We propose two types of novel morphological metrics for quantifying the geometry of tubular structures on computed tomography (CT) images. We apply our metrics to identify irregularities in the airway of patients with chronic obstructive pulmonary disease (COPD) and demonstrate that they provide complementary information to the conventional metrics used to assess COPD, such as the tissue density distribution in lung parenchyma and the wall area ratio of the segmented airway. The three-dimensional shape of the airway and its abstraction as a rooted tree with the root at the trachea carina are automatically extracted from a lung CT volume, and the two metrics are computed based on a mathematical tool called persistent homology; treeH0 quantifies the distribution of branch lengths to assess the complexity of the tree-like structure and radialH0 quantifies the irregularities in the luminal radius along the airway. We show our metrics are associated with clinical outcomes.

中文翻译：

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通过持续同源性对气道结构进行量化


我们提出了两种新颖的形态学指标，用于量化计算机断层扫描（CT）图像上管状结构的几何形状。我们应用我们的指标来识别慢性阻塞性肺病 (COPD) 患者气道的不规则性，并证明它们为用于评估 COPD 的传统指标提供了补充信息，例如肺实质中的组织密度分布和壁面积比的分段气道。气道的三维形状及其抽象为根部位于气管隆突的有根树，是从肺部 CT 体积中自动提取的，并且这两个指标是基于称为持久同源性的数学工具计算的； treeH0 量化分支长度的分布以评估树状结构的复杂性，radialH0 量化沿气道的管腔半径的不规则性。我们证明我们的指标与临床结果相关。