SEMINAR ON
ARCH FORMS
By Dr. Riddhi M Rathi PG student Guid : Dr.G.S Patil
Department of Orthodontics and Dentofacial Orthopedics, Dayananda Sagar College of Dental Sciences CONTENTS:
1. Int Introdu roduct ctiion 2. Impor Importa tance nce of Arc Arch h Form Formss 3. Normal Normal growth growth & Devel Developm opment ent of of Arche Archess 4. Differ Different ent concept conceptss of Arch Arch Form Formss 5. Relaps Relapsee Tende Tendency ncy of Arch Arch Form Formss 6. Practi Practical cal solut solution ionss to mainta maintain in Arch Arch Forms Forms 7. Rece Recent nt Deve Develo lopm pmen ents ts 8. Concl nclusion 9. References ces
INTRODUCTION:
Arch form may be described as the arch formed by the buccal and facial surfaces of the teeth when viewed from their occlusal surfaces. To the orthodontist, the shape of this arch form holds the key to the final result of any case. Which arch form do we follow? , has been the central question that has been raised time and again and has haunted the orthodontist. Many orthodontists have sought to find a universal ideal arch form and although most studies have used similar materials- a collection of untreated samples, there has been very little agreement about the natural shape of this ideal arch. A review of literature shows the following assumptions: •
Algebraic or geometric formula
•
The arches may be ellipsoidal, hyperbolic, parabolic, square, omega etc.
•
All ideal arch forms are of the same shape and differ only in size
•
Ideal arches are symmetrical
The basic principle of archform in orthodontic treatment should be preserved, that would place the teeth in a position of maximum stability IMPORTANCE OF ARCH FORMS: 1) STABILITY: Relationship between the arch form and stability cannot be ignored Joondeph & Reidel in one of their nine theorems for stability have stressed on the need to maintain the existing arch form, particularly in the mandibular arch for stability 2) OCCLUSION: Unless the teeth are aligned in a proper arch form in both upper and lower arches, the occlusion will not be normal. Angle(1907) emphasised this with his concept of Line of Occlusion. 3) ESTHETICS: Primary reason for the patient to take treatment. Teeth arranged in proper arch form, will improve smile value as proposed by Sarver(2003).
NORMAL GROWTH & DEVELOPMENT OF ARCHES
Arch dimensions change with growth hence it is important to distinguish changes induced by appliance therapy and by growth. Acc. To Scott(1967) arch form is determined prior to muscular development and is independent of functional activity of the oral musculature. Moorrees(1969) pointed out that considerable individual variation in arch form will occur with normal growth, with a tendency toward an increase in inter-molar width during change over from deciduous to permanent dentition. A review of the change in arch form show the following findings: Male arches grow wider that female arches Lower inter- canine width increases significantly in changeover dentition but doesn’t change in permanent dentition after 12 years. Upper and lower inter-molar widths increase spontaneously to a considerable extent between 7-18 years especially in males. Little change in arch width in premolar region after 12 years Changes in arch width may not be accompanied by changes in arch length. Tendency towards a decrease in arch depth in the 33 rd and 4th decades.
DIFFERENT CONCEPTS OF ARCH FORM : BONWILL CONCEPT BONWILL HAWLEY CONCEPT ANGLES LINE OF OCCLUSION APICAL BASE CONCEPT CATERNARY ARCH FORM BRADER ARCH FORM ROCKY MOUNTAIN DATA SYSTEM ROTH’S TRU ARCH FORM RICKETTS PENTA MORPHIC ARCH FORM MATHEMATIC & GEOMETRIC MODELS FOR ARCH FORMS ARCH FOR DETERMINATION TOMOGRAPHY
USING
CONE
BEAM
COMPUTED
BONWILL’S CONCEPT OF ARCH FORM: Developed certain postulates for artificial dentures in 1885 He noted the tripod shape of the mandible is formed by an equilateral triangle, with its base between the condyles and the apex between the central incisors. length of each side approx 4 inches.
Hawley in 1905, modified Bonwill’s concept. He recommended that the combined widths of the 6 anterior teeth serve as the radius of a circle and the teeth be placed on that circle. From this circle he constructed an equilateral triangle with the base representing the intercondylar width. The radius of each arch varied depending on size of teeth, so the arch dimensions differed as a function of tooth size but the arch form was constant. This was used as a guide for establishing arch form.
