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The relationship of arch length to alterations in dental arch width
ORIGINAL ARTICLE
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The relationship of arch length to alterations in dental arch width William P. Hnat, PhD,a Stanley Braun, DDS, MME,b Antony Chinhara, DMD, MS,c and Harry L. Legan, DDS,d Louisville, Ky, Harare, Zimbabwe, and Indianapolis, Ind An accurate method is presented for forecasting alterations in arch length related to various width increases in each dental arch. It is based on combined beta and hyperbolic cosine functions which express the expanded dental arches with correlation coefficients of r = 0.98, between measured data and representations of the dental arch. When the midpalatal suture is expanded, canine width and molar width alterations are not equal because the line of action of the expanding force is anterior to the center of resistance of the dentomaxillary complex. Therefore, canine to molar width ratio alterations of 1:1, 1.25:1, and 1.5:1 are examined, and simple linear functions are presented for purposes of predicting changes in arch length. (Am J Orthod Dentofacial Orthop 2000;118:184-8)
ncreases in arch width have been recommended for a variety of reasons: (1) the correction of posterior crossbites, (2) to “redirect dentoskeletal development of the developing dentition to achieve more normal relationships that may consequently reduce or eliminate later treatment,”1-8 (3) the elimination of potential deleterious effects on the temporomandibular structures,9,10 (4) the improvement of nasal respiratory competence.11 More recently, altering arch widths has become popular as it potentiates nonextraction therapy.12-14 It should be noted, however, that the clinician does not yet have adequate diagnostic criteria to identify those patients who may have their dental arches expanded with acceptable long-term stability.15-20 It has been reported by various clinicians11,21-23 that the anterior portion of the dental arch expands more than the posterior portion during maxillary sutural expansion and is likely to be related to the resistance of the zygomatic buttresses. Others24-26 have reported that the mandibular arch is observed to “follow” maxillary arch expansion because of the influence of occlusion and alterations in the extraoral tissue drape. Some investigators have attempted to quantify the peripheral arch length changes related to arch width expansion. Adkins et al27 found an average increase in arch perimeter of 4.7 mm for an average molar expansion of 6.5 mm. This finding was obtained by recording dental landmarks of 21 orthodontic patients who had undergone rapid palatal expansion and did not attempt
I
aAssociate Professor of Mechanical Engineering, J. B. Speed Scientific School, University of Louisville. bClinical Professor of Orthodontics, Vanderbilt University Medical Center. cPrivate Practice. dProfessor and Chairman of Orthodontics, Vanderbilt University Medical Center. Reprint requests to: Stanley Braun, DDS, MME, 7940 Dean Road, Indianapolis, IN 46240 Submitted, August 1999; Revised and accepted, January 2000. Copyright © 2000 by the American Association of Orthodontists. 0889-5406/2000/$12.00 + 0 8/1/105570 doi.10.1067/mod.2000.105570
184
to account for any related canine expansion. General guidelines have been reported by Ricketts et al,28 stating that each millimeter of canine expansion provides for a 1 mm increase in arch perimeter, and 1 mm of molar expansion increased the peripheral arch length 0.25 mm. The method of obtaining these guidelines was not revealed. Germane et al29 quantified the increase in arch perimeter related to orthodontic expansion based on the premise that the mathematic spline function describes the dental arch with acceptable accuracy. When the canine width and incisor positions were held constant, an initial 1 mm increase in molar width produced an approximate 0.27 mm increase in perimeter, the second millimeter produced an additional 0.31 mm, and the fifth millimeter of molar width increase was related to a perimeter increase of 0.41 mm. When the incisor positions were fixed, each millimeter of canine expansion provided a 0.73 mm increase in arch perimeter. As Germane et al29 pointed out, individual isolation of the width changes will cause an abnormal arch form, and alterations in the canine region will alter the incisor positions and premolar/molar widths. Because the natural maxillary and mandibular arch forms have recently been accurately described30 by the mathematical beta function with a correlation coefficient (r) of 0.98, it is the purpose of this study to more precisely relate alterations in arch width to arch length. MATERIAL AND METHODS
Because the force systems related to maxillary sutural expansion are applied anterior to the center of resistance of the dentomaxillary complex,31,32 the canine width commonly changes more rapidly than molar widths. Consequently, the alterations in arch length are examined for canine width changes to molar width changes (canine width/molar width) in ratios of 1:1, 1.25:1, and 1.5:1. In the early phase of this study, it was found that the correlation coefficients for the beta function describing
Hnat et al 185
American Journal of Orthodontics and Dentofacial Orthopedics Volume 118, Number 2
Fig 1. Correlation coefficients vs incremental arch width increases for various canine/molar width ratios.
