Ferrario V F, Sforza C, Guazzi M, Serrao G
Laboratorio di Anatomia Funzionale dell'Apparato Stomatognatico, Facoltà di Medicina e Chirurgia, Università degli Studi di Milano, Italy.
J Craniofac Genet Dev Biol. 1996 Oct-Dec;16(4):208-17.
Craniofacial growth and development involve both size and shape variations. Shape variations can be assessed independently from size using mathematical methods such as the elliptic Fourier analysis, which allows a global evaluation of the shape of organs identified by their outlines independently from size, spatial orientation, and relation to reference planes. The mandibular outlines were digitized from the tracings of the Bolton standards (lateral view) from 1 to 18 years of age, and the age differences in shape independently from size were quantified using the elliptic Fourier series. A "morphologic distance" MD (i.e., a measurement of differences in shape) between each younger mandible and the oldest one was computed using the relevant Fourier coefficients like the cartesian coordinates in standard metric measurements. MD equals 0 when the profiles are identical. MD (Y) between the Bolton standard at 18 years of age and all the other Bolton tracings were significantly correlated (correlation coefficient r = 0.987, P < or = 0.001) with age (X) (semi-logarithmic interpolation Y = -3.87.log(e) X + 13.593). Differences between the size-independent shape of the Bolton standard at 18 years and the relevant plot at 1 year were located at the chin, gonion, coronoid process, anterior border of the ramus. Size differences were measured from the areas enclosed by the mandibular outlines. Mandibular area (Y) increased about 2.58 times from 1 to 18 years of age (X) (Y = -0.071.X2 + 4.917.X + 35.904, r = 0.997, P < or = 0.001). The shape effect was largely overwhelmed by the very evident size increments, and it could be measured only using the proper mathematical methods. The method developed could also be applied to the comparison between healthy and diseased individuals.
颅面生长发育涉及大小和形状的变化。形状变化可以使用诸如椭圆傅里叶分析等数学方法独立于大小进行评估，该方法允许对由其轮廓识别的器官形状进行全局评估，而与大小、空间方向以及与参考平面的关系无关。下颌轮廓是从1至18岁的博尔顿标准（侧视图）描图中数字化得到的，并且使用椭圆傅里叶级数对独立于大小的形状年龄差异进行了量化。使用与标准度量测量中的笛卡尔坐标类似的相关傅里叶系数，计算每个较年轻下颌骨与最老下颌骨之间的“形态距离”MD（即形状差异的度量）。当轮廓相同时，MD等于0。18岁的博尔顿标准与所有其他博尔顿描图之间的MD（Y）与年龄（X）显著相关（相关系数r = 0.987，P≤0.001）（半对数插值Y = -3.87.log(e) X + 13.593）。18岁博尔顿标准的与大小无关的形状与1岁时的相关图之间的差异位于下巴、下颌角、冠状突、下颌支前缘。大小差异是从下颌轮廓所包围的面积测量的。下颌面积（Y）从1岁到18岁（X）增加了约2.58倍（Y = -0.071.X2 + 4.917.X + 35.904，r = 0.997，P≤0.001）。形状效应在很大程度上被非常明显的大小增加所掩盖，并且只能使用适当的数学方法来测量。所开发的方法也可应用于健康个体与患病个体之间的比较。
