Mathematical modeling is a powerful tool to study the complex and orchestrated biological process of cardiac electrical activity. By integrating experimental data from key components of cardiac electrophysiology, systems biology simulations can complement empirical findings, provide quantitative insight into physiological and pathophysiological mechanisms of action, and guide new hypotheses to better understand this complex biological system to develop novel cardiotherapeutic approaches. In this chapter, we briefly introduce in silico methods to describe the dynamics of physiological and pathophysiological single-cell and tissue-level cardiac electrophysiology. Using a "bottom-up" approach, we first describe the basis of ion channel mathematical models. Next, we discuss how the net flux of ions through such channels leads to changes in transmembrane voltage during cardiomyocyte action potentials. By applying these fundamentals, we describe how action potentials propagate in models of cardiac tissue. In addition, we provide case studies simulating single-cell and tissue-level arrhythmogenesis, as well as promising approaches to circumvent or overcome such adverse events. Overall, basic concepts and tools are discussed in this chapter as an accessible introduction to nonmathematicians to foster an understanding of electrophysiological modeling studies and help facilitate communication with dry lab colleagues and collaborators.
Keywords: Arrhythmias; Cardiac electrophysiology; Ion channels; Models of disease; Quantitative systems pharmacology; Systems biology; Torsades de pointes.