A method for maintaining blood flow in a patient comprising the steps of providing a total artificial heart comprising a first surgically implantable pump and a second surgically implantable pump, each pump including a hollow cylinder, a piston slidably positioned in the cylinder for longitudinal movement therein, a permanent magnet member fixedly attached to the piston for movement therewith and having axially spaced magnet poles directed radially outwardly toward the outer surface of the piston, an array of electrical windings spaced axially along the hollow cylinder, and high permeability, high saturation magnetic material between the spaced electrical windings, whereby the flux produced by the permanent magnet poles links the electrical windings, the inlet end of the first pump being connectable to a right atrium, the outlet end of the first pump being connectable to a pulmonary artery, the inlet end of the second pump being connectable to a left atrium, and the outlet end of the second pump being connectable to an aorta, and control means for sequentially energizing the electrical windings in the array in each pump in a controlled manner so as to exert an axial force on the piston in each pump causing the corresponding piston to move longitudinally through the hollow cylinder and blood to flow into and through each pump, the piston moving in a controlled manner in synchrony with the sequential energization of the electrical windings, connecting the inlet end of the first pump to a patient's right atrium and the outlet end of the first pump to a patient's pulmonary artery and connecting the inlet end of the second pump to a patient's left atrium and the outlet end of the second pump to a patient's aorta.