Two-Dimensional Finite Element Model to Study Calcium Distribution in Astrocytes in Presence of VGCC and Excess Buffer

Abstract

Astrocyte plays a pivotal role in synaptic transmission with neuron. It maintains the ionic concentration in synapse to regulate signals from one cell to another. Calcium known as second messenger plays an important role in signal transduction. There are so many physiological processes that affect the cytosolic calcium concentration [ Ca 2+]i like calcium buffering, flow of calcium ion through channels, etc. The modeling of calcium signaling in astrocytes has become more sophisticated. The modeling effort has provided insight to understand the cell contraction. Main objective of this work is to study the effect of voltage-gated calcium channel on calcium profile under excess buffer approximation in the form of diffusion equation. A mathematical model is developed in the form of diffusion equation for the calcium profile. The model incorporates the important physiological parameter like diffusion coefficient association rate constant, etc. Appropriate boundary conditions have been framed. Finite element method is employed to solve the problem. A MATLAB program has been developed for the entire problem and simulated to compute the numerical results.

Finite element model to study two dimensional unsteady state calcium distribution in cardiac myocytes

“…To show this consider the steady state of Eqs. (6)- (8) in the absence of influx (J = 0). Setting the left hand sides of Eqs.…”

“…1,2 Attempts are reported in the literature for the study of calcium regulation in neuron cell, astrocyte cell, fibroblast cell, oocyte cell, acinar, etc. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] But very few attempts are reported in the literature for the study of calcium dynamics in myocytes. 1,2,20,21 Most of the studies reported on calcium diffusion in myocytes are experimental.…”

Two dimensional finite element estimation of calcium ions in presence fo NCX and Buffers in Astrocytes

“…The numbers without circles denote the node numbers. The element information is taken from jha et al [6,7,18] Figure 1: Discretization of the solution region [6,7,18] Here, we have used ′ u ′ in lieu of [Ca 2+ ] for our convenience, e = 1, 2 .......50. In the term outside the integral, µ e = 1 for e = 1 and µ e = 0 for rest of the elements.…”

“…Triangular ring element and coaxial circular elements are used to discretize the region. Jha et al [6,7] have studied the effect of buffer and VGCC on [Ca 2+ ] in astrocytes. Finite element method employed to solve the model using triangular element with rectangular region.…”

Nonlinear Dynamic Modeling of 2-Dimensional Interdependent Calcium and Inositol 1,4,5-Trisphosphate in Cardiac Myocyte

“…Pathak et al [18] have developed a two dimensional mathematical model to understand Ca 2+ signaling process in cardiac myocyte but they have not considered the impact of IP 3 dynamics in their model. There are other studies of different cells in literature like hepatocytes [19], neurons [20,21], astrocytes [22,23], fibroblasts [24,25], pancreatic acinar [26,27] and oocytes [28]. But in the existing literature, many mathematical work on Ca 2+ signaling in cardiac myocyte have not paid attention on the role of IP 3 signaling in their mathematical model [29] while those works which state about the impact of IP 3 signaling on Ca 2+ signaling are experimental [30,31,32].…”