Zana Coulibaly

Insight into spontaneous recurrent calcium waves in a 3-D cardiac cell based on analysis of a 1-D deterministic model

Calcium dynamics in a cardiac cell are described by a system of 3-D non-linear stochastic partial differential equations. To obtain solutions that have biophysical properties, it is necessary to explore the model parameter space. To decrease the complexity of the parameter search, we reduce the 3-D stochastic model to a 1-D deterministic model. The reduction of the problem from 3-D to 1-D is done through an asymptotic approximation after non-dimensionalization and based on rational biophysical assumptions of the 3-D domain; the stochastic to deterministic transformation is based on the regular property of the 3-D solution. The result of the model reduction proves very effective in reducing the time required to get qualitative as well as quantitative information about parameter regions in the 3-D stochastic model including calcium dynamics (sparks, wave propagation, and recovery) observed in cardiac cells.

Mechano-chemo-transduction is attenuated in a rabbit model of heart failure

Author(s): Shimkunas, Rafael; Hegyi, Bence; Jian, Zhong; Coulibaly, Zana; Lam, Kit S; Ginsburg, Kenneth S; Bossuyt, Julie; Bers, Donald M; Izu, Leighton T; Chen-Izu, Ye

Modeling the Links Between the Chemical, Electrical and Contractile Calcium Dynamics in a Heart Cell

These results were obtained as part of the REU Site: Interdisciplinary Program in High Performance Computing (hpcreu.umbc.edu) in the Department of Mathematics and Statistics at the University of Maryland, Baltimore County (UMBC), in Summer 2016. This program is funded by the National Science Foundation (NSF), the National Security Agency (NSA), and the Department of Defense (DOD), with additional support from UMBC, the Department of Mathematics and Statistics, the Center for Interdisciplinary Research and Consulting (CIRC), and the UMBC High Performance Computing Facility (HPCF). HPCF 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 UMBC. Co-author Uchenna Osia was supported in part by the UMBC National Security Agency (NSA) Scholars Program through a contract with the NSA. Graduate assistant Jonathan Graf was supported by UMBC.