Cordato M A
Aust Orthod J. 1995 Mar;13(4):249-52.
A mathematical study of the anterior dental relations could provide a rationale for the work of Neff and Bolton. Bolton used normal occlusions of permanent teeth to obtain his range of comparisons of tooth width ratios; a model that needs no normals is described in this study. Use of this model and its development could support or disprove further hypotheses regarding anterior occlusion. Manipulation of the model could allow a means of estimating the influence of several dental measurement variables on the relation between upper and lower dental arches. The formulae allow changes in the form and size of one or both arches individually and a comparison of an upper arch to different upper arches and a lower arch to different lower arches; and further, they allow these combinations of upper and lower arches to relate to each other. A reference plane between the arches is established to relate opposing arches to each other. The model is developed using the archform and angular measures of Bonwill and the mesiodistal widths of Bolton. Scope is provided in the model to allow for alteration of antero-posterior relations, spacing and crowding. Values for different amounts of overjet of incisors and maxillary canine tip could be generated by altering the figures to those of other authors' hypotheticals or by the use of individual patient data.
对前牙关系进行数学研究可为内夫和博尔顿的工作提供理论依据。博尔顿利用恒牙的正常咬合来获取其牙齿宽度比的比较范围；本研究描述了一种无需正常咬合的模型。使用该模型及其拓展可能支持或反驳关于前牙咬合的进一步假设。对该模型进行操作可以提供一种方法，用以估计几个牙齿测量变量对上、下牙弓关系的影响。这些公式允许单独改变一个或两个牙弓的形态和大小，以及将一个上牙弓与不同的上牙弓进行比较，将一个下牙弓与不同的下牙弓进行比较；此外，它们还允许上、下牙弓的这些组合相互关联。在牙弓之间建立一个参考平面，以使相对的牙弓相互关联。该模型是利用邦威尔的牙弓形态和角度测量值以及博尔顿的近远中宽度来构建的。该模型提供了一定范围，以允许改变前后关系、间隙和拥挤情况。通过将数据改为其他作者假设的数据或使用个体患者的数据，可以得出不同程度的切牙覆盖和上颌尖牙牙尖覆盖的值。
