1. A method for four-dimensional (4D) intensity modulated radiation therapy (IMRT) planning for motion compensated treatments, comprising: obtaining a four dimensional (4D) computed tomography (CT) reference scan for a patient, the reference scan containing a plurality of phases of a tumor in irregular periodic motion; creating a deliverable IMRT treatment plan for said tumor in irregular periodic motion, said treatment plan being adapted for execution by a linear accelerator and a dynamic multi-leaf collimator and responding to said irregular period of motion by variation in monitor unit (MU) and breathing phase (θ), said treatment plan comprising treatment plans for each of said plurality of phases, each said treatment plan considering each degree of freedom of a 4D planning optimization problem; and delivering said treatment plan using a dynamic multi-leaf collimator, leaf positions of said dynamic multi-leaf collimator being adapted separately for each respective phase and for each of a plurality of beam positions, the beam being collimated by said multi-leaf collimator, wherein leaf motion in successive phases does not exceed a predetermined maximum leaf velocity.