  We use a lattice model to study first-passage time distributions of target
finding events through complex environments with elongated fibers distributed
with different anisotropies and volume occupation fractions. For isotropic
systems and for low densities of aligned fibers, the three-dimensional search
is a Poisson process with the first-passage time exponentially distributed with
the most probable finding time at zero. At high enough densities of aligned
fibers, elongated channels emerge, reducing the dynamics dimensionality to one
dimension. We show how the shape and size of the channels modify the behavior
of the first-passage time distribution and its short, intermediate, and long
time scales. We develop an exactly solvable model for synthetic rectangular
channels, which captures the effects of the tortuous local structure of the
elongated channels that naturally emerge in our system. For arbitrary values of
the nematic order parameter of fiber orientations, we develop a mapping to the
simpler situation of fully aligned fibers at some other effective volume
occupation fraction. Our results shed light on the molecular transport of
biomolecules between biological cells in complex fibrous environments.