Fig 2. Arch shape for the combined beta and hyperbolic cosine functions.
the entirety of the natural untreated dental arch diminished significantly as the arch widths were increased as shown in Fig 1. Therefore, the expanded (altered) dental arch is best modeled by 2 mathematical functions: the hyperbolic cosine function for the 6 anterior teeth,33 and the beta function for the dentition posterior to the canines. High correlation coefficients are consequently maintained. Using average values for the initial
pre-expanded arch widths and depths of untreated dental arches,30 alterations in arch length related to changes in molar and canine widths are studied with accuracy. The arch shapes were assumed symmetric and the coordinates were identified for the initial overall arch depth, initial molar width, and initial canine width. These points were subsequently used to curvefit the beta and hyperbolic cosine functions to the
186 Hnat et al
American Journal of Orthodontics and Dentofacial Orthopedics August 2000
Fig 3. Six anterior teeth described by the hyperbolic cosine function.
expanded dental arch. The overall arch depth and the anterior arch depth were held constant while the canine and molar widths were varied. Each time the widths were altered, the curve-fit routines were used to emulate the new arch shape as shown in Fig 2. The arch length was calculated by summing the length of segments between the calculated coordinates. This provides a satisfactory simulation for the arch length since 36 coordinates were calculated for each dental arch. Microsoft Excel (Microsoft Corp, Redmond, Wash) was used to perform all calculations including curvefits for the hyperbolic cosine and beta functions. The anterior arch segment, described by the hyperbolic cosine function, is given by
x Y = –cosh cosh–1(h+1) + 1.0 + h b where b represents one-half the cross-arch distance between the normal distal contacts of the right and left canines, and h represents the distance measured along a line from the contacts of the central incisors perpendicular to a line connecting the distal contacts of the canines as shown in Fig 3. The dental arch posterior to the distal contacts of the canines bilaterally, described by the beta function, is given by
x 1 Y = 3.0314D + w 2
0.8
1 x – 2 w
0.8
where W represents the cross-arch distance between the second molar contact points, in millimeters, and D the perpendicular distance from a line joining the distal contact points of the canines anteriorly to a similar line joining the mesial contact points of the second molars, in millimeters.
Because the geometric relationship of the maxillary and mandibular arches have been well described by earlier investigators,34-36 the coordinated alterations in mandibular arch length relative to that of the maxillary arch can be calculated. This is limited to Angle Class I occlusion because a previous study has shown that the relationship of the mandibular arch form to that of the maxillary arch form is significantly altered in occlusions other than Angle Class I.30 RESULTS
Fig 4 illustrates alterations in maxillary arch length for changes in the canine width to molar width ratios of 1:1, 1.25:1, and 1.5:1, in increments of 2 mm to 14 mm of molar expansion. Fig 5 illustrates alterations in mandibular arch length for the same canine width to molar width ratios up to 14 mm of molar expansion. DISCUSSION AND CONCLUSIONS
A high correlation coefficient is maintained to the form (coordinates) of the expanded maxillary and related mandibular arches when the hyperbolic cosine function is used to represent the 6 anterior teeth and the beta function is used to represent the remaining posterior teeth. Because the canine to molar width expansion ratios are a function of the point of application of the expansion force relative to the center of resistance of the dentomaxillary complex, 3 canine/molar ratios: 1:1, 1.25:1, and 1.5:1 were examined. Alterations in arch length were calculated with the curve-fit routines. As an example, if the maxillary molar width is expanded 6 mm (3 mm per side), and the canine/molar expansion ratio is 1.25:1, then the arch length alteration is +5.4 mm (L = 0.9236[6] – 0.1154). See Fig 4. Correspondingly, the mandibular arch length alteration
American Journal of Orthodontics and Dentofacial Orthopedics Volume 118, Number 2
Hnat et al 187
Fig 4. Changes in maxillary arch length for canine/molar width ratios 1:1, 1.25:1, and 1.5:1.