ANGLE’S LINE OF OCCLUSION
Angle in 1906,described the LINE OF OCCLUSION – “The line of greatest normal occlusal contact” . But in 1907, he rediscribed it as “ the line with which in form and in position according to type, the teeth must be in harmony if in normal occlusion.” Ricketts(1997) redefined the line of occlusion to its contemporary definition – “ A distinctively individual line at the inciso-buccal contact, with a location, position & form to which the teeth must conform to be in normal occlusion”
In 1942, Gray’s Anatomy stated the following about human arch form:
“The maxillary dental arch forms an elliptical curve.
The mandibular dental arch forms a parabolic curve”.
In 1934, Chuck7 noted the variation in human arch form and pointed out that arch forms had been referred to as square, round, oval, tapering, etc.
He stated that while the Bonwill-Hawley arch form was not suitable for use in each patient, it could serve as a template for the construction ofindividualized arch forms.
Chuck superimposed this arch form on a millimeter grid and used this template for archwire construction according to Angle’s method. Chuck suggested
that the bicuspid regions should be wider than the cuspids to prevent excessive expansion of the cuspids.
In 1963, Boone8 proposed the similar superimposition of the Bonwill- Hawley arch form on a millimeter template for construction of the individualized edgewise arch form. APICAL BASE CONCEPT:
Was proposed by Lundstorm. He highlighted the need to consider the apical base when determining the arch form for the patient.
“Orthodontic experiments showed that a normal occlusion attained by mechanical treatment is not necessarily accompanied by a development of apical base in harmony with the position of the teeth, with the result that the occlusion cannot be maintained.”
“Occlusion doesn’t control form and amount of apical base development but apical base is capable of affecting the dental occlusion” CATENARY ARCH FORM:
Catenary curve was made popular by work of McConaill & Scher1949, who felt that from an engineering and biological point of view, the Catenary curve was the simplest curve possible and could be easily explained mathematically
Bruide & Lilley 1966 found that the shape of basic bony arch at 9.5 weeks I.U , was Catenary design.
When the width across the first molars is used to establish the posterior attachments, a caternary curve fits the dental arch form nicely for most individuals. Preformed archwires based on average intermolar dimensions.
Concept first proposed by David Musich & James Ackerman(1973). To measure the arch perimeter they used an instrument that was a modified Boley Guage with a chain incorporated in it - CATANOMETER Schulhoff(1997) used the same concept to describe the lower arch. Catenary curve is the shape that the loop of a chain would take if it were suspended from 2 hooks. Shape of the curve depends on the length of the chain and the distance between the hooks. BRADER ARCH FORM
Brader in 1972, presented a mathematical model of dental arch form at the annual session of A.A.O for which he won Milo Hellman Research Award Of Special Merit. He proposed that the arch form was a trifocal ellipse, which was based on the findings of Proffit, Norton & Winders. The trifocal ellipse was patterned after the shape of an eggextremely resistant to collapse & produced stable arch form.
He proposed that the arch form was a trifocal ellipse, which was based on the findings of Proffit, Norton & Winders. The trifocal ellipse was patterned after the shape of an egg- extremely resistant to collapse & produced stable arch form.
Not only pressure but duration of pressure should also be considered. Therefore Brader hypothesized the arch form was a Trifocal Ellipse and PR=C Where, P = Pressure R = Radius of curvature of ellipse curve at the pressure site C = Mathematical Constant He also took data from Winders study and calculated the pressure exerted at different regions of the arch BUCCOLABI AL
P
R
C
MOLARS
4
28
112. 0
PREMOLAR
4.9
23
112. 7
CANINE
6.9
16. 3
112. 5
INCISOR
11. 3
10
113
LINGUA L
P
R
C
MOLAR
9.2
12. 2
112. 2
INCISOR S
15. 2
7.5
112. 5
PR=C, was applied and was noted that the product of P and R was the same Thus the equation expressed the most fundamental association between forces and shape and revealed an inverse relation between force and curvature. Then to find the tension exerted by the lips and cheeks, he used the Laplace Formula for elastic container, Pi=Pe+T(1/R+ 1/R’), where; Pi= internal pressure Pe= external forces T= tension of elastic envelope R= radius in horizontal plane R’= radius in vertical plane Pe=0, since atmospheric pressure is equal on both sides R’ not considered as its contribution not known and may be of very small magnitude. Therefore, Pi=T/R T=PiR. Since T=C, Thus, the dental arch remains in a state of equilibrium coz the product of P & R on the lingual side (C) is always equal and opposite to the product of P & R on facial side (T).
