Respiratory motion is a major problem in cardiac MRI. In this work, the displacement of the heart relative to the diaphragm was investigated. A subject-specific nonlinear elliptical affine model has been developed to incorporate the effect of hysteresis in motion correction. Nine healthy volunteers participated in a study in which the diaphragm position and an image of the heart were acquired during each cardiac cycle, while breathing freely. The elliptical model was compared to a linear affine model, and the results show that the elliptical model performed significantly (P < 0.05) better than the linear model. Further, it has been established that the model can be constructed from 25 s of prescan data, which makes it feasible to perform a short prescan to construct the model, so that subject-specific prospective motion correction of the heart can be integrated into structural cardiac MRI sequences.