Fig 5. Changes in mandibular arch length for canine/molar width ratios 1:1, 1.25:1, and 1.5:1.
is +5.6 mm (L = 0.9469[6] – 0.1305), when the 2 arches are in Angle Class I occlusion. The relationship between arch length alteration and molar width expansion is linear as illustrated by the high correlation coefficients (r = 0.999) of the linear fit equations in Figs 4 and 5. In this example, when the mandibular molar width is increased 6 mm, a total of 5.6 mm mandibular arch length increase occurs. Based on previously reported research,33 the arch length increase in the anterior
segment (canine to canine) is 5.95 mm (L = 0.779 [1.25][∆W] + 0.111). For canine to molar width expansion ratios of 1.25:1 and 1.5:1, a small decrease in the posterior arch length actually occurs. This is due to a reduction in the curvature of the arch form from distal to the canines, and accounts for the small variation in the results. Consequently, the clinician can assume that most of the arch length gain occurs in the anterior segment for all alterations in arch width.
188 Hnat et al
When the arch width ratio is 1:1 (canine/molar), the arch length gain in the anterior segment represents 95% of the total alteration. The clinician now has a method, which was not previously available with any degree of accuracy, to forecast alterations in arch length related to arch width expansion. The clinician should be aware that if the entirety of the arch length gain is not used in reconciling a pre-existing arch length deficiency, the incisors’ anteroposterior position (arch depth) will change.33 REFERENCES 1. Barnes RE. The early expansion of deciduous arches and its effect on the developing permanent dentition. Am J Orthod 1956;42:83-97. 2. Clifford FO. Crossbite correction in the deciduous dentition: principals and procedures. Am J Orthod 1971;59:343-9. 3. Harrold E. Some biological aspects of orthodontic treatment in the transitional dentition. Am J Orthod 1963;49:1-14. 4. Haas AJ. The treatment of maxillary deficiency by opening the midpalatal suture. Angle Orthod 1965;35:200-17. 5. Haas AJ. Palatal expansion: just the beginning of dentofacial orthopedics. Am J Orthod 1970;57:219-55. 6. Moyers RF. Handbook of Orthodontics, 3d Ed. Chicago: Yearbook Medical Publications; 1974. 7. Ricketts RM. Early treatment. J Clin Orthod 1979;13:181-99. 8. Kutin G, Hawes RR. Posterior crossbites in the deciduous and mixed dentition. Am J Orthod 1969;56:491-504. 9. Cheney EA. Indications and methods for the interruption of functional cross-bite. Dent Clin N Am 1958; July 385-92. 10. Myers DR. Condylar position in children with functional posterior crossbites: before and after crossbite correction. Ped Dent 1980;2:190-4. 11. Haas AJ. Rigid expansion of the maxillary dental arch and nasal cavity by opening of the midpalatal suture. Angle Orthod 1961:31:73-90. 12. Bishara SE, Staley RV. Maxillary expansion: clinical implications. Am J Orthod Dentofacial Orthop 1987;91:13-4. 13. Bereocher WC, Mueller BH, Tinasff N. The effect of maxillary palatal expansion on the primary dental arch circumference. J Pediatr Dent 1980;2:27-30. 14. Guerrero C, Covtasti G. Transverse (horizontal) mandibular deficiency. In: Bell WH, editor. Modern practice in orthognathic and reconstructive surgery (Vol 3). Philadelphia: WB Saunders; 1992. p. 2382-2402. 15. Schuler RJ. Cephalometric diagnosis of the increase in mandibular arch length by utilizing buccal expansion for the individual patient [Unpublished Master’s Thesis]. Loma Linda University, 1975. 16. Gardner SD, Chaconas SJ. Posttreatment and postretention changes following orthodontic therapy. Angle Orthod 1976;46:151-61.
