Chinese Journal of Tissue Engineering Research ›› 2010, Vol. 14 ›› Issue (13): 2315-2318.doi: 10.3969/j.issn.1673-8225.2010.13.010

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Curve fitting of soft and hard tissue relation using mathematics models: Functional treatment and natural growth of Class II malocclusion

Liu Ya-fei1, Cui Li-juan2, Zuo Yan-ping1, Liu Xue-cong3, Liu Xin4   

  1. 1 Department of Orthodentics, First Hospital of Hebei Medical University, Shijiazhuang   050031, Hebei Province, China; 2 Teaching and Research Section of Mathemathics, Basic Medical College, Hebei Medical University, Shijiazhuang   050017, Hebei Province, China; 3 Department of Stomatology, Hebei Provincial Children’s Hospital, Shijiazhuang   050031, Hebei Province, China; 4 Department of Oral Medicine, Clinical Medical College, Hebei Medical University, Shijiazhuang   050031, Hebei Province, China
  • Online:2010-03-26 Published:2010-03-26
  • Contact: Zuo Yan-ping, Doctor, Professor, Chief physician, Department of Orthodentics, First Hospital of Hebei Medical University, Shijiazhuang 050031, Hebei Province, China zyp6381@sina.com
  • About author:Liu Ya-fei★, Master, Attending physician, Department of Orthodentics, First Hospital of Hebei Medical University, Shijiazhuang 050031, Hebei Province, China yafei_lyf@sina.com

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Abstract:

BACKGROUND: With development of the digitization in cephalometry and model, increasing mathematical methods are applied in studies of orthodontics.
OBJECTIVE: To investigate whether the relationship between soft- and hard-tissue changed before and after the functional treatment and to build up mathematical models.
METHODS: A total of 67 early permanent dentition Class II Division 1 malocclusion patients were selected, including 40 with functional treatment and 27 with no functional treatment. They were examined cephalometrially before and after treatment. Mathematical methods were used to evaluate effect of treatment, including 4 items, APDI, Ls-EP, U1-NA (mm) and U1-NA. To evaluate the relationship between soft- and hard-tissue movements, a linear function was initially fitted to the data. A quadratic function was fitted to the data when the linear term was not significant. 
RESULTS AND CONCLUSION: Mathematical models confirmed that the association for the soft and hard tissues was quadratic, by using curve-fitting polynomial approach to the cephalometric data of 4 indicators before and after the functional treatment. The pre-treatment  functional formula were: U1–NAmm =-0.012 7 (APDI)2 +1.705 2 (APDI) -0.686 1; U1–NA =-0.025 5 (APDI)2 +3.234 3 (APDI) -67.831 8; Ls–EP =-0.003 7 (APDI)2 +0.380 2(APDI) -3.267 3. The post-treatment  functional formula were: U1–NAmm =-0.003 1(APDI)2 +0.495 8(APDI) -14.248 4; U1–NA =0.01 32 (APDI)2 -1.993 9 (APDI) +98.104 5; Ls–EP =0.007 4 (APDI)2 -1.264 7(APDI) + 55.412 4. The results showed obvious changed in the relationship between soft- to hard-tissue pre- and post the functional treatment. The functional treatment effectively improved the profile of soft-tissues of Class II malocclusion cases.

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