One Dimensional Numerical Study of Advection Diffusion of Calcium in a Hepatocyte Cell

Y.D. Jagtap¹ , N. Adlakha²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.311-316, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.311316

Online published on Feb 28, 2019

Copyright © Y.D. Jagtap, N. Adlakha . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In a human body, in almost all types of cells, the calcium plays a vital role in chemical signalling required for communication and maintenance of structure and functions of a cell. Almost all chemicals and proteins are produced in liver therefore, it is also known as body`s chemical factory. The calcium regulates all vital functions of a hepatocyte cell. The calcium concentration is tightly regulated by various processes like diffusion and advection in cytosol, binding with buffers etc. In this paper an unsteady state numerical approach is prefer to investigate the effect of advection and diffusion of calcium in a hepatocyte cell. The initial and boundary conditions are formulated according to physiology of a hepatocyte cell. The finite volume approach is used for simulation on MATLAB to obtain numerical results. The results are used to analyze the effect of advection, diffusion and buffer concentration on calcium profiles in a hepatocyte cell.

Key-Words / Index Term :
Calcium, Advection, Diffusion, Hepatocyte cell, Finite Volume Method

References :
[1] G .Dupont, S. Stephanne, C. Clair, T. Tordjmann, L. Combettes, “Hierarchical organization of calcium signals in hepatocytes: from experiments to models”, Biochimica et Biophysica Acta (BBA)-Molecular Cell Research, Vol. 1498, Issue.2, pp.134-152, 2000.
[2] I. Garcin, T. Tordjmann, “Calcium signalling and liver regeneration”, International journal of hepatology, Vol. 2012, pp.1-6, 2012.
[3] G.D. Smith, J. Wagner, J. Keizer, “Validity of the rapid buffering approximation near a point source of calcium ions”, Biophysical Journal, Vol. 70, Issue.6, pp.2527-2539, 1996.
[4] A Jha, N. Adlakha, “Analytical solution of two dimensional unsteady state problem of calcium diffusion in a neuron cell”, Journal of medical imaging and health informatics, Vol. 4, Issue.4, pp.547-553, 2014.
[5] S. Tewari, K.R. Pardasani, “Finite element model to study two dimensional unsteady state cytosolic calcium diffusion in presence of excess buffers, IAENG International Journal of Applied Mathematics”, Vol. 40, Issue.3, pp.108-112, 2010.
[6] B.K. Jha, N. Adlakha, M.N. Mehta, “Two-dimensional finite element model to study calcium distribution in astrocytes in presence of vgcc and excess buffer”, Int. J. Model. Simul. Sci. Comput, Vol. 4, Issue.2, pp.1250030, 2012.
[7] B.K. Jha, N. Adlakha, M.N. Mehta, “Two-dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer”, International Journal of Biomathematics, Vol. 7, Issue.3, pp.1450031, 2014.
[8] K . Pathak, N. Adlakha, “Finite element model to study two dimensional unsteady state calcium distribution in cardiac myocytes”, Alexandria Journal of Medicine, Vol. 52, Issue.3, pp.261-268, 2016.
[9] K. B. Pathak, N. Adlakha, “Finite Element Model to Study One Dimensional Calcium Dyanmics in Cardiac Myocytes”, Journal of Multiscale Modelling, Vol. 6, Issue.2, pp.1550003, 2015.
[10] M. Kotwani, N. Adlakha, “Modeling of endoplasmic reticulum and plasma membrane Ca 2+ uptake and release fluxes with excess buffer approximation (EBA) in fibroblast cell”, International Journal of Computational Materials Science and Engineering, Vol. 6, Issue.1, pp.1550004, 2017.
[11] M. Kotwani, N. Adlakha, M.N. Mehta, “Numerical model to study calcium diffusion in fibroblasts cell for one dimensional unsteady state case” , Applied Mathematical Sciences, Vol. 6, Issue.102, pp.5063-5072, 2012.
[12] Y. D. Jagtap, N. Adlakha, “Finite volume simulation of two dimensional calcium dynamics in a hepatocyte cell involving buffers and fluxes” Communications in Mathematical Biology and Neuroscience. Vol. 2018, pp.1-6, 2018.
[13] N. Manhas, K.R. Pardasani, “Mathematical model to study IP3 dynamics dependent calcium oscillations in pancreatic acinar cells”, Journal of Medical Imaging and Health Informatics, Vol. 4, Issue.6, pp.874-880, 2014.
[14] N. Manhas, K.R. Pardasani, “Modelling mechanism of calcium oscillations in pancreatic acinar cells”, Journal of bioenergetics and biomembranes, Vol. 46, Issue.5, pp.403-420, 2014.
[15] N. Manhas, K.R. Pardasani, J. Sneyd , “Modelling the transition from simple to complex Ca2+ oscillations in pancreatic acinar cells”, Journal of biosciences, Vol. 39, Issue.3, pp.463-484, 2014.
[16] P. A. Naik, K.R. Pardasani, “One Dimensional Finite Element Model to Study Calcium Distribution in Oocytes in Presence of VGCC, RyR and Buffers”, J. Medical Imaging Health Informatics, Vol. 5, Issue.3, pp.471-476, 2015.
[17] P. A. Naik, K.R. Pardasani, “One dimensional finite element method approach to study effect of ryanodine receptor and serca pump on calcium distribution in oocytes”, Journal of Multiscale Modelling, Vol. 5, Issue.2, pp.1350007, 2013.
[18] S. Panday, K.R. Pardasani, “Finite element model to study effect of advection diffusion and Na+/Ca2+ exchanger on Ca2+ distribution in Oocytes”, Journal of medical imaging and health informatics, Vol. 3, Issue.3, pp.374-379, 2013.
[19] S. Panday, K.R. Pardasani, “Finite element model to study the mechanics of calcium regulation in oocyte”, Journal of Mechanics in Medicine and Biology, Vol. 14, Issue.2, pp.145002223, 2014.
[20] A. P. Thomas, D. C. Renard, T. A. Rooney, “Spatial and temporal organization of calcium signalling in hepatocytes” Cell Calcium, Vol. 12, Issue. -2-3, pp.111-126, 1991.
[21] L. D. Gaspers, A. P. Thomas, “Calcium signaling in liver” Cell calcium, Vol. 38, Issue.3, pp.329-342, 2005.
[22] B. K. Jha, N. Adlakha, M. N. Mehta, “Finite Volume Model to Study The Effect of Voltage Gated Ca2+ Channel on Cytosolic Calcium Advection Diffusion” International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol. 8, Issue.8, pp.1379-1383, 2011.
[23] K. B. Pathak, N. Adlakha, “Finite Element Simulation of Advection Diffusion of Calcium in Myocyes Involving Influx and Excess Buffer” Advances in Computational Sciences and Technology, Vol. 10, Issue.1, pp.11-23, 2017.
[24] G. D. Smith, “Analytical steady-state solution to the rapid buffering approximation near an open Ca2+channel” Biophysical Journal, Vol.71, Issue.6, pp.3064-3072, 1996.
[25] C. Fall, “Computational cell biology”, Interdisciplinary Applied Mathematics: V. Springer-Verlag New York Incorporated, pp.173-176, 2002.
[26] J. Keener, J. Sneyd, “Mathematical physiology: I: cellular physiology”, Springer Science and Business Media. pp.283-312, 2010.
[27] H. K. Versteeg, W. Malalasekera, “An introduction to computationnal Fluid Dynamics, The finite volume method”, Longman, Londres, pp.243-266, 1995.