  The Helfrich energy is commonly used to model the elastic bending energy of
lipid bilayers in membrane mechanics. The governing differential equations for
certain geometric characteristics of the shape of the membrane can be obtained
by applying variational methods (minimization principles) to the Helfrich
energy functional and are well-studied in the axisymmetric framework. However,
the Helfrich energy functional and the resulting differential equations involve
a number of parameters, and there is little explanation of the choice of
parameters in the literature, particularly with respect to the choice of the
"spontaneous curvature" term that appears in the functional. In this paper, we
present a careful analytical and numerical study of certain aspects of
parametric sensitivity of Helfrich's Using simulations of specific model
systems, we demonstrate the application of our scheme to the formation of
spherical buds and pearled shapes in membrane vesicles.
