÔappleÙÈÎ. È appleúôëáô ÌÂÓÔÈ Û ÁÁÚ Ê appleúôûapple ıëû Ó Ó Û ÁÎÚ ÓÔ Ó ÙÈ ÂÚÁ Û Â ÙˆÓ Vanden Bulcke Î È Û Ó. (1987), Pedersen Î È Û Ó. (1991) Ì ÙË ÈÎ ÙÔ ÌÂÙÚÒ- ÓÙ applefi ÙËÓ ÎÔappleÙÈÎ ÂappleÈÊ ÓÂÈ ÙˆÓ Óˆ ÙÔÌ ˆÓ. Ìʈ- Ó Ì ÙÔ Î Ù ÙËÓ ÏÍË, ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Ô Óˆ ÎÂÓÙÚÈÎÒÓ ÙÔÌ ˆÓ Ê ÓÂÙ È Ó Ú ÛÎÂÙ È ÌÂÙ Í ÙˆÓ 10,3 Î È 11,1 mm, ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ ÌÂÙ Í ÙˆÓ 8,1 Î È ÙˆÓ 12,3 mm Î È ÙˆÓ ÍÈ Óˆ appleúôûı ˆÓ ÌÂÙ - Í ÙˆÓ 10,5 Î È 13,7 mm applefi ÙËÓ ÎÔappleÙÈÎ ÂappleÈÊ ÓÂÈ ÙˆÓ Óˆ ÙÔÌ ˆÓ (Vanden Bulcke Î È Û Ó., 1987; Pedersen Î È Û Ó., 1991; Yoshida Î È Û Ó., 2001a). ÂÓ Â Ó È ÁÓˆÛÙ ÂappleÔÌ Óˆ Ë ÎÚÈ ı ÛË ÙˆÓ Î ÓÙÚˆÓ ÓÙ ÛÙ ÛË, È ˆ ÙˆÓ Óˆ ÙÔÌ ˆÓ Î È ÙˆÓ Óˆ appleúôûı ˆÓ ÏÏ Ë appleâúèô Á Úˆ applefi ÙËÓ ÔappleÔ appleèı ÓfiÓ Ó ÂÓÙÔapple ÔÓÙ È. ÏÔ, ÔÈ Matsui Î È Û Ó. (2000) ÛÂ Ó ÊˆÙÔÂÏ ÛÙÈÎfi ÈÎfiÓ 2. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ appleúôûı ˆÓ Û ÌÊˆÓ Ì ÙÔ Melsen Î È Û Ó. (1990). ( applefi: Melsen Î È Û Ó. (1990), Î ÙfiappleÈÓ Â - ÙÔ J Clin Orthod.) Figure 2. 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.) 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. Location of the center of resistance of other groups of teeth 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 midsagittal 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). 54 HELLENIC ORTHODONTIC REVIEW 2005 ñ VOLUME 8 ñ ISSUE 1

13 ÌÔÓÙ ÏÔ Ú Î Ó fiùè ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ ÙÔappleÔıÂÙÂ Ù È ÛÙÔ Ì ÛÔ Ô ÂÏÈ Ô Âapple appleâ Ô 4 mm apple Ûˆ Î È 6 mm apple Óˆ applefi ÙË ÂÈÏÈÎ Ê ÙÓÈ Î ÎÚÔ- ÏÔÊ ÙˆÓ ÎÂÓÙÚÈÎÒÓ Óˆ ÙÔÌ ˆÓ. È Û ÁÁÚ Ê apple ˆ- Û Ó ÙË È ÊÔÚ Ì ÙÈ ÏÏ ÌÂÏ Ù ÛÙË Ú ÛË ÊˆÙÔÂ- Ï ÛÙÈÎÔ ÏÈÎÔ Î È ÛÙÔ È ÛÙËÌ ÙˆÓ 6 mm appleô apple Ú-  ÌÂÙ Í ÙÔ appleï Á Ô Óˆ ÙÔÌ Î È ÙÔ Î Ófi ÔÓÙ. Àapple Ú Ô Ó appleôïï ÂÚÁ Û Â ÁÈ ÙËÓ appleâúòè ÌÂÙ Î ÓËÛË ÙˆÓ Óˆ ÙÔÌ ˆÓ. Ó ÂÈÎÙÈÎ Ó Ê ÚÔ Ì ÌÂÚÈÎ ÔÈ ÔappleÔ -  ÚËÛÈÌÔappleÔÈÔ Ó È ÊÔÚÂÙÈÎ Î ÓÙÚ ÓÙ ÛÙ ÛË. È Park Î È Û Ó. (2000) ÈÛ Ú ÔÓÙ È fiùè Âapple Ù Ó apple Ú Ï- ÏËÏË ÌÂÙ Î ÓËÛË ÙˆÓ appleúôûı ˆÓ ÔÓÙÈÒÓ ÌÂ Ó Û ÛÙËÌ lever-arm Î È ÁψÛÛÈÎ ÁÎ ÏÈ ˆÚ Ó Ó Ê ÚÔ Ó ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÔÓÙÈÒÓ apple Ú ÌfiÓÔ ÙÔ Û Â Û Ó. È Choy Î È Û Ó. (2002) ÂappleÈÓÔÔ Ó Ó Û