Multiscale Computational Methods with Applications in Materials Science and Tissue Engineering

在这个项目中，研究者将开发新的计算多尺度方法来建模和模拟(a)材料科学中的外延生长；(b)细胞聚集体融合在器官生物制造和组织工程中的应用。尽管这两个问题来自不同的学科，但它们都涉及多个时空尺度上跨越几个数量级的复杂现象。用标准算法直接在最精细的尺度上对这些问题进行数值求解，不可避免地会导致巨大的计算成本。因此，有必要开发多尺度方法，既能共享宏观模型的效率，又能实现微观模型的精度。在我们的方法中，微观尺度的动力学用基于动力学蒙特卡罗算法的晶格模型来描述，而宏观尺度的动力学用常/偏微分方程在连续体水平上建模。研究中有几个具有挑战性的问题需要解决：(1)详细了解不同尺度水平上物理或生物模型之间的关系；(2)如何为微观模型应用合适的边界条件和约束；(3)系统准确的粗粒化程序。一旦这些问题得到解决，研究者将在本研究中产生的想法扩展到广泛的相关多尺度问题。这种计算方法也将为研究(a)使用不同材料的同质外延和异质外延生长建立一个范例；(b)细胞融合和组织/器官制造一般通过逐渐加入额外的化学意义显著的蛋白质动力学。本研究对材料科学、组织工程和细胞生物学的相关应用具有显著和积极的影响。它可以帮助我们(a)了解外延生长过程中的物理和机械过程，这是许多半导体材料的高质量晶体生长的一种负担得起的方法，在纳米技术和半导体制造中很重要；(b)了解细胞内细胞反应和组织融合引起的细胞间力的起源，定量表征组织形态发生过程中的机械化学过程，准确预测和优化器官生物制造中的打印后结构形成，并智能地开发药物设计和组织工程方法。通过与这些学科的科学家和工程师合作，研究者将开发一个合适的计算多尺度框架来解决这些问题，以更好地理解这些系统中的复杂现象。教育影响包括对计算数学感兴趣的研究生和本科生的跨学科培训。将特别注意包括少数民族在内的代表性不足的群体。

In this project the investigator will develop new computational multiscale methods to model and simulate (a) epitaxial growth in materials science; (b) cellular aggregate fusion in organ biofabrication and tissue engineering. Even though the two problems arise from distinct disciplines, they all involve complex phenomena on multiple spatio-temporal scales across several orders of magnitude. Numerically solving these problems directly at the finest scale with standard algorithms inevitably leads to an enormous computational cost. Therefore, it is necessary to develop multiscale methods that share the efficiency of the macroscopic models while achieving the accuracy of the microscopic models. In our methods, the microscale dynamics is described by a lattice model based on the kinetic Monte Carlo algorithm, while ordinary/partial differential equations are used for modeling the macroscale dynamics on continuum level. There are several challenging issues to be addressed in the research: (1) a detailed understanding of the relation between the physical or biological models at different scale levels; (2) how to apply suitable boundary conditions and constraints for microscopic models; (3) systematic and accurate procedures of coarse-graining. Once these issues are addressed, the investigator will extend the ideas produced in this research to a broad range of relevant multiscale problems. This computational approach will also set up a paradigm for investigating (a) both homoepitaxial and heteroepitaxial growth using various material species; (b) cell fusion and tissue/organ fabrication in general by incrementally incorporating additional chemically significant protein dynamics.This research has the potential to significantly and positively impact relevant applications in materials science, tissue engineering, and cell biology. It can help us to (a) understand the physical and mechanical processes during epitaxial growth, which is an affordable method of high-quality crystal growth for many semiconductor materials and is important in nanotechnology and in semiconductor fabrication; (b) understand the origin of intercellular forces due to cellular responses in cells as well as tissue fusion and quantitatively characterize the mechanochemical process during tissue morphogenesis, accurately predict and optimize postprinting structure formation in organ biofabrication, and intelligently develop approaches in drug design and tissue engineering. Through collaborating with scientists and engineers from these disciplines, the investigator will develop a suitable computational multiscale framework for solving these problems to better understand complex phenomena in these systems. Educational impact includes interdisciplinary training of graduate and undergraduate students interested in computational mathematics. Special attention will be paid to underrepresented groups including minorities.