Abstract: We present in this paper a fully implicit finite element
method tailored for the numerical modeling of inextensible fluidic
membranes in a surrounding Newtonian fluid. We consider a highly
simplified version of the Canham-Helfrich model for phospholipid
membranes, in which the bending force and spontaneous curvature
are disregarded. The coupled problem is formulated in a fully
Eulerian framework and the membrane motion is tracked using
the level set method. The resulting nonlinear problem is solved
by a Newton-Raphson strategy, featuring a quadratic convergence
behavior. A monolithic solver is implemented, and we report several
numerical experiments aimed at model validation and illustrating
the accuracy of the proposed method. We show that stability is
maintained for significantly larger time steps with respect to an
explicit decoupling method.
Abstract: Liver segmentation from medical images poses more
challenges than analogous segmentations of other organs. This
contribution introduces a liver segmentation method from a series of
computer tomography images. Overall, we present a novel method for
segmenting liver by coupling density matching with shape priors.
Density matching signifies a tracking method which operates via
maximizing the Bhattacharyya similarity measure between the
photometric distribution from an estimated image region and a model
photometric distribution. Density matching controls the direction of
the evolution process and slows down the evolving contour in regions
with weak edges. The shape prior improves the robustness of density
matching and discourages the evolving contour from exceeding liver’s
boundaries at regions with weak boundaries. The model is
implemented using a modified distance regularized level set (DRLS)
model. The experimental results show that the method achieves a
satisfactory result. By comparing with the original DRLS model, it is
evident that the proposed model herein is more effective in addressing
the over segmentation problem. Finally, we gauge our performance of
our model against matrices comprising of accuracy, sensitivity, and
specificity.
Abstract: Transient shape variation of a rotating liquid dropletis
simulated numerically. The three dimensional Navier-Stokes
equations were solved by using the level set method. The shape
variation from the sphere to the rotating ellipsoid, and to the two-robed
shapeare simulated, and the elongation of the two-robed droplet is
discussed. The two-robed shape after the initial transient is found to be
stable and the elongation is almost the same for the cases with different
initial rotation rate. The relationship between the elongation and the
rotation rate is obtained by averaging the transient shape variation. It is
shown that the elongation of two-robed shape is in good agreement
with the existing experimental data. It is found that the transient
numerical simulation is necessary for analyzing the largely elongated
two-robed shape of rotating droplet.