ÛÙËÌ (SDRS) ÁÈ ÙËÓ appleâúòè ÌÂÙ Î ÓËÛË ÙˆÓ Óˆ appleúôûı ˆÓ, ÂÓ Ó Ê - ÚÔ Ó fiìˆ Ô Ù ÙÔ ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÏÏ ÌfiÓÔ ÙÔ Û Â È Ô Ó. È Kim Î È Û Ó. (2004) ÚËÛÈÌÔappleÔÈÔ Ó ÙÔÓ C-lingual retractor ÁÈ ÙËÓ appleâúòè ÌÂÙ Î ÓËÛË Î È ÂÌ ıèûë ÙˆÓ Óˆ appleúôûı ˆÓ. È ÙÔÓ ÔÚÈÛÌfi ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ appleúôûı ˆÓ ÛÙËÚ ÔÓÙ È ÛÙË ÌÂÏ ÙË ÙˆÓ Vanden Bulcke Î È Û Ó. (1986). È Guray Î È Orhan (1997) ÚËÛÈÌÔappleÔÈÔ Ó Â͈ÛÙÔÌ ÙÈÎfi ÙfiÍÔ (anterior headgear) ÁÈ ÙËÓ appleâúòè ÌÂÙ Î ÓËÛË ÙˆÓ Óˆ appleúôûı ˆÓ. È Ó ÔÚ ÛÔ Ó ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ appleúôûı ˆÓ ÂappleÈÏ ÁÔ Ó ÙËÓ ÂÚÁ Û ÙË Melsen Î È Û Ó. (1990). Gjessing (1992) ÂappleÈÓÔ ÙÔ ÂÏ Ù ÚÈÔ PG ÁÈ ÙËÓ appleâúò- È ÌÂÙ Î ÓËÛË ÙˆÓ Óˆ ÙÔÌ ˆÓ. È ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ appleúôûı ˆÓ ÚËÛÈÌÔappleÔÈ ÙÔÓ ÔÚÈÛÌfi ÙÔ Pedersen. ÙÈ ÂÚÁ Û Â Ù Ó Ê ÚÔÓÙ È ÛÙÔ ıâˆúëùèîfi Ì ÚÔ ÔÈ Ú ÏÂÈÙÔ ÚÁ ÙÔ Û ÛÙ Ì ÙÔ appleô appleúôùâ ÓÂÙ È ÁÈ ÙËÓ appleâúòè ÌÂÙ Î ÓËÛË ÙˆÓ Óˆ appleúôûı ˆÓ, ÌÂÚÈÎ ÊÔÚ Î appleôè appleâèú Ì ÙÈÎ Â ÔÌ Ó Î È Ù ÏÔ apple ÚÔ ÛÈ - ÂÙ È Ó ÎÏÈÓÈÎfi appleâúèûù ÙÈÎfi ÛÙÔ ÔappleÔ Ô Â ÓÂÙ È Ë ÏÂÈ- ÙÔ ÚÁ ÙÔ ÌË Ó Ì ÙÔ. Û ÛÙ Ì Ù Ù Â Ó È ÛÎÔÏÔ Ó Û ÁÎÚÈıÔ Ó ÌÂÙ Í ÙÔ Ô Ó fiìˆ ÌÈ ÛˆÛÙ ıâˆúëùèî ÛË Î È Ù appleôùâï ÛÌ Ù ÙÔ Ï ÈÛÙÔÓ ÛÙ ÎÏÈÓÈÎ appleâúèûù ÙÈÎ Â Ó È ÂÍ ÈÚÂÙÈÎ. È appleâúèûûfiùâúôè Û ÁÁÚ Ê ÚËÛÈÌÔappleÔÈÔ Ó Ó ÌÂÈ Ó ÌÂÈ Î È ÚÔapple ÁÈ ÙËÓ ÏÍË ÙˆÓ Óˆ ÙÔÌ ˆÓ ÙˆÓ Óˆ appleúôûı ˆÓ, ÂappleÈÏ ÁÔ Ó Ó Î ÓÙÚÔ ÓÙ ÛÙ ÛË ˆÚ fiìˆ Ó apple Ú ÂÈ Ó ÙfiÙËÙ Ó ÎÚ ÓÔ Ì appleôèô Â Ó È Ô ÛˆÛÙfi ÔÚÈÛÌfi Ó apple Ú ÂÈ ÛˆÛÙfi. È ÔÚÈÛÌÔ fiìˆ ÙˆÓ Pedersen Î È CONCLUSIONS The center of resistance of single-rooted teeth is located between 33% and 42% of the root length when measured from the alveolar crest. The center of resistance of a group of teeth varies according to the number of teeth. Most research studies concern maxillary incisors and maxillary anterior teeth. However, there are serious objections about CR location during palatal movement and intrusion, which may challenge the clinical orthodontist. Furthermore, our knowledge concerning the factors affecting the location of the CR of tooth groups is very limited; this may be due to the fact that these factors are