Mathematical medicine: modeling cancer and its treatments

物理学和数学在医学中的应用是跨学科研究中发展最快的领域之一。数学建模可以提供一个定量的框架来详细讨论复杂生物系统的所有组成部分之间的相互作用，以及测试各种治疗干预措施。新的计算技术和数学模型的结合，以实验和临床数据为基础，从而为生物医学研究提供了一个强大的新工具。一个重要的应用是模拟肿瘤生长及其治疗。癌症是一种不受控制的细胞生长，可以发生在身体的任何组织中。肿瘤不能通过简单的氧气和其他必需营养物质扩散到肿瘤中而生长超过一定的大小。血管生成，即从预先存在的血管形成血管，是肿瘤获得自身血液供应的关键和可观察的步骤。抑制肿瘤血管生成（抗血管生成疗法），以补充传统的放疗和化疗治疗，可能是控制癌症的有效策略，其中这种组合将破坏癌症和内皮细胞。然而，随着肿瘤血管的破坏，化疗和氧气不能有效地到达肿瘤细胞。此外，与正常组织的脉管系统不同，肿瘤血管在结构和功能上都是异常的。全面了解肿瘤微环境以及肿瘤（及其异常血管系统）对各种治疗的反应，对于确定最佳剂量以及联合治疗策略的安排和排序至关重要。基于现有和新的生物物理模型以及临床前和临床数据的数学建模对于研究肿瘤生长和血管生成以及不同治疗的效果肯定非常有用。该提案包括研究肿瘤生长和各种类型的癌症治疗，主要是放疗，化疗和抗血管生成治疗。建模范围从分子和细胞水平到宏观尺度。

The application of physics and mathematics to medicine is one of the most rapidly growing areas of interdisciplinary research. Mathematical modeling can provide a quantitative framework to discuss, in detail, the interaction between all components of complex biological systems, as well as to test various therapeutic interventions. The combination of novel computational techniques and mathematical models, grounded in experimental and clinical data, thus provides a powerful new tool in biomedical research. One important application is to modeling tumor growth and its treatment.Cancer is an uncontrolled growth of cells that can occur in any tissue of the body. Tumors cannot grow beyond a certain size through simple diffusion of oxygen and other essential nutrients into the tumor. Angiogenesis, the formation of blood vessels from pre-existing vessels, is a crucial and observed step, through which a tumor obtains its own blood supply. Inhibition of tumor angiogenesis (anti-angiogenic therapy), to complement conventional radiotherapy and chemotherapy treatments, could be an effective strategy for the control of cancer, where such combinations would destroy both cancer and endothelial cells. However, with the destruction of the tumor blood vessels, chemotherapies and oxygen cannot effectively reach the tumor cells. Additionally, unlike the vasculature of normal tissues, tumor vessels are structurally and functionally abnormal. A complete understanding of the tumor microenvironment, and the response of a tumor (and its abnormal vasculature) to various treatments, is essential in determining optimal dosage, and in the scheduling and sequencing of combined treatment strategies. Mathematical modeling based on existing and novel biophysical models, as well as pre-clinical and clinical data, would certainly be very useful to study tumor growth and angiogenesis, and the effects of different treatments. The proposal includes the study of tumor growth and various types of cancer treatments, mainly radiotherapy, chemotherapy, and anti-angiogenic therapy. The modeling ranges from the molecular and cellular levels to macroscopic scales.