Dental arch forms /certified fixed orthodontic courses by Indian dental academy


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Dental arch forms /certified fixed orthodontic courses by Indian dental academy

  1. 1. DENTAL ARCH FORMS INDIAN DENTAL ACADEMY Leader in continuing dental education
  2. 2. INTRODUCTION The basic pattern of tooth position is the arch. The arch has long been known architecturally (as the word architecture itself implies) as a strong, stable arrangement. The maxillary and the mendibular teeth are positioned on the maxilla and the mandible respectively to produce a curve “arch” when viewed from the occlusal surface. This form is determined gy the underlying basel bone. Malpositioning of individual teeth does not alter the arch form. However, when multiple teeth are misplaced, irregularities and asymmetries may develop in the arch form. Proper arch form in addition to improving the occlusion, also contributes significantly to the esthetic value of face.
  3. 3. DEFINITION OF DENTAL ARCH FORM “Dental arch form is the arch, formed by the buccal and facial surfaces of the teeth when viewed from their occlusal surfaces.”
  4. 4. IMPORTANCE OF ARCH FORM The arch form is important mainly from three points of view : • Stability • Occlusion • Esthetics
  5. 5. STABILITY From the area of Angle till date, researcher and clinicians have unarguably accepted the relationship between dental arch form and the stability of the orthodontic result. Donald Joondeph and Richard Reidel in one of their nine theorems for stability have stressed on the need to maintain the existing arch form for stability, particularly in the mandibular arch.
  6. 6. OCCLUSION Unless the teeth are aligned in a proper arch form in both the maxillary and mandibular arches, the occlusion will not be normal. Angle described his lines of occlusion in 1907, as one of the criteria for normal occlusion. He described the line of occlusion as “the line with which in form and position, according to type, the teeth must be in harmony if in normal occlusion”.
  7. 7. ESTHETICS Esthetics is the driving force for the patients to seek orthodontic treatment. A good smile, among other things depends on how the teeth are arranged. Teeth arranged in a proper arch no doubt increases the smile value.
  8. 8. BASIC TYPES OF DENTAL ARCH FORM Many kinds of arch forms have been described in the literature. Majority of them fall into one of the following types :  (1).Parabolic :  (2).Hyperbolic :  (3).Ellipsoidal :  converging (4).Square :  (5).Omega : It is shaped like a parabola, with an anterior curve and slightly diverging posterior legs. It is shaped like a hyperbola, with a flatter anterior curve and markedly diverging posterior legs. It is shaped like an ellipse with a curved anterior segment and slightly posterior legs. It has a flat anterior segment and relatively parallel posterior legs. It has a curved anterior segment and posterior legs that converge then diverge.
  9. 9. DIFFERENT CONCEPTS OF ARCH FORMS Many researchers have described a variety of arch forms. The following six concepts may be considered as milestones in the development of so called ideal arch forms.        (1). (2). (3). (4). (5). (6). (7). Bonwill’s concept of the arch form Bonwill – Hawley arch form Angel’s line of occlusion Catenary curve of Schulhof Brader’s arch form Rocky Mountain Data System computer derived arch design Individualized Ideal Arches by Larry White
  10. 10. BONWILL’S CONCEPT OF ARCH FORM The question, “What is the normal arch form?”, has interested dentists since 1885, when Bonwill attempted to establish certain postulates for constructing artificial dentures. He noted that the tripod shape of the mandible formes an equilateral triangle, with the base between the condyles and the apex between the central incisors. The average length of the sides was 4 inches, with a variation of not maore that ¼ inch. Bonwill emphasized the principle that “human anatomy is in perfect consonance with geometry, physics and mechanism…. If nature is given a fair chance to right herself, she will return to normal standard of mathematical and mechanical precision. To do otherwise would annihilate creation”.
  11. 11. BONWILL – HOWLEY ARCH FORM Hawley in 1904, modifies the Bonwill approach an recommended that the combined widths of the six anteriors teeth should serve as the radius of a circle, and the teeth should be placed on that circle. From this circle, he constructed an equilateral triangle with the base representing the intercondylar width. The radius of the circle varied depending on the size of the anterior teeth, so that the dimensions differed as a function of tooth size, but arch form was constant for all individuals. This construction was to serve as a guide for establishing arch form, though not an absolute orthodontic treatment objective.
