Applications of a new In vivo tumor spheroid based shell-less chorioallantoic membrane 3-D model in bioengineering research

The chicken chorioallantoic membrane (CAM) is a classical in vivo biological model in studies of angiogenesis. Combined with the right tumor system and experimental configuration this classical model can offer new approaches to investigating tumor processes. The increase in development of biotechnolo- gical devices for cancer diagnosis and treatment, calls for more sophisticated tumor models that can easily adapt to the technology, and provide a more accurate, stable and consistent platform for rapid quantitative and qualitative analysis. As we discuss a variety of applications of this novel in vivo tumor spheroid based shell-less CAM model in biomedical engineering research, we will show that it is extremely versatile and easily adaptable to an array of biomedical applications. The model is particularly useful in quantitative studies of the progression of avascular tumors into vascularized tumors in the CAM. Its environment is more stable, flat and has a large working area and wider field of view excellent for imaging and longitudinal studies. Finally, rapid data acquisition, screening and validation of biomedical devices and therapeutics are possible with the short experimental window.

Numerical Study on Viscous Fingering Using Electric Fields in a Hele-Shaw Cell

We investigate the nonlinear dynamics of amoving interface in aHele-Shaw cell subject to an in-plane applied electric field.We develop a spectrally accurate numerical method for solving a coupled integral equation system.Although the stiffness due to the high order spatial derivatives can be removed using a small scale decomposition technique,the long-time simulation is still expensive since the evolving velocity of the interface drops dramatically as the interface expands.We remove this physically imposed stiffness by employing a rescaling scheme,which accelerates the slow dynamics and reduces the computational cost.Our nonlinear results reveal that positive currents restrain finger ramification and promote the overall stabilization of patterns.On the other hand,negative currents make the interface more unstable and lead to the formation of thin tail structures connecting the fingers and a small inner region.When no fluid is injected,and a negative current is utilized,the interface tends to approach the origin and break up into several drops.We investigate the temporal evolution of the smallest distance between the interface and the origin and find that it obeys an algebraic law(t∗−t)b,where t∗is the estimated pinch-off time.

Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics

Geometrical evolution laws are widely used in continuum modeling of surface and interface motion in materials science.In this article,we first give a brief review of various kinds of geometrical evolution laws and their variational derivations,with an emphasis on strong anisotropy.We then survey some of the finite element based numerical methods for simulating the motion of interfaces focusing on the field of thin film growth.We discuss the finite element method applied to front-tracking,phase-field and level-set methods.We describe various applications of these geometrical evolution laws to materials science problems,and in particular,the growth and morphologies of thin crystalline films.

Numerical Study of Surfactant-Laden Drop-Drop Interactions

In this paper,we numerically investigate the effects of surfactant on dropdrop interactions in a 2D shear flow using a coupled level-set and immersed interface approach proposed in(Xu et al.,J.Comput.Phys.,212(2006),590–616).We find that surfactant plays a critical and nontrivial role in drop-drop interactions.In particular,we find that the minimum distance between the drops is a non-monotone function of the surfactant coverage and Capillary number.This non-monotonic behavior,which does not occur for clean drops,is found to be due to the presence of Marangoni forces along the drop interfaces.This suggests that there are non-monotonic conditions for coalescence of surfactant-laden drops,as observed in recent experiments of Leal and co-workers.Although our study is two-dimensional,we believe that drop-drop interactions in three-dimensional flows should be qualitatively similar as the Maragoni forces in the near contact region in 3D should have a similar effect.

An Efficient Rescaling Algorithm for Simulating the Evolution of Multiple Elastically Stressed Precipitates

In this paper,we propose a space-time rescaling scheme for computing the long time evolution of multiple precipitates in an elastically stressed medium.The algorithm is second order accurate in time,spectrally accurate in space and enables one to simulate the evolution of precipitates in a fraction of the time normally used by fixed-frame algorithms.In particular,we extend the algorithm recently developed for single particle by Li et al.(Li,Lowengrub and Leo,J.Comput.Phys.,335(2007),554)to the multiple particle case,which involves key differences in the method.Our results show that without elasticity there are successive tip splitting phenomena accompanied by the formation of narrow channels between the precipitates.In presence of applied elastic field,the precipitates form dendrite-like structures with the primary arms aligned in the principal directions of the elastic field.We demonstrate that when the far-field flux decreaseswith the effective radius of the system,tip-splitting and dendrite formation can be suppressed,as in the one particle case.Depending on the initial position of the precipitates,we further observe that some precipitates grow while others may shrink,even when a positive far field flux is applied.