An adaptive isogeometric analysis for three-dimensional phase-field modeling of morphological evolution of lipid bilayers in interactions with fluid flow and electric field

在广泛的生物技术应用中，利用电场作为外部刺激是一种有效的工程囊泡行为的技术。电穿孔技术已被用于将基因或药物导入细胞和癌症治疗。电场作为一种强大的细胞操纵手段，已被应用于组织消融、伤口愈合、电铸和巨泡电融合等领域。这些应用推动了对囊泡电流体动力学的计算研究，以便更好地了解在电场和流场的影响下膜响应的变化。在多组分囊泡的情况下，由于相分离动力学和电流体动力学的耦合，问题变得更加复杂。本研究的主要目标是开发一个三维计算框架来模拟同时与流体流动和电场相互作用的单组分和多组分脂质双层膜的形态演化。我们将建立一个细胞内外流体影响下的多组分囊泡热力学一致的相场模型，将相分离动力学、萌发和分裂过程与囊泡流体动力学相耦合。该模型将进一步扩展，以包括膜上的吸附/解吸过程的细节以及曲率诱导分子在主体流体中往返于膜的传输。我们还将我们的相场模型扩展到囊泡电流体动力学，以研究流体流动和电场对单组分/多组分囊泡的联合影响。因此，我们将设计一种基于截断分层B-样条(THB-Splines)的三维自适应等几何分析(IGA)公式，该公式具有计算效率所必需的局部细化和粗化特征。另外，THB-Spline是分段光滑的，全局连续的，因此可以直接处理高阶多物理偏微分方程组。开发的模型将被用来更好地了解单组分和多组分小泡的流体动力学和电流体动力学，以及内吞过程的细节，特别是在惯性效应不可忽视的情况下。这项研究还将通过识别膜中潜在的孔形成位置来理解细胞电穿孔，因为根据最近的研究，穿孔预计发生在高张力区域。此外，我们的三维数值框架使得捕捉囊泡行为的其他模式成为可能，这可能是在早先的轴对称或2D模拟中没有观察到的。可以肯定的是，更好地了解囊泡在不同生物物理情况下的行为有助于设计更有效的生物技术技术来进行细胞操作。

The use of electric fields as external stimulus is an effective technique for engineering vesicle behavior in a wide range of biotechnological applications. Electroporation has been used for introducing genes or drugs into cells and cancer treatments. As a powerful cell manipulation method, electric fields have been used in tissue ablation, wound healing, electroformation and electrofusion of giant vesicles. These applications have motivated computational studies on electrohydrodynamics of vesicles in order to gain a better understanding of the variety of membrane responses under the influence of electric and flow fields. The problem becomes even more complicated in case of multicomponent vesicles due to the coupling of the phase separation dynamics with electrohydrodynamics.The main objective of this research proposal is to develop a three-dimensional computational framework to model morphological evolutions of single- and multi-component lipid bilayer membranes interacting simultaneously with fluid flow and electric fields. We will develop a thermodynamically-consistent phase-field model of multicomponent vesicles under the influence of intracellular and extracellular fluids, which couples the phase separation dynamics, budding and fission processes to vesicle hydrodynamics. This model will be further extended to incorporate the details of adsorption/desorption processes at the membrane and the transport of curvature-inducing molecules in the bulk fluid to and from the membrane. We also will extend our phase-field model to vesicle electrohydrodynamics in order to study the combined effect of fluid flows and electric fields on the single/multi-component vesicles. Therefore, we will devise a three-dimensional adaptive isogeometric analysis (IGA) formulation based on Truncated Hierarchical B-splines (THB-splines) with local refinement and coarsening features necessary for computational efficiency. Additionally, THB-splines are piecewise smooth and globally C1-continuous and therefore can straightforwardly treat the high-order multi-physics partial differential equations. The developed model will be exploited to gain a better understanding of hydrodynamics and electrohydrodynamics of single- and multicomponent vesicles, and of the details of endocytosis processes, particularly when inertial effects are not negligible. This research will also give insights to understanding the cell electroporation by identifying the potential sites of pore formation in the membrane since according to recent studies the poration is expected to happen in the areas of high tension. Moreover, our three-dimensional numerical framework makes it possible to capture additional modes of vesicle behavior, which might not have been observed in previous axisymmetric or 2D simulations. Assuredly, a better understanding of vesicle behaviors in different biophysical situations can help to design more efficient biotechnological techniques for cell manipulations.