Document Type : Full Research Paper


1 Associate Professor, Department of Mechanical Engineering, Engineering Faculty, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 MS.D Student, Department of Mechanical Engineering, Engineering Faculty, Shahid Chamran University of Ahvaz, Ahvaz, Iran

3 Assistant Professor, Department of Mechanical Engineering, Engineering Faculty, Shahid Chamran University of Ahvaz, Ahvaz, Iran


A two-dimensional-in-space mathematical model of amperometric micro biosensors with selective and perforated membranes has been proposed and analyzed. The model involves the geometry of micro or nano meter holes partially or fully filled with an enzyme. The model is based on a system of the reaction-diffusion equations containing a nonlinear term related to the Michaelis-Menten enzymatic reaction. In this study, in order to generate general equation, first, dimensionless parameters are introduced and then by replacing them into governing equation are converted to dimensionless equations.The general equations have been solved numerically in 2D space.. Using numerical simulation of the biosensor action, the influence of the geometry of the holes as well as of the filling level of the enzyme in the holes on the biosensor response was investigated. For this purpose three different geometries including cylindrical, upright circular and downright circular cone for cavities are considered and the impact of these geometries on the response of the biosensor in different levels of enzyme are obtained. Biosensor's respond based on rate of enzyme level variations to slope of the cone variations are determined. In the biosensor, as the level of enzyme rises in all three geometries, the biosensor output current increases. Under the same conditions, the sensitivity of biosensor in upright circular cone is more than the other two geometries and increases with a decrease in conical gradient. As long as the enzymatic properties are the same, the more biosensor's number, the more sensitivity.Moreover, a concept known as reduced dimensionless current is introduced by providing and calculating dimensionless current in the biosensor.


Main Subjects

[1]     K. S. Hwang, S. M. Lee, S. K. Kim, J. H. Lee, T. S. Kim, Micro-and nanocantilever devices and systems for biomolecule detection, Annual Review of Analytical Chemistry, Vol. 2, No. 1, pp. 77-98, 2009.
[2]     A. Turner, I. Karube, G. S. Wilson, Biosensors: fundamentals and applications, pp. 456-487, NewYork: Oxford University Press, 1987.
[3]     F. W. Scheller, F. Schubert, Biosensors, Elsevier, Vol. 7, No 1–3, pp. 412-415, 1992.
[4]     K. R. Rogers, Biosensors for environmental applications, Biosensors and bioelectronics, Vol. 10, No. 6, pp. 533-541, 1995.
[5]     U. Wollenberger, F. Lisdat, F. W. Scheller, Frontiers in Biosensorics 2: Practical Applications, pp. 45-71, Basel, Birkhäuser, 1997.
[6]     H. K. Lee JH, Park J, Yoon KH, Yoon DS, Kim TS, Immunoassay of prostate-specific antigen (PSA) using resonant frequency shift of piezoelectric nanomechanical microcantilever, Biosens. Bioelectron, Vol. 20, No. 2005, pp. 2157–2162, 2005.
[7]     C. Dhand, M. Das, M. Datta, B. D. Malhotra, Recent advances in polyaniline based biosensors, Biosensors and Bioelectronics Vol. 26, No. 6, pp. 2811–2821, 2011.
[8]     M. R. Romero, M. Baruzzi, F. Garay, Mathematical modeling and experimental results of a sandwich-type amperometric biosensor, Sensors and
[9]     P. Kotzian, P. Brázdilová, K. Kalcher, K. Handlíř, K. Vytřas, Oxides of platinum metal group as potential catalysts in carbonaceous amperometric biosensors based on oxidases, Sensors and Actuators B: Chemical, Vol. 124, No. 2, pp. 297-302, 2007.
[10] G. Tsiafoulis, I. Prodromidis, I. Karayannis, Development of an amperometric biosensing method for the determination of l-fucose in pretreated urine, Biosensors and Bioelectronics, Vol. 20, No. 3,  pp. 620–627, 2004.
[11] A. A. Aziz, Mathematical modeling of an amperometric glucose sensor: the effect of membrane permeability and selectivity on performance, Jurnal teknologi, Vol. 51, No. 1, pp. 77–94, 2012.
[12] V. Rossokhaty, N. Rossokhata, Mathematical model of a biosensor with multilayer charged membrane, Computer physics communications, Vol. 147, No. 1, pp. 366-369, 2002.
[13] R. Baronas, J. Kulys, F. Ivanauskas, Computational modelling of biosensors with perforated and selective membranes, Journal of mathematical chemistry, Vol. 39, No. 2, pp. 345-362, 2006.
[14] L. Michaelis, M. L. Menten, Die kinetik der invertinwirkung, Biochem. z, Vol. 49, No. 3, pp. 333-369, 1913.
[15] F. W. Scheller, F. Schubert, Techniques and Instrumentation in Analytical Chemistry, Elsevier Science, Vol. 11, No. 260,pp. 412-465, 1992.
[16] E. Seibert, T. S. Tracy, Fundamentals of enzyme kinetics, Enzyme Kinetics in Drug Metabolism: Fundamentals and Applications, Volume 1113, No. 2, pp. 9-22, 2014.
[17] A. Cornish-Bowden, Fundamentals of enzyme kinetics, pp. 430-451, London:  Portland Press, 2013.
[18] R. Baronas, Numerical simulation of biochemical behaviour of biosensors with perforated membrane, Zelinka, Z. Oplatkova, A. Orsoni (Eds.), pp. 214-217, 2007.
[19] F. Heineken, H. Tsuchiya, R. Aris, On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics, Mathematical Biosciences, Vol. 1, No. 1, pp. 95-113, 1967.
[20] L. A. Segel, M. Slemrod, The quasi-steady-state assumption: a case study in perturbation, SIAM review, Vol. 31, No. 3, pp. 446-477, 1989.
[21] Q. Wang, Y. Liu, Mathematical Methods for Biosensor Models,  Thesis, PhD Thesis. Dublin Institute of Technology, Dublin, pp. 16-19, 2011.
[22] E. Gaidamauskaitė, R. Baronas, A Computational Investigation of the Optical Biosensor by a Dimensionless Model, Informacijos Mokslai/Information Sciences, Vol. 50, No. 1, pp. 306-310, 2009.
[23] D. Šimelevičius, R. Baronas, Computational modelling of amperometric biosensors in the case of substrate and product inhibition, Journal of mathematical chemistry, Vol. 47, No. 1, pp. 430-445, 2010.
[24] R. Baronas, R. Šimkus, Modeling the bacterial self-organization in a circular container along the contact line as detected by bioluminescence imaging, Nonlinear Analysis: Modeling and Control, Vol. 16, No. 3, pp. 270-282, 2011.
[25] R. Šimkus, R. Baronas, Ž. Ledas, A multi-cellular network of metabolically active E. coli as a weak gel of living Janus particles, Soft matter, Vol. 9, No. 17, pp. 4489-4500, 2013.
[26] Reddy, J.N., An introduction to the finite element method. Vol. 2. 1993: McGraw-Hill New York.