Stanley Braun

The form of the human dental arch.

The human dental arch form is shown to be accurately represented mathematically by the beta function. The average correlation coefficient between measured arch-shape data and the mathematical arch shape, expressed by the beta function, is 0.98 with a standard deviation of 0.02. Forty sets of casts--15 Class I, 16 Class II, and 9 Class III--were examined. A precision machine tool device was used to record the X-, Y-, and Z-coordinates of selected dental landmarks on all casts to 0.001 mm accuracy. The coordinates were processed through a computer curve-fitting program. The Class III mandibular arches had smaller arch depth and greater arch width (beginning in the premolar area) than the Class I arches. The Class II mandibular arches exhibited generalized reduced arch width and depth compared with the Class I arches. Maxillary arch depths were similar in all three groups. However, the Class III maxillary arch widths were greater from the lateral incisor-canine area distally compared with the Class I maxillary arch, and the Class II maxillary arch form was narrower than the Class I arch form from the lateral incisor-canine area distally. The beta function more accurately described the dental arch form than representations previously reported.

A study of bite force, part 1: Relationship to various physical characteristics.

A new device for measuring and recording bilateral bite force in the molar/premolar region has been developed. Because this new device is elastic and conforms to the occlusal surfaces of the teeth, and because the sensing element is relatively comfortable, it is believed that experimental subjects are less reluctant to register true maximal forces than in earlier studies. Potential correlations of maximum bite force to gender, age, weight, body type, stature, previous history of orthodontic treatment, presence of TMJ symptoms (jaw motion limitation, clicking with pain, or joint pain), or missing teeth were studied in a sample of 142 dental students. The mean maximum bite force of the sample was found to be 738 N, with a standard deviation of 209 N. The mean maximum bite force as related to gender was found to be statistically significant, while the correlation coefficients for age, weight, stature, and body type were found to be low. Even so, all data scatterplots exhibited relatively positive relationships. Correlations of maximum bite force to an earlier history of orthodontic treatment or to the absence of teeth were not found. Subjects reporting TMJ symptoms did not exhibit a significantly different maximum bite force than subjects without symptoms.

A study of maximum bite force during growth and development

Bilateral bite force was measured in a sample of 457 subjects (231 males and 226 females) from 6 years through 20 years. The mean maximum bite force was found to increase from 78 Newtons at 6 to 8 years to 176 Newtons at 18 to 20 years. While earlier studies have shown adult males have a greater mean bite force than females, this difference is not evident during growth and development. Gender-related bite force difference likely develops during the postpubertal period in association with greater muscle mass development in males.

A study of bite force, part 2: Relationship to various cephalometric measurements.

Maximum bilateral bite force, determined in 129 dental students, was evaluated with regard to six skeletal and eight dental measurements acquired from conventional lateral cephalometric radiographs. Statistically significant correlations for three of the skeletal measurements were found. Maximum bite force increased with regard to decreasing mandibular plane/palatal plane angle and to decreasing mandibular plane angles. Maximum bite force increased with an increasing ratio of posterior facial height to anterior facial height. Significant statistical correlation for only one of the eight dental measurements was found: maximum bite force related directly with increasing maxillary and/or mandibular dentoalveolar heights, and unexpected finding.

The curve of Spee revisited

Through the use of a sophisticated measuring device and support computer technology, accurate arch circumferences were determined for 27 casts that exhibited moderate to severe curves of Spee. Arch circumference differences were subsequently obtained by comparing the measured arch length to a planar projection formed by the center of the incisal tips anteriorly and the distobuccal cusp tips of the second molars distally. A general relationship has been derived for the arch circumference differential, resulting from the elimination of the curve of Spee, versus the severity of the curve. The arch circumference reduction is considerably less than that found by earlier investigators, implying that the incisor protrusion often associated with leveling the curve of Spee is not primarily due to the aforementioned differential, but rather more directly due to the mechanics used in leveling the curve of Spee.

Biomechanical considerations in distraction of the osteotomized dentomaxillary complex

The completely osteotomized dentomaxillary complex is essentially a free body constrained only by its soft tissue attachments. Therefore the line of action and point of application of any protractive force(s) used during distraction osteogenesis must be considered relative to its center of mass. This is in contrast to the nonsurgically separated dentomaxillary complex, which is a constrained body, and therefore the application of protractive force(s) must be considered relative to its center of resistance. These two centers are not coincident. With knowledge of the location of the center of mass, predictable protraction of the dentomaxillary complex can be achieved. In this study, the center of mass of an adult maxillary specimen osteotomized to emulate a Le Fort I osteotomy was determined. Protractive force(s) through the center of mass will produce linear advancement along its line of action. Protractive movement of the dentomaxillary complex can be adjusted downward and forward or upward and forward by locating the protractive force(s) line of action superior or inferior to the center of mass. A cleft patient is described wherein the surgically separated dentomaxillary complex is protracted downward and forward with a force vector superior to its approximate center of mass. This results in a predictable increase in overbite and overjet with negligible mandibular rotation.

On the management of extraction sites

Extraction sites may be needed to achieve specific orthodontic goals of positioning the dentition within the craniofacial complex. The fundamental reality that determines the final position of the dentition, however, is the control exercised by the clinician in closure of the extraction sites. A specific treatment objective may require the posterior teeth to remain in a constant position anteroposteriorly as well as vertically, while the anterior teeth occupy the entire extraction site. Another treatment objective may require the reverse, or any number of purposeful alternatives of extraction site closure. An appliance system developed over time, which provides this control, is described. The system takes advantage of aspects of continuous arch therapy that provides constant, positive orientation of the anterior and posterior groups of teeth to each other in three-dimensional space across an extraction site, combined with aspects of the segmented arch technique that permit definable and predictable force systems to be applied to these teeth. Consequently, the clinician has the ability to forecast treatment outcomes with confidence.

Changes in occlusion related to the cant of the occlusal plane

It is known that dental occlusion is influenced by changes in the cant of the occlusal plane. This study has defined the geometric and mathematical relationships between dental occlusion and rotations of the occlusal plane in the sagittal view. As a general clinical guide, each degree of rotation of the occlusal plane will result in a half millimeter change in the dental occlusal relationship. This is of importance, because changes in the cant of the occlusal plane are sometimes unintentional, as well as intentional, during orthodontic therapy. An earlier study has also documented that the occlusal plane rotates naturally upward and forward approximately 6 degrees during growth and development. This phenomenon tends to develop a Class II dental relation and therefore has important implications for the developing dentition.

Rationale of the segmented approach to orthodontic treatment

Modern orthodontics requires defined treatment goals. To achieve them, known force systems must be used to control the active units (teeth being moved) and the reactive units (anchorage teeth). This article discusses the methods of controlling the force systems through the variables of spring design and anchorage selection. Continuous and segmented arch treatment are contrasted in their ability to achieve optimal and defined force systems with minimal side effects.

Dynamic relationships of the mandibular anterior segment

The hyperbolic cosine function is shown to be an accurate representation of the form of the mandibular anterior teeth from the canine/first premolar contact on one side around the perimeter to the opposite side (r = 0.951). On the basis of this mathematical function, the changes in canine width, anterior segment depth, arch perimeter, and their related incisor angular alterations are forecastable. This knowledge will allow the clinician to predict the effects on various aspects of the anterior segment arch form as one or more of these variables are altered without resorting to trial and error or performing a wax-up. For example, the clinician can predict the change in the anterior segment arch depth and incisor angulation that would occur with alterations in canine width.