American Journal of Orthodontics and Dentofacial Orthopedics August 2000
17. Strang RHW. The fallacy of dental expansion as a treatment procedure. Angle Orthod 1949;19:12-7. 18. Litowitz R. A study of the movements of certain teeth during or following orthodontic therapy. Angle Orthod 1948;18:113-31. 19. Dona A. An analysis of dental casts of patients made before and after orthodontic treatment [Unpublished Master’s Thesis]. University of Washington, 1952. 20. Little LR, Riedel R. Mandibular arch length increase during the mixed dentition, postretention evaluation of stability and relapse. Am J Orthod Dentofacial Orthop 1990;97:393-404. 21. Ekstrom C, Henrikson CO, Jensen R. Mineralization in the midpalatal suture after orthodontic expansion. Am J Orthod 1977; 71:449-55. 22. Wertz RA. Skeletal and dental changes accompanying rapid midpalatal suture opening. Am J Orthod 1970;58:41-66. 23. Bell RA, LeCompte EJ. The effects of maxillary expansion using a quad-helix appliance during the deciduous and mixed dentition. Am J Orthod 1981;79:152-61. 24. Walter CW. Changes in the form and dimensions of dental arches resulting from orthodontic treatment. Angle Orthod 1953;23:3-18 25. Haas AJ. Long-term posttreatment evaluation of rapid palatal expansion. Angle Orthod 1980;50:189-217. 26. Cotton LA. Slow maxillary expansion: skeletal vs dental response to low magnitude force in Macaca Mulatta. Am J Orthod 1978;73:1-23. 27. Adkins MD, Nanda RS, Currier GF. Arch perimeter changes in rapid palatal expansion. Am J Orthod Dentofacial Orthop 1990;97:194-9. 28. Ricketts RM, Roth RH, Chaconis SJ, Schulhof RJ, Engel GA. Orthodontic diagnosis and planning. USA Rocky Mountain Data Systems 1982:194-200. 29. Germane N, Lindauer SJ, Rubenstein LK, Revere JH Jr, Isaacson RJ. Increase in arch perimeter due to orthodontic expansion. Am J Orthod Dentofacial Orthop 1991;100:421-7. 30. Braun S, Hnat WP, Fender DE, Legan HL. The form of the human dental arch. Angle Orthod 1998;68:29-36. 31. Lee K, Ryu Y, Park Y, Rudolph DJ. A study of holographic interferometry on the initial reaction of the maxillofacial complex during protraction. Am J Orthod Dentofacial Orthop 1997; 111:623-32. 32. Braun S, Lee K, Legan HL. A re-examination of various extraoral appliances in light of recent research findings. Angle Orthod 1999;69:81-4. 33. Braun S, Hnat WP. Dynamic relationships of the mandibular anterior segment. Am J Orthod Dentofacial Orthop 1997;111:518-24. 34. Wheeler RC. A textbook of dental anatomy and physiology. Philadelphia: WB Saunders; 1965. 35. Marcotte MR. The use of the occlusogram in planning orthodontic treatment. Am J Orthod 1976;69:655-67. 36. White LW. The clinical use of occlusograms. J Clin Orthod 1982;2:92-103.
