Hybrid Multiscale Methods with Applications in Biomaterials and Bioengineering

在研究方面，该项目旨在开发实验指导的混合多尺度模型和方法，以研究复杂的生物系统和生物材料和生物工程中出现的问题：(A)在血管形成过程中萌发血管生成；(B)在生物膜形成过程中细菌聚集。这项研究将对多尺度问题及其在生物材料、组织再生和生物医学工程中的相关应用具有重要意义，包括组织器官制造的生物打印技术、细胞运动研究、药物设计以及最终的再生医学。这些方法可以作为生物学家和生物工程师的假设生成和检验工具。通过与实验者的合作，PI将开发一种混合的多尺度方法，以更好地了解血管形成和生物膜生长的复杂机制。在教育方面，这个项目不仅将为研究生和本科生提供多学科的研究培训，还将促进未被充分代表的少数群体对计算数学和数学生物学的认识和兴趣。特别是，我们使用了典型的粗粒度连续介质模型(反应扩散系统)来描述血管内皮生长因子(VEGF)和营养物质/氧气的动力学，基于有限元方法(FEM)的细胞外基质(ECM)的力学模型，以及基于动力学蒙特卡罗(KMC)算法的离散多细胞格子模型来描述细胞动力学。微尺度模型和连续介质模型之间的通信通过一套多尺度协议来实现。对于推力(B)，PI将研究生物膜形成过程中导致细菌聚集的几种机制，如细菌趋化性、细菌之间的相互作用、细菌形状等。在所提出的基于杂交剂的模型中，细菌由自推进颗粒(SPP)或自推进杆(SPR)表征，环境中胞外聚合物(EPS)的动态由连续变化的场来描述。多尺度模型由常微分方程组和偏微分方程组描述。研究成果包括一套混合的多尺度模型，模型的详细实施，以及用于模拟组织形成和最终涉及血管生成和血管形成的3D生物制造的电子分析工具。这些工具可以提供有效的方法来系统地测试个体细胞特征在一系列环境条件下的影响，并研究细菌菌落的集体行为。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

On the research side, this project aims to develop experimentally guided, hybrid multiscale models and methods to study complex biological systems and problems arising in biomaterials and bioengineering (a) sprouting angiogenesis during vascularization; (b) bacterial swarming during biofilm formation. This research will have many benefits to multiscale problems and relevant applications in biomaterials, tissue regeneration and biomedical engineering, which include bioprinting technology for fabricating tissues and organs, study of cell motions, drug design and ultimately regenerative medicine. These methods can be used as hypothesis generating and testing tools for biologists and bioengineers. Through collaboration with experimentalists, the PI will develop a hybrid multiscale approach to better understand complex mechanisms in the vascularization and the biofilm growth. On the educational side, this project will not only provide multidisciplinary research training to graduate and undergraduate students, but also promote awareness and interest in computational mathematics and mathematical biology among underrepresented minority groups.For the thrust (a), motivated by new findings in sprouting angiogenesis in bioprinting technology, the PI will integrate models for angiogenic signaling pathways with that for the mechanical motion. In particular, we employ typically coarse-grained continuum models (reaction-diffusion (RD) systems) to describe the dynamics of vascular-endothelial-growth-factor (VEGF) and nutrients/oxygen, a mechanical model for the extra-cellular matrix (ECM) based on the finite element method (FEM), and couple a discrete multicellular lattice model based on the kinetic Monte Carlo (KMC) algorithm to describe the cellular dynamics. Communication between the microscale model and the continuum ones is carried out via a suite of multiscale protocols. For the thrust (b), the PI will study several mechanisms responsible for bacterial swarming during biofilm formation, such as bacterial chemotaxis, interaction between bacteria, bacterial shapes, etc. In the proposed hybrid agent-based model, bacteria are characterized by self-propelled particles (SPP) or self-propelled rods (SPR) and the dynamics of extracellular polymeric substances (EPS) in the environment is described by continuously changing fields. The multiscale model is described by a system of ordinary and partial differential equations. The research outcomes consist of a set of hybrid multiscale models, detailed implementation of the models, and accompanying in silico analysis tools for simulating tissue formation and ultimately 3D biofabrication involving angiogenesis and vascularization. The tools can provide efficient ways to systematically test the influence of individual cellular features under a spectrum of environmental conditions and to study the collective behavior of bacterial colonies.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.