The model equations were solved using the standard Galerkin
finite element method, as described previously.
10 The
solution method was modified by allowing finite element nodes to slide
along the surface of the lens to minimize element distortion.
During accommodation, the lens deforms anteriorly toward the iris and
nearly comes into contact with the iris. In theory, actual contact
between two smooth surfaces is impossible because of the infinite
stress developed in the lubricating fluid layer on incipient contact.
Inaccuracies in numerical solution, however, can cause the computed
position of the iris to overlap slightly with the lens, leading to
breakdown of the simulation. Various methods have been developed to
combat this sort of problem, such as the use of a Lagrange multiplier
to push back the nodes that have penetrated the lubrication
layer.
23 Our approach was to enforce a no-contact zone by
introducing a stress on the iris normal to the lens. The additional
stress is related to the distance between the iris and lens by the
equation
\[{\varsigma}_{\mathrm{iris}}{=}A{\cdot}\mathrm{e}^{-\ \frac{d}{{\epsilon}}}\mathbf{n}_{\mathrm{lens}}\mathbf{n}_{\mathrm{lens}}\]
where
n lens is the vector normal to
the lens surface at the nearest point on the lens surface,
A and ε are adjustable coefficients, and
d is the minimum
distance from the iris to the lens. The coefficient ε corresponds to
how far the no-contact zone extends into the aqueous humor, and the
coefficient
A corresponds to how strongly the no-contact
zone is enforced. The contact prevention force can affect the results
if it is applied at greater distances (or equivalently greater
strength), as shown in
Figure 2 . Based on the data in
Figure 2 , the maximum value of ε used in all
studies was 3 μm. In addition to having little effect on the
hydrodynamics of interest, the use of a small separation layer is
consistent with the fact that the posterior iris surface is
rough,
24 and therefore, although some regions may contact
the lens, the entire surface is unlikely to make contact.