not easily measured in groups of teeth; e.g., what root length or what alveolar plate height should be measured when intrusion of the four upper incisors is attempted? Perhaps mathematical models will resolve this issue in the future. However, an orthodontist treats patients rather than centers of resistance. If a method is successfully tested in the clinical practice, a clinician may use it. References Bassigny F. Le traitement des anomalies orthodontiques. In Bassigny F. Manuel d orthopedie dento-faciale. Paris: Masson, 1983: Bourauel C, Drescher D. Retraction of the upper incisors with pseudoplastic treatment elements. Their computational and biomechanical testing and clinical use. Fortschr Kieferorthop 1994;55: Burstone CJ, Every TW, Pryputniewicz RJ. Holographic measurement of incisor extrusion. Am J Orthod 1982;82:1-9. Burstone CJ. Deep overbite correction by intrusion. Am J Orthod 1977;72:1-22. Burstone CJ, Pryputniewicz RJ. Holographic evaluation of centers of rotation produced by orthodontic forces. Am J Orthod 1980;77: Choy K, Pae EK, Kim KH, Park YC, Burstone CJ. Controlled space closure with a statically determinate retraction system. Angle Orthod 2002;72: Christiansen RL, Burstone CJ. Centers of rotation within the periodontal space. Am J Orthod 1969;55: Davidian EJ. Use of a computer model to study the force distribution on the root of a maxillary central incisor. Am J Orthod 1971;59: Dermaut LR, Vanden Bulcke MM. Evaluation of intrusive mechanics of the type "segmented arch" on a macerated human skull using the laser reflection technique and holographic interferometry. Am J Orthod 1986;89: Fung YC. Biomechanics, the mechanical properties of living tissues. E HNIKH OP O ONTIKH E I EøPH H 2005 ñ TOMO 8 ñ TEYXO 1 55

14 HELLENIC ORTHODONTIC REVIEW Û Ó. (1991) Î È ÙˆÓ Melsen Î È Û Ó. (1990) Ú ÛÎÔÓÙ È appleôï ÎÔÓÙ Ô Ó Ì ÙÔÓ ÏÏÔ. applefi ÙËÓ Ó ÛÎfiappleËÛË ÙË È ÏÈÔÁÚ Ê Á ÓÂÙ È Ê ÓÂÚfi fiùè ÔÈ appleâúèûûfiùâúôè ÂÚ ÓËÙ ÛÙÈ appleâèú Ì ÙÈÎ ÙÔ ÂÚÁ - Û Â ÂÓ ÂÍÂÙ Ô Ó Ó ÂÓÈ Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÔÓÙÈÒÓ ÏÏ ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË Î Ù ÙËÓ appleâúòè ÌÂÙ Î ÓËÛË ÙËÓ ÂÌ ıèûë ˆÚ Ó Ó Ê ÚÔÓÙ È Û ÏÏ ÌÔÚÊ ÌÂÙ Î ÓËÛË ÙˆÓ ÔÓÙÈÒÓ (Ì ÛËÙÈÎ ÌÂÙ Î - ÓËÛË, Î.