Journal of Mathematical Chemistry

, Volume 49, Issue 5, pp 995–1010 | Cite as

Modelling carbon nanotube based biosensor

  • Romas Baronas
  • Juozas Kulys
  • Karolis PetrauskasEmail author
  • Julija Razumiene
Original Paper


This paper presents a two-dimensional-in-space mathematical model of an amperometric biosensor based on an enzyme-loaded carbon nanotubes layer deposited on a perforated membrane. The developed model is based on non-linear non-stationary reaction-diffusion equations. By changing input parameters the output results are numerically analysed with a special emphasis to the influence of the geometry and the catalytic activity of the biosensor to its response. The numerical simulation at transition and steady state conditions was carried out using the finite difference technique. The mathematical model and the numerical solution were validated by experimental data. The obtained agreement between the simulation results and experimental data was admissible at different concentrations of the substrate and the mediator.


Modelling Simulation Reaction-diffusion Biosensor SWCNT 


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  1. 1.
    Scheller F., Schubert F.: Biosensors. Elsevier, Amsterdam (1992)Google Scholar
  2. 2.
    Turner A.P.F., Karube I., Wilson G.S.: Biosensors: Fundamentals and Applications. Oxford University Press, Oxford (1987)Google Scholar
  3. 3.
    Malhotra B.D., Chaubey A.: Sens. Actuators, B 91, 117 (2003)CrossRefGoogle Scholar
  4. 4.
    Wollenberger U., Lisdat F., Scheller F.W.: Frontiers in Biosensorics 2, Practical Applications. Birkhauser Verlag, Basel (1997)Google Scholar
  5. 5.
    Yu D., Blankert B., Virè J.-C., Kauffmann J.-M.: Anal. Lett. 38, 1687 (2005)CrossRefGoogle Scholar
  6. 6.
    Iijima S.: Nature 354, 56 (1991)CrossRefGoogle Scholar
  7. 7.
    Ahammad A.J.S., Lee J.-J., Rahman M.A.: Sensors 9, 2289 (2009)CrossRefGoogle Scholar
  8. 8.
    Balasubramanian K., Burghard M.: Anal. Bioanal. Chem. 385, 452 (2006)CrossRefGoogle Scholar
  9. 9.
    Huang Y., Sudibya H.G., Fu D., Xue R., Dong X., Li L.-J., Chen P.: Biosens. Bioelectron. 24, 2716 (2009)CrossRefGoogle Scholar
  10. 10.
    Jiang H.-J., Yang H., Akins D.: J. Electroanal. Chem. 623, 181 (2008)CrossRefGoogle Scholar
  11. 11.
    Wang S., Zhang Q., Wang R., Yoona S.: Biochem. Biophys. Res. Commun. 311, 572 (2003)CrossRefGoogle Scholar
  12. 12.
    J. Razumienė, J. Gurevičienė, J. Barkauskas, V. Bukauskas , A. Šetkus, in Biodevices 2009: Proceedings of the International Conference on Biomedical Electronics and Devices (2009), pp. 448–452Google Scholar
  13. 13.
    Amatore C., Oleinick A., Svir I., da Mota N., Thouin L.: Nonlinear Anal. Model. Contr. 11, 345 (2006)Google Scholar
  14. 14.
    Stamatin I., Berlic C., Vaseashta A.: Thin Solid Films 495, 312 (2006)CrossRefGoogle Scholar
  15. 15.
    Mell L.D., Maloy T.: Anal. Chem. 47, 299 (1975)CrossRefGoogle Scholar
  16. 16.
    Kulys J.: Anal. Lett. 14, 377 (1981)Google Scholar
  17. 17.
    Bartlett P.N., Whitaker R.G.: J. Electroanal. Chem. 224, 27 (1987)CrossRefGoogle Scholar
  18. 18.
    Schulmeister T.: Sel. Elect. Rev. 12, 203 (1990)Google Scholar
  19. 19.
    Baronas R., Ivanauskas F., Kulys J.: Mathematical Modeling of Biosensors, Springer Series on Chemical Sensors and Biosensors, vol. 9. Springer, Berlin (2010)Google Scholar
  20. 20.
    Lyons M.E.G.: Int. J. Electrochem. Sci. 4, 77 (2009)Google Scholar
  21. 21.
    Lyons M.E.G.: Int. J. Electrochem. Sci. 4, 1196 (2009)Google Scholar
  22. 22.
    Baronas R., Kulys J., Ivanauskas F.: J. Math. Chem. 39, 345 (2006)CrossRefGoogle Scholar
  23. 23.
    Britz D.: Digital Simulation in Electrochemistry, Lecture Notes in Physics, vol. 666, 3rd edn. Springer, Heidelberg (2005)Google Scholar
  24. 24.
    Samarskii A.A.: The Theory of Difference Schemes. Marcel Dekker, New York-Basel (2001)CrossRefGoogle Scholar
  25. 25.
    Deslous C., Gabrielli C., Keddam M., Khalil A., Rosset R., Trobollet B., Zidoune M.: Electrochim. Acta 42, 1219 (1997)CrossRefGoogle Scholar
  26. 26.
    Baronas R., Ivanauskas F., Survila A.: J. Math. Chem. 27, 267 (2000)CrossRefGoogle Scholar
  27. 27.
    Levich V.: Physicochemical Hydrodynamics. Prentice Hall, Englewood Cliffs (1962)Google Scholar
  28. 28.
    Gooding J.J., Chou A., Liu J., Losic D., Shapter J.G., Hibbert D.B.: Electrochem. Commun. 9, 1677 (2007)CrossRefGoogle Scholar
  29. 29.
    Whitaker S.: The Method of Volume Averaging, Theory and Applications of Transport in Porous Media, vol. 13. Kluwer, Boston (1999)Google Scholar
  30. 30.
    Bakhvalov N., Panasenko G.: Homogenisation: Averaging Processes in Periodic Media, Mathematics and its Applications, vol. 36. Kluwer, Dordrecht (1989)Google Scholar
  31. 31.
    Bertram R., Pernarowski M.: Biophys. J. 74, 1722 (1998)CrossRefGoogle Scholar
  32. 32.
    Yankov D.: Enzyme Microb. Technol. 34, 603 (2004)CrossRefGoogle Scholar
  33. 33.
    Mu M., Clarke N., Composto R.J., Winey K.I.: Macromolecules 42, 7091 (2009)CrossRefGoogle Scholar
  34. 34.
    Lyons M.E.G., Bannon T., Hinds G., Rebouillat S.: Analyst 123, 1947 (1998)CrossRefGoogle Scholar
  35. 35.
    Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P.: Numerical Recipes in C++: The Art of Scientific Computing, 2nd edn. Cambridge University Press, New York (2002)Google Scholar
  36. 36.
    Lide, D.R. (ed): CRC Handbook of Chemistry and Physics, 85th edn. CRC Press, New York (2004)Google Scholar
  37. 37.
    Petrauskas K., Baronas R.: Nonlinear Anal. Model. Contr. 14, 85 (2009)Google Scholar
  38. 38.
    Baronas R., Ivanauskas F., Kulys J.: Sensors 3, 248 (2003)CrossRefGoogle Scholar
  39. 39.
    Baronas R., Ivanauskas F., Kaunietis I., Laurinavicius V.: Sensors 6, 727 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Romas Baronas
    • 1
  • Juozas Kulys
    • 2
  • Karolis Petrauskas
    • 1
    Email author
  • Julija Razumiene
    • 3
  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Department of Chemistry and BioengineeringVilnius Gediminas Technical UniversityVilniusLithuania
  3. 3.Department of Bioanalysis, Institute of BiochemistryVilnius UniversityVilniusLithuania

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