References
- A. Tripathi and N. Adlakha, Finite Volume Model to Study Calcium Diffusion in Neuron Cell under Excess Buffer Approximation, Int. J. of Math. Sci. and Engg. Appls. (IJMSEA) 5(III)(2011), 437-447.
- A. Tripathi and N. Adlakha, Finite Element Model to Study Calcium Diffusion in Neuron Cell in Presence of Excess Buffer for One Dimensional Steady State, Global Journal of Computational Science and Mathematics (GJCSM), I(1) (2011), 21-30.
- A. Tripathi and N. Adlakha, Two Dimensional Coaxial Circular Elements in Fem to Study Calcium Diffusion in Neuron Cells, Applied Mathematical Sciences, 6(10) (2012), 455-466.
- B. K. Jha, N. Adlakha, and M. N. Mehta, Finite element model to study calcium diffusion in astrocytes, Int. J. of Pure and Appl. Math. 78(7) (2012), 945-955.
-
B. K. Jha, N. Adlakha, and M. N. Mehta, Finite volume model to study the effect of buffer on cytosolic
$Ca^{2+}$ advection diffusion, Int. J. of Engg. and Nat. Sci. 4(3) (2010), 160-163. - C. P. Fall, Computational Cell Biology, Springer Verlag Berlin Heidelberg NewYork, (2002).
- D. Holcman and Z. Schuss, Modeling Calcium Dynamics in Dendritic Spines, SAIM J. of App Maths, (2005), 1-21.
- G. D. Smith, Miura and Sherman, Asymptotic analysis of buffered calcium diffusion near a Point Source, SIAM J. APPL. MATH. 61(5)(2001),1816-1838. https://doi.org/10.1137/S0036139900368996
- G. D. Smith, Modeling Intracellular Calcium diffusion, dynamics and domains, 10(2004), 339-371.
-
G. D. Smith, Analytical steady-state solution to the rapid buffering approximation near an open
$Ca^{2+}$ channel, Biophys J, 71(6)(1996), 30643072. -
G. D. Smith and J. Keizer, Spark- to-wave transition: salutatory transmission of
$Ca^{2+}$ waves in cadiac mayocytes, Biophys Chem, 72(1998), 87-100. https://doi.org/10.1016/S0301-4622(98)00125-2 - G. L. Fain, Molecular and Cellular Physiology of Neuron, Prentice- Hall of India (2005).
- J. Crank, The mathematics of diffusion, Oxford, U.K.: Clarendon Press (1975).
- J. Mean, G. D. Smith, Shephered, F. shaded, D. Smith, wilson, M. Wojcikiewicz, Reaction Diffusion Modeling of Calcium Dynamics with Realistic ER Geometry, Biophys J, 91(2006), 537-557. https://doi.org/10.1529/biophysj.105.075036
- M. Fill and J. A. Copello, Ryanodine Receptor Calcium Release Channels, Phyl. Rev. 82(2002) 893922.
- M. Kotwani, N. Adlakha, and M. N.Mehta, Numerical model to study calcium diffusion in fibroblasts cell for one dimensional unsteady state case, Appl. Mathematical Sci., 102(6)(2012), 5063 5072.
-
M. Naraghi and E. Neher, Concentration profiles of intracellular
$Ca^{2+}$ in the presence of diffusible chelator, Exp Brain Res, 14(1986), 8096. - N. Volfovsky, H. Parnas, M. Segal and E. Korkotian, Geometry of Dendritic Spines Affects Calcium Dynamics in Hippocampal Neurons, Theory and Experiments Journal of Neurophysiology 82 (1999), 450-462. https://doi.org/10.1152/jn.1999.82.1.450
-
R. Bertram, C. Rudy, Arceo, A Mathematical Study of the Differential Effects of Two SERCA Isoforms on
$Ca^{2+}$ Oscillations in Pancreatic Islets, Bulletin J. of Mathematical Biology, 70(2008) 1251-1271. https://doi.org/10.1007/s11538-008-9298-1 - S. S. Rao, The Finite Element Method in Engineering, Elsevier Science and Technology Books, (2004).
- S. Tewari and K. R. Pardasani, Finite Element Model to Study Two Dimensional Unsteady State Cytosolic Calcium Diffusion, J. Appl. Math. and Informatics 29(1-2)(2011), 427-442. https://doi.org/10.14317/JAMI.2011.29.1_2.427
-
S. Tewari and K. R. Pardasani,, Finite Difference Model to Study the effects of Na+ Influx on Cytosolic
$Ca^{2+}$ Diffusion,Int. J. of Bio. and Medical Sci. (2009), 205-209. - T. Meyer and L. Stryer, Molecular Model for Receptor- Stimulated Calcium 5. Spiking, PNAS, 85(14)(1988), 5051-5055. https://doi.org/10.1073/pnas.85.14.5051
- Y. Tang, T. Schlumpberger, T. Kim, M. Lueker, and R. S. Zucker, Effects of Mobile Buffers on Facilitation: Experimental and Computational Studies, Biophys. J., 78(2000), 27352751.
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