Clinical Implications Of PR=C
1) Growth of Dental Arches
Brader suggested that the dental arches grow as a total curve, enlarging about its geometric centre. This internally centered curve orientation provides a new method for reliable comparison of arch forms in both serial and cross sectional investigations. Effect of muscle forces can be noted in cases with patients with scars, hemifacial hypertrophy, atrophy and macroglossia. 2) Lower Incisor Crowding
PR=C, explains why mandibular incisor teeth exhibit many crowded positional variations and of all the teeth in the mouth, the least stability following positional changes due to treatment. In this anterior segment, the radius is smallest and the pressure is greatest, thus having a critical influence on this segment.
ROCKY MOUNTAIN DATA SYSTEM
ROCKY MOUNTAIN DATA SYSTEM computer derived formula relies upon measurements taken from inter molar width, inter cuspid width and arch depth as measured from the facial surface of the incisors to the distal surface of the terminal molar. This allows computer to be programmed with Cartesian X & Y co-ordinates that are necessary for arch computation.
Facial type is also considered Arch design applicable only to the lower arch INDIVIDUALIZED IDEAL ARCHES
Proposed by Larry White in 1978. Undertook a study to see how a collection of ideal, untreated arches conformed to the predetermined arch forms of the most popular formulae. Models of 24 orthodontically untreated superior, adult occlusions were collected and tracings made on acetate paper & overlays were superimposed. The closeness of fit was evaluated and graded as ‘ good fit ’ , ‘moderately good fit ’ and TYPE
GOOD FIT
MODERAT E
POOR FIT
BONWILLHAWLEY
4 (8.33%)
19 (39.5%)
25 (52.8%)
BRADER
6 (12.5%)
21 (43.7%)
21 (43.7%)
CATERNAR Y
3 (27.08% )
22 (45.8%)
13 (27.08% )
RMDS
2 (8.33%)
22 (91.6%)
-
‘ poor fit ’.
➢
Absence of Arch Symmetry
White also evaluated the symmetry of arches and the most conspicuous finding was the total absence of arch symmetry. Thus reached to 2 conclusions: 1. 2.
No generalised, universal arch forms seems to be applicable. Majority of dental arches are assymmetrical
3.
Thus he advocated individualising arches by simple technique called “OCCLUSAL MAPPING”.
4.
Draw occlusal surfaces of teeth from xray or photos. Proximal contacts are marked and a line is drawn through the mesio-distal dimensions of each tooth & connecting the lines across the proximal contacts.
5. This line represents the centre of the basic arch perimeter.
RICKETTS PENTAMORPHIC ARCH FORMS
Considered the following factors in the determination of the arch form: Arch correlation, size, arch length, where the arch was measured, contact details and form at the bracket location. Originally 12 arch forms were identified from different studies. These were narrowed to 9 by computer analysis. Studies of other normal and stable treated patients resulted in elimination of all but 5 forms. These Pentamorphic arch forms were such that they would fit most facial forms
ROTH TRU ARCH FORM
Developed from biologically and clinically derived broad curves observed in patients treated with Cetlin mechanics of functional appliances such as FR which are referred to as “ Natural or Non-Orthodontic”. The Roth Tru Arch was derived from his extensive clinical testing & recording of jaw movement patterns in treated patients who were out of retention and had remained stable.
This arch form mainly was wider by a few millimeters, primarily in bicuspid area when compared of Andrews norms and coincided exactly when superimposed on Ricketts pentamorphic arch forms. This arch form over corrects arch width slightly: over correction in all 3 planes of space is a part of Roth’s end of fixed appliance therapy goal.
