Collaborative Research: Mechanistic modeling of cell encapsulation

细胞封装是一种受生物学启发的技术，可将活细胞从恶劣环境中分离出来。这是通过将细胞包装在支架中来完成的，支架包裹在半透性隔离膜中。被包装的细胞通过一根管子（吻合移植物）与宿主的脉管系统相连，将氧气和富含营养的血液输送到细胞中。这种半透性的包封膜位于移植物血液流动和细胞支架之间的界面，旨在阻止宿主的免疫细胞攻击移植细胞，同时允许氧气和营养物质进入细胞。细胞包封的一个主要挑战是要有足够的氧气和营养供应来维持细胞的长期生存能力。该项目的主要目标是开发一个综合的多尺度和多物理场的数学和计算框架来模拟细胞封装。利用这一框架，pi将通过(1)研究水凝胶结构和弹性如何影响细胞的氧气和营养供应，以及(2)探索水凝胶内超滤通道的设计，以最大限度地向细胞供应氧气和营养，来解决被封装细胞的长期生存能力。细胞包封的概念与生物人造器官的设计和生物治疗药物的控制递送高度相关。这个跨学科的项目将为本科生和研究生在数学和生物学之间的界面提供指导。德克萨斯理工大学将开设一门新的研究生课程，以培训学生使用该项目开发的最新数学方法。为了促进女性参与STEM，将在加州大学伯克利分校数学系组织一系列高中女生暑期研讨会，并对加州大学旧金山分校生物设计实验室进行科学访问。本课题的目标是建立一个综合性的多尺度、多物理场的细胞封装数学和计算模型，用于生物人工器官的设计。在宏观尺度上，将建立和分析两组时间相关的耦合模型：(1)Stokes/Navier-Stokes方程与耦合非线性Biot孔弹性介质方程的Biot膜方程之间的流固耦合（FSI）模型；(2)在描述被封装器官中氧浓度的运动域上定义的非线性耦合平流-反应-扩散方程。将开发两个分区方案来解决FSI问题和耦合的平流-反应-扩散问题。数值格式将被设计用于处理在“混合”2D/3D域上定义的跨Biot孔弹性膜界面的新型耦合条件。将进行稳定性分析和收敛性试验。为了捕捉微尺度水凝胶结构对局部导电性的影响，将使用平滑粒子流体动力学（SPH）模拟。SPH模拟的结果将为编码器-解码器卷积神经网络训练（离线）提供合成数据，以产生宏观尺度模拟所需的宏观参数，如水凝胶渗透率张量。验证和参数估计将由UCSF生物设计实验室的实验提供。本研究的结果将促进涉及孔弹性介质和运动域上耦合非线性平流-反应-扩散系统的数学FSI的知识。这些发现的结果将促进生物人工器官设计和生物治疗药物控制递送的细胞封装知识。本提案由数学科学部（DMS）的数学生物学项目、流体动力学项目和生物医学系统工程（EBMS）项目共同资助，这三个项目都隶属于工程理事会化学、生物工程、环境和运输系统（CBET）部门。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Cell encapsulation is a biologically inspired technology that isolates live cells from the hostile environment. This is done by packaging the cells in a scaffold, which is encapsulated in a semi-permeable isolating membrane. The packaged cells are connected to the host’s vasculature via a tube (anastomosis graft) transporting oxygen and nutrients rich blood to the cells. The semi-permeable encapsulating membrane, located at the interface between the blood flow in the graft and the cell scaffold, is designed to block the host’s immune cells from attacking the transplanted cells, while allowing passage of oxygen and nutrients to the cells. A major challenge in cell encapsulation is sufficient oxygen and nutrients supply to maintain the long-term viability of cells. The main goal of this project is to develop a comprehensive multi-scale and multi-physics mathematical and computational framework modeling cell encapsulation. Using this framework, The PIs will address the long-term viability of encapsulated cells by (1) studying how hydrogel architecture and elasticity affect oxygen and nutrients supply to the cells, and by (2) exploring design of ultrafiltrate channels within the hydrogel to maximize oxygen and nutrients supply to the cells. The concept of cell encapsulation is highly relevant for bioartificial organs design and for controlled delivery of biological therapeutics. This interdisciplinary project will provide mentoring of undergraduate and graduate students at the interface between mathematics and biology. A new graduate course at Texas Tech will be introduced to train students in the state-or-the-art mathematical methods developed in this project. To promote participation of women in STEM, a series of Summer Workshops for High School girls will be organized at the UC Berkeley Mathematics Department with scientific visits to the UCSF Biodesign Laboratory. The goal of this project is to develop a comprehensive multi-scale, multi-physics mathematical and computational model of cell encapsulation for bioartificial organs design. At the macro-scale, two sets of time-dependent coupled models will be developed and analyzed: (1) a fluid-structure interaction (FSI) model between the Stokes/Navier-Stokes equations and the Biot membrane equations coupled to the nonlinear Biot poroelastic medium equations, and (2) a set of coupled nonlinear advection-reaction-diffusion equations defined on moving domains describing oxygen concentration in the encapsulated organ. Two partitioned schemes will be developed to solve the FSI problem and the coupled advection-reaction-diffusion problems. The numerical schemes will be designed to deal with the novel coupling conditions holding across a Biot poroelastic membrane interface, defined on a “mixed’’ 2D/3D domain. Stability analysis and convergence tests will be performed. To capture the impact of micro-scale hydrogel architecture on local hydraulic conductivity, Smoothed Particle Hydrodynamics (SPH) simulations will be used. The results of the SPH simulations will provide synthetic data for the Encoder-Decoder Convolution Neural Networks training (offline) to produce macro-scale parameters, such as the hydrogel permeability tensor, needed in macro-scale simulations. Validation and parameter estimation will be provided by the experiments at the UCSF Biodesign Laboratory. The results from this research will advance the knowledge in mathematical FSI involving poroelastic media and in coupled nonlinear advection-reaction-diffusion systems on moving domains. The outcomes of the findings will advance the knowledge in cell encapsulation for bioartificial organ design and in controlled delivery of biological therapeutics.This proposal is jointly funded by the Mathematical Biology Program of the Division of Mathematical Science (DMS), the Fluid Dynamics Program and the Engineering of Biomedical Systems (EBMS) Program, both in the Chemical, Bioengineering, Environmental, and Transport Systems (CBET) Division, Directorate for Engineering.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.