1. A process of acquiring ultrasound data and magnetic resonance imaging (MRI) data of a patient in an MRI scanner such that a magnetic resonance (MR) imaging volume moves relative to the MRI scanner, under guidance from said ultrasound data, to track movement of an organ of the patient that moves relative to the MRI scanner to a plurality of different positions relative to the MRI scanner, comprising: acquiring ultrasound data indicative of a changing position of a body organ of the patient while the organ is moving relative to the MRI scanner; acquiring MRI data from an MR imaging volume in the patient substantially concurrently with the acquisition of the ultrasound data; computer-processing the ultrasound data to generate guidance information causing said MR imaging volume to move relative to the MRI scanner to track the changing position of said body organ such that the MR imaging volume and said moving organ undergo matching movement with respect to the MRI scanner during said MRI data acquisition; and computer-processing the MRI data to generate images of at least said body organ with inherent correction for motion artifacts due to said movement of the organ relative to the MRI scanner.