Ï.apple.) (Dermaut Î È Vanden Bulcke, 1986; Vanden Bulcke Î È Û Ó., 1986; Vanden Bulcke Î È Û Ó., 1987; Yoshida Î È Û Ó., 2001b). Ù Û ÌappleÂÚ ÛÌ Ù ÙÔ Î ÓÔ Ó Ó ÊÔÚ ÛÙË ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË Î Ù ÙËÓ appleâ- ÚÒ ÌÂÙ Î ÓËÛË ÙËÓ ÂÌ ıèûë apple ÓÙÔÙ fiìˆ ÛÂ Ì È ÛÙ ÛË. ÎfiÌ Î È ÔÈ ÂÚ ÓËÙ appleô ÂÍ Ù Û Ó ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ - ÛË Î Ù ÙËÓ appleâúòè ÌÂÙ Î ÓËÛË Î È ÙËÓ ÂÌ ıèûë fiappleˆ ÔÈ Pedersen Î È Û Ó. (1991) ÛÙÔ ÈÔ ÎÚ Ó Ô Î È ÔÈ Vanden Bulcke Î È Û Ó. (1986) Î È Vanden Bulcke Î È Û Ó. (1987) ÛÂ Ô ˆÚÈÛÙ ÂÚÁ Û Â Ì apple ÚfiÌÔÈ ÌÂıÔ ÔÏÔÁ ÂÓ Ó Ê ÚÔ Ó fiùè Ù Ô Î ÓÙÚ Û Ìapple appleùô Ó. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÔÓÙÈÒÓ ÌappleÔÚÂ Ó È Ê ÚÂÈ Ó ÏÔÁ Ì ÙË È ı ÓÛË ÙË ÂÊ ÚÌÔ fiìâóë Ó ÌË. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË apple.. ÂÓfi ÌÔÓfiÚÚÈ Ô ÔÓÙÈÔ È - Ê ÚÂÈ ÛÙËÓ appleâúòè ÌÂÙ Î ÓËÛË Î È ÛÙËÓ ÂÌ ıèûë (Nagerl Î È Û Ó., 1991).  ÔÚÈÛÌ Ó ÙÌËÌ ÙÈÎ Ù ÓÈÎ fiappleˆ ÙÔ ÙÌËÌ ÙÈÎfi ÙfiÍÔ ÙÚÈÒÓ ÙÂÌ ˆÓ (three-piece intrusion arch) Ë Ó ÌË, Ó Î È Â Ó È Î Ú ˆ ÂÌ ıèûë, ÂÈ Î È Ì appleâúòè Û ÓÈÛÙÒÛ Ë ÔappleÔ fiìˆ Ûˆ ÏÏ - ÂÈ ÙÔ ıâˆúëùèîfi Î ÓÙÚÔ ÓÙ ÛÙ ÛË. ÙÌËÌ ÙÈÎ Ù ÓÈÎ ÁÈ ÙËÓ ÂÌ ıèûë ÙˆÓ Óˆ ÙÔÌ ˆÓ ÂÈ appleôïï appleïâôóâîù - Ì Ù Î È appleôïï ÊÔÚ ÛÙËÓ Î ıëìâúèó ÎÏÈÓÈÎ appleú ÍË Â Ó È Ë ÌfiÓË appleôùâïâûì ÙÈÎ. ÚfiÏ Ù, Ù appleú ÎÙÈÎ appleôùâï ÛÌ Ù ÌappleÔÚÂ Ó È Ê ÚÔ Ó Ï ÁÔ appleôï applefi Ù ıâˆúëùèî. 2. ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÏÏˆÓ ÔÌ ˆÓ ÔÓÙÈÒÓ ÚÈÛÌ ÓÔÈ Û ÁÁÚ Ê ÔÚ Ô Ó Î ÓÙÚ ÓÙ ÛÙ ÛË ÛÙËÚÈ fi- ÌÂÓÔÈ Û ÎÏÈÓÈÎ apple Ú ÙËÚ ÛÂÈ Î È fi È Û appleâèú Ì ÙÈÎ ÂÚÁ ÛÙËÚÈ Î Â ÔÌ Ó Î È ÂappleÔÌ Óˆ Ù Â Ú Ì Ù ÙÔ appleú appleâè Ó ÂÍÂÙ ÔÓÙ È Ì ÌÂÁ ÏË appleúôûô (Papadopoulos Î È Christou, 2000). Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ Óˆ ÙÔÌ ˆÓ Î È ÙˆÓ appleúòùˆó ÁÔÌÊ ˆÓ ÔÈ ÔappleÔ ÔÈ Û Ó ÔÓÙ È ÌÂ Ó ÙÌË- Ì ÙÈÎfi ÙfiÍÔ Ú ÛÎÂÙ È ÛÙÔ ÛËÌÂ Ô ÙÔÌ ÙÔ Ì ÛÔ Ô ÂÏÈ- Ô ÂappleÈapple Ô Î È ÂÓfi ÂappleÈapple Ô apple Ú ÏÏËÏÔ Ì ÙÔ ÌÂÙˆappleÈ Ô appleô appleâúó applefi ÙÈ ÂÁÁ apple ÚÂÈ Î Ú Â ÙˆÓ appleúòùˆó 2nd ed. New York: Springer-Verlag, Gjessing P. Controlled retraction of maxillary incisors. Am J Orthod Dentofacial Orthop 1992;101: Greenfield RL. Simultaneous torquing