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The relationship of arch length to alterations in dental arch width William P. Hnat, PhD,a Stanley Braun, DDS, MME,b Antony Chinhara, DMD, MS,c and Harry L. Legan, DDS,d Louisville, Ky, Harare, Zimbabwe, and Indianapolis, Ind An accurate method is presented for forecasting alterations in arch length related to various width increases in each dental arch. It is based on combined beta and hyperbolic cosine functions which express the expanded dental arches with correlation coefficients of r = 0.98, between measured data and representations of the dental arch. When the midpalatal suture is expanded, canine width and molar width alterations are not equal because the line of action of the expanding force is anterior to the center of resistance of the dentomaxillary complex. Therefore, canine to molar width ratio alterations of 1:1, 1.25:1, and 1.5:1 are examined, and simple linear functions are presented for purposes of predicting changes in arch length. (Am J Orthod Dentofacial Orthop 2000;118:184-8)
ncreases in arch width have been recommended for a variety of reasons: (1) the correction of posterior crossbites, (2) to “redirect dentoskeletal development of the developing dentition to achieve more normal relationships that may consequently reduce or eliminate later treatment,”1-8 (3) the elimination of potential deleterious effects on the temporomandibular structures,9,10 (4) the improvement of nasal respiratory competence.11 More recently, altering arch widths has become popular as it potentiates nonextraction therapy.12-14 It should be noted, however, that the clinician does not yet have adequate diagnostic criteria to identify those patients who may have their dental arches expanded with acceptable long-term stability.15-20 It has been reported by various clinicians11,21-23 that the anterior portion of the dental arch expands more than the posterior portion during maxillary sutural expansion and is likely to be related to the resistance of the zygomatic buttresses. Others24-26 have reported that the mandibular arch is observed to “follow” maxillary arch expansion because of the influence of occlusion and alterations in the extraoral tissue drape. Some investigators have attempted to quantify the peripheral arch length changes related to arch width expansion. Adkins et al27 found an average increase in arch perimeter of 4.7 mm for an average molar expansion of 6.5 mm. This finding was obtained by recording dental landmarks of 21 orthodontic patients who had undergone rapid palatal expansion and did not attempt
I
aAssociate Professor of Mechanical Engineering, J. B. Speed Scientific School, University of Louisville. bClinical Professor of Orthodontics, Vanderbilt University Medical Center. cPrivate Practice. dProfessor and Chairman of Orthodontics, Vanderbilt University Medical Center. Reprint requests to: Stanley Braun, DDS, MME, 7940 Dean Road, Indianapolis, IN 46240 Submitted, August 1999; Revised and accepted, January 2000. Copyright © 2000 by the American Association of Orthodontists. 0889-5406/2000/$12.00 + 0 8/1/105570 doi.10.1067/mod.2000.105570
184
to account for any related canine expansion. General guidelines have been reported by Ricketts et al,28 stating that each millimeter of canine expansion provides for a 1 mm increase in arch perimeter, and 1 mm of molar expansion increased the peripheral arch length 0.25 mm. The method of obtaining these guidelines was not revealed. Germane et al29 quantified the increase in arch perimeter related to orthodontic expansion based on the premise that the mathematic spline function describes the dental arch with acceptable accuracy. When the canine width and incisor positions were held constant, an initial 1 mm increase in molar width produced an approximate 0.27 mm increase in perimeter, the second millimeter produced an additional 0.31 mm, and the fifth millimeter of molar width increase was related to a perimeter increase of 0.41 mm. When the incisor positions were fixed, each millimeter of canine expansion provided a 0.73 mm increase in arch perimeter. As Germane et al29 pointed out, individual isolation of the width changes will cause an abnormal arch form, and alterations in the canine region will alter the incisor positions and premolar/molar widths. Because the natural maxillary and mandibular arch forms have recently been accurately described30 by the mathematical beta function with a correlation coefficient (r) of 0.98, it is the purpose of this study to more precisely relate alterations in arch width to arch length. MATERIAL AND METHODS
Because the force systems related to maxillary sutural expansion are applied anterior to the center of resistance of the dentomaxillary complex,31,32 the canine width commonly changes more rapidly than molar widths. Consequently, the alterations in arch length are examined for canine width changes to molar width changes (canine width/molar width) in ratios of 1:1, 1.25:1, and 1.5:1. In the early phase of this study, it was found that the correlation coefficients for the beta function describing
Hnat et al 185
American Journal of Orthodontics and Dentofacial Orthopedics Volume 118, Number 2
Fig 1. Correlation coefficients vs incremental arch width increases for various canine/molar width ratios.
