Computational Methods and Software for Structured Multiscale Models of Tumor Invasion

这位研究人员和学生建议开发计算方法和软件来求解出现在肿瘤侵袭的多尺度模型中的偏微分方程组。这些系统的行为不仅取决于时间和空间，还取决于大小或年龄等生理特征。该方法将时间与生理变量解耦。在这样做的过程中，与以前的方法不同，它们防止了通常精细分辨率的时间离散化推断生理变量中的节点数。与癌症生物学家的合作是这项研究计划的关键组成部分。该软件将在范德比尔特大学癌症生物学家开发和参数化的模型的背景下开发和使用，期望它们将对理解肿瘤侵袭机制产生重大和近期的影响。这种合作对于确保方法和软件的相关性和实用性也是至关重要的；在应用真空中开发的方法往往缺乏实用性。研究人员和他的学生提议开发计算机软件和算法--决定软件如何工作的数学规则--以研究癌症肿瘤在其发展的中后期是如何侵入附近组织的。特别是，该软件将处理复杂的情况，即肿瘤内大量单个细胞的不同遗传特征，以及每个细胞的细胞分裂周期的不同阶段，与物理上更大的完整肿瘤有关。例如，在研究化疗的整体效果时，这一点很重要，因为使用的药物会根据细胞的遗传类型或细胞分裂周期的哪个部分而对细胞产生不同的影响。这项提议中的算法背后的数学比以前的要先进得多，导致软件可以在今天和不久的将来有效地在计算机上使用。这项研究提案的一个重要部分是田纳西州纳什维尔的范德比尔特大学和苏格兰邓迪大学的研究人员和数学和癌症生物学方面的同事之间的合作。

The investigator and student propose to develop computational methods and software to solve systems of partial differential equations that arise in multiscale models of tumor invasion. The behavior of these systems depends not only on time and space, but also on physiological traits such as size or age. The methods decouple time from the physiological variables. In doing so they, unlike previous methods, prevent the often fine-resolution time discretization from infl ating the number of nodes in the physiological variables. Collaboration with cancer biologists is a critical component of this research plan. The software will be developed and used in the context of models developed and parameterized with cancer biologists at Vanderbilt University, with the expectation that they will have a significant and near-term impact on understanding the mechanisms of tumor invasion. This collaboration is also vital to ensure the relevance and usefulness of the methods and software; methods developed in an application vacuum tend to lack utility.The investigator and his student propose the development of computer software and algorithms -- the mathematical rules that determine how the software works -- to study how cancer tumors, in middle and later stages of their development, invade nearby tissue. In particular, the software will handle the complicated situation where the different genetic profiles of the multitudes of individual cells within a tumor, and the different stages in the cell-division cycle of each of these cells, are linked to the physically larger complete tumor. This is important, for example, in studying the overall effects of chemotherapy when using drugs that affect cells differently depending on their genetic type or what part of the cell-division cycle they are in. The mathematics behind the algorithms in this proposal are significantly more advanced than what came before, resulting in software that can be used effectively with the computers of today and the near future. An important part of this research proposal is the collaboration between the investigators and colleagues in mathematics and cancer biology at Vanderbilt University in Nashville, TN, and at the University of Dundee in Scotland.