An mpeg movie and movie for iPad are available.
Calcium Induced Calcium Release (CICR) is the phenomenon of calcium ion entry into a heart cell triggering even greater release of calcium from the cellular stores. Normally, CICR is induced uniformly in the cell, but under pathological conditions, spontaneous localized release can occur potentially leading to self-organizing calcium waves. If the anomalous wave is triggered coincident to the normal physiological signaling, then it can lead to irregular heart beats and possibly a life threatening ventricular fibrillation.
Our mathematical model for CICR involves the superposition of point sources at several thousand calcium release units (CRUs) in one cell, which results in several challenges. First, realistic simulations for the mathematical model of CICR require long-time simulations on high-resolution numerical meshes of the three-dimensional cell domain, which necessitates sophisticated numerical methods on high performance computing clusters. Second, the point sources are modeled by non-smooth Dirac delta distributions as forcing terms, for which the convergence of the numerical methods is not covered by standard numerical analysis; knowledge of the convergence of numerical methods is vital in order to be able to rely on the results of simulations.
It is the contribution of CSE to provide carefully designed and tested computer code that provided numerical evidence of the convergence that can be expected [Gobbert 2008], which then inspired rigorous analysis that guarantees the convergence of the numerical method [Seidman et al. 2012]. With this reliable basis, we can on the one hand proceed to make the code more efficient by using state-of-the-art GPUs [Huang et al. 2015] and by implementing alternative methods [Schäfer et al. 2015]. And on the other hand, reliable physiological simulations are now possible with confidence.
The plot shows an isosurface of the elevated calcium concentration that brings out the three-dimensional shape of the region of highly elevated calcium concentration and which also shows the initiation of scroll wave in the right half of the cell.
This result demonstrates the significance of the accomplishments in that our simulator produces physiologically correct behavior in full three-dimensional simulations and can provide a better understanding of physiological processes than available from other simulators to date [Coulibaly et al. 2015]. With this ability, we will be able to provide input to help guide in what ranges of parameters to focus laboratory experiments, thus making research significantly more effective. The importance of efficient simulations is also apparent in the context of uncertainty quantification (UQ), an area rapidly growing in importance that needs a large number of simulations to ensure the statistical validity of conclusions in the face of uncertain parameters [Brewster 2014].
For more information and more results, please go to the project web page.
The hardware used in the computational studies is part of the UMBC High Performance Computing Facility (HPCF). The facility is supported by the U.S. National Science Foundation through the MRI program (grant nos. CNS-0821258 and CNS-1228778) and the SCREMS program (grant no. DMS-0821311), with additional substantial support from the University of Maryland, Baltimore County (UMBC). See www.umbc.edu/hpcf for more information on HPCF and the projects using its resources.