Patient specific simulations enhance the planning of the therapeutic interventions and help in predicting the clinical outcomes. However, the high computational effort linked to the solution of the coupled problems limits its use in the medical practice. In this context, isogeometric analysis offers the possibility of discretizing the partial differential equations in a cost-effective way by means of the collocation scheme . When applied to the monodomain equation, it results in an efficient scheme suitable for simulating tissues composed by different types of cells and pathological activation patterns. Moreover, the electrophysiological solver can be coupled with the mechanics to investigate the myocardial contractility. In coupling the two sub-problems, we focus on the possibility of adopting two different discretizations to properly represent the two length scales of the sub-problems, improving the computational performance. Furthermore, we develop an immersed method to handle complex geometries within the collocation framework, that is based on the solution of the strong form of the partial differential equation. It simplifies the definition of the mesh and it allows for a direct integration of diagnostic images into the analysis to better model pathological conditions. Numerical tests present and demonstrate the capabilities of the constituent blocks of the isogeometric framework.