and intrusion auxiliary. J Clin Orthod 1993;27: Guray E, Orhan M. "En Masse" retraction of maxillary anterior teeth with anterior headgear. Am J Orthod Dentofac Orthop 1997;112: Halazonetis DJ. Computer experiments using a two-dimensional model of tooth support. Am J Orthod Dentofacial Orthop 1996;109: Kim SH, Park YG, Chung K. Severe class II anterior deep bite malocclusion treated with a C-lingual retractor. Angle Orthod 2004;74: Lindauer SJ, Isaacson RJ. One-couple orthodontic appliance systems. Sem Orthod 1995;1: Moyers RE. Force systems and tissue responses to forces in orthodontics and facial orthopedics. In Moyers RE. Handbook of orthodontics, 4th edition. Chicago: Year Book Medical Publishers Inc, 1988: Matsui S, Caputo AA, Chaconas SJ. Center of resistance of anterior arch segment. Am J Orthod Dentofacial Orthop 2000; McGuiness NJP, Wilson AN, Jones ML, Middleton J. A stress analysis of the periodontal ligament under various orthodontic loadings. Eur J Orthod 1991;13: Melsen B, Fotis V, Burstone CJ. Vertical forces considerations in differential space closure. J Clin Orthod 1990;24: Nagerl H, Burstone CJ, Becker B, Kubein-Messenburg D. Centers of rotation with transverse forces: an experimental study. Am J Orthod Dentofacial Orthop 1991;99: Nanda R, Kuhlberg A. Principles of biomechanics. In: Nanda: R, ed. Biomechanics in clinical orthodontics. Philadelphia: WB Saunders Company, 1997:1-22. Nikolai RJ. Periodontal ligament reaction and displacements of a maxillary central incisor subjected to transverse crown loading. J Biomech 1974;7:93-9. Papadopoulos MA, Christou PK. Centers of resistance of the maxillary complex: Theoretical models and practical applications in orthodontics. Hell Orthod Rev 2000;3: Park JB, Lakes RS. Biomaterials: an introduction. 2nd edition. New York: Plenum press, Park YC, Choy K, Lee JS, Kim TK. Lever-arm mechanics in lingual orthodontics. J Clin Orthod 2000;34: Pedersen E, Isidor F, Gjessing P, Andersen K. Location of centres of resistance for maxillary anterior teeth measured on human autopsy material. Eur J Orthod 1991;13: Poppe M, Bourauel C, Jager A. Determination of the elasticity parameters of the human periodontal ligament and