  A model for computing acoustic scattering by a swimbladdered fish with
coupling to surrounding fish tissue that is assumed to behave as a homogeneous
fluid, is presented. Mathematically, this corresponds to considering the
problem of two penetrable scatterers immersed in a homogeneous medium, one of
which is wholly embedded in the other. The model is formulated in the frame of
boundary integral equations whose solution is achieved using the Boundary
Element Method (BEM) for a planar triangle mesh. The numerical implementation
is verified against benchmark solutions reported in the literature. The model
is then applied to a specimen of \textit{Merluccius hubbsi}, whose morphometry
was determined by CT scanning, for evaluating its forward and backscattering
responses. From the acoustic scattering viewpoint, the swimbladder is
considered as a gas-filled object while the flesh constituting the fish body
acts like a weak scatterer. The numerical results suggest the swimbladder and
the fish body responses, when fully coupled, can lead to substantial
differences with respect to the simplified models normally in use in the area
of aquatic ecosystem research.
