A Multimodal Topological Approach to Brain Cancer: Unifying Molecular and Imaging Data

胶质母细胞瘤（GBM）是在成人中发现的最常见和最具侵袭性的恶性脑肿瘤类型之一，诊断后平均存活率仅为15个月，并且只有3%至5%的GBM患者存活超过三年。由于该疾病的高度异质性，GBM对传统治疗具有抗性并且易于复发。此外，由于GBM患者的预期寿命短，可用的数据是sparse.In本项目中，我们研究了两种不同模式的GBM数据，成像数据的形式，组织病理学图像和分子数据，涉及GBM的某些特征基因的表达。我们希望在拓扑数据分析（TDA）的统一框架下捕获这两种类型的数据，TDA是数据科学的一个新的分支，使用代数拓扑的数学工具，使用统计推理方法来帮助我们更好地理解和解释GBM。更好的诊断可以帮助临床医生改善治疗和患者的生活质量。特别是，我们使用持久的同源性，TDA内的一个重要的拓扑不变量，总结的形状和大小的拓扑特征，持续跨多个尺度内的数据。我们受益于持久同源性的灵活性，因为它的计算可以适应不同形式的数据，使我们能够在相同的基础上研究成像和分子数据，同时还可以在局部和全球范围内捕获特征。例如，在组织学图像上应用持续同源性，我们的目标是通过其细胞核分布捕获肿瘤的细胞间结构，其可能包括GBM的一些标志，例如不同于正常细胞排列的坏死和细胞过多。所有功能都将包含在功能摘要中。因此，对于推理，我们寻求构建功能模型的功能数据分析中的统计技术，并受益于工具从经典的功能分析，这可能有助于我们处理有关的问题，既高维的数据和小样本size.This项目属于福尔斯的EPSRC数学生物学研究领域。我们将使用在查令十字医院的帝国学院医疗保健NHS信托神经肿瘤服务中收集的脑肿瘤数据。

Glioblastoma (GBM) is one of the most common and aggressive types of malignant brain tumour found in adults with a dismal rate of survival of on average only fifteen months after diagnosis and only three to five percent of GBM patients survive longer than three years. Due to the high heterogeneity of the disease, GBM is resistant to traditional treatments and prone to recurrence. Moreover, owing to the short life expectancies of GBM patients, the data available is sparse.In this project, we study two different modes of GBM data, imaging data in the form of histopathology images and molecular data involving the expression of certain characteristic genes for GBM. We look to capture both types of data under the unifying framework of topological data analysis (TDA), a novel branch of data science using mathematical tools from algebraic topology, with statistical inference methods to help us better understand and prognosticate GBM. Better prognostication can help clinicians improve treatments and the quality of life for patients. In particular, we use persistent homology, an important topological invariant within TDA, to summarize the shapes and sizes of topological features which persist across multiple scales within the data. We benefit from the flexible nature of persistent homology as its computations can be adapted to data of vastly different forms, allowing us to study both imaging and molecular data on the same basis, whilst also capturing features both on a local and global scale. For example, applying persistent homology on histology images, we aim to capture the intercellular structure of the tumours through their nuclei distributions which may include some of the hallmarks of GBM such as necrosis and hypercellularity which differ from normal cell arrangements. All features will be encapsulated within a functional summary. As such, for inference, we seek to construct functional models building on statistical techniques within functional data analysis and benefitting from tools from classical functional analysis, which may help us to deal with problems relating to both the high dimensionality of the data and the small sample size available.This project falls within the EPSRC mathematical biology research area. We will be working with the brain tumour data collected within the Imperial College Healthcare NHS Trust Neuro-Oncology Service at Charing Cross Hospital.