Mathematical and Computational Modeling of Poroelastic Cell Scaffolds Used in the Design of an Implantable Bioartificial Pancreas
Mathematical and Computational Modeling of Poroelastic Cell Scaffolds Used in the Design of an Implantable Bioartificial Pancreas
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DOI：
10.3390/fluids7070222
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发表时间：
2022-07
期刊：
影响因子：
1.9
通讯作者：
Yifan Wang;S. Čanić;M. Bukač;C. Blaha;Shuvo Roy
中科院分区：
文献类型：
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作者：
Yifan Wang;S. Čanić;M. Bukač;C. Blaha;Shuvo Roy
我们提出了一个多尺度的数学模型和一种新的数值求解器，以研究血浆流量和氧浓度的原型模型的植入式生物人工胰腺（iBAP）的动静脉压差下运行，而不需要免疫抑制治疗。iBAP设计由含有健康移植细胞的多孔弹性细胞支架组成，封装在两个半渗透纳米孔径膜之间，以防止患者自身的免疫细胞攻击移植物。该装置通过吻合移植物连接到患者的血管系统，将氧气和营养物带到移植的细胞，其中氧气是长期存活的限制因素。在数学上，我们提出了一个（非线性）流体-多孔弹性结构相互作用模型来描述血浆通过含有细胞的支架的流动，和一组（非线性）对流-反应-扩散方程定义在移动域上来研究细胞的氧气供应。这些宏观尺度的模型求解使用有限元方法为基础的求解器。这项工作的新颖之处之一是设计一种新的二阶精确的流体-多孔弹性结构相互作用求解器，我们证明了它是无条件稳定的。在微/纳米尺度上，光滑粒子流体动力学（SPH）模拟用于捕获细胞支架的微/纳米结构（架构），并从微尺度支架特定架构获得宏观尺度参数，例如水力传导性/渗透性。为了避免对每个新的支架架构进行基于SPH模拟的昂贵的微尺度模拟，我们使用编码器-解码器卷积神经网络。基于我们的数值模拟，我们提出了改进目前的原型设计。例如，我们发现高弹性支架具有更高的氧转移能力，这是一个重要的发现，考虑到支架弹性可以在其制造过程中控制，并且弹性支架可以提高细胞活力。在这项工作中开发的数学和计算方法提供了一个基准工具，不仅iBAP的计算分析，而且，更一般地说，用于细胞治疗和生物人工器官的设备的设计中使用的细胞封装策略。
We present a multi-scale mathematical model and a novel numerical solver to study blood plasma flow and oxygen concentration in a prototype model of an implantable Bioartificial Pancreas (iBAP) that operates under arteriovenous pressure differential without the need for immunosuppressive therapy. The iBAP design consists of a poroelastic cell scaffold containing the healthy transplanted cells, encapsulated between two semi-permeable nano-pore size membranes to prevent the patient’s own immune cells from attacking the transplant. The device is connected to the patient’s vascular system via an anastomosis graft bringing oxygen and nutrients to the transplanted cells of which oxygen is the limiting factor for long-term viability. Mathematically, we propose a (nolinear) fluid–poroelastic structure interaction model to describe the flow of blood plasma through the scaffold containing the cells, and a set of (nonlinear) advection–reaction–diffusion equations defined on moving domains to study oxygen supply to the cells. These macro-scale models are solved using finite element method based solvers. One of the novelties of this work is the design of a novel second-order accurate fluid–poroelastic structure interaction solver, for which we prove that it is unconditionally stable. At the micro/nano-scale, Smoothed Particle Hydrodynamics (SPH) simulations are used to capture the micro/nano-structure (architecture) of cell scaffolds and obtain macro-scale parameters, such as hydraulic conductivity/permeability, from the micro-scale scaffold-specific architecture. To avoid expensive micro-scale simulations based on SPH simulations for every new scaffold architecture, we use Encoder–Decoder Convolution Neural Networks. Based on our numerical simulations, we propose improvements in the current prototype design. For example, we show that highly elastic scaffolds have a higher capacity for oxygen transfer, which is an important finding considering that scaffold elasticity can be controlled during their fabrication, and that elastic scaffolds improve cell viability. The mathematical and computational approaches developed in this work provide a benchmark tool for computational analysis of not only iBAP, but also, more generally, of cell encapsulation strategies used in the design of devices for cell therapy and bio-artificial organs.