Back
 JAMP  Vol.5 No.5 , May 2017
Stochastic Modelling of Solution Particle Movement: An Individual Case of Coupled Concentration Gradient Dependent and Independent Movements of Efavirenz
Abstract: This work proposed a coupled model of diffusion. It adopted two forms of coupled movement, the interacting and non-interacting driven forms of movement of a solution particle of efavirenz concentration measured in blood plasma. Data from projected pharmacokinetics in a patient on efavirenz were used. A relationship between interacting and non-interacting diffusion was suggested through a stochastic differential equation. The solution particle with a small value of relative acceleration drift to its active neighbourhood was projected to have a corresponding high transport/interacting diffusion.
Cite this paper: Nemaura, T. (2017) Stochastic Modelling of Solution Particle Movement: An Individual Case of Coupled Concentration Gradient Dependent and Independent Movements of Efavirenz. Journal of Applied Mathematics and Physics, 5, 1027-1034. doi: 10.4236/jamp.2017.55090.
References

[1]   Philibert, J. (2005) One and a Half Century of Diffusion: Fick, Einstein, before and Beyond. Diffusion Fundamentals, 2, 1-10.

[2]   Fieldman, J. (2007) The Heat Equation (One Space Dimension).
http://www.math.ubc.ca/~feldman/m267/heat1d.pdf

[3]   Mehrer, H. and Stolwijk, N.A. (2009) Heroes and Highlights in the History of Diffusion. Diffusion Fundamentals, 11, 1-32.

[4]   Narasimhan, T.N. (1999) Fourier’s Heat Conduction Equation: History, Influence, and Connections. Reviews of Geophysics, 37, 151-172.
https://doi.org/10.1029/1998RG900006

[5]   Donnet, S. and Samson, A. (2013) A Review on Estimation of Stochastic Differential Equations for Pharmacokinetic/Pharmacodynamic Models. Advanced Drug Delivery Reviews, 65, 929-939.

[6]   Nemaura, T. (2016) The Advection Diffusion-in-Secondary Saturation Movement Equation and Its Application to Concentration Gradient-Driven Saturation Kinetic Flow. Journal of Applied Mathematics and Physics, 4, 1998-2010.
https://doi.org/10.4236/jamp.2016.411200

[7]   Silvester, D.J., Griffiths, D.F. and Dold, J.W. (2015) Essential Partial Differential Equations: Analytical and Computational Aspects. Springer Undergraduate Mathematics Series, Springer Verlag, Heidelberg.

[8]   Kärger, J. (2015) Transport Phenomena in Nanoporous Materials. ChemPhysChem, 16, 24-51.
https://doi.org/10.1002/cphc.201402340

[9]   Nemaura, T. (2015) Modeling Transportation of Efavirenz: Inference on Possibility of Mixed Modes of Transportation and Kinetic Solubility. Frontiers in Pharmacology, 6, 121.
https://doi.org/10.3389/fphar.2015.00121

[10]   Øksendal, B. (2003) Stochastic Differential Equations: An Introduction with Applications. 6th Edition, Springer, New York.
https://doi.org/10.1007/978-3-642-14394-6

[11]   Gonze, D. (2015) The Logistic Equation.
http://homepages.ulb.ac.be/dgonze/TEACHING/logistic.pdf

[12]   Nemaura, T. (2014) Projections of Pharmacokinetic Parameter Estimates from Middose Plasma Concentrations in Individuals on Efavirenz; A Novel Approach. African Journal of Pharmacy and Pharmacology, 8, 929-952.

 
 
Top