  We present a pilot study on the nearby massive barred galaxy NGC 1291, in
which we use dynamical modelling to constrain the disc mass-to-light ratio
(M/L), thus breaking the degeneracy between the baryonic and dark matter in its
central regions. We use the gas, specifically the morphology of the dust lanes
on the leading side of the bar, as a tracer of the underlying gravitational
potential. We run a large number of hydrodynamic gas response simulations, in
potentials obtained directly from near-infrared images of the galaxy, which
have three free parameters: the M/L, the bar pattern speed and the height
function. We explore the three-dimensional parameter space, by comparing the
morphology of the shocks created in the gas response simulations with those of
the observed dust lanes, and find the best-fitting models; these suggest that
the M/L of NGC 1291 agrees with that predicted by stellar population synthesis
models in the near-infrared ($\approx$0.6\,$M_{\odot}/L_{\odot}$), which leads
to a borderline maximum disc for this galaxy. Furthermore, we find that the bar
rotates fast, with a corotation radius which is $\leq$ 1.4 times the bar
length.