Fig 2. Arch shape for the combined beta and hyperbolic cosine functions.
the entirety of the natural untreated dental arch diminished significantly as the arch widths were increased as shown in Fig 1. Therefore, the expanded (altered) dental arch is best modeled by 2 mathematical functions: the hyperbolic cosine function for the 6 anterior teeth,33 and the beta function for the dentition posterior to the canines. High correlation coefficients are consequently maintained. Using average values for the initial
pre-expanded arch widths and depths of untreated dental arches,30 alterations in arch length related to changes in molar and canine widths are studied with accuracy. The arch shapes were assumed symmetric and the coordinates were identified for the initial overall arch depth, initial molar width, and initial canine width. These points were subsequently used to curvefit the beta and hyperbolic cosine functions to the
186 Hnat et al
American Journal of Orthodontics and Dentofacial Orthopedics August 2000
Fig 3. Six anterior teeth described by the hyperbolic cosine function.
expanded dental arch. The overall arch depth and the anterior arch depth were held constant while the canine and molar widths were varied. Each time the widths were altered, the curve-fit routines were used to emulate the new arch shape as shown in Fig 2. The arch length was calculated by summing the length of segments between the calculated coordinates. This provides a satisfactory simulation for the arch length since 36 coordinates were calculated for each dental arch. Microsoft Excel (Microsoft Corp, Redmond, Wash) was used to perform all calculations including curvefits for the hyperbolic cosine and beta functions. The anterior arch segment, described by the hyperbolic cosine function, is given by
x Y = –cosh cosh–1(h+1) + 1.0 + h b where b represents one-half the cross-arch distance between the normal distal contacts of the right and left canines, and h represents the distance measured along a line from the contacts of the central incisors perpendicular to a line connecting the distal contacts of the canines as shown in Fig 3. The dental arch posterior to the distal contacts of the canines bilaterally, described by the beta function, is given by
x 1 Y = 3.0314D + w 2
0.8
1 x – 2 w
0.8
where W represents the cross-arch distance between the second molar contact points, in millimeters, and D the perpendicular distance from a line joining the distal contact points of the canines anteriorly to a similar line joining the mesial contact points of the second molars, in millimeters.
Because the geometric relationship of the maxillary and mandibular arches have been well described by earlier investigators,34-36 the coordinated alterations in mandibular arch length relative to that of the maxillary arch can be calculated. This is limited to Angle Class I occlusion because a previous study has shown that the relationship of the mandibular arch form to that of the maxillary arch form is significantly altered in occlusions other than Angle Class I.30 RESULTS
Fig 4 illustrates alterations in maxillary arch length for changes in the canine width to molar width ratios of 1:1, 1.25:1, and 1.5:1, in increments of 2 mm to 14 mm of molar expansion. Fig 5 illustrates alterations in mandibular arch length for the same canine width to molar width ratios up to 14 mm of molar expansion. DISCUSSION AND CONCLUSIONS
A high correlation coefficient is maintained to the form (coordinates) of the expanded maxillary and related mandibular arches when the hyperbolic cosine function is used to represent the 6 anterior teeth and the beta function is used to represent the remaining posterior teeth. Because the canine to molar width expansion ratios are a function of the point of application of the expansion force relative to the center of resistance of the dentomaxillary complex, 3 canine/molar ratios: 1:1, 1.25:1, and 1.5:1 were examined. Alterations in arch length were calculated with the curve-fit routines. As an example, if the maxillary molar width is expanded 6 mm (3 mm per side), and the canine/molar expansion ratio is 1.25:1, then the arch length alteration is +5.4 mm (L = 0.9236[6] – 0.1154). See Fig 4. Correspondingly, the mandibular arch length alteration
American Journal of Orthodontics and Dentofacial Orthopedics Volume 118, Number 2
Hnat et al 187
Fig 4. Changes in maxillary arch length for canine/molar width ratios 1:1, 1.25:1, and 1.5:1.
