I read with keen interest the article by Simon et al in the June issue of the AJO-DO . (Simon M, Keilig L, Schwarze J, Jung BA, Bourauel C. Forces and moments generated by removable thermoplastic aligners: Incisor torque, premolar derotation, and molar distalization. Am J Orthod Dentofacial Orthop 2014;145:728-35). The authors are to be commended for tackling a difficult problem and for devising a simulator system with computer-controlled 3-dimensional sensors. At present, suitable direct sensors are not available.

A distinction is made between vacuum-formed appliances and pressure-formed appliances. Both are pressure formed in that they use air pressure to form the appliances. In vacuum forming, atmospheric air pressure is used with a theoretical maximum of 15 pounds per square inch (PSI). Pressures from 3 to 14 PSI are obtained, depending on the efficiency of the vacuum pump. In other systems, compressed air up to 100 PSI is used. The inner detail of the aligner depends on the magnitude of the air pressure, up to a maximum. The more detailed the inner surface, the more force is generated and the greater the precision.

The authors referred to “incisor torque” as one of their measurements. Unlike wire appliances that use torsion for changing the axial inclination of incisors, thermoplastics use 2 or more balanced force vectors for this correction. Orthodontic force vectors rarely, if ever, pass through the center of gravity of a tooth. Hence, these forces generate moments (“moment” and “torque” are synonymous). It is the careful balancing of these forces that produces translation or changes in the axial inclination of a tooth.

The authors stated that “clinical parameters such as periodontal ligaments, mastication, saliva, and soft-tissue reactions could not be simulated and considered.” In addition, an ideal center of resistance was used for each tooth. A tooth in its periodontal space does not follow simple Newtonian physics but follows the principles of deformable media. The exact center of resistance is not known. Therefore, it is critical that it be emphasized that a simulation is useful in understanding this problem, but it is far from a solution.

There is no indication that the authors made an allowance for the fact that aligners do not always begin in their final seated position. There is slippage between the inner surface of the aligner and the teeth. The force system is constantly changing as the patient occludes his or her teeth.

For the record, the authors listed several articles as the source for the basic principles of the Invisalign system. They did not include the contour appliance of Nahoum. In 1959, I developed vacuum-formed thermoplastic appliances for dental use. In addition to retainers made of clear plastic, I developed the concept of using serial (successive) appliances, with small incremental changes, to obtain major corrections. The Invisalign system and the others are based on this technology.

The Kesling positioner is a short-term (90 days) finishing appliance that was made of black rubber and covered both dental arches. It is powered when the patient bites into the rubber. The positioner was designed to close interdental spaces after debanding and to make minor interarch corrections. It was worn mainly at night. An acrylic and wire retainer was made after this phase of treatment.