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Estimation of stochastic behaviour in cardiac myocytes: I. Calcium Ca2+ movements inside the cytosol and sarcoplasmic reticulum on curvilinear domains

Estimation of stochastic behaviour in cardiac myocytes: I. Calcium Ca2+ movements inside the cytosol and sarcoplasmic reticulum on curvilinear domains

Arif, Serife, Lai, Choi-Hong ORCID: 0000-0002-7558-6398 and Ramesh, Nadarajah I. (2019) Estimation of stochastic behaviour in cardiac myocytes: I. Calcium Ca2+ movements inside the cytosol and sarcoplasmic reticulum on curvilinear domains. JRSM Cardiovascular Disease, 8. ISSN 2048-0040 (Print), 2048-0040 (Online) (doi:https://doi.org/10.1177/2048004018822428)

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Abstract

Background:
Since the discovery of Ca2+ sparks and their stochastic behaviour in cardiac myocytes, models have focused on the inclusion of stochasticity in their studies. While most models pay more attention to the stochastic modelling of cytosolic Ca2+ concentration the coupling of Ca2+ sparks and blinks in a stochastic model has not been explored fully. The cell morphology in past in silico studies is assumed to be Cartesian, spherical or cylindrical. The application on curvilinear grids can easily address this restriction and provide more realistic cell morphology. This paper presents a stochastic reaction-diffusion model that couples Ca2+ sparks and blinks applied to curvilinear domains.

Methodology:
Transformation of the model was performed to the curvilinear coordinate system. A set of differential equations is used to produce Ca2+ waves initiated from sparks and blinks. A non-buffered and non-dyed version as well as a buffered and dyed version of these equations were studied in light of observing the effects of reactions on the Ca2+ wave properties. For comparison, results for both the Cartesian and curvilinear grids are provided.

Results and Conclusions:
A successful demonstration of the application of curvilinear grids serving as basis for future developments.

Item Type: Article
Additional Information: Creative Commons Non Commercial CC BY-NC: This article is distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 License (http://www.creativecommons.org/licenses/by-nc/4.0/) which permits non-commercial use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage).
Uncontrolled Keywords: Stochastic calcium waves, Ca2+ sparks and blinks, curvilinear domain.
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 24 Jan 2019 11:07
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/22523

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