用拓扑方法量化胶质母细胞瘤坏死区的几何特征，发现四种新亚型。
A Topological Data Analysis Framework for Quantifying Necrosis in Glioblastomas
- 提出'内部函数'和子复形空隙度，刻画坏死区域结构
- 基于磁共振成像识别出四类具有不同几何特征的胶质母细胞瘤
- 适用于肿瘤形态学分析，对精准诊疗有参考价值
本文提出一种名为'内部函数'的形状描述符，基于拓扑数据分析（TDA）改进了图像分析中的已有描述符。基于此概念，我们定义了一种新的指标——子复形空隙度，用于量化肿瘤坏死区域的几何特性，如聚集程度。在此框架基础上，我们构建了一系列指数以分析坏死形态，并生成图表，揭示坏死区域独特的结构与几何属性。该方法应用于胶质母细胞瘤（GB）的MRI研究中，通过聚类分析，识别出四类反映坏死区域几何特性的不同亚型。
原文摘要 · Abstract (English)
In this paper, we introduce a shape descriptor that we call "interior function". This is a Topological Data Analysis (TDA) based descriptor that refines previous descriptors for image analysis. Using this concept, we define subcomplex lacunarity, a new index that quantifies geometric characteristics of necrosis in tumors such as conglomeration. Building on this framework, we propose a set of indices to analyze necrotic morphology and construct a diagram that captures the distinct structural and geometric properties of necrotic regions in tumors. We present an application of this framework in the study of MRIs of Glioblastomas (GB). Using cluster analysis, we identify four distinct subtypes of Glioblastomas that reflect geometric properties of necrotic regions.
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