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graph between calcium concentration and distance in x and y direction. u = 0.1μm/s , v = 10μm/s Dx=20 and Dy-250 is taken
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Mathematical and computational modeling of calcium signalling in astrocytes has produced considerable insights into how the astrocytes contracts with other cells under the variation of biophysical and physio-logical parameters. The modeling of calcium signaling in astrocytes has become more sophisticated. The modeling effort has provided insight to...
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... calcium concentration is decreasing uniformly in both direction x and y form its initial value .35μM . Figure 3 Shows calcium concentration is decreasing as y increasing when x is constant for any time t > 0 and it is observed that calcium concentration is linearly decreasing as y increasing for t > 0. Figure 4 represents the calcium concentration is decreasing when x in- creasing for some fix value of y for t > 0 . It is observed that when the value of x approaches to .50μm the calcium concentration decreasing and then it be- comes at steady state when x > 50μm which is obvious in physical phenomena in calcium signalling in cytosol. ...
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... The control of the cells' impact and functions depends significantly on calcium signaling. The calcium advection analytical solution in astrocytes and nerve cells has been solved by [27][28][29][30]. A different mathematical model is developed to get further knowledge on calcium signaling in alpha cells, Cholangiocyte cells, Oocyte cells, Hepatocyte cells, etc. [16,17,[31][32][33][34][35]. ...
Free Calcium ions in the cytosol are essential for many physiological and physical functions. The free calcium ions are commonly regarded as a second messenger, are an essential part of brain communication. Numerous physiological activities, such as calcium buffering and calcium ion channel flow, etc. influence the cytosolic calcium concentration. In light of the above, the primary goal of this study is to develop a model of calcium distribution in neuron cells when a Voltage-Gated Calcium Channel and Sodium Calcium Exchanger are present. As we know, decreased buffer levels and increased calcium activity in the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger lead to Alzheimer’s disease. Due to these changes, the calcium diffusion in that location becomes disrupted and impacted by Alzheimer’s disease. The model has been constructed by considering key factors like buffers and ER fluxes when Voltage-Gated Calcium Channels and Sodium Calcium Exchangers are present. Based on the physiological conditions of the parameters, appropriate boundary conditions have been constructed in the fuzzy environment. This model is considered a fuzzy boundary value problem with the source term and initial boundary conditions are modeled by triangular fuzzy functions. In this, paper we observed the approximate solution of the mathematical model which was investigated by the fuzzy undetermined coefficient method. The solution has been performed through MATLAB and numerical results have been computed using simulation. The observation made that the proper operation of the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger is critical for maintaining the delicate equilibrium of calcium ions, which regulates vital cellular activities. Dysregulation of Voltage-Gated Calcium Channel and Sodium Calcium Exchanger activity has been linked to neurodegenerative illnesses like Alzheimer’s disease.
... The control of the cells' impact and functions depends significantly on calcium signaling. The calcium advection analytical solution in astrocytes and nerve cells has been solved by [14][15][16][17]. A different mathematical model is developed to get further knowledge on calcium signaling in alpha cells, Cholangiocyte cells, Oocyte cells, Hepatocyte cells, etc. [18][19][20][21]. ...
Free Calcium ions in the cytosol are essential for many physiological and physical functions. The free calcium ions are commonly regarded as a second messenger, are an essential part of brain communication. Numerous physiological activities, such as calcium buffering and calcium ion channel flow, etc. influence the cytosolic calcium concentration. In light of the above, the primary goal of this study is to develop a model of calcium distribution in neuron cells when a Voltage-Gated Calcium Channel and Sodium Calcium Exchanger are present. As we know, decreased buffer levels and increased calcium activity in the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger lead to Alzheimer’s disease. Due to these changes, the calcium diffusion in that location becomes disrupted and impacted by Alzheimer’s disease. The model has been constructed by considering key factors like buffers and ER fluxes when Voltage-Gated Calcium Channels and Sodium Calcium Exchangers are present. Based on the physiological circumstances of the parameters, appropriate boundary conditions have been constructed in the fuzzy environment. This model is considered a fuzzy boundary value problem with the source term and initial boundary conditions are modeled by triangular fuzzy functions. In this, paper we observed the approximate solution of the mathematical model which was investigated by the fuzzy undetermined coefficient method. The solution has been performed through MATLAB and numerical results have been computed using simulation. The observation made that the proper operation of the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger is critical for maintaining the delicate equilibrium of calcium ions, which regulates vital cellular activities. Dysregulation of Voltage-Gated Calcium Channel and Sodium Calcium Exchanger activity has been linked to neurodegenerative illnesses like Alzheimer’s disease.
... The authors of [14] examined the analytic solution of ADE. The analytical solution of 2-D ADEs occurring in the distribution of cytosolic calcium concentration was investigated in [15]. In [16], the author obtained semi analytic solution of ADE for modelling solute transport in layered porous media using LT. ...
... A mathematical model is developed in the form of two dimensional advection diffusion equation for calcium profile and solved analytically by B. K. Jha et al. [7]. A. Fedi et al. [8] analytically solved two dimensional advection diffusion equation in porous media where a laterally bounded domain is considered. ...
