A mathematical model of mandibular protrusion

Development of a New Type of Incisal Table for Prosthetic Articulators

This study illustrates the effectiveness of an advanced incisal table surface, featuring adjustable curvature, in the sake of more accurate articulator kinematics in anterior teeth reconstruction. Prosthetic articulators, used by dental technicians in reconstructive dentistry, are adjustable instruments that simulate the motion of mastication between dental casts: usually, the forward motion (protrusion) of the mandible is guided by sliding a pin over a flat table in order to recreate those movements when incisal teeth are missing. However, such protrusion is an approximation of the exact motion, since flat incisal tables have a limited set of adjustments. Customized software has been developed in order to simulate the kinematics of articulators in three-dimensional space: animations and measures of the envelope of teeth profiles show the unfeasibility of reconstructing with good approximation the profile of incisive teeth, when a simple ‘flat' incisal table is used. A new incisal table with an adjustable curvature has been proposed, simulated, and built, and computer simulations demonstrated the superior precision of the new design when compared to a conventional articulator which uses a flat incisal table.

A mathematical model of mandibular movement on the Hanau articulator and computerized simulation system of dynamic occlusion for complete denture

This study is concerned with the construction of a mathematical model of mandibular movement on the Hanau articulator and a complete denture occlusion simulation system (CDOSS) in the field of dental restoration. On the basis of the theory of spatial mechanisms, degrees of freedom in the kinematic chain of the Hanau articulator are analysed, and a hypothesis of constraints is presented to obtain constrained motion. Then, a series of mathematical expressions are derived to describe the three dimensional mandibular movement on the Hanau articulator. By adopting techniques and tools such as laser scanning, computer graphics, and computer databases, a 3D digitized model of complete denture is reconstructed, and a CDOSS is developed. With the aid of this software, the visualization and diagnosis of mandibular movement can be easily realized. One edentulous case discussed in this study shows that CDOSS provides a useful tool to deal with the functional aspects of occlusal morphology in a diagnostic and therapeutic sense.

Computer-aided axiography of asymptomatic individuals with Class II/2

The condylar axiographic tracings of 23 asymptomatic adult volunteers (Helkimo-index DiO) with Class II/2 axiography relationships were compared to tracings of an analogous group (DiO; n = 30) with normal occlusion. The obtained measurements were evaluated statistically and discussed with respect to possible recording errors.

RESULTS

The open-close movement proceeded uncharacteristically, differences existed only in protrusion, mediotrusion and their combined rotation component. In Class II/2 cases an approximately 7 degrees higher angle of the condylar path inclination (CPI) was measured. The Class II/2 group rotated to a significantly higher angle in protrusive and mediotrusive movements and showed longer condylar path lengths than the control group. Another significant difference was found in the location of maximum CPI values and maximum rotation angles within the condylar path, because in no case was isolated rotation or translation of the hinge axis observed.

CONCLUSION

The temporomandibular joint of Class II/2 individuals shows a wider range of motion than joints of subjects with normal occlusion. The reduced capacity of motion which was assumed to exist in a so-called hack-bite could not be backed up for Class II/2 deep bite cases. The investigated differences cannot be seen as pathomechanisms, because all participants were clinically free of dysfunction. The neuromuscular engram to overcome the overbite controls a complex spatial motion pattern which cannot be described by a simplified mechanical abstraction of motion in the sagittal plane. The temporomandibular joint with its complex pattern of movement is able to create physiological mechanisms of compensation to react to different dental and skeletal features.

A mathematic model of occlusal adjustment

A mathematic algorithm was developed to calculate mandibular repositioning resulting from occlusal equilibration. A formula to determine the amount of tooth reduction necessary for the adjustment also was derived.