A method is presented for generating a time-dependent parametric surface. The application on which this paper concentrates is that of producing a parametric surface description of the surfaces of the left and right ventricles of the human heart. The model is generated from two-dimensional section data obtained from MRI images of the heart. The method views surface generation as a boundary-value problem and produces surfaces as the solutions to elliptic partial differential equations. Shape parameters controlling the geometry of the surface model are introduced through the boundary conditions on the solution of the partial differential equation. These parameters are functions of time, and the surface model can be used to produce an animation of the heart during the cardiac cycle.