Multiscale Mathematical Modeling of Cancer Invasion

描述（由申请人提供）：这个跨学科项目的目标是建立数学模型和模拟软件，定量描述癌症侵袭的过程，并将从广泛的实验观察中获得的知识封装为相关和预测工具，供所有研究人员使用。癌症侵袭被认为涉及许多细胞参数（包括细胞增殖、凋亡、迁移、粘附、代谢和突变的改变率）以及微环境参数（包括细胞外基质组成、血管生成、炎症和蛋白酶）。从数学的观点来看，这些参数有些是连续的，有些是离散的。因此，我们的主要方法是基于一个混合模型，其中连续确定性和离散随机参数和变量是集成的。由于其混合性质，该模型可以直接与癌症生物学家认为在癌症侵袭中重要的细胞和微环境参数的实验测量相关联。基于混合模型的预测将通过实现入侵计算机模拟的软件可视化。这些模型和相关的模拟将成为产生假设的基础，这些假设将在体外、二维（2D）和三维（3D）癌细胞培养系统以及体内、异种移植和人类癌症遗传小鼠模型中进行测试。实验验证将用于以迭代的方式完善和改进数学模型和仿真程序，并为模型提供新的输入参数。最初，我们将在不妨碍数学和实验可行性的复杂程度上建立入侵参数模型，但这已经提供了癌症入侵的现实表现。随着我们的进展，我们将能够引入越来越复杂的水平，因为模型是开放的，从几个尺度，如宏观尺度（组织），微观尺度（细胞），亚细胞和分子尺度的参数和实验数据的结合。长期目标是对癌症侵袭的主要机制进行全面、定量的描述。这一描述以及相关的计算机模拟，应该能够为癌症进展的侵袭/转移阶段的准确诊断分期和治疗靶向提供合理的方法。

DESCRIPTION (provided by applicant): The goal of this cross-disciplinary project is to produce mathematical models and simulation software that describe quantitatively the process of cancer invasion and encapsulate the knowledge derived from a wide range of experimental observations into a correlative and predictive tool, available to all researchers. Cancer invasion is thought to involve a number of cellular parameters (including altered rates of cell proliferation, apoptosis, migration, adhesion, metabolism, and mutation), as well as microenvironmental parameters (including extracellular matrix composition, angiogenesis, inflammation, and proteases). From a mathematical point of view, some of these parameters are continuous and some discrete. Therefore, our primary approach is based on a hybrid model in which both continuum deterministic and discrete stochastic parameters and variables are integrated. Because of its hybrid nature, the model can be directly linked to experimental measurements of those cellular and microenvironmental parameters recognized by cancer biologists as important in cancer invasion. Predictions based on the hybrid models will be visualized by software that implements computer simulations of invasion. These models and the associated simulations will be the basis for generating hypotheses that will be tested in vitro, in two-dimensional (2D) and three-dimensional (3D) cancer cell culture systems, as well as in vivo, in xenograft and genetic mouse models for human cancers. Experimental validation will be used to both refine and improve the mathematical models and simulation programs in an iterative fashion and provide new input parameters for the models. Initially, we will model invasion parameters at a level of complexity that does not hinder mathematical and experimental feasibility, but that already provides a realistic representation of cancer invasion. As we progress, we will be able to introduce increasing levels of complexity, since the model is open to incorporation of parameters and experimental data from several scales, e.g., the macro-scale (tissue), micro-scale (cells), subcellular, and molecular scales. The long-term goal is to produce a comprehensive, quantitative description of the major mechanisms underlying cancer invasion. This description, and the associated computer simulations, should enable a rational approach for accurate diagnostic staging and therapeutic targeting of the invasion/metastasis step of cancer progression.