We consider Isogeometric Analysis (IGA) for the numerical solution of the electrophysiology of the atria, which in this work is modeled by means of the bidomain equations on thin surfaces. First, we consider the bidomain equations coupled with the Roger-McCulloch ionic model on simple slabs. Here, our goal is to evaluate the effects of the spatial discretization by IGA and the use of different B-spline basis functions on the accuracy of the approximation, in particular regarding the accuracy of the front velocity and the dispersion error. Specifically, we consider basis functions with high polynomial degree, p, and global high order continuity, Cp-1, in the computational domain: our results show that the use of such basis functions is beneficial to the accurate approximation of the solution. Then, we consider a realistic application of the bidomain equations coupled with the Courtemanche-Ramirez-Nattel ionic model on the two human atria, which are represented by means of two NURBS surfaces. (C) 2018 Elsevier B.V. All rights reserved.