Tensor approximation methods for modeling tumor progression

用于建模肿瘤进展的张量近似方法

• 批准号: 458051812
• 负责人: Professor Dr. Lars Grasedyck
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/458051812?language=en
• 关键词: Tensor; approximation; methods; modeling; tumor

Our project is motivated by current problems in cancer research, in particular tumor progression modeling. Tumors progress by the accumulation of mutations and other progression events, such as epigenetic alterations, inflammation or structural changes of the genome. The better we understand the forces that drive this process, the better we understand which events drive expansion, dissemination, formation of metastasis, therapy resistance, and patient death. The combination of pre-existing events in a tumor determines the rates of events that have not occurred yet. In other words, tumor progression is a Markov process on the state space of tumor geno-/phenotypes (all possible combinations of events), a space that grows exponentially in the number of binary progression events.Our goal is to develop a hierarchical low-rank tensor framework in which we can model tumor progression and find approximations in linear complexity. We also want to understand the patient-specific evolution of tumors in terms of the emerging tensor hierarchy in the mathematical model. In the long term, we aim to predict and influence the individual evolution of the tumor.In preparation for this project, we have formulated a basic tumor progression model in suitable low-rank tensor form and verified in a small-scale numerical test that a hierarchical low-rank structure is present in the given real-world data. In order to find and exploit this low-rank structure we propose three main lines of research: First, we develop novel tensor operations, with particular emphasis on the Kullback-Leibler divergence for low-rank tensors. These require closed-form formulas for basic functions of tensors and a deep theoretical understanding of low-rank structures. Second, we will expand the basic tumor progression model in order to allow for reversible events, missing data, hidden events, and higher-order interactions. Third, our methods will be integrated in a high-performance open-source solver library. This will allow us to perform numerical experiments in realistic (and large-scale) tumor progression models.

我们的项目是由于癌症研究中目前问题的动机，特别是肿瘤进展建模。肿瘤是由于突变和其他进展事件的积累而进行的，例如基因组的表观遗传改变，炎症或结构变化。我们越理解推动这一过程的力量，我们就会越理解哪些事件会促进扩张，传播，抗药性，耐药性和患者死亡的扩张。肿瘤中现有事件的结合决定了尚未发生的事件率。换句话说，肿瘤进展是马尔可夫的一个过程，在肿瘤生物/表型的状态空间（事件的所有可能组合）上，该空间在二进制进展事件的数量中成倍增长。我们的目标是在层次的低秩量张量框架中开发出我们可以在层次肿瘤进展和近似近似值中建立近似值。我们还想从数学模型中新兴的张量层次结构来理解肿瘤的患者特异性演变。从长远来看，我们旨在预测和影响肿瘤的个体演变。在为该项目的准备准备中，我们以合适的低级张量形式制定了基本的肿瘤进展模型，并在小规模的数值测试中进行了验证，即给定的现实世界中存在层次低级别结构。为了查找和利用这种低级结构，我们提出了三个主要研究线：首先，我们开发了新型的张量操作，特别强调了低级别张量的Kullback-Leibler差异。这些需要封闭形式的公式，以进行张量的基本功能以及对低级别结构的深刻理论理解。其次，我们将扩展基本的肿瘤进展模型，以允许可逆事件，丢失的数据，隐藏事件和高阶相互作用。第三，我们的方法将集成到高性能的开源求解器库中。这将使我们能够在现实（和大规模）肿瘤进展模型中执行数值实验。