the location of the center of resistance of single-root teeth. Fortschr Kieferorthop 2002;63: Proffit WR, Fields HW. Mechanical principles in orthodontic force control. In Proffit WR, Fields HW. Contemporary orthodontics. St Louis: CV Mosby, 2000: Provatidis CG, Toutountzakis NE. A critical review of older and contemporary applications of biomechanical method in orthodontics. Hell Orthod Rev 1998;1: HELLENIC ORTHODONTIC REVIEW 2005 ñ VOLUME 8 ñ ISSUE 1

15 Óˆ ÌfiÓÈÌˆÓ ÁÔÌÊ ˆÓ (Stoeckli Î È Teuscher, 1985). ÏÔ ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙÔ Óˆ Ô ÔÓÙÈÎÔ ÊÚ ÁÌÔ Ô ÔappleÔ Ô Û Ó ÂÙ È Ì ΠÓËÙ ÔÚıÔ ÔÓÙÈÎ Û ÛÎÂ Ú ÛÎÂÙ È ÛÙÔ ÛËÌÂ Ô ÙÔÌ ÙÔ Ì ÛÔ Ô ÂÏÈ Ô ÂappleÈapple - Ô Î È ÂÓfi ÂappleÈapple Ô apple Ú ÏÏËÏÔ Ì ÙÔ ÌÂÙˆappleÈ Ô Î È È Ú ÂÙ È ÌÂÙ Í ÙˆÓ ÚÈ ÒÓ ÙˆÓ Ô appleúôáôìê ˆÓ Î È Â Ó È Î ıâùë ÛÙÔ Û ÁÎÏÂÈÛÈ Îfi Âapple appleâ Ô (Stoeckli Î È Teuscher, 1985). Àª ƒ ª Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙˆÓ ÌÔÓfiÚÚÈ ˆÓ ÔÓÙÈÒÓ Ú ÛÎÂÙ È Ó ÌÂÛ ÛÙÔ 33-42% ÙÔ Ì ÎÔ ÙË Ú fiù Ó Ë Ì ÙÚË- ÛË Á ÓÂÙ È applefi ÙË Ê ÙÓÈ Î ÎÚÔÏÔÊ. Ô Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÌÈ ÔÌ ÔÓÙÈÒÓ È Ê ÚÂÈ Ó - ÏÔÁ Ì ÙÔÓ ÚÈıÌfi ÙˆÓ ÔÓÙÈÒÓ. È appleâúèûûfiùâúâ Ú - ÓÂ Ô Ó Á ÓÂÈ ÁÈ ÙÔ Óˆ ÙÔÌÂ Î È ÙÔ Óˆ appleúôûı - Ô. ÚfiÏ Ù, apple Ú Ô Ó ÛÔ Ú È ÊˆÓ Â ÁÈ ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÙfiÛÔ Î Ù ÙËÓ appleâúòè ÌÂÙ Î ÓËÛË fiûô Î È Î Ù ÙËÓ ÂÌ ıèûë ÔÈ ÔappleÔ Â appleèı ÓfiÓ Ó appleúô ÏË- Ì Ù Ô Ó ÙÔÓ ÎÏÈÓÈÎfi ÔÚıÔ ÔÓÙÈÎfi. appleèappleï ÔÓ ÔÈ ÁÓÒÛÂÈ Ì ÁÈ ÙÔ apple Ú ÁÔÓÙ appleô ÂappleËÚÂ Ô Ó ÙË ı ÛË ÙÔ Î ÓÙÚÔ ÓÙ ÛÙ ÛË ÔÌ ˆÓ ÔÓÙÈÒÓ Â Ó È appleôï appleâúèôúè- ÛÌ Ó ۈ ÂappleÂÈ ÔÈ apple Ú ÁÔÓÙ ÙÔ Â Ó È ÛÎÔÏÔ Ó ÌÂÙÚËıÔ Ó Û ÔÌ Â ÔÓÙÈÒÓ (apple.. appleôèô Ô ÙË Ú ı appleú appleâè Ó ÌÂÙÚËı appleôèô Ô Ê ÙÓÈ ÎÔ appleâù ÏÔ fiù Ó ÂappleÈ ÂÈÚÂ Ù È ÂÌ ıèûë ÙˆÓ ÙÂÛÛ ÚˆÓ Óˆ ÙÔÌ ˆÓ). ÿûˆ Ù Ì ıëì ÙÈÎ ÌÔÓÙ Ï ÌappleÔÚ ÛÔ Ó ÛÙÔ Ì ÏÏÔÓ Ó appleúôûâáá ÛÔ Ó appleâúèûûfiùâúô ÙÔ ÙÔ apple Ú ÁÔÓÙÂ. ÔÚıÔ ÔÓÙÈÎfi fiìˆ ÂÓ ıâú appleâ ÂÈ Î ÓÙÚ ÓÙ ÛÙ ÛË ıâú appleâ ÂÈ ÛıÂÓÂ. Ó Ì Ì ıô Ô ÂÈ ÔÎÈÌ ÛÙ ÎÏÈ- ÓÈÎ Ì ÂappleÈÙ ı appleú appleâè Ó ÙË ÚËÛÈÌÔappleÔÈÂ. È ı ÓÛË ÁÈ Ó Ù apple : πˆ ÓÓË. apple ÁˆÚÁ Ô ÂÛÛ Ï ˆÁÚ ÊÔ [email protected] Qian H, Chen J, Katona TR. The influence of PDL principal fibers in a 