Abstract: A method for estimating a dose gradient of the parameters of a beam of ionizing particles, the dose being deposited by the beam in a voxel of a meshed phantom of a patient, each mesh cell comprising voxels of one and the same material, the parameters of the beam comprising a fluence parameter and geometric parameters, the method comprises the determination of the analytic function for the gradient of the dose, deposited per mesh cell, of the parameters of the beam; and the determination of the estimation of the gradient of the dose in the voxel. Certain procedures for estimating the dose deposited are described. Developments deal with configurations having several independent of partially dependent irradiating beams, optimizations of the treatment plan using cost functions and the management of beams moving along trajectories. The use of servo-controlled robotic arms or of other mobile systems during irradiation is described.