Heart disease is the leading cause of mortality in the United States. One cause of heart arrhythmia is calcium (Ca2+) mishandling in cardiac muscle cells. We adapt Izu's et al. mathematical reaction-diffusion model of calcium in cardiac muscle cells, or cardiomyocytes implemented by Gobbert, and analyzed in Coulibaly et al. to include calcium being released from the sarcoplasmic reticulum (SR), the effects of buffers in the SR, particularly calsequestrin, and the effects of Ca2+ influx due to voltage across the cell membrane. Based on simulations of the model implemented in parallel using MPI, our findings aligned with known biological models and principles, giving us a thorough understanding of several factors that influence Ca2+ dynamics in cardiac myocytes. Specifically, dynamic calcium store will cap previous calcium blow-up seen in the model. Calcium channels located in spatial opposition of calcium release units produce more predictable intracellular calcium propagation. And we used multi-parametric calcium dynamics tables, which act as a multidimensional bifurcation diagram, to visualize parameter boundaries between different biophysical dynamics.
Alexander, Amanda M.; DeNardo, Erin K.; Frazier, Eric III; McCauley, Michael; Rojina, Nicholas; Coulibaly, Zana; Peercy, Bradford E.; and Izu, Leighton T.
"Spontaneous Calcium Release in Cardiac Myocytes: Store Overload and Electrical Dynamics,"
Spora: A Journal of Biomathematics: Vol. 1:
Available at: https://ir.library.illinoisstate.edu/spora/vol1/iss1/6