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Discontinuity, Nonlinearity, and Complexity 2(4) (2013) 357--368 | DOI:10.5890/DNC.2013.11.005

Clara M. Ionescu; Dana Copot; Robin De Keyser

Department of Electrical energy, Systems and Automation, Gent University, Technologiepark 913, 9052 Gent, Belgium

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Abstract

This paper presents the initial steps towards the development of a compartmental model for drug diffusion in the human body, using fractional calculus. The model presented here preserves the mass balance, therefore it maintains the link between physiological and mathematical concepts. The final purpose of this model is to predict drug pharma-cokinetics and pharmacodynamics during general anesthesia. However, in this case the model is derived for a general class of drugs, therefore it can be employed in many biomedical applications.

Acknowledgments

Clara M. Ionescu is a post-doc fellow of the Research Foundation - Flanders (FWO). This research is supported by Flemish Research Foundation - Research Project FWOPR2013 005101.

References

1. [1]	Macheas, P. and Iliadis, A. (2006), A Modeling in Biopharmaceutics, Pharmacokinetics, and Phamacodynamics: Homogeneous and Heterogeneous Approaches, Springer Verlag, New York.

2. [2]	Trujillo, J.J. (2006), Fractional models: Sub and super-diffusives, and undifferentiable solutions, Innovation in Engineering Computational Technology, 371-401.

3. [3]	West, B.J. (1990), Fractal Physiology and Chaos in Medicine, Studies of Nonlinear Phenomena in Life Sciences, vol.1, World Scientific, Singapore.

4. [4]	Magin, R.L. (2006), Fractional Calculus in Bioengineering, Begell House Publishers, Redding, Connecticut.

5. [5]	Kilbas, A.A., Srivastava, H.M., and Trujillo, J.I. (2006), Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.

6. [6]	Gutierrez, E., Mauricio Rosario, J., and Machado, J.T. (2010), Fractional Order Calculus: Basic Concepts and Engineering Applications, Mathematical Problems in Engineering, doi:10.1155/2010/375858.

7. [7]	Losa, G.A., Merlini, D., Nonnenmacher, T.F., and Weibel, E.R. (2005), Fractals in Biology and Medicine, vol IV, Birkhaser, Berlin.

8. [8]	Oustaloup, A. (1995), La derivation non entiere, Hermes, Paris. (in French)

9. [9]	Podlubny, I. (1999), Fractional Differential Equations, Academic Press, San Diego.

10. [10]	Lundstrom, B., Higgs, M., Spain, W., and Fairhall, A. (2008), Fractional differentiation by neocortical pyramidal neurons, Nature Neuroscience,11, 1135-1342.

11. [11]	Teich, M. (1997), Fractal character of the auditory neural spike train, IEEE Transactions on Biomedical Engineering, 36, 150-160.

12. [12]	Lowen, S.B., Cash, S., Poo, M., and Teich, M. (1997), Quantal neurotransmitter secretion rate exhibits fractal behavior, Journal of Neuroscience, 17, 5666-5677.

13. [13]	Gilboa, G., Chen, R., and Brenner, N. (2005), History-dependent multiple-timescaledynamics in a single-neuron model, Journal of Neuroscience, 25 (28), 6479-6489.

14. [14]	Tal, D., Jacobson, E., Lyakov, V., and Marom, S. (2001), Frequency tuning of input-output relation in a rat cortical neuron in vitro, Neuroscience, 300, 21-24.

15. [15]	Ionescu, C.M. (2012), Phase constancy in a ladder model of neural dynamics, IEEE Transactions on Systems, Man and Cybernetics, part A: Systems and Humans, 42(6),.

16. [16]	Dokoumetzidis, A. and Macheras, P. (2009), Fractional kinetics in drug absorption and disposition processes, Journal of Pharmacokinetics and Pharmacodynamics, 36, 165-178.

17. [17]	Kytariolos, J., Dokoumetzidis, A., and Macheras, P.(2010), Power law IVIVC: an application of fractional kinetics for drug release and absorption, European Journal of Pharmaceutical Sciences ,41, 299-304.

18. [18]	Absalom, A.R., De Keyser, R., and Struys, M.M.R.F. (2004), Closed Loop Anesthesia: Are We Getting Close to Finding the Holy Grail? Anesthesia and Analgesia,112 (3), 364-381.

19. [19]	Steen-Knudsen,O. (2002), Biologicalmembranes. Theory of transport, potential and electric impulses, Cambridge University Press, Cambridge.

20. [20]	Popovic, J.K., Atanackovic, M.T., Pilipovic, A.S., Rapaic, M.R., Pilipovic, S., and Atanackovic, T.M. (2010), A new approach to the compartmental analysis in pharmacokinetics: fractional time evolution of diclofenac, J Pharmacokinet Pharmacodyn., 37, 119-134.

21. [21]	Hilfer, R. (2000), Fractional Calculus in Physics, World Scientific, Singapore.

22. [22]	Petras, I. and Magin, R.L. (2011), Simulation of drug uptake in a two compartmental fractional model for a biological system, Communications in Nonlinear Science and Numerical Simulation, 16, 4588-4595.

23. [23]	Mortier, E., Struys, M., De Smet, T., Versichelen, L., and Rolly, G. (1998), Closed-loop controlled administration of Propofol using bispectral analysis, Anaesthesia, 53, 749-754.

24. [24]	Schnider, T.W., Minto, C.F., Shafer, S.L., Gambus, P.L., Andresen, C., Goodale, D.B., and Youngs, E.J. (1999), The influence of age on Propofol pharmacodynamics, Anaesthesiology,90, 1502-1516.

25. [25]

    Coppens, M., Van Limmen, J.G.M., Schnider, T., Wyler, B., Bonte, S., Dewaele, F., Struys, M.M.R.F., Vereecke, H.E.M. (2010), Study of the time course of the clinical effect of propofol compared with the time course of the predicted effect-site concentration: performance of three pharmacokinetic-dynamic models, British Journal of Anaesthesia, 104(4), 452-458.

26. [26]	Marsh, B., White, M., Morton, N., and Kenny, G.N. (1991), Pharmacokinetic model driven infusion of Propofol in children, British Journal of Anaesthesia, 67, 41-48.