The relation between reentrant activity and occurrence of cardiac arrhythmias still is a topic of intensive investigation. Reentries are strictly related to and enhanced by the complex structure of cardiac tissue, characterized by multi-sized electrophysiological and spatial heterogeneities. However, the structure and the function of the tissue can sometimes also promote phenomena of spontaneous termination of waves. The role played by the tissue in this scenario is not well understood and yet under investigation. In this study, we implemented a bidomain formulation of the phase I of the Luo and Rudy action potential model in 2D under ischemic conditions. We investigate how the size of ischemic heterogeneities and tissue conduction properties may affect the system dynamics and drive it towards maintenance of reentrant activity or quiescence. The main findings show that: (a) for the stability of the waves, changes of conductivity in the intracellular space are more critical than alterations in the extracellular space; (b) the maintenance or the self-termination of pinned spirals is strongly dependent not only on the size of the heterogeneities but also on the degree of intracellular anisotropy. These findings confirm and extend results obtained from previous investigations. In addition, since experimental values of conductivity tensors reported in the literature are not consistent, an overview of possible scenarios arising from a broader range of assumed anisotropy values is provided in relation to different sizes of ischemic heterogeneities. In this perspective, simulations are shown to compare the impact of different degrees of tissue anisotropy on wave dynamics.(C) 2016 The Authors. Published by Elsevier B.V.