Thank you to Henry Nahoum for carefully reading and commenting on our article regarding the force systems of removable thermoplastic appliances.

In fact, there are several different parameters that can influence the biomechanics of the aligners, including (but not limited to) the material properties of the aligner, its thickness, and the fitting accuracy. We are aware that these parameters do influence the clinical outcome, but the evaluation of these parameters was out of the scope of our study. However, such investigations might be the focus of future studies.

According to the correspondent, using an in-vitro setup for simulating tooth movements might limit the applicability of the presented approach. Furthermore, he stated that using a “center of resistance” for describing a tooth movement (as it is done in our setup) does not reflect the correct mechanical behavior of the tooth in the alveolus. We are aware that we could not consider the clinical parameters in our study, and we hope that these limitations are clearly expressed in the discussion of the article. However, the use of the center of resistance is an accepted idealization used to describe the tooth movement, and after using the presented approach of experimental simulation of the orthodontic tooth movement in several previous studies, we feel confident that the results of these simulations provide a rather good approximation of the clinical outcome. This holds especially for this study, since we were able to analyze the clinical outcome of these cases in another part of this study, which was in good correlation with the results of the simulations.

Furthermore, Dr Nahoum pointed out that we did not pay attention to the fact that force systems of aligners are constantly changing while being worn. Although this is not stated directly in our article, we repeatedly inserted each aligner and performed the simulation at least 3 times in a row for each aligner to allow the teeth to “slip in the aligner.” Unfortunately, this part of the text was accidentally removed in an attempt to improve the readability of that section. Altogether, the tooth movement was implemented in increments. After every increment movement (transformed by the stepping motors of the positioning tables), the force systems currently generated by the aligners were remeasured, and the updated forces were used for the simulation.

Finally, Dr Nahoum emphasized that we did not mention Nahoum’s contour appliance. We included the Kesling article because it is one of the oldest articles that reported the use of elastic positioners in orthodontics (here still primary for minor tooth movements after debonding), and many other publications refer to this article as the basic idea that finally led to aligner systems. Due to the limited space available in the article, it was not possible to mention every available article on this topic.