William P. Hnat

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.

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.

Design and development of a MEMS capacitive bending strain sensor

The design, modeling, fabrication and testing of a MEMS-based capacitive bending strain sensor utilizing a comb drive is presented. This sensor is designed to be integrated with a telemetry system that will monitor changes in bending strain to assist with the diagnosis of spinal fusion. ABAQUS/CAE finite-element analysis (FEA) software was used to predict sensor actuation, capacitance output and avoid material failure. Highly doped boron silicon wafers with a low resistivity were fabricated into an interdigitated finger array employing deep reactive ion etching (DRIE) to create 150 ?m sidewalls with 25 ?m spacing between the adjacent fingers. The sensor was adhered to a steel beam and subjected to four-point bending to mechanically change the spacing between the interdigitated fingers as a function of strain. As expected, the capacitance output increased as an inverse function of the spacing between the interdigitated fingers. At the unstrained state, the capacitive output was 7.56 pF and increased inversely to 17.04 pF at 1571 ?? of bending strain. The FEA and analytical models were comparable with the largest differential of 0.65 pF or 6.33% occurring at 1000 ??. Advantages of this design are a dice-free process without the use of expensive silicon-on-insulator (SOI) wafers.

Stress Analysis of Human Tooth Root Using Various Root Canal Instruments

This study compared external root stresses from instrumentation by several motor-driven nickel-titanium instruments to stresses developed by hand files. Twelve curved first molar mesial roots were invested in PLM-9 photoelastic material to disclose net stress transmitted from the canal through the dentin. Minimal fringe patterns were observed during instrumentation with all techniques. Light-speed yielded the least change. In no case was a complete 60 psi fringe change noted.

Optical measurement of discharge valve modal parameters for a rolling piston refrigeration compressor

In this paper we describe the methodology and results of an experiment to measure the fundamental undamped natural frequency and damping ratio for the discharge reed valve in a rolling piston rotary compressor. The small size and extreme flexibility of the valve assembly required the use of a non-contacting measurement technique; thus, an optical displacement follower was chosen as the primary transducer. The measurement system also incorporated a strain gage load cell and PC-based signal processing software. The sensitivity of the system modal parameters to design variables such as valve preload geometry, lubricant viscosity, and retaining screw torque was investigated. Eventually, the measured stiffness, fundamental natural frequency and equivalent viscous damping ratio were incorporated as valve model parameters in a comprehensive computer simulation program for the compressor. Results show that this reed valve design is lightly damped, and that the fundamental natural frequency is a strong function of preload geometry. Lubricant viscosity and retaining screw torque had little effect on the modal parameters.

A new accurate approach to the anterior ratio with clinical applications: Part 1: A computer program

The arcs of the six anterior maxillary and mandibular teeth have recently been described mathematically by the hyperbolic cosine function with a maxillary correlation coefficient (r ) of 0.885 and a mandibular correlation coefficient (r ) of 0.951. Because the geometric relationships of the anterior dental arcs are known when the occlusion is Class I, a computer program has been developed for use in clinical practice. Rapid forecasting of the interrelationships between the maxillary and mandibular arc depths (related to overjet) with variations in the mesiodistal sums of the six maxillary and mandibular anterior teeth for various intercanine widths is now possible with ease and accuracy (+/- 0.1 mm). Clinical applications are illustrated.