  We study complex structure deformations of special Lagrangian cycles
associated to fractional D-branes at $\mathbb{Z}_2$ singularities in Type
II/$\Omega \mathcal{R}$ orientifold models. By means of solving hypersurface
constraints, we show how to compute the volumes of the most simple D-brane
configurations. These volumes are given as a function of the deformation
parameters depending on the D-brane position relative to the smoothed out
singularity. We observe which cycles keep the special Lagrangian property in
various deformation scenarios and what orientifold involutions are allowed.
  As expected, the volume and thus the tree level value of the gauge coupling
hardly change for D-branes not wrapping the exceptional cycle on the deformed
singularity, whereas the volume of D-branes passing through the singularity
depends on the deformation parameter by some power law.
