Research Projects

Cell motility

Cell migrations could be powered by both actin recycling and osmotic water flow. Cells may use different driving mechanism to navigate in their environment, especially in confined spaces. In this area of research, we use a multiphase model to study the driving machanism of cell migration, and the energy expenditure. Results can be found in "On the energy efficiency of cell migration in diverse physical environments", a research paper published in PNAS, November 12, 2019 (with Y. Li, Y. Mori and S. X. Sun). Our results show that with high fluid resistance, water driving is much more efficient than actin driving in cell migrations. Also, the water flow helps cell move faster even in actin driving migrations. The 2D calculation in this paper is based on the numerical methods we developed in the numerical algorithm section bellow.

Polyelectrolyte hydrogels

Rhythmic drug delivery device driven by volume phase transition of hydrogels has great potential to deliver physiological substances to human body periodically in time, which are necessary for many medical treatments. One of the promising biochemical oscillator built in Dr. Siegel's lab consists of a pH-sensitive, hydrophobic polyelectrolyte hydrogel membrane, and the enzyme glucose oxidase. The membrane's response to hydrogen ion exhibits hysteresis, and leads to oscillations in membrane swelling and permeability to glucose. We team with the designer of the device Dr. Siegel to analyze and summarize in a paper: "Rhythmomimetic Drug Delivery: Modeling, Analysis, and Numerical Simulation" in SIAM J. Appl. Math. in 2017 (with C. Calderer, Y. Mori and R. Siegel), how the chemo-mechanical oscillator is driven by the gel volume phase transition and how to understand the detailed dynamics in the mathematical model behind the experimental devices built.

Numerical Algorithm and Simulation

In Cell Migrations

To study the osmotic effect in cell motility, we design a mathematical model in 2D. In the model, cell membranes, which are permeable to both water and ionic flows, divide the domain into intracellular and extracellular regions. The cell membranes also move with the flow it is embedded in, while its elastic force and osmotic forces due to ions will in turn affect fluid properties. So our model consists of fluid-structure interactions and chemical advection-reaction-diffusion in a fluid domain with deformable (moving) internal interfaces. The model system presents great challenges to the numerical methods for computations. The numerical framework we developed in a paper "A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension" in J. of Comp. Phys. in 2017 (with Y. Mori), for the system is a fixed Cartesian method for chemical and immersed boundary for fluid structure interactions. It is shown to be stable and effective, and is capable of producing accurate results for all the fluid and chemical variables in the model.

In blood clotting

Numerical methods for enzyme advection-diffusion-reaction in blood flow need to deal with irregular shape of platelets and red blood cells in the computational domain and mixed boundary conditions on the surfaces of the moving objects. In addition to stability and accuracy, the numerical algorithms have to resolve large numbers of platelets so the simulation could be in realistic physiological conditions. Our Cartesian grid method developed in "Simulations of Chemical Transport and Reaction in a Suspension of Cells I: An Augmented Forcing Point Method for the Stationary Case", published in International J. of Numer. Methods in Fluids in 2012 (with A. Fogelson), are based on the idea of an augmented forcing function and a general saddle point formulation; these methods successfully achieve good efficiency, accuracy and stability. We showed analytically and confirm numerically that these methods, which can handle mixed boundary conditions on each platelet easily, have the same accuracy and stability as the ghost cell method \cite{IB-ghostcell-JCP2003} does, but our method provides better computation efficiency.

Modeling and simulation in complex fluids

Liquid Crystal Polymers (LCPs)

Diffusions of micro-beads in complex fluids

Financial Support

NSF-DMS 1852597, $95,274, 2018-2021. Algorithm and Theory for Interface Computations.