According to Jerry Sellwood of Rutgers University, in the article What process creates and maintains the beautiful spiral arms around spiral galaxies?:
Fortunately, nearly every one agrees that spiral patterns extract gravitational energy from the field of a galaxy. The inexorable force of gravity tries to pull the stars in a galaxy closer towards the center. The gravitational force is balanced by the orbital motion of a star (like a stone whirled on a string) which generally prevents it from settling any deeper on average into the galaxy. The spiral arms are a kind of catalyst that brakes the orbital motion of some stars, allowing them to sink slightly closer to the middle. Those with technical training will realize that if some stars lose angular momentum others must gain equally and, in fact, the stars that lose are near the inner end of the arms while those at the outer end gain. The gravitational stresses arising from the spiral density wave provide the torque.
In other words, the spiral arms tend to reduce the rotational speeds in the central portions of galaxies and increase them in the outer regions.
I have not heard of this effect being considered when relating the rotation curves to the distributions of matter in the galaxies, so I'm wondering how significant this effect may be.