Peng Hao, Wang Xu, Duan Ye, Frey Scott H, Gu Xianfeng
Department of Computer Science, Stony Brook University, Stony Brook, NY 11794.
Department of Computer Science, University of Missouri, Columbia, MO 65211.
Comput Aided Des. 2015 Jan;58:84-91. doi: 10.1016/j.cad.2014.08.024.
Congenital Hand Deformities (CHD) are usually occurred between fourth and eighth week after the embryo is formed. Failure of the transformation from arm bud cells to upper limb can lead to an abnormal appearing/functioning upper extremity which is presented at birth. Some causes are linked to genetics while others are affected by the environment, and the rest have remained unknown. CHD patients develop prehension through the use of their hands, which affect the brain as time passes. In recent years, CHD have gain increasing attention and researches have been conducted on CHD, both surgically and psychologically. However, the impacts of CHD on brain structure are not well-understood so far. Here, we propose a novel approach to apply Teichmüller space theory and conformal welding method to study brain morphometry in CHD patients. Conformal welding signature reflects the geometric relations among different functional areas on the cortex surface, which is intrinsic to the Riemannian metric, invariant under conformal deformation, and encodes complete information of the functional area boundaries. The computational algorithm is based on discrete surface Ricci flow, which has theoretic guarantees for the existence and uniqueness of the solutions. In practice, discrete Ricci flow is equivalent to a convex optimization problem, therefore has high numerically stability. In this paper, we compute the signatures of contours on general 3D surfaces with surface Ricci flow method, which encodes both global and local surface contour information. Then we evaluated the signatures of pre-central and post-central gyrus on healthy control and CHD subjects for analyzing brain cortical morphometry. Preliminary experimental results from 3D MRI data of CHD/control data demonstrate the effectiveness of our method. The statistical comparison between left and right brain gives us a better understanding on brain morphometry of subjects with Congenital Hand Deformities, in particular, missing the distal part of the upper limb.
先天性手部畸形（CHD）通常发生在胚胎形成后的第四至第八周。臂芽细胞向上肢的转化失败会导致出生时出现上肢外观或功能异常。一些病因与遗传有关，而其他病因则受环境影响，其余病因仍不明。CHD患者通过手部的使用来发展抓握能力，随着时间的推移，这会影响大脑。近年来，CHD越来越受到关注，并且已经在外科手术和心理学方面对CHD进行了研究。然而，到目前为止，CHD对脑结构的影响尚未得到充分理解。在此，我们提出一种新方法，应用泰希米勒空间理论和共形焊接方法来研究CHD患者的脑形态学。共形焊接特征反映了皮质表面不同功能区域之间的几何关系，这是黎曼度量所固有的，在共形变形下不变，并编码了功能区域边界的完整信息。该计算算法基于离散曲面里奇流，其解的存在性和唯一性具有理论保证。在实际应用中，离散里奇流等同于一个凸优化问题，因此具有较高的数值稳定性。在本文中，我们用曲面里奇流方法计算一般三维曲面上轮廓的特征，该特征编码了全局和局部曲面轮廓信息。然后，我们评估了健康对照者和CHD受试者中央前回和中央后回的特征，以分析脑皮质形态学。来自CHD/对照数据的三维磁共振成像数据的初步实验结果证明了我们方法的有效性。左右脑之间的统计比较使我们能更好地了解先天性手部畸形患者，特别是上肢远端缺失患者的脑形态学。