  12. 12. ANGLE’S LINE FOR OCCLUSION  Angle in 1906, described the line of occlusion as “the line of greatest normal occlusal contact”. But in 1907, he redescribed it as “the line with which in form and position, according to type, the teeth must be in harmony if in normal occlusion”  The interpretation of Angle’s above statement and his intended use became confusing. Some believed that Angle was thinking of a line through the contact points as used for calculating arch lengths. Others imagined a line through the centers of the clowns, while still others used a line through a line at the middle of the buccal surface as the circumference of each arch, such as would be necessary for the arch wire attached to brackets.
  13. 13.   .  Ricketts in 1977, studied the writings of Dr. angle and made use of cephalometrics and computerized occlusograms. He redefined the Angle’s line of occlusion and gave contemporary definition as :“A distinctively individual line at the incisobuccal contact, with a location, position and form to which the teeth must to be in its normal occlusion” In other words, the line of occlusion is an imaginary line through the labioinsical and bucco occlusal contact points of the teeth.
  14. 14. CATENARY ARCH FORM OF SCHULHOF  The concept of catenary arch was first used by David Musich and James Ackerman in 1973 for determining the arch perimeter. The instrument they used to measure the arch perimeter was a modified Boley gauge with chain incorporated in it. They named the instrument a Catenometer.  In the year 1977, Schulhof used the same concept to explain the arch form for the lower arch. Catenary curve is the shape that the loop of chain would take if it were suspended by two hooks the length of the chain and the width between the supports determines the precise shape of the curve. When the width across the first molars is used to establish the posterior attachments, a catenary curve fits the dental arch form of the premolar canine incisor segment of the arch very nicely for most individuals.
  15. 15.  . Exceptions includes, patients whose arches would fall into the prosthodontists classification of square of tapering arch forms. For all individuals, the fit is not as the catenary curve is extended posteriorly, because the dental arch normally curves lingually in the 2nd and 3rd molar region  Most of the performed archwires offered by contemporary manufacturers are based on a catenary curve, with average intermolar dimensions.  Although these archwires are good starting point, it is apparent that even if one accepts the catenary curve as ideal, their shape should be modified if the first molar widths are unusually wide or narrow. Modification to accommodate for a generally more tapering or more square morphology are also appropriate, and the second molar must be “tucked in” slightly.
  16. 16. BRADRER ARCH FORM  Brader in the year 1971, presented a mathematical model of dental arch form at the annual session of the American Association of orthodontists for which he won the prestigious Milo Hellman Research Award of special merit. It was a great leap forward in understanding the arch form and revolutionized the thinking about the dental arch forms related with intra oral forces.  It is interesting to note that he gave that mathematical model not by his own clinical research but based on findings reported by other researchers, like Proffit, Norton, Winders.
  17. 17.  Traditional belief in orthodontics was that the tongue pressure at the lip and the cheek pressure are equal in magnitude and opposite in direction, this Hypothesis was disproved by Lear and Moorees in the year 1969. They stated that lingual/tongue pressure is more than lip and cheek pressure. They even verified the time-pressure equilibrium hypothesis. This hypothesis states that it is not just the pressure of tongue, cheek and lip that should be considered for equilibrium but also the duration (or time) of pressure, mathematically it can be illustrated as follows :  {E (+Pat) + (+Pbt) + (+Pct)……….} + {E (-Pxt) + (-Pyt) + (-Pzt) ………} = 0 Where P is the pressure t is the time a, b, c…… represents positive forces, and x, y, z…… represents negative forces.    
  18. 18.  Lear and Moorees also found that 24-hour muscle forces on the dental arches is more on lingual side than on the buccal side and said that “ ……… enigma of the relationship between dental arch form and muscle function remains”.  To solve this puzzle/enigma Brader hypothesized the arch form as a trifocal ellipse and PR=C; where P is pressure in Gm/Cm2, R is the radius of curvature of the elliptical curve at the pressure site in mm and C is a mathematical constant.  The trifocal ellipse, which more or less resembles a hen-egg in longitudinal section, fitted well with many ideal untreated arches in patients (the samples were taken from Down’s study of variations in facial relationships, AJO, 1948).  Secondly, he took the data from the electrodynamics study done by Winders, which is as follows :
  19. 19.         -------------------------------------------------------------------------------------------------------------------------------SITE PRESSURE (gm/cm2) -------------------------------------------------------------------------------------------------------------------------------Bucco labial At lower 6 region 4.0 At lower 4 region 4.9 At lower 3 region 6.9 At lower 1 region 11.3       Lingual At lower 6 region 9.2 At lower 1 region 15.2 -------------------------------------------------------------------------------------------------------------------------------In the above sample Brader found out the radius of curvature at given site and applied the formula, PR=C, to calculate the mathematical constant.