MATHEMATIC & GEOMETRIC MODELS FOR ARCH FORMS
Mathematic models have been used for describing arch forms. Lu(1964) claimed that the dental arch could be satisfactorily described by a polynomial equation of the 4th degree. Sanin(1970) investigated the size and shape of ideal arches and confirmed the views of Lu. Pepe(1975) analyzed a sample of 7 models of normal occlusion by digitization and curve fits. The results showed that 4th order polynomial equations were better than Catenary curve fits and also suggested that 6th degree polynomial equations appear to have potential as clinical indicators of arch form. Cubic Spline Function : used for modelling of various assymmetrical objects. Is an adaptation of the draftsmans spline. The mathematical adaptation of physical spline consists of a set of individual cubic polynomials between successive knot points and has been developed for use in describing normal dental arches
RESEARCH ARCH FORM/ CLINICAL ARCH FORM
Acc. To McLaughlin & Bennet , there is a difference between the clinical and research arch form. Braun etal (1966) represented arch form by a complex mathematical formula known as “ Beta Function”. They measured the center of each incisor incisal edge, cusp tips of canines and premolars and the M-D and D-B cusp tips of molars. This research arch form can be surprisingly tapered. In contrast clinicians arch wire shape must be based on the points where the wire will lie in the bracket slots of correctly positioned brackets. This arch form relates to the mid point on the labial surface of the clinical crowns of the teeth, and should include estimation for the in out which is built into the bracket system.
Results were
CL III mandibular arches had smaller arch depth and greater arch width( beginning in premolar area) than CL I
CL II mandibular arches exhibited generalized reduced arch width compared with CL I arches
The maxillary arch depth were similar in all the cases but arch width was more in lat incisor canine area in CL III then in CL I And CL II was less then CL I in lat incisor canine area distally
Beta function more accurately described the dental arch form than representations previously reported Hassan Noroozi, Tahereh Hosseinzadeh Nik, Reza Saeeda – revisited the dental arch form
The coordinates of the midincisal edges and buccal cusp tips of each dental arch were measured, and the correlation coefficient of each dental arch with its corresponding sixth order polynomial function was calculated.
The polynomial function Y = AX
+ BX
was the
nearest to the generalized beta function and could be an accurate substitute for the beta function in less common forms of the human dental arch ( Angle Orthod 2001;71:386– 389.) Felton(1987) evaluated a wide range of manufactured arch wires from orthodontic companies and found that the arch forms fell into tapered, ovoid or square groups( first classified by Chuck in 1932). When superimposed they differed only in ICW (approx 6mm).
Facial type and Dental arches. Dolichocephalic individuals have long and narrow faces and relatively narrow dental arches Brachycephalic individuals have very broad and relatively short faces and broad , round dental arches Mesocephalic individuals fit somewhere in between , paraboloid or average dental arches A long-face individual usually has narrower transverse
dimensions (dolichofacial) and a short-face individual wider transverse dimensions (brachyfacial), according to Ricketts et al. (1982) , Enlow and Hans (1996) , and Wagner and Chung (2005) . Toru Kageyama et al (2006) studied dental arch forms associated with various facial types in adolescents with Class II Division 1 malocclusions by using mathematical functions to describe the arch form at clinical bracket point. They concluded 1 The dental arch forms associated with different facial types can be characterized by using mathematical functions. 2 The mathematical features of the maxillary arch forms indicate that the dolichofacial type has a tapered arch and the brachyfacial type has a wide arch in male subjects. 3 The mandibular arch forms and sizes of the 3 facial types have similar mathematical features. 4 No significant difference was observed in all degrees of the polynomial equations between boys and girls. 5 The beta function is appropriate for predicting the finishing arch form, and the polynomial equation is appropriate for the analysis (diagnosis) of various Class II malocclusions, including ovoid, tapered, and square arch forms and dental arch asymmetry The fourth-degree polynomial equation was described by y = α4x4+ α3x3+ α2x2+ α1x + b (α4, α3, α2 and α1: coefficients; b: constant term) A new concept of mandibular dental arch forms with normal occlusion
Tarcila Triviñoa Danilo Furquim Siqueira b and Marco Antonio Scanavinic Form A(22%)- flattening of the anterior curve region and the origin of the curvature at the distal region of the lateral incisors Form B(15%)- similar configuration as form A—ie, mandibular incisors arranged in a straight line. However, its intercanine distance was slightly wider than in form A. Form C(10%)- the anterior teeth are roundly arranged, as in an ellipsis
Form D(9%)- anterior region of form D is analogous with form C, although this form has a greater intercanine distance, and the incisors are positioned nearly in a plane, giving a quadrangular configuration for this form. Form E(11%)- had a semicircular arrangement of the anterior teeth; therefore, the posterior region is not strictly straight. Form F(13%)- this is an example of a catenary curve Form G( 2%)- a pointed anterior region like a groin Form H(18%)- similar to the shape of archwires advocated by Angle, Chuck, and Boone.Form H has a morphology that describes the projection of the mandibular central incisors and had the second highest frequency in this study, subgroup 2 (medium size) had the most curve segments in forms A (46.4%), B (52.6%), C (50.0%), D (63.6%), E (71.4%), and F (43.8%), whereas forms G (66.7%) and H (47.8%) had a higher incidence of subgroup 1 (small size), even though form G had no segment in subgroup 2 because of sample size. These results might be related to the anterior curve of each dental arch form. Forms G and H had pointed alignments of the incisors, with a smaller distance between homologous teeth at the canine region, and reduced sizes and more components with small size, as also observed for form F, which had a high incidence in subgroup 1 (31.25%).
