Advection diffusion model to study the astrocyte calcium regulation in neurodegenerative disease

  • Hardik Joshi Department of Mathematics, LJ Institute of Engineering and Technology,\\ LJ University, Ahmedabad-382210, Gujarat, India
  • Brajesh Kumar Jha Department of Mathematics, School of Technology,\\ Pandit Deendayal Energy University, Gandhinagar-382007, Gujarat, India.


Calcium ion plays a pivotal role in regulating the astrocyte calcium signaling phenomena. Astrocyte is a part of the glial cells that perform various functions in the human brain in a calcium-dependent manner. A free cytosolic calcium concentration provides a better insight to understand besides physiological process. Thus modelling of astrocytes calcium activity is necessary to study the role of aberrant calcium and leads to neurodegenerative disease. In view of this, a mathematical model is framed in the form of an advection-diffusion equation to study the cytosolic calcium concentration. The apposite boundary and initial condition are framed and found the solution of the model by using the Laplace transform technique. The obtained results are interpreted with the neurodegenerative disease.