FINITE ELEMENT MODEL TO STUDY EFFECT OF Na+−Ca2+ EXCHANGERS AND SOURCE GEOMETRY ON CALCIUM DYNAMICS IN A NEURON CELL

Abstract

The study of calcium diffusion in neuron cells has gained interest among research workers during the last two decades, due to its wide variety of roles in human body like muscle contraction, secretion, metabolism, signal transduction etc. Na[Formula: see text] is the first ion that comes in the hierarchy of ions affecting cytosolic Ca[Formula: see text] concentration. This Na[Formula: see text] ion helps in intracellular Ca[Formula: see text] regulation in cytosol via Na[Formula: see text]/Ca[Formula: see text] exchanger protein (NCX protein). Most of the theoretical investigations on calcium diffusion in neuron cells have been carried out for one and two dimensional cases by various research workers and that too by incorporating a point source of influx. In order to have more realistic study the more details of geometry, microstructure and physiological parameters need to be incorporated in the models. In view of above a three dimensional unsteady state model of Calcium dynamics in a neuron cell has been developed. Apart from the point source, the line and surface sources of an influx of Ca[Formula: see text]as well as the Na[Formula: see text]/Ca[Formula: see text] exchanger, have been incorporated in the model. Appropriate initial and boundary conditions have been framed. The region is discretized using three dimensional circular sectoral elements. Variational finite element method has been employed to obtain the solution. The numerical results have been computed to study effect of Na[Formula: see text]/Ca[Formula: see text] exchanger, point source, line source and surface source of an influx on Ca[Formula: see text] distribution in a neuron cell.

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

“…In our model we have taken an exchange ratio of 3:1 with respect to sodium and calcium ions respectively. The net transport of Ca 2+ ions through N a + /Ca 2+ exchanger is given by : [1,8,13,16] …”

“…Brajesh Kumar Jha and Amrita Jha exchanger etc [1,2,4,8,14,16,20]. In present study calcium buffering and NCX is taken into consideration to study the effect of them on free Ca 2+ concentration.…”

“…Only the effect of buffer was studied in one dimensional unsteady state case. Jha et al [1] have studied the effect of N a + /Ca 2+ exchangers on Ca 2+ in neuron cell using finite element method. Coaxial circular sector element has been used to discretize the circular region.…”

Chaos of calcium diffusion in Parkinson s infectious disease model and treatment mechanism via Hilfer fractional derivative

“…That is three sodium ions enter into the cytosol and one calcium ion exists from the cytosol. In the present study, we have considered the sodium calcium exchanger with an exchange ratio of 3Na + : 1Ca ++ [5,6,7]. The alteration in the process to manage free calcium in the cells for long periods may result in various neurological diseases namely Parkinson's, Alzheimer's, Amyotrophic lateral sclerosis, etc [8,9].…”

“…Tewari and Pardasani have employed Gear's method to study the role of sodium calcium exchanger, calcium channel, plasma membrane, sodium pump and buffer on calcium diffusion in neuron cells [6]. Jha et al have employed the finite element method to study the role of sodium calcium exchanger by considering a point source and line source of calcium flux on calcium diffusion in neuron cells [7]. Also, there have been several experimental attempts that were performed in the past to identify the role and physiological impact of sodium calcium exchangers on various cells [13,14,15,16].…”