Recently my research interest has moved into the area of biology. For example, two problems of considerable interest have been the dynamics of lipid bilayer vesicles and biopreservation by way of desiccation and vitrification (conversation to a glassy state), a technique known as anhydrobiosis.
Lipid bilayers are the basic component of cell membranes. Our aim is to develop solution methods and to investigate the behavior of the mathematical models governing the dynamics of these biological interfaces. Besides being used to enhance our basic understanding of cell membranes, this investigation may have applications to enhanced drug delivery. Our investigations have been directed to developing models which allow for the dynamics of the lipids along the membranes in flows, and we have been interested in understanding the effect of a DC electric pulse on the stability of the membrane. A controlled application of an DC electric pulse can induce transient pores in the cell or vesicle membrane, which can reseal after the pulse is turned off but may allow the delivery of exogenous molecules. Both small amplitude perturbation analysis and numerical methods have been used in our investigations.
Featured Research
THE EFFECT OF GLASS-FORMING SUGARS ON VESICLE MORPHOLOGY AND WATER DISTRIBUTION DURING DRYING
To explore the hypothesis that incomplete vitrification of the cells is causing current desiccation techniques to produce invalid cells, a cell is modeled as a lipid vesicle to monitor the water content and membrane deformation during desiccation.
VESICLE ELECTROHYDRODYNAMICS IN DC ELECTRIC FIELD
We employ the boundary integral method to investigate the dynamics of a 2D vesicle exposed to a uniform DC electric field. The vesicle membrane is modeled as an infinitely thin, capacitive, area-incompressible interface, with the surrounding fluids acting as leaky dielectrics. Our investigations reveal dynamic transitions between oblate and prolate ellipsoidal shapes which depend on the ratio of the conductivities of the surrounding fluids. These transitions are characterized by a ‘squaring’ motion in which vesicles deform into rectangular profiles with corner-like regions of high curvature.