3D mathematical modeling of calcium signaling in Alzheimer’s disease

  • Devanshi D. DaveEmail author
  • Brajesh Kumar Jha
Original Article


The present paper focuses on the solution of the three-dimensional calcium advection–diffusion equation in the presence of calcium-binding buffers. As buffers play an important role in maintaining cytosolic calcium concentration level, decrease in buffers leads to increase in cytoplasmic calcium which may further lead to toxicity of Alzheimer’s disease. The governing three-dimensional differential equation has been further converted into one-dimensional equation using similarity transforms. The solution is obtained analytically using Laplace transforms and suitable boundary conditions. The obtained solution is simulated in MATLAB. The graphs clearly show the impact of buffers on calcium concentration level for normal and Alzheimeric cells.


Calcium Buffers 3D-advection–diffusion Alzheimer’s disease Analytical solution 

Mathematics Subject Classification

92B05 92C30 35K57 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, School of TechnologyPDPUGandhinagarIndia

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