Earlier simulation studies have modelled the nucleus as a region lacking a releasable calcium pool with lower diffusion coefficient (about 50 μm²/s) compared with cytoplasm (about 300 μm²/s), where nuclear calcium rises only because of passive diffusion [1]. However, the magnitude and duration of nuclear calcium transient can be both significantly greater than that of cytosolic calcium transient, which indicates other potential nuclear calcium release sources [2]. Given the importance of nuclear calcium in the regulation gene transcription and expression, we introduce a nulcear envelope into the 3Dv E-Cell, which has been used to model stochastic intracellular calcium wave phenomena of an isolated ventricular cell [3], as a barrier with low diffusion coefficient D_NE < 5 μm²/s to maintain spatial heterogeneity, and nuclear calcium handling as a CICR type process with longer Ca²⁺ release duration (about 200 ms) and relative high diffusion coefficient (about 200 μm²/s). A nuclear envelope with a very low diffusion coefficient (D_NE = 0.1 μm²/s), isolates the nucleus from the cytosol, and cytosolic calcium waves neither enter the nucleus nor initiate nuclear calcium transients. The nucleus acts simply as an obstacle that splits the calcium wave front into two fronts that travel around the nucleus. For intermediate values (D_NE = 1.0 μm²/s) a Ca²⁺ wave can trigger a confined nuclear Ca²⁺ transient, and lead to a nuclear Ca²⁺ excitation. Since the nucleus has a much longer Ca²⁺ release duration, nuclear Ca²⁺ concentration remains at a high level for a relatively long period after the cytosolic Ca²⁺ wave passed. At higher values (D_NE = 5.0 μm²/s) a nuclear calcium transient can be activated when cytosolic calcium wave reached an end of the elongated nucleus. The nuclear Ca²⁺ transient can re-invade neighbouring cytosol and trigger a Ca²⁺ wave. This can allow a Ca²⁺ spark located near the nucleus to be amplified by the nuclear transient and nuclear envelope, and initiate a spontaneous cytosolic Ca²⁺ wave due to a high D_NE. Examples of these phenomena are illustrated in Fig. 1.