One aspect of an intravascular ventricular assist device is an implantable blood pump where the pump includes a housing defining a bore having an axis, one or more rotors disposed within the bore, each rotor including a plurality of magnetic poles, and one or more stators surrounding the bore for providing a magnetic field within the bore to induce rotation of each of the one or more rotors. Another aspect of the invention includes methods of providing cardiac assistance to a mammalian subject as, for example, a human. Further aspects of the invention include rotor bodies having helical channels formed longitudinally along the length of the body of the rotor where each helical channel is formed between peripheral support surface areas facing radially outwardly and extending generally in circumferential directions around the rotational axis of the rotor.