According to results of this study , the mandibular dental arch can be represented by 8 forms. There is not 1 ideal or representative form of normal occlusion. Most arch forms were medium size, and the incidence of the 8 groups of forms according to sex was homogeneous.
Conclusion : Current literature illustrates many divergent views on the shape of arch form. It is now generally believed that the arch shape is determined by an interplay between genetic and many varied environmental factors such as pressure from soft tissues; shape and position of jaws; alteration in eruptive mechanism and morphology of teeth Clinicians should therefore be cautious when treating individuals to a mathematically derived ideal. The common consensus though seems to be that individualization and coordination of arch forms for each patient is a must to obtain optimum long term stability.
References 1.
SystemizedOrhtodontic Treatment Trevisi
Mechanics-
McLaughlin,Bennet
&
2.
Bioprogressive Therapy, Book 1- Ricketts, Bench, Gugino, Hilgers, Schulhof
3. Rocky Mountain Data System arch forms. JCO 1975,9:776 4. Dental Arch form related to intraoral force PR=C, Brader.AJO1972;61:541561 5.
Polynomial Caternary Curve fits, Pepe. J Dent Res,1975;54:1124
6.
Dental Arch Analysis : A literaature review, Rudge. Eujo,1981;3:279
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archform and Archwire sequencing
11. Contemporary
Orthodontics- William Proffit , Mosby, 3 rd edition
12.The Essence of Orthodontics,-Graber Lee 13. Text
book of Orthodontics- Graber Vanarsdall
14.Orthodontics- Tweed 15. 15.A
new method for analyzing change in dental arch form BeGole, Raymond C. Lyew, : AJO-DO 1998 April (394-401)
16. 16.
Ellen A.
A new concept of mandibular dental arch forms with normal occlusion;Tarcila Triviño a Danilo Furquim Siqueira b and Marco Antonio Scanavini ;AJO-DO jan 2008 vol 133 (1)
17.
17. The Dental Arch Form Revisited -Hassan Hosseinzadeh Nik; Angle Orthod 2001;71:386–389
Noroozi,Tahereh
18. 18.
Longitudinal Dental Arch Changes in the Mixed Dentition-Mladen Sˇ laj, Marina A. Jezˇina, Tomislav Lauc,Senka Rajic´-Mesˇtrovic, Martina Miksˇ ic´; ( Angle Orthod 2003;73:509–514
19. 19.
A comparison of dental arch forms between Class II Division 1 and normal occlusion assessed by euclidean distance matrix analysis Qiong Nie,and Jiuxiang Lin ajo-do, April 2006 vol 6, Pages 528-535
20. 20.A
mathematic geometric model to calculate variation in mandibular arch ;Sabirina Muteinelli et al; EJO 2000 (113-125).
21. 21.The
form of human dental arch ; Stanely Braun et al ; Angle Orthod 1998;68(1): 29-36.
22.22. Mathematical Analyses of Dental Arch Curvature in Normal Occlusion. 23. Seba
AlHarbia; Eman A. Alkofideb; Abdulaziz AlMadic ; Orthodontist, Vol 78, No 2, 2008 .
Angle