  20. 20.             It is shown in the following table-------------------------------------------------------------------------------------------------------------------SITE P (gm/cm2) R (mm) C --------------------------------------------------------------------------------------------------------------------------------Bucco labial At lower 6 region 4.0 28.0 112.0 At lower 4 region 4.9 23.0 112.7 At lower 3 region 6.9 16.3 112.5 At lower 1 region 11.3 10.0 113.0 Lingual At lower 6 region 9.2 12.2 112.2 At lower 1 region 15.2 7.5 112.5 --------------------------------------------------------------------------------------------------------------------
  21. 21.                Thus, the equation PR=C expresses the most fundamental associations between forces and shape and reveals an inverse relation between force and curvature; that is to say the tighter the curve the greater Pr/unit area and the converse would follow. To find out the tension exerted by the lips and cheeks, he used Laplace formula for elastic container. He considered the circumora structures as an elastic envelope and applied Laplace formula: Pi = Pe + T (1/R + 1/R’), where Pi = Internal forces Pe = External forces T = Tension of the elastic envelope R = Radius of curvature in horizontal plane R’ = Radius of curvature in vertical plane Value for Pe is 0 since the atmospheric pressure is equal on both the sides. R’ is not considered because its contribution is presently unknown and may be of small magnitude for mathematical reasons. Therefore substituting Pe = 0, and neglecting R’, we get Pi = T/R T = Pi * R Brader found out that T is always equal to C. The dental arch remains in a state of equilibrium because the product of P and R on the lingual side(C) is always equal and opposite to the product of P and R on the facial side(T).
  22. 22. CLINICAL IMPLICATIONS OF PR=C (1).Growth of dental arches  The traditional view of growth of dental arches, with the form considered as an open curve like the catenary where superimposed of serial events is possible only on the single point they share in common the medical approximal contacts of the central incisor teeth. This view point implies little or no dimensional change in the outer and of the arch curve; form such interpretations, restrictive conclusions have been drawn about the movement of teeth during Orthodontic therapy.  Taking advantage of the geometric characteristics of the closed elliptical curve Brader suggested that the dental arches grow total curve enlargement about geometric centers. This closed curve concepts, he says, places the arch into different but more satisfying architectural context with generally accepted understanding about the growth of the face and head. But more important, a total internally centered curve orientation provides a new method for the reliable comparison of arch forms in both serial and cross-sectional investigations into the nature of growth of the dental arches.
  23. 23. (2).Lower Incisor Crowding:  Since pressure (P) and radius of curvature (R) are inversely related, PR=C explains why the mandibular incisor teeth exhibit many crowded positional variations and of all the teeth in the mouth, the least stability following positional changes produced by orthodontic movements. It is precisely here, in the anterior segment of the madibular dental arch, where the radius of curvature is smallest, that the pressure are greatest and therefore exercise the most critical influence on tooth positions.
  24. 24. LIMITATIONS OF BRADER’S ARCH FORM  The Brader’s arch form explains a typical normal arch form. It may not be applicable in different maloccusions.  Although it fits majority of cases, there are exception to this, they include what the Prosthodontists would call as tapering or square arch form. In such case the arch form of the wire should be altered accordingly.  Brader’s PR=C is just a hypothesis and not theory and it is incompletely verified. Further, long term studies are requires to verify the stability.  The main clinical criticism of the Brader’s arches is that when those forms are followed explicitly, there is often severe narrowing in cuspid region.
  25. 25. COMPUTER DERIVED ARCH DESIGN The Rocky Mountain Data System computer derived formula that relies upon measurements taken from intermolar width, intercuspid width and arch depth as measured from the facial surface of incisors to the distal surface of the terminal molar. This allows the computer to be programmed with Cartesian X and Y co-ordinates that are necessary for a two-dimensional, computer derived formula. Facial type is also considered in this arch computation. This arch design is applicable only for the lower arch.
  26. 26. RELATIONSHIP BETWEEN FACIAL FORM AND ARCH FORM Most Prosthodontists believe there is a definite correlation between the arch form and facial form. They state that dolicofacial individual have long narrow arches; brachyfacial individuals have broad and squarish dental arches the mesofacial individuals have arch forms which fit somewhere in between these two and described as average.
  27. 27.  However it must not be assumed that narrow arches inevitably go with narrow faces and broad arches go with broad faces. In biology, every rule has exceptions. Despite the general trend in this direction clinical examination frequently will reveal exception and gradations in the degree of narrowness and broadness of dental arches, as correlated with facial type. Some anthropologists would claim that there are so many, exceptions to this trend that the correlation between facial form and the arch form has only limited value.
  28. 28. INDIVIDUALIZED IDEAL ARCHES  The technique of individualizing arch form was proposed by Larry White in the year 1978  Even though various researchers have arrived at different conclusions while using similar data, a review of literature shows that most have labored under at least three common presumption:-  There must be algebraic or geometric formula to determine ideal arch form.  Every ideal arch form must adhere to a generalized scheme; that is, a form that is of some quality differing only in size.  Every arch is considered to be symmetrical, this last presumption is directly related to mathematical equation used, which make it impossible to produce asymmetry. Equations are by definition, equal values.
  29. 29.  White undertook a study to see how a collection of ideal untreated arches conformed to the predetermined arch forms of the most popular formula and to come to conclusions, if possible about how reasonable, ideal arch forms can be derived for individual patients.  Dental casts of 24 orthodontically untreated superior adult occlusions were collected, tracings of the teeth were made on acetate papes and overlays were super imposed, the closeness of fit was evaluated and graded as “good fit”, “moderately good fit” and “poor fit”. The evaluation was of course, subjective and not without some degree of error .  Yet the results were interesting (shown in the table)
  30. 30. Table 1 – 24 untreated superior adult occlusion evaluated for fit various arch designs :----------------------------------------------------------------------------------------Good Fit Moderately Good Fit Poor Fit ----------------------------------------------------------------------------------------Bonwill-Hawley 4 (8.33%) 19 (39.53%) 25 (52.08%) Brader 6 (12.50%) 21 (43.75%) 21 (43.75%) Catenary 3 (27.08%) 22 (45.83%) 13 (27.08%) RMDS 2 (8.33%) 22 (91.67%) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  31. 31.  Only 8% of Bonwill-Hawley designs couls be considered a bood fit, while 52% were poor fits. The Brader designs has two more good fits, but the percentage was still low at 12.5%. Catenaries had more good fits than the previous two combined, but the percentage was still only 27% and there was an equal percentage of poor fits. The RDMS computer derived arch designs impressively, had no poor fitting designs. Since lower arches are computed by RMDS, the sample number is one half that of the other designs 92% of the RMDS designs were judged to be moderately good fits.
  32. 32. Absence of arch symmetry White also evaluated the symmetry of the arches of the ideal orthodontically untreated models. The most conspicuous finding was that total absence of true arch symmetry among his collection of models. Each occlusal tracing was copied onto graph paper and set within a rectangle to study arch symmetry. Symmetry displayed by the arches was scored at ‘symmetrical’, ‘moderately symmetrical’ and ‘asymmetrical’. Tabulation showed only 6.25% were evaluated as symmetrical.
  33. 33. Table – 2 ------------------------------------------------------------------------------Symmetrical Moderately Symmetrical Asymmetrical --------------------------------------------------------------------------------------------------------------------------------------------------Number 3 27 18 Percent 6.25% 56.25% 37.5% -----------------------------------------------------------------------------------------------------------------------------------------------------------By the above observations he came to two conclusions: No generalized, universal arch form seems to be applicable. Majority of normal arches are asymmetrical.
  34. 34.  Because of these two observations, White advocated individualizing arches to the patients by a simple technique called “occlusal mapping”. The technique involved drawing an outline of occlusal surfaces of all the teeth on a piece of acetate paper from an occlusal x-ray. Photo or the study cast. On this the contact points are marked.  A dotted line is drawn through the masidosital dimension of each and connecting the lines across the proximal contacts. This line will represent the center of the basic arch perimeter that is available for the support of the teeth. The occlusal shape of each tooth can then be traced in an ideal position on this basic arch and a customized ideal arch form can be constructed and used through out the treatment.
  35. 35. PHYSIOLOGIC ARCH FORMS Charles Oakes and James Hatcher Dallas, Texas (JCO 1991) Determining arch form is one of the most misunderstood and neglected aspects of orthodontic treatment. The arch form, especially in the mandible cannot be permanently expanded by appliance therapy. There is a lack of stability in both intercanine and intermolar width after expansion. Today, many treatment modalities are aimed at widening the arch as a means of avoiding extractions. Orthodontists might be well advised to work within the tested limits.
  36. 36.        With few exceptions, the mandibular model with all permanent teeth present provide the best basis for construction of a correct or “physiologic” arch form. The arch form can easily be determined from an initial model as follows. Attach small beads, representing the ideal bracket positions to the mandibular model with toothpaste. A piece of clear glass, plastic or even acetate paper is placed over the model. Viewing the model from directly overhead, transfer the bead positions to the glass, plastic or acetate paper with a permanent marker. Remove the glass / plastic / acetate paper from the model and connect the dots as symmetrically as possible. Place the lower arch wire directly over the traced arch form. Bend the upper wire to lie outside the traced arch form. Physiologic arch forms are difficult to construct in cases with severe intercanine construction. If the intercanine width is maintained in such case, the arch form will be unacceptable. In these cases, expansion is necessary and retainer is encouraged.
  37. 37. THE FORM OF THE HUMAN DENTAL ARCH Stanley Braun et al        The human dental arch form is shown to be accurately represented mathematically Forts sets of casts – 15 Class I, 16 Class II and 9 Class III – were examined. A precision machine tool was used to record the x, y and z coordinates of selected dental landmarks on all casts. The coordinates were processed through a computer curve-fitting programme. The were as follows : The Class III mandibular arches had smaller arch depth and greater arch width (beginning from the premolar area) than the class I arches. The Class II mandibular arches exhibited generalized reduced arch width and depth compared with Class I arches. Maxillary arch depths were similar in all three groups. The Class III maxillary arch width were greater from the lateral incisorcanine area distally compared with the Class I maxillary arch. The Class II maxillary arch form was narrower than the Class I arch form from the lateral incisor-canine area distally.
  38. 38. ARCH SIZE AND FORM IN UNTREATED ADULTS  Edward Harris, Memphis (AJO, 1997)  Adulthood - the lengthy phase following attainment of biologic maturity – often is perceived as a period of “no change”, or one of slow deterioration. Recent skeletodental studies discount this stereotype.Teeth consolidate during the adolescent age interval, apparently by mesial drift, and the arch length decreases. Arch widths also change with age, but the magnitude of the change is smaller. Changes in arch size and shape were studied in 60 adults with intact dentitions. Full mouth models were taken at about 20 years of age and again 55 years of age. Some variables – particularly those between arches (incisor overbite and overjet, molar relationship) and mandibular intercanine measures of arch width and length changed significantly. Arch widths increased over time, especially in distal segments, whereas arch lengths decreased. These changes significantly altered arch shape towards shorter-broader arches. The data suggests that changes during adulthood occur most rapidly during the second and third decades of life, but do not stop thereafter.  
  39. 39.       CONCLUSION A study of any aspect of orthodontics immediately involves the problem of variations in size of structures, variations in the form of parts, variations in functions; and the dental arch form is no exception to this. The form and size of dental arches is influenced at least by four factors. Firstly, the skeletal parts may not be harmonious or in proportion, and this will mean that appropriate compromises will be indicated from otherwise ideal relations. Secondly, functional problems may alter the oral environment when muscle structure itself may be inadequate. Thirdly, psychologic factors may be present, causing prolonged habits and fourthly, discrepancies in tooth size and tooth form may alter an otherwise harmonious situation. Because of these complex problems, there is no universally accepted arch form. The irony is that, the more we know about a particular subject, the more our ignorance unfolds and the goal seems farther ahead. Accepting there is no generalized, universal, ideal arch form, the question remains, “to which arch form should we treat our patients?”. To answer that, I would like to quote none other than the Father of Modern Orthodontics, Dr. Edward H. Angle. He made this statement nearly eight decades ago and it is still relevant today. “The best Orthodontists can do is to secure normal relations of the teeth and correct general form of the arch, leaving the finer adjustments to individual typal form to be worked out by nature through her forces, which must, in any event, finally triumph”.
  40. 40. REFRENCES         Begole EA et al. Analysis of change in arch form with premolar expansion. Am J orthod 1998 ; 113: 307-15. Brader AC. Dental arch form related to intraoral forces, PR=C. Am J Orthod 1972 ; 61: 541-562. Braun S et al. The form of the human dental arch. Angle Orthod 1998 ; 68:29-36. Musich DR, and Ackerman JL. The catenometer: A reliable device for estimating arch perimeter. Am J Orthod 1973 ; 63: 366-375 Oakes C, Hatcher JE. Determining physiologic arch forms. J Clin Orthod 1991 ; 25:79-80 Wheeler RC. A textbook of Dental Anatomy, physiology and occlusion. 7th ed. W.B. Saunders Co. 1993 ; 418-420. Valiathan A, Oberoi S. Dental Arch Forms. KDJ 1996 ; 19(2): 39-42 White LW. Individualized ideal arches. J Clin Orthod 1978 ; 12:779-87.
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  42. 42. Leader in continuing dental education