Abstract
Usually, when modeling a biosensor as a flat electrode having one or several layers sandwich-likely applied onto the electrode surface, a mathematical model of the biosensor is formulated in a one-dimensional-in-space domain. This chapter deals with the modeling of biosensors for which two-dimensional-in-space domains are used when describing mathematically the biosensor action.
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References
Amatore C, Oleinick AI, Svir I (2006) Construction of optimal quasi-conformal mappings for the 2d-numerical simulation of diffusion at microelectrodes. Part 1: Principle of the method and its application to the inlaid disk microelectrode. J Electroanal Chem 597:69
Amine A, Kauffmann JM, Patriarche GJ (1991) Long-term operational stability of a mixed glucose oxidase-redox mediator-carbon paste electrode. Anal Lett 24:1293
Antiochia R, Lavagnini I, Magno F (2004) Amperometric mediated carbon nanotube paste biosensor for fructose determination. Anal Let 37:1657
Bacon NC, Hall EAH (1999) A sandwich enzyme electrode giving electrochemical scavenging of interferents. Electroanal 11:749
Bakhvalov NS, Panasenko GP (1989) Homogenization: averaging processes in periodic media. Kluwer, Dordrecht
Barnaby W (1997) Biological weapons: an increasing threat. Med Confl Surviv 13:301
Baronas R, Ivanauskas F, Kulys J (1998) Modeling of a microreactor on heterogeneous surface and an influence of geometry to microreactor operation. Nonlinear Anal Model Contr 3:19
Baronas R, Ivanauskas F, Survila A (2000) Simulation of electrochemical behavior of partially blocked electrodes under linear potential sweep conditions. J Math Chem 27:267
Baronas R, Ivanauskas F, Kulys J (2003) Computer simulation of the response of amperometric biosensors in stirred and non stirred solution. Nonlinear Anal Model Contr 8:3
Baronas R, Ivanauskas F, Kulys J, Sapagovas M (2003) Modeling of amperometric biosensors with rough surface of the enzyme membrane. J Math Chem 34:227
Baronas R, Ivanauskas F, Kulys J, Sapagovas M (2004) Computational modeling of a sensor based on an array of enzyme microreactors. Nonlinear Anal Model Contr 9:203
Baronas R, Ivanauskas F, Kulys J (2005) Modelling biosensors with perforated membrane. Lith Math J 45(spec issue):449
Baronas R, Kulys J, Ivanauskas F (2006) Computational modeling of biosensors with perforated and selective membranes. J Math Chem 39:345
Baronas R, Ivanauskas F, Kulys J (2006) Mathematical modeling of biosensors based on an array of enzyme microreactors. Sensors 6:453
Baronas R, Ivanauskas F, Kaunietis I, Laurinavicius V (2006) Mathematical modeling of plate-gap biosensors with an outer porous membrane. Sensors 6:727
Bertram R, Pernarowski M (1998) Glucose diffusion in pancreatic islets of Langerhans. Biophys J 74:1722
Bieniasz LK, Britz D (2004) Recent developments in digital simulation of electroanalytical experiments. Polish J Chem 78:1195
Bindra DS, Zhang Y, Wilson GS et al (1991) Design and in vitro studies of a needle-type glucose sensor for subcutaneous monitoring. Anal Chem 63:1692
Boujtita E, el Murr N (2006) Biosensors for analysis of ethanol in food. J Food Sci 60:201
Britz D (2005) Digital simulation in electrochemistry, 3rd edn. Springer, Berlin
Buerk DG (1995) Biosensors: theory and applications. CRC Press, Lancaster
Crank J (1975) The mathematics of diffusion, 2nd edn. Clarendon, Oxford
Devlin JP (ed) (1997) High throughput screening. Marcel Dekker, New York
Dirks JL (1996) Diagnostic blood analysis using point-of-care technology. AACN Clin Issues 7:249
Dormieux L, Lemarchand E (2001) Homogenization approach of advection and diffusion in cracked porous material. J Eng Mech ASCE 127:1267
Eggins BR (2002) Chemical sensors and biosensors. Analytical techniques in the sciences. Wiley, Chichester
Ehrfeld W, Hessel V, Lwe H (2000) Microreactors: new technology for modern chemistry. Wiley-VCH, New York
Forrow NJ, Bayliff SW (2005) A commercial whole blood glucose biosensor with a low sensitivity to hematocrit based on an impregnated porous carbon electrode. Biosens Bioelectron 21:3581
Garboczi EJ (1990) Permeability, diffusivity and microstructural parameters: a critical review. Cem Concr Res 20:591
Gorton L (1995) Carbon paste electrodes modified with enzymes, tissues, and cells. Electroanal 7:23
Guilbault GG (1970) Enzymatic methods of analysis. Pergamon, Oxford
Ivanauskas F, Kaunietis I, Laurinavicius V et al (2008) Apparent Michaelis constant of the enzyme modified porous electrode. J Math Chem 43:1516
Kulys J, Razumas V (1986) Bioamperometry. Mokslas, Vilnius (in Lithuanian)
Kulys J (1999) The carbon paste electrode encrusted with a microreactor as glucose biosensor. Biosens Bioelectron 14:473
Laurinavicius VA, Kulys JJ, Gureviciene VV, Simonavicius KJ (1989) Flow through and cateter biosensors with an extended concentration range. Biomed Biochem Acta 48:905
Laurinavicius V, Razumiene J, Kurtinaitiene B et al (2002) Bioelectrochemical application of some PQQ-dependent enzymes. Bioelectrochem 55:29
Luckarift HR (2008) Silica-immobilized enzyme reactors. J Liq Chromatogr R T 31:1568
Moreira JE, Midkiff SP, Gupta M et al (2000) Java programming for high performance numerical computing. IBM Systems J 39:21
