Mathematical modeling and computational studies for proliferation kinetics of tumor growth with spatial-temporal dynamics

实体瘤在组成上是异质的。癌症干细胞（CSC）是在发育多样的肿瘤中发现的高度致瘤性细胞类型，其被认为对标准化疗药物具有抗性并负责肿瘤复发。因此，了解肿瘤生长动力学和空间组成对于开发癌症治疗的新策略至关重要，而肿瘤生长是一种非常复杂的现象，涉及广泛的空间和时间尺度上的许多相互关联的过程，这使得数学建模和计算非常具有挑战性。本项目的主要目标是：（1）进一步开发和评估数学模型，以探索控制肿瘤生长平衡的潜在机制和生物学因素;（2）开发随机和连续数学模型，以更好地了解肿瘤生长过程中CSC群体的空间结构;（3）建立肿瘤生长模型。（3）设计快速有效的数值方法来求解所提出的具有运动和复杂区域的数学模型。本研究旨在利用建模技术和计算研究来解决数学，化学工程和生物学之间的肿瘤生长所引起的复杂问题。因此，将采用多尺度、随机和连续模型的原理和技术，并结合新的计算算法来实现研究目标。通过整合肿瘤生长过程中复杂的调控网络和营养物质的空间分布来控制CSC的增殖、分化和细胞层，本项目的变革性研究和新方法将有助于揭示调控CSC衍生细胞谱系的动力学和空间分布的潜在机制。 该项目的成功完成也将对公共卫生产生重大影响，因为研究结果可用于开发诊断，免疫学和治疗方法，以更具体地针对癌症干细胞。该项目将通过多学科培训来指导学生，以提高他们自己的科学知识，并为更广泛的科学机构做出贡献。在这项工作中开发的数学和计算工具箱也将有助于启动一个新的项目为导向的计算生物学课程，更好地培训研究生和本科生。

Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are a highly tumorigenic cell type found in developmentally diverse tumors that are believed to be resistant to standard chemotherapeutic drugs and responsible for tumor recurrence. Thus understanding the tumor growth kinetics and spatial composition is critical for development of novel strategies for cancer treatment, while tumor growth is a very complicated phenomenon involving many inter-related processes across a wide range of spatial and temporal scales, which makes the mathematical modeling and computation very challenging. With a close integration with designed experiments, the main aims of this project are (1) to further develop and evaluate mathematical models to explore underlying mechanisms and biological factors to control the balance of tumor growth; (2) to develop both stochastic and continuous mathematical models to better understand the spatial structures of CSC populations during tumor growth; (3) to design fast and efficient numerical methods to solve the proposed mathematical models with moving and complex domains.This research seeks to employ modeling techniques and computational studies to address complex issues arising from tumor growth at the interface of mathematics, chemical engineering and biology. Therefore, principles and techniques from multi-scale, stochastic and continuous models incorporated with new computational algorithms will be employed to achieve the study goals. By integrating complex regulatory networks and spatial distributions of nutrients during tumor growth to control proliferation, differentiation and cell layers of CSCs, the transformative studies and novel methodologies in this project will help revealing the underlying mechanisms to regulate the dynamics and spatial distributions of CSC derived cell lineages. Successful completion of this project will also have a significant impact on public health, as the research findings can be used to develop diagnostics, prognostics, and therapeutics to more specifically target cancer stem cells. This project will mentor students through multidisciplinary training to advance their own scientific knowledge as well as contribute to the wider scientific body. The mathematical and computational toolbox to be developed in this work will also help to initiate a new project oriented course on computational biology for better training of both graduate and undergraduate students.