Two-dimensional finite element model to study unsteady state Ca2+ diffusion in neuron involving ER LEAK and SERCA

2015 ◽  
Vol 08 (01) ◽  
pp. 1550002 ◽  
Author(s):  
Amrita Jha ◽  
Neeru Adlakha
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Element Model ◽  
Diffusion Problem ◽  
Physiological Parameters ◽  
Communication Process ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Unsteady State

In this paper, finite element approach using two-dimensional unsteady state problem has been developed to study radial and angular calcium diffusion problem in neurons. Calcium is responsible messenger for transmitting information in communication process between neurons. The most important Ca 2+ binding proteins for the dynamics of Ca 2+ is itself buffer and other physiological parameters are located in Ca 2+ stores. In this study, the model incorporates the physiological parameters like diffusion coefficient, receptors, exogenous buffers etc. Appropriate boundary conditions have been framed in view of the physiological conditions. Computer simulations in MATLAB 7.11 are employed to investigate mathematical models of reaction–diffusion equation, the details of the implementation can heavily affect the numerical solutions and, thus, the outcome simulated on Core(TM) i3 CPU M 330 @ 2.13 GHz processing speed and 3 GB memory.

A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation

2020 ◽  
Vol 11 (02) ◽  
pp. 2050016
Author(s):  
Yaping Zhang ◽  
Jiliang Cao ◽  
Weiping Bu ◽  
Aiguo Xiao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Time Space ◽  
Distributed Order ◽  
Fractional Reaction ◽  
Element Method

In this work, we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation (2D-DOTSFRDE) with low regularity solution at the initial time. A fast evaluation of the distributed-order time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the sum-of-exponentials. The stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are discussed. For the spatial approximation, the finite element method is employed. The convergence of the corresponding fully discrete scheme is investigated. Finally, some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.

scholarly journals Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Nauman Raza ◽  
Asma Rashid Butt
Keyword(s):  
Finite Element ◽  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Singularly Perturbed ◽  
Three Dimensions ◽  
Reaction Diffusion Equation ◽  
Sobolev Gradients ◽  
Sobolev Gradient

Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.

Finite element model to study the effect of exogenous buffer on calcium dynamics in dendritic spines

2014 ◽  
Vol 05 (02) ◽  
pp. 1350027 ◽  
Author(s):  
Amrita Jha ◽  
Neeru Adlakha
Keyword(s):  
Finite Element ◽  
Dendritic Spines ◽  
Element Model ◽  
Storage Site ◽  
Calcium Dynamics ◽  
Two Dimensional ◽  
Unsteady State ◽  
Triangular Elements ◽  
State Case ◽  
Single Synapse

Dendritic spine plays an important role in calcium regulation in a neuron cell. It serves as a storage site for synaptic strength and receives input from a single synapse of axon. In order to understand the calcium dynamics in a neuron cell, it is crucial to understand the calcium dynamics in dendritic spines. In this paper, an attempt has been made to study the calcium dynamics due to the exogenous buffers, in dendritic spines with the help of a sectional model. The compartments of dendritic spines are discretized using triangular elements. Appropriate boundary conditions have been framed. Finite element method has been employed to obtain the solution in the region for a two-dimensional unsteady state case. MATLAB 7.11 is used for simulation of the problem and numerical computations. The numerical results have been used to study the effect of exogenous buffers on calcium distribution in dendritic spines.

scholarly journals Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

Meccanica ◽  
2020 ◽  
Author(s):  
P. Pandey ◽  
S. Das ◽  
E-M. Craciun ◽  
T. Sadowski
Keyword(s):  
Diffusion Equation ◽  
Present Article ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Linear Algebraic Equations ◽  
Non Linear

AbstractIn the present article, an efficient operational matrix based on the famous Laguerre polynomials is applied for the numerical solution of two-dimensional non-linear time fractional order reaction–diffusion equation. An operational matrix is constructed for fractional order differentiation and this operational matrix converts our proposed model into a system of non-linear algebraic equations through collocation which can be solved by using the Newton Iteration method. Assuming the surface layers are thermodynamically variant under some specified conditions, many insights and properties are deduced e.g., nonlocal diffusion equations and mass conservation of the binary species which are relevant to many engineering and physical problems. The salient features of present manuscript are finding the convergence analysis of the proposed scheme and also the validation and the exhibitions of effectiveness of the method using the order of convergence through the error analysis between the numerical solutions applying the proposed method and the analytical results for two existing problems. The prominent feature of the present article is the graphical presentations of the effect of reaction term on the behavior of solute profile of the considered model for different particular cases.

Two-dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer

2014 ◽  
Vol 07 (03) ◽  
pp. 1450031 ◽  
Author(s):  
Brajesh Kumar Jha ◽  
Neeru Adlakha ◽  
M. N. Mehta
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Concentration Distribution ◽  
Calcium Concentration ◽  
Reaction Diffusion ◽  
Element Model ◽  
Cytosolic Calcium ◽  
Numerical Results ◽  
Two Dimensional ◽  
Diffusion Phenomena

In this paper a finite element model is developed to study cytosolic calcium concentration distribution in astrocytes for a two-dimensional steady-state case in presence of excess buffer. The mathematical model of calcium diffusion in astrocytes leads to a boundary value problem involving elliptical partial differential equation. The model consists of reaction–diffusion phenomena, association and dissociation rates and buffer. A point source of calcium is incorporated in the model. 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. The numerical results have been used to plot calcium concentration profiles in astrocytes. The effect of EGTA, BAPTA and σCa influx on calcium concentration distribution in astrocytes is studied with the help of numerical results.

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

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