Fig 5. Changes in mandibular arch length for canine/molar width ratios 1:1, 1.25:1, and 1.5:1.
is +5.6 mm (L = 0.9469[6] – 0.1305), when the 2 arches are in Angle Class I occlusion. The relationship between arch length alteration and molar width expansion is linear as illustrated by the high correlation coefficients (r = 0.999) of the linear fit equations in Figs 4 and 5. In this example, when the mandibular molar width is increased 6 mm, a total of 5.6 mm mandibular arch length increase occurs. Based on previously reported research,33 the arch length increase in the anterior
segment (canine to canine) is 5.95 mm (L = 0.779 [1.25][∆W] + 0.111). For canine to molar width expansion ratios of 1.25:1 and 1.5:1, a small decrease in the posterior arch length actually occurs. This is due to a reduction in the curvature of the arch form from distal to the canines, and accounts for the small variation in the results. Consequently, the clinician can assume that most of the arch length gain occurs in the anterior segment for all alterations in arch width.
188 Hnat et al
When the arch width ratio is 1:1 (canine/molar), the arch length gain in the anterior segment represents 95% of the total alteration. The clinician now has a method, which was not previously available with any degree of accuracy, to forecast alterations in arch length related to arch width expansion. The clinician should be aware that if the entirety of the arch length gain is not used in reconciling a pre-existing arch length deficiency, the incisors’ anteroposterior position (arch depth) will change.33 REFERENCES 1. Barnes RE. The early expansion of deciduous arches and its effect on the developing permanent dentition. Am J Orthod 1956;42:83-97. 2. Clifford FO. Crossbite correction in the deciduous dentition: principals and procedures. Am J Orthod 1971;59:343-9. 3. Harrold E. Some biological aspects of orthodontic treatment in the transitional dentition. Am J Orthod 1963;49:1-14. 4. Haas AJ. The treatment of maxillary deficiency by opening the midpalatal suture. Angle Orthod 1965;35:200-17. 5. Haas AJ. Palatal expansion: just the beginning of dentofacial orthopedics. Am J Orthod 1970;57:219-55. 6. Moyers RF. Handbook of Orthodontics, 3d Ed. Chicago: Yearbook Medical Publications; 1974. 7. Ricketts RM. Early treatment. J Clin Orthod 1979;13:181-99. 8. Kutin G, Hawes RR. Posterior crossbites in the deciduous and mixed dentition. Am J Orthod 1969;56:491-504. 9. Cheney EA. Indications and methods for the interruption of functional cross-bite. Dent Clin N Am 1958; July 385-92. 10. Myers DR. Condylar position in children with functional posterior crossbites: before and after crossbite correction. Ped Dent 1980;2:190-4. 11. Haas AJ. Rigid expansion of the maxillary dental arch and nasal cavity by opening of the midpalatal suture. Angle Orthod 1961:31:73-90. 12. Bishara SE, Staley RV. Maxillary expansion: clinical implications. Am J Orthod Dentofacial Orthop 1987;91:13-4. 13. Bereocher WC, Mueller BH, Tinasff N. The effect of maxillary palatal expansion on the primary dental arch circumference. J Pediatr Dent 1980;2:27-30. 14. Guerrero C, Covtasti G. Transverse (horizontal) mandibular deficiency. In: Bell WH, editor. Modern practice in orthognathic and reconstructive surgery (Vol 3). Philadelphia: WB Saunders; 1992. p. 2382-2402. 15. Schuler RJ. Cephalometric diagnosis of the increase in mandibular arch length by utilizing buccal expansion for the individual patient [Unpublished Master’s Thesis]. Loma Linda University, 1975. 16. Gardner SD, Chaconas SJ. Posttreatment and postretention changes following orthodontic therapy. Angle Orthod 1976;46:151-61.
