Tumor shape plays a critical role in influencing both growth and metastasis. We introduce a novel topological radiomic feature derived from persistent homology to characterize tumor shape, focusing on its association with time-to-event outcomes in gliomas. These features effectively capture diverse tumor shape patterns that are not represented by conventional radiomic measures. To incorporate these features into survival analysis, we employ a functional Cox regression model in which the topological features are represented in a functional space. We further include interaction terms between shape features and tumor location to capture lobe-specific effects. This approach enables interpretable assessment of how tumor morphology relates to survival risk. We evaluate the proposed method in two case studies using radiomic images of high-grade and low-grade gliomas. The findings suggest that the topological features serve as strong predictors of survival prognosis, remaining significant after adjusting for clinical variables, and provide additional clinically meaningful insights into tumor behavior.

翻译：肿瘤形态在影响其生长和转移过程中起着关键作用。我们引入了一种源自持续同调的新型拓扑影像组学特征，用于表征肿瘤形态，并重点研究其与胶质瘤时间-事件结局的关联。这些特征能有效捕捉传统影像组学指标无法表征的多样化肿瘤形态模式。为将这些特征纳入生存分析，我们采用函数型Cox回归模型，将拓扑特征映射至函数空间进行表征。我们进一步纳入形态特征与肿瘤位置间的交互项，以捕捉脑叶特异性效应。该方法能够可解释地评估肿瘤形态学特征与生存风险间的关联。我们在两个案例研究中，利用高级别与低级别胶质瘤的影像组学图像对提出方法进行评估。研究结果表明，拓扑特征可作为生存预后的强预测因子，在调整临床变量后仍保持显著性，并为肿瘤行为提供了具有临床意义的新见解。