Analysis of the disturbance effect in intracellular calcium dynamic on fibroblast cells with an exponential kernel law

Hardik Joshi; Mehmet Yavuz; Ivanka Stamova

doi:10.59292/bulletinbiomath.2023002

Authors

Hardik Joshi Department of Mathematics, LJ Institute of Engineering and Technology, LJ University, Ahmedabad-382210, India https://orcid.org/0000-0003-2014-3765
Mehmet Yavuz Department of Mathematics and Computer Sciences, Necmettin Erbakan University, 42090 Konya, Türkiye https://orcid.org/0000-0002-3966-6518
Ivanka Stamova Department of Mathematics, The University of Texas at San Antonio, San Antonio, TX 78249, USA https://orcid.org/0000-0001-6723-2699

DOI:

https://doi.org/10.59292/bulletinbiomath.2023002

Keywords:

Calcium concentration, buffer, fibroblast cells, fractional advection reaction-diffusion equation, Caputo-Fabrizio fractional derivative

Abstract

The maintenance of free calcium in the cytoplasm is requisite for cell integrity and the regime of the multi-cellular process. Overproduction and degradation to manage this cellular entity produce offensive changes in tissue performance and as a result, commence fibrotic diseases. Thus, there is a necessity to know the cellular process for the inclusion and extrusion of free calcium. Here, a mathematical model is framed to investigate the role of buffer and calcium concentration on fibroblast cells. In this context, the Caputo-Fabrizio advection reaction-diffusion model along with apposite biophysical initial and boundary conditions is considered. The analytical solution is obtained and used to analyze the diverse mechanisms of calcium on fibroblast cells. The obtained results reveal that when the fractional order goes to one, the Caputo–Fabrizio fractional derivative provides a concise calcium profile and well-managed cellular entity due to the exponential kernel law.

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