Development and application of a system for 3-D measurement of biostructures by computational geometry

虽然病理学研究涉及人和动物的器官、组织和细胞等三维生物结构，但实际的观察手段仅限于二维切片图像，基于随机几何的体视学技术不能适用于病理学的大多数方面，即人们往往无法用相关的几何模型来同化实际的生物结构。有鉴于此，我们设计了一个从连续切片输入的结构数据通过计算几何进行生物结构三维测量的系统。我们成功地为以下三个任务建立了算法，其中，系统已经准备好应用于实际研究1。计算机辅助粒度测量：这是为了获得有关朗格汉斯的细胞、细胞核或胰岛等颗粒状生物结构的数量和大小分布的信息。计算机通过“取样砖”进行扫描，这是一种在含有颗粒的组织空间中构建的三维取样探头，从连续切片输入。血管图案与空间距离分布的表达：设计了一种算法，将三维建筑图案与从随机放置的点到感兴趣结构的距离分布进行比较。将该方法应用于慢性肝炎和肝硬变患者肝脏的血管构筑分析，定量描述随着肝硬变的进展，肝组织的血管构筑如何偏离正常。三维拓扑分析：有一些病变器官的特征只能用拓扑学的术语来分析，如癌细胞巢的形式。通过开发一种计算机辅助测量拓扑不变性(1Betti数)的算法，满足了这一要求。我们现在正在为生物结构的三维细化找到解决方案，这将给我们一种可视化它们骨骼的方法。

Although the pathological studies deal with 3-dimensional biostructures such as the organs, tissues and cells of man and animals, the actural means of observation is confined to 2-dimensional sectional pictures, The tchniques of stereology, which is based on stochastic geometty, cannot work in most aspects of pathology where one is often unable to assimilate actual biostructures with pertinent geometric models. In view of this, we designed a system by which to perform 3-dimensional measurement of biostructures by computational geometry from structural data in putted from serial sections. We managed to establish algorithms for the following three tasks, in which, the system is ready to application to actual studies.1. Computer-assisted granulometry : This is to obtain information on the number and size distribution of granular biostructures such as the cells, their nuclei or the islets of Langerhans. The computer scans through "sampling bricks, " a 3-dimensional sampling probe constructed in a tissue space containing granules and inputted from serial sections.2. Expression of vascular pattern with the spatial distance distribution : An algorithm was devised to compare the pattern of 3-dimensional architecture with the distribution of distances from randomly positioned points to the structure of interest. The method was applied to the analysis of vasculature in livers with chronic hepatitis and cirrhosis, to quantitatively describe how the vascular arrangement deviates from the norm with the progress of cirrhogenesis.3. Three-dimensional topological analysis : There are features of diseased organs that can be analyzed only in topological terms, such as the form of carchinoma cell nests. This requirement was met by developing an algorithm for computer-aided measurement of topological invariable (1st Betti number). We aere now finding a solution for the three-dimensional thinning of biostructures, which will give us a method to visualize their skeleton.