We propose a curve-based Riemannian geometric approach for general shape-based statistical analyses of tumours obtained from radiologic images. A key component of the framework is a suitable metric that enables comparisons of tumour shapes, provides tools for computing descriptive statistics and implementing principal component analysis on the space of tumour shapes and allows for a rich class of continuous deformations of a tumour shape. The utility of the framework is illustrated through specific statistical tasks on a data set of radiologic images of patients diagnosed with glioblastoma multiforme, a malignant brain tumour with poor prognosis. In particular, our analysis discovers two patient clusters with very different survival, subtype and genomic characteristics. Furthermore, it is demonstrated that adding tumour shape information to survival models containing clinical and genomic variables results in a significant increase in predictive power.

中文翻译：

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基于放射图像的脑肿瘤统计形状分析。

我们提出了一种基于曲线的黎曼几何方法，用于对从放射图像获得的肿瘤进行一般基于形状的统计分析。该框架的一个关键组成部分是一个合适的度量，它能够比较肿瘤形状，提供计算描述性统计数据和在肿瘤形状空间上实施主成分分析的工具，并允许肿瘤形状的丰富类别的连续变形。该框架的实用性通过对诊断为多形性胶质母细胞瘤（一种预后不良的恶性脑肿瘤）患者的放射图像数据集的特定统计任务来说明。特别是，我们的分析发现两个患者群的生存率、亚型和基因组特征截然不同。此外，研究表明，将肿瘤形状信息添加到包含临床和基因组变量的生存模型中可以显着提高预测能力。