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

• Applicant: Professor Dr.-Ing. Timon Rabczuk, Ph.D.
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 405890576

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.

• DFG Programme: Research Grants