The electrical activity of the heart is the result of complex biophysical and biochemical processes occurring at different scales ranging from submicroscopic to macroscopic. The variability arising from these processes has important effects on cardiac function under both physiological and pathological conditions. In this review, mathematical modeling and simulation of cardiac electrical variability at the level of the cell, tissue and whole organ will be reviewed. A set of studies will be presented, which investigate the role that the stochastic gating of ion channels of cardiac cell membranes plays in the generation of electrical voltage variations along time. Also, methodologies for the development, calibration and evaluation of populations of mathematical models able to represent variations in cardiac electrophysiology across space, i.e. among cells, tissues or individuals, will be described. In particular, methods based on state-space representations, dimension reduction techniques and nonlinear adaptive filtering will be presented and their capacity to replicate experimentally measured spatio-temporal variability will be illustrated. The importance of these methodologies will be shown as a means to ascertain the mechanisms underlying variability, to establish the link between variability and cardiac arrhythmias (irregularities in heart beating) and to propose clinical markers for diagnosis, monitoring and treatment of cardiac diseases