American Journal of Orthodontics and Dentofacial Orthopedics August 2000
17. Strang RHW. The fallacy of dental expansion as a treatment procedure. Angle Orthod 1949;19:12-7. 18. Litowitz R. A study of the movements of certain teeth during or following orthodontic therapy. Angle Orthod 1948;18:113-31. 19. Dona A. An analysis of dental casts of patients made before and after orthodontic treatment [Unpublished Master’s Thesis]. University of Washington, 1952. 20. Little LR, Riedel R. Mandibular arch length increase during the mixed dentition, postretention evaluation of stability and relapse. Am J Orthod Dentofacial Orthop 1990;97:393-404. 21. Ekstrom C, Henrikson CO, Jensen R. Mineralization in the midpalatal suture after orthodontic expansion. Am J Orthod 1977; 71:449-55. 22. Wertz RA. Skeletal and dental changes accompanying rapid midpalatal suture opening. Am J Orthod 1970;58:41-66. 23. Bell RA, LeCompte EJ. The effects of maxillary expansion using a quad-helix appliance during the deciduous and mixed dentition. Am J Orthod 1981;79:152-61. 24. Walter CW. Changes in the form and dimensions of dental arches resulting from orthodontic treatment. Angle Orthod 1953;23:3-18 25. Haas AJ. Long-term posttreatment evaluation of rapid palatal expansion. Angle Orthod 1980;50:189-217. 26. Cotton LA. Slow maxillary expansion: skeletal vs dental response to low magnitude force in Macaca Mulatta. Am J Orthod 1978;73:1-23. 27. Adkins MD, Nanda RS, Currier GF. Arch perimeter changes in rapid palatal expansion. Am J Orthod Dentofacial Orthop 1990;97:194-9. 28. Ricketts RM, Roth RH, Chaconis SJ, Schulhof RJ, Engel GA. Orthodontic diagnosis and planning. USA Rocky Mountain Data Systems 1982:194-200. 29. Germane N, Lindauer SJ, Rubenstein LK, Revere JH Jr, Isaacson RJ. Increase in arch perimeter due to orthodontic expansion. Am J Orthod Dentofacial Orthop 1991;100:421-7. 30. Braun S, Hnat WP, Fender DE, Legan HL. The form of the human dental arch. Angle Orthod 1998;68:29-36. 31. Lee K, Ryu Y, Park Y, Rudolph DJ. A study of holographic interferometry on the initial reaction of the maxillofacial complex during protraction. Am J Orthod Dentofacial Orthop 1997; 111:623-32. 32. Braun S, Lee K, Legan HL. A re-examination of various extraoral appliances in light of recent research findings. Angle Orthod 1999;69:81-4. 33. Braun S, Hnat WP. Dynamic relationships of the mandibular anterior segment. Am J Orthod Dentofacial Orthop 1997;111:518-24. 34. Wheeler RC. A textbook of dental anatomy and physiology. Philadelphia: WB Saunders; 1965. 35. Marcotte MR. The use of the occlusogram in planning orthodontic treatment. Am J Orthod 1976;69:655-67. 36. White LW. The clinical use of occlusograms. J Clin Orthod 1982;2:92-103.