Computational Methods and Software for Structured Multiscale Models of Tumor Invasion

研究者和学生建议开发计算方法和软件来解决肿瘤侵袭的多尺度模型中出现的偏微分方程系统。 这些系统的行为不仅取决于时间和空间，还取决于生理特征，如大小或年龄。该方法将时间与生理变量解耦。在这样做时，他们，不像以前的方法，防止经常细分辨率的时间离散化的生理变量中的节点的数量膨胀。 与癌症生物学家的合作是这项研究计划的重要组成部分。该软件将在范德比尔特大学的癌症生物学家开发和参数化的模型的背景下开发和使用，预计它们将对理解肿瘤侵袭的机制产生重大的近期影响。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出开发计算机软件和算法-确定软件如何工作的数学规则-以研究癌症肿瘤如何在其发展的中期和后期侵入附近组织。 特别是，该软件将处理复杂的情况，其中肿瘤内大量单个细胞的不同遗传特征以及这些细胞中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相关联。 这一点很重要，例如，在研究化疗的总体效果时，使用药物对细胞的影响不同，这取决于它们的遗传类型或它们处于细胞分裂周期的哪一部分。 该提案中的算法背后的数学比以前先进得多，从而产生了可以在今天和不久的将来有效使用的软件。 这项研究计划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.