3-dimensional analysis of orthodontic tooth movement. Am J Orthod Dentofacial Orthop 2001;120: Schneider J, Geiger M, Sander FG. Numerical experiments on longtime orthodontic tooth movement. Am J Orthod Dentofacial Orthop 2002;21: Shroff B, Lindauer SJ, Burstone CJ, Leiss JB. Segmented approach to simultaneous intrusion and space closure: Biomechanics of the three-piece base arch appliance. Am J Orthod Dentofacial Orthop 1995;107: Stoeckli PW, Teuscher UM. Combined activator headgear orthopedics. In Graber TM, Swain BF, eds. Orthodontics: Current principles and techniques. St Louis: CV Mosby, 1985: Tanne K, Koenig HA, Burstone CJ. Moment to force ratio and the center of rotation. Am J Orthod Dentofacial Orthop 1988;94: Tanne K, Nagataki T, Inoue Y, Sakuda M, Burstone CJ. Patterns of initial tooth displacements associated with various root lengths and alveolar bone heights. Am J Orthod Dentofacial Orthop 1991;100: Toutountzakis N, Mavreas D. Segmented arch technique and incisor intrusion for deep overbite correction. Orthod Epitheorese 1989;1: Vanden Bulcke MM, Dermaut LR, Sachdeva RCL, Burstone CJ. The center of resistance during intrusion using the laser reflection technique and holographic interferometry. Am J Orthod Dentofacial Orthop 1986;90: Vanden Bulcke MM, Burstone CJ, Sachdeva RCL, Dermaut LR. Location of the centers of resistance for anterior teeth during retraction using the laser reflection technique. Am J Orthod Dentofacial Orthop 1987;91: Vollmer D, Bourauel C, Maier K, Jager A. Determination of the centre of resistance in an upper human canine and idealized tooth model. Eur J Orthod 1999;21: Yoshida N, Jost-Brinkmann PG, Koga Y, Mimaki N, Kobayashi K. Experimental evaluation of initial tooth displacement, center of resistance, and center of rotation under the influence of an orthodontic force. Am J Orthod Dentofacial Orthop 2001a;120: Yoshida N, Koga Y, Mimaki N, Kobayashi K. In vivo determination of the centres of resistance of maxillary anterior teeth subjected to retraction forces. Eur J Orthod 2001b;23: Reprint requests to: Ioannis S. Papageorgiou Thessalias Str. 27 GR Zografou Greece [email protected] E HNIKH OP O ONTIKH E I EøPH H 2005 ñ TOMO 8 ñ TEYXO 1 57