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. 2021 Aug 4;11:15853. doi: 10.1038/s41598-021-95002-w

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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The average actual facial changes in the Surgery group for pre-treatment (top-left) and the superimposition of the actual facial changes between pre-treatment (blue) and post-treatment (yellow). For the significance probability maps, significant changes between pre-treatment and post-treatment are indicated as follows: blue, P < 0.05; pale pink, P < 0.01; dark pink, P < 0.001; purple, P < 0.000. For the distance maps, yellow indicates that the treatment changed from pre-treatment to post-treatment (post-treatment minus pre-treatment is a positive value, whereas blue indicates that the change had a negative value. Thus, in the horizontal direction in the Surgery group, yellow in the left-half face indicates lateral displacement and blue in the right-half face also indicates lateral displacement after treatment. In the vertical direction, blue indicates a downward displacement after treatment in the Surgery group and yellow indicates upward displacement after treatment. In the anteroposterior direction, yellow indicates a protrusive movement, whereas blue indicates a retrusive movement after treatment. The figures were created using a custom MATLAB software (MATLAB 2020a, The Math Works, Natick, MA, USA).