Flow in amoeboid movement: modeling and numerical methods
Creators: name: University Of California Office Of The President
Publisher: name: University of California Office of the President
publisherIdentifier: https://ror.org/00dmfq477
publisherIdentifierScheme: ROR
Year: 2024

description: Biofluid dynamics problems often involve complex, active elastic structures whose dynamics are coupled to the surrounding fluid. Studying these problems involves both sophisticated numerical methods and modeling. This research will accomplish two goals: (1) develop a computational model that explores how amoeboid cells use forces to produce shape changes yielding directed movement, and (2) develop efficient and robust implicit immersed boundary methods. The model organism we study is the giant amoeboid cell, Physarum polycephalum. The cytoplasm of Physarum shows regular, periodic shuttle streaming driven by pressure gradients generated by actin-myosin contractions of the cortical gel. Published data by our collaborator show that changes in velocity and boundary deformations propagate as waves along the length of the cell. These bidirectional fluid flows result in a net motion of the entire cell generated by the phase difference between the velocity and deformation waves. The cell does not directly control its intracellular flows and boundary deformations. Instead, these are the product of the spatiotemporal pattern of contraction within cortical gel, the material properties of the cortex, and the shape of the cell. This raises several questions: What boundary contractions are necessary to generate the observed patterns in flow and deformation? What is responsible for the phase difference in the velocity and deformation waves? How do the passive mechanical properties and cell shape contribute to generating directed motion? This research will answer these questions by developing a computational model of the cell. We will prescribe contraction waves with different wave profiles and velocities and compute the resulting flows and boundary deformations to explore how the pattern of contraction is related to the observed flows and deformations. We will explore both simple, idealized cell shapes with uniform material properties, and boundaries based on realistic cell shapes with heterogeneous structure in order to quantify these effects. Simulations of the boundary mechanics and flows will be done using the immersed boundary (IB) method. The IB method is used for many different biofluids applications, and is increasingly being used in engineering applications that involve moving boundaries. The IB method with explicit time discretization requires a very small time step to maintain numerical stability. Recently, we proved that unconditional stability can be achieved using an implicit discretization provided it satisfies certain energy principles. Although these implicit methods are unconditionally stable and a larger time step can be used, the work per time step is much greater. Computational comparisons show that the efficiency of implicit IB methods is problem dependent, and without preconditioning they do not always offer a significant improvement over existing explicit methods. Making implicit methods efficient and robust requires the development of preconditioners, which is a difficult problem, and is generally problem specific. One strategy that has been successful for variety of problems is to use multilevel methods as preconditioners for Krylov methods. This approach has never been applied to the implicit IB equations. We will develop multilevel preconditioners for the implicit IB equations, and we will benchmark our new methods against explicit methods to demonstrate the improved efficiency and robustness for a variety of problems. In our previous work, we have shown that implicit methods together with adaptive mesh refinement (AMR) are highly effective for problems involving widely varying temporal and spatial scales. Adaptive methods are especially important for IB methods because much of the discretization error is concentrated near the immersed boundary. Our new methods will combine implicit discretizations with AMR for the IB equations. We will use these new methods to explore efficiently a wide range of parameters for our computational model of the cell.