... Zoppou and Knight [15] investigated the analytic solution of an ADE with variable coefficients. In [16], the analytic solution of 2D ADE, arising in cytosolic calcium concentration distribution, was examined. Further information on other analytic methods for ADEs can be found in [17][18][19] and the references therein. ...
Partial differential equations arising in engineering and other sciences describe nature adequately in terms of symmetry properties. This article develops a numerical method based on the Laplace transform and the numerical inverse Laplace transform for numerical modeling of diffusion problems. This method transforms the time-dependent problem to a corresponding time-independent inhomogeneous problem by employing the Laplace transform. Then a local radial basis functions method is employed to solve the transformed problem in the Laplace domain. The main feature of the local radial basis functions method is the collocation on overlapping sub-domains of influence instead of on the whole domain, which reduces the size of the collocation matrix; hence, the problem of ill-conditioning in global radial basis functions is resolved. The Laplace transform is used in comparison with a finite difference technique to deal with the time derivative and avoid the effect of the time step on numerical stability and accuracy. However, using the Laplace transform sometimes leads to a solution in the Laplace domain that cannot be converted back into the real domain by analytic methods. Therefore, in such a case, the Laplace transform is inverted numerically. In this investigation, two inversion techniques are utilized; (i) the contour integration method, and (ii) the Stehfest method. Three test problems are used to evaluate the proposed numerical method. The numerical results demonstrate that the proposed method is computationally efficient and highly accurate.
... [1], [2]), to two dimensions, 2D, (e.g. [3], [4], [5], [6], [7], [8]) to three dimensions, 3D, (e.g. [9], [10], [11], [12], [13], [14], [15]). ...
... They validated both of the hydrodynamic and transport models with experimental data. Jha, B.K et al studied the calcium profile in the form of 2D advection diffusion equation [5]. A mathematical model is developed that incorporates the important physiological parameters like the diffusion coefficient. ...
Abstract:
A three dimensional unsteady finite element environmental model, SUITE-3D (Solving Unsteady Incompressible Transport Equation in Three Dimensions, 3D), is developed to solve the advection-diffusion transport equation with decay and source terms. Since there is no general analytical solution to the full advection-diffusion transport equation under all possible boundary conditions and under the different equation parameters, an additional model such as SUITE-3D will aid in giving more insights into the phenomenon of advection-diffusion and pollutant transport. It is important to investigate air pollution modelling in the era of climate change and global warming, that our planet earth is facing nowadays. SUITE-3D uses the standard Galerkin’s method without upwinding. Difference schemes are used (central, backward, forward) for the time integration. The finite elements are 8-node cubic brick elements (hexahedrons). Eight Gaussian quadrature points are used for the numerical integration of the element matrices. SUITE-3D is validated against exact solutions of two problems; one has only advection and diffusion terms while the other has advection-diffusion-decay-source terms. The total percentage relative error for the first case was less than 0.61% while it reached 1.0% in the second case. The model is applied to study air pollution dispersion due to a point source pollutant. It is noted that neglecting the x-diffusion term in the Gaussian plume model under calm wind conditions (velocity = 0.2 m/s) results in under-prediction of concentration by 81% at 180 m downstream of the pollutant source. This proves that Gaussian models such as AERMOD provide poor results in situations with low wind speeds, where the three-dimensional diffusion is significant.
Keywords: Three dimensional (3D); Environmental flows, unsteady; advection-diffusion-decay-source; Finite Element Method; Air pollution modeling; Gaussian plume models, AERMOD model
... Analytical, traditional finite element method and various numerical methods have been extensively used by the researchers in past to obtain the approximate solution. Jha et al. (2012) have found the analytical solution of calcium advection diffusion in astrocytes, whereas, have found the significance of excess buffering phenomenon on calcium concentration level using Laplace and Fourier transforms. Dave and Jha have analytically found the solution to calcium advection reaction diffusion in presence of several parameters like buffers, VGCC and ER, taking place in normal and Alzheimer's affected neuron cells Jha 2018a, b, 2020). ...
The present paper discusses the estimation of calcium ions in presence of calcium binding buffer, voltage-gated calcium channel (VGCC) and sodium calcium exchanger (NCX) for normal and Alzheimer’s affected neuronal cells. In Alzheimer’s disease (AD), amount of buffer decreases whereas the calcium activities increase in VGCC and NCX. Due to these alterations, the normal calcium diffusion in that area gets disturbed and gets affected by AD. The governing equation of this physiological phenomena is in the form of calcium diffusion equation which is solved along with initial and boundary conditions. The approximate solution to this problem has been obtained using finite element technique in MATLAB. The significance of buffers at cytosolic level has been shown using single and multiple buffering phenomena. Moreover, to check the influence of fluxes mediated by VGCC and NCX at cytosolic level, for normal and Alzheimer’s affected cells, the single and multiple fluxes are assumed and the results are obtained. The obtained results clearly show the significance of the assumed parameters on calcium concentration at the cytosolic level. The hike in the calcium concentration due to decrease in buffer and increase in VGCC and NCX mediated fluxes may lead to neurodegenerativity of AD. This study may help the theoretical scientists in knowing the role of calciumopathy in AD.
... Much information has not been found for the Alzheimer's disease and less computational work has been done to understand the impact of variations in parameters on calcium concentration in Alzheimeric condition. Jha et al., in 2012, found the analytical solution to two-dimensional calcium diffusion problem using Laplace technique (Jha et al. 2012). Moreover, Dave and Jha have adopted analytic approach to delineate calcium concentration distribution. ...
... Much information has not been found for the Alzheimer's disease and less computational work has been done to understand the impact of variations in parameters on calcium concentration in Alzheimeric condition. Jha et al., in 2012, found the analytical solution to two-dimensional calcium diffusion problem using Laplace technique (Jha et al. 2012). Moreover, Dave and Jha have adopted analytic approach to delineate calcium concentration distribution. ...
... The trend of the calcium profile obtained in this article for normal cell matches well with the results obtained by Smith. Also, Jha and Adlakha have used similarity and Laplace transforms for simple two-dimensional calcium reaction-advection-diffusion phenomenon (Jha et al. 2012). ...
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.
... Experiments are limited by protocol and therefore computational studies, across different spatial and temporal scales, are a significant and indispensable tool. Various attempts for the study of calcium regulation in other cells [6,7,8,9,10,11,12,13,14] are reported in the literature. Pathak et al. [15] have developed mathematical models to understand independent Ca 2+ signaling process in cardiac myocyte. ...
Calcium governs the most versatile and universal signaling mechanism in living systems which includes contraction of the cardiac tissues, information processing in the brain, release of digestive enzymes by the liver etc. High blood calcium leads to various diseases and problems like chronic fatigue and tiredness, poor memory, atherosclerosis, muscle aches and cramps, bone pain, poor sex drive, osteoporosis and broken bones, kidney stones and heart rhythm problems such as atrial fibrillation. Various investigators have been made on study of calcium signaling in cardiac myocyte to understand its mechanisms. But most of existing investigators have mainly focused on study of calcium signaling in cardiac myocyte without paying attention on interdependence of calcium signaling and inositol−1; 4; 5 trisphosphate (IP 3) signaling. In the present work, we have studied a mathematical model to understand the impact of source influx of calcium and maximum rate of production of IP 3 on these coupled signaling processes. This study suggests that maximum rate of production of IP 3 plays a more significant role in these coupled dynamics. Also, calcium and IP 3 shows a beautiful coordination with each other, which explains the role of IP 3 in calcium signaling in cardiac myocyte. Such studies will provide the better understanding of various factors involved in calcium signaling in cardiac myocyte, which as a result will be of great use to biomedical scientists for making protocols for various heart diseases.
... On the other hand, one of the mechanisms of the killing of the cancerous cell is through elevation of intracellular calcium level (Wang et al. 2012). Various attempts for the study of calcium regulation in various cells such as neuron Adlakha 18 Page 2 of 15 2014a, b, 2015;Jha et al. 2016;Tewari andPardasani 2008, 2010;Tripathi and Adlakha 2011), astrocyte (Jha et al. 2011(Jha et al. , 2012(Jha et al. , 2013, fibroblast (Kotwani and Adlakha 2017;Kotwani et al. 2012Kotwani et al. , 2014, oocyte Pardasani 2015, 2018;Pardasani 2013, 2014) and pancreatic acinar cell (Manhas and Pardasani 2014a, b;) are reported in the literature and some attempts are reported in the literature for the study of calcium dynamics in myocytes (Luo and Rudy 1994a, b;Michailova et al. 2002;Shannon et al. 2004;Smith et al. 1998). It is found that various parameters such as source, pump, Leak, and inositol 1,4,5-trisphosphate ( IP 3 ) play an important role in this Ca 2+ regulation within the cell which is essential for Ca 2+ signaling and other activities of the cell. ...
Calcium Ca2+ signaling is the secondary signaling processes which have been one of the most vital intracellular signaling mechanisms. Over recent decades, this signaling process has been studied a lot in various cells to understand its mechanisms and also cure of various health hazards. In this paper, an attempt has been made to propose a model for coupled dynamics of Ca2+ and inositol 1,4,5-trisphosphate IP3 in cardiac myocyte for a better understanding of the dependence of Ca2+ signaling on other chemical ions such as \IP3 ions. The parameters such as influx, outflux, diffusion coefficient, SERCA pump, and Leak have been incorporated into the model and the finite differences scheme has been employed for the solution of the problem. The numerical results have been used to study the interdependence of Ca2+ and IP3 in the cardiac myocyte. It is observed that this interdependence is quite significantly affected by all these parameters except Leak. Also, the relationship between Ca2+ and IP3 dynamics is found to be non-linear. Such realistic models can be useful to generate the information of these dynamics in cardiac cells which can be useful for developing protocols for diagnosis and treatment of heart diseases like abnormal calcium signaling due to mutation of calsequestrin which results in sudden cardiac death and cardiomyopathy that affects the squeezing of the heart muscle.
This article is available at : https://rdcu.be/bLwCn
