The analysis of the pure motion of subnuclear structures without influence of the cell nucleus motion and deformation is essential in live cell imaging. In this work, we propose a 2D contour-based image registration approach for compensation of nucleus motion and deformation in fluorescence microscopy time-lapse sequences. The proposed approach extends our previous approach which uses a static elasticity model to register cell images. Compared to that scheme, the new approach employs a dynamic elasticity model for forward simulation of nucleus motion and deformation based on the motion of its contours. The contour matching process is embedded as a constraint into the system of equations describing the elastic behavior of the nucleus. This results in better performance in terms of the registration accuracy. Our approach was successfully applied to real live cell microscopy image sequences of different types of cells including image data that was specifically designed and acquired for evaluation of cell image registration methods. An experimental comparison with existing contour-based registration methods and an intensity-based registration method has been performed. We also studied the dependence of the results on the choice of method parameters.