Cardiovascular System Modeling

Mathematical models and numerical simulations of the cardiovascular system are very useful for understanding the mechanisms influencing its function and its physiological and pathological processes. This modeling research increases the potential for developing new diagnostic and therapeutic cardiovascular techniques or devices and is also helpful for pharmacological research [1]. The recent development of computational methods to solve modeling difficulties in diverse disciplines such as systems biology and computer science led to the idea of compiling a special volume on the subject. This special issue mainly focuses on computational and mathematical methods in cardiovascular system modeling. The research papers cover the topics of cellular or subcellular cardiac cell modeling, cardiovascular anatomical structure modeling, cardiac electrophysiology modeling and simulation , cardiac mechanics modeling and analysis, heart failure modeling and simulation, GPU-based cardiac computational technology, modeling and simulation of the vascular system and mechanics, and computational methods in cardiovas-cular imaging. In the following, we briefly summarize the twelve papers included in this issue. Calcium dynamics is very important in cardiac cell modeling and is often modeled using deterministic ordinary differential equations (ODEs). However, is it appropriate to model the dynamics of the subspace calcium using deterministic ODEs? Do we require a stochastic description that accounts for the fundamentally discrete nature of the calcium-regulated calcium influx? To answer these questions, constructed and analyzed a minimal Markov model of a calcium-regulated calcium channel and associated subspace and also compared the expected steady-state subspace calcium concentration in the stochastic model (a result that accounts for the small subspace volume) with the corresponding deterministic ODE model (an approximation that assumes large system size). L. Lu et al. developed a coupled calcium dynamics model by integrating the spatiotemporal Ca 2+ reaction-diffusion system into the cellular electrophysiological model. Their model was applied to study the effect of rogue RyRs on Ca 2+ cycling and membrane potential in failing heart. Their simulation showed that rogue RyR with tiny Ca 2+ release flux is an important factor in triggering arrhythmia in failing cardiac cells and suggested that rogue RyRs could influence the initiation of Ca 2+ release events (especially Ca 2+ waves) and consequently delayed afterdepolarizations or triggered action potentials. Modeling and simulation of the high complexity of the cardiac electrophysiological processes and the detailed microstructure of cardiac tissue face the challenges of the high computational cost. B. G. de Barros et al. developed a cardiac electrophysiological model using a very …