The scientific goal of the present paper is to develop a three-dimensional physical dynamic model of the plasmasphere that is constrained by realistic data. The core of the plasmasphere is obtained from the kinetic exospheric approach assuming a kappa velocity distribution function for the particles. The relative abundance of trapped particles is constrained in such way that the density profiles correspond to Carpenter and Anderson's (1992) observations. The position of the plasmapause is determined by the interchange instability mechanism for the formation of the plasmapause, which is a function of the level of geomagnetic activity. The deformation of the plasmasphere during quiet and disturbed geomagnetic periods is illustrated and compared with the results of other plasmaspheric models and observations of IMAGE and Cluster.