Phase-Field Models for Biological Cells in Flow

• Applicant: Professor Dr. Sebastian Aland
• Subject Area: Mathematics
• Term: since 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 328170591

Recent techniques for medical diagnostics use flow scenarios to measure properties of biological cells in high-speed. The interpretation of the measurement data requires numerical methods which are capable to realistically simulate the complex interaction of biological cells with a surrounding fluid. At the considered time scales, cells can neither be approximated as fluid vesicles nor as elastic solids, but a good model must rather regard a combination of different mechanical components. The combination of flow, surface tension, membrane stretch elasticity and viscoelasticity of the cell bulk requires novel mathematical models for a fairly accurate description of cells in a viscous fluid.The goal of this project is to develop a phase field model that can describe the interplay of cells with a fluid and combines the advantages of interface capturing methods with the elastic contributions of the cell components. In the first funding period we have developed the first phase-field model for the interaction of an elastic bulk material with a viscous fluid. The model includes surface contributions from bending stiffness and active tension.The only missing part to get an accurate mechanical model of a biological cell is the in-plane elasticity of the surface which stems from the actin cortex. For the present second funding period we will include this surface stretching elasticity and derive efficient numerical algorithms using adaptive methods and robust time discretizations.In collaboration with experimentalists the method will be applied to a revolutionary new technique to measure cell elasticity, termed Real-Time-Deformability-Cytometry (RTDC). In this technique cells are immersed in a viscous fluid and flown through a narrow channel at a rate of 1000 cells per second. Camera snapshots provide cell shapes in the channel that can be used to compare and validate the numerical results. In the first funding period we have presented the first numerical results of RTDC which shed a first light on the mechanical properties of biological cells on the considered timescales. Our results are now used in RTDC devices around the world to extract cell mechanical properties. One of our main findings so far was, that for many cell types the actin cortex gives the dominant contribution to cell stiffness in RTDC. Including this component in the second funding period will thus enable significant new insight on the mechanics of cells and thereby directly contribute to improve medical diagnostics by RTDC. Since the cell surface will not be represented by a mesh, the model will also be capable to describe surface fluidization by actin depolymerization. This will provide the opportunity to simulate for the first time a viscoelastic surface Maxwell fluid. In collaboration with partners from biology and physics, the model will be applied to active gel theory of viscoelastic membranes and novel thin-shell microswimmers.

• DFG Programme: Research Grants