Robert H. Biggerstaff

Three Variations in Dental Arch Form Estimated by a Quadratic Equation

The shape of the human dental arcades has been qualitatively described as semiellipsoid (G. V. BLACK, Descriptive Anatomy of the Human Teeth, 1894), paraboloid (E. H. ANGLE, Dent Cosmos 41:248, 1899), U-shaped (R. MARTIN, Lehrbuch der Anthropologie, 1914), horseshoe-shaped (A. HR.DLICKA, Practical Anthropometry, 1920) and catenary (M. A. MACCONAIL and E. A. SCHER, Dent Rec 69:285302). More recently, the computer has been used to mathematically fit the curvature of the dental arches by exponential (T. HAYASHI, Bull Tokyo Med Dent Univ 3:175-218, 1957), Fourier series (K. H. Lu, Biometrics 21:491-502, 1965), and fourth degree polynomial equations (K. H. Lu, Arch Oral Biol 11:1057-1069, 1966). Of these methods the fourth, fifth, or sixth degree least squares polynomial regression equations give the most accurate and reproducible likeness of arch form (faithfully reproducing symmetries and asymmetries) and arch length (C. SANIN ET AL, J Dent Res 49: 885, 1970). However, the fitted curves are not descriptive and no satisfactory statistical method exists for comparing the coefficients. Furthermore, the statistics of coefficients are difficult to interpret. The known variability of the human dental arch is responsible, at least partially, for the many qualitative descriptions. Generally, one of three curves (ellipsoidal, parabolic, or hyperbolic) will compare favorably with a human dental arch. But, some humans may have Ushaped or horseshoe-shaped dental arches. This paper describes a method for defining the individual arch form as one of three mathematical curves.

The short-term and long-term soft-tissue profile changes accompanying mandibular advancement surgery

To provide an improved data base for predicting the soft-tissue changes that accompany mandibular advancement surgery, short- and long-term serial cephalograms from the records of eighteen patients were analyzed. Hard- and soft-tissue landmarks were located on serial tracings and later were reduced to rectangular X-Y coordinates for computer-generated measurement data and statistical analyses. The interpretation of mean value, ratio, and regression equation data showed that the lower lip, inferior labial sulcus, and chin tissues moved forward and downward. The mandibular short-term (mean = 3.7 months postsurgery) horizontal change means were greater than the long-term (mean = 18 months postsurgery) horizontal change means. The posteriorly directed long-term means may result from functional adaptations that follow the short-term surgery-related spatial changes. These data also show the need for long-term prediction data to supplement the short-term data base.

Heritability of the Carabelli Cusp in Twins

The study of the Carabelli trait among 199 monozygotic and dizygotic twin pairs failed to demonstrate a high degree of heritability. Analyses of antimere differences in individuals indicated a lack of mirroring and no sexual dimorphism. Monozygotic twin pairs exhibited a higher concordance rate for corresponding tooth comparisons than dizygotic twin pairs.

A vertical cephalometric analysis of the human craniofacial complex

A vertical analysis involving ten linear measurements was developed to localize skeletal and dentoalveolar dysplasias. The measurements are of biologic relevance, reflecting the amount of growth harmony or disharmony to the examination and record-taking time. The vertical dimensional analysis uses the age- and sex-related University of Michigan mean values for comparative data for each measurement. Ratios were computed for a five-unit proportional analysis. Both analyses were applied to assess the vertical problems of three female patients. The analyses detected specific areas of dysplasia for each patient.

Cusp Size, Sexual Dimorphism, and the Heritability of Maxillary Molar Cusp Size in Twins

The quantitative hierarchy for maxillary molar cusp size is established. Sexual dimorphism, not present in measures of individual cusp size, is present when the size contributions of individual cusps and ridges are summed. The twin data analyses show a low level of hereditary variability for these dental traits.

A quantitative comparison of paralleling long-cone and bisection-of-angle periapical radiography

Quantitative data permit the variability comparison of crown-root ratios computed from periapical films of a single central incisor taken by five technicians using the bisection-of-angle and the paralleling long-cone techniques. The paralleling long-cone technique produces significantly less distortion and is less variable. It is the method of choice for assessing natural root resorption and resorption due to orthodontic therapy.

Orthodontic classifications: Mystique or reality?

F or years those who have attempted to create systems for orthodontic classifications have been shackled by the bonds of the E. H. Angle paradigm.’ The two-dimensional constraints of the most widely used and accepted orthodontic classification preclude advancement in this field. Therefore, orthodontics may be called a “science art” and/or a “transscience.“’ These terms are interpreted broadly in this article in an attempt to focus on the problem of classification and to create an awareness of the necessity to link the etiology of malocclusion accurately with a rational plan of therapy. The future of orthodontics becomes dimensionless if past biases are eliminated and today’s problems are resolved under an evolved or synthetic philosophy. Orthodontics has borrowed heavily from other disciplines, such as physical anthropology, anatomy, and metallurgical sciences. By doing so, it has utilized considerable data and adapted it, rightly or wrongly, to orthodontics. “We have acquired notions and compiled precious materials which will later have their place and be of importance.“3 However, the compiled data cannot properly explain biologic phenomena if they are acquired erroneously or if the interpretations are directed to other seemingly related or unrelated processes. In this sense, orthodontics must function under the nineteenth century philosophy that a discipline deserves its name only when it establishes quantitative relations between phenomena. However, biologic entities have not been reduced to an exact science. They often appear identical but are the results of different determinants. Further, biologic observations may be asymmetric, comprised of numerous components, each with its unique potential for growth. Pasteur stated: “The universe is a big dissymmetrical whole. I am inclined to believe that lift such as it is manifested to us must be a function of the dissymmetry of the universe and of the consequences which it entails. Life is dominated by dissym-

A Photogrammetric Mandible Holder

The mandible, because of its shape, is a difficult bone to describe by measurements. In the past, the mandible has been described craniometrically, cephalometrically, and by radiographic cephalometric methods. Each method uses caliper measurements to describe the mandible in terms of defined dimensions. Unfortunately, these measurements do not describe adequately the U-shaped mandible. As an alternative to the customary measurement methods, I propose the use of photogrammetric methods similar to those used (R. H. BIGGERSTAFF, Amer J Phys Anthrop 31:163170, 235-242, 1969) to generate mensurational data describing the mandible. These methods have the capability of reducing the images of the complex occlusal surfaces of molars and premolars to a two dimensional model for the study of crown component variation, ie, the basal areas of cusps and ridges. A mandible holding device was designed and fabricated for this purpose. This device was attached to a radiographic craniostat (R. H. BIGGFRSTAFF, J Dent Res 47:1186, 1968), in such a way that the equipment and methods were adaptable to field use without sacrificing accuracy. Figure 1 shows the mandible holding device with a mandible affixed. This device has the capability of positioning the mandible so that the occlusal plane (or plane of the alveolar bone) is parallel to the plane of photographic film. Fiducials are machined on both sides of the holder for the adjustment of minor errors because of the enlargement or diminution of the photographic image (Figs 1, 2). Rotation of the oriented mandible through 1800 allows photographing of the occlusal and basal views of the mandible (Fig 2). Points defined along the lingual margin of the alveolar bone, in addition to an analogous series along the lower border of the mandible, can be transformed into coordinate X and Y coordinate data for analysis. When applied to a suitable population, these methods may provide important data that describe the shape of the mandible body and the metric explication of the origin and evolution of the chin. The mandible holder makes it possible to test the hypothesis that chin formation is a sequel to the peculiar backward and forward shifting relationships between the basal bone and alveolar bone during the processes of maturation.