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Fractional Reaction Diffusion Model for Parkinson’s Disease

  • Hardik JoshiEmail author
  • Brajesh Kumar Jha
Conference paper
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 30)

Abstract

Calcium (Ca2+) ion known as a second messenger, involve in variety of signalling process, and directly link with the intracellular calcium concentration ([Ca2+]) that are continuously remodelled for the survival of the nerve cell. Buffer, also refer as a protein, react with Ca2+ and significantly lower down the intracellular [Ca2+] in nerve cell. There are numerous signalling processes in mammalian brain which can initiate at the high level of intracellular [Ca2+]. Voltage gated calcium channel (VGCC), and ryanodine receptor (RyR) are work as an outward source of Ca2+ which initiate, and sustain the signalling process for smooth functioning of the cells. Parkinson’s disease (PD) is a brain disorder of the central nervous system accompanied with the alteration of the signalling process. In present paper, a one dimensional fractional reaction diffusion model is consider to understand the physiological role of buffer, VGCC, and RyR in view of the PD.

Keywords

Fractional approach Buffer Voltage gated calcium channel Ryanodine receptor Calcium concentration Parkinson’s disease 

Notes

Acknowledgements

We are very grateful to the reviewers for their fruitful comments and suggestions for making updation in the research article.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, School of TechnologyPandit Deendayal Petroleum UniversityGujaratIndia

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