arXiv subjects

Shuwang Li

Publications and source records attributed to Shuwang Li.

21 records · Page 2Linked to original sources

arXiv2020

Complex Far-Field Geometries Determine the Stability of Solid Tumor Growth with Chemotaxis

In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient uptake rates inside and outside the tumor, this introduces variability in spatial diffusion gradients. Linear stability analysis suggests that the uptake rate in the tumor microenvironment, together with chemotaxis, may induce unstable growth, especially when the nutrient gradients are large. We investigate the fully nonlinear dynamics using a spectrally accurate boundary integral method. Our nonlinear simulations reveal that vascular heterogeneity plays an important role in the development of morphological instabilities that range from fingering and chain-like morphologies to compact, plate-like shapes in two-dimensions.

math.NA↗

arXiv2019

Nonlinear simulation of an elastic tumor-host interface

We develop a computational method for simulating the nonlinear dynamics of an elastic tumor-host interface. This work is motivated by the recent linear stability analysis of a two-phase tumor model with an elastic membrane interface in 2D. Unlike the classic tumor model with surface tension, the elastic interface condition is numerically challenging due to the 4th order derivative from the Helfrich bending energy. Here we are interested in exploring the nonlinear interface dynamics in a sharp interface framework. We consider a curvature dependent bending rigidity (curvature weakening) to investigate metastasis patterns such as chains or fingers that invade the host environment. We solve the nutrient field and the Stokes flow field using a spectrally accurate boundary integral method, and update the interface using a nonstiff semi-implicit approach. Numerical results suggest curvature weakening promotes the development of branching patterns instead of encapsulated morphologies in a long period of time. For non-weakened bending rigidity, we are able to find self-similar shrinking morphologies based on marginally stable value of the apoptosis rate.

math.NA↗

arXiv2016

Dynamics of a multicomponent vesicle in shear flow

We study the fully nonlinear, nonlocal dynamics of two-dimensional multicomponent vesicles in a shear flow with matched viscosity of the inner and outer fluids. Using a nonstiff, pseudo-spectral boundary integral method, we investigate dynamical patterns induced by inhomogeneous bending for a two phase system. Numerical results reveal that there exist novel phase-treading and tumbling mechanisms that cannot be observed for a homogeneous vesicle. In particular, unlike the well-known steady tank-treading dynamics characterized by a fixed inclination angle, here the phase-treading mechanism leads to unsteady periodic dynamics with an oscillatory inclination angle. When the average phase concentration is around 1/2, we observe tumbling dynamics even for very low shear rate, and the excess length required for tumbling is significantly smaller than the value for the single phase case. We summarize our results in phase diagrams in terms of the excess length, shear rate, and concentration of the soft phase. These findings go beyond the well known dynamical regimes of a homogeneous vesicle and highlight the level of complexity of vesicle dynamics in a fluid due to heterogeneous material properties.

cond-mat.soft↗