Multiscale Computational Methods with Applications in Materials Science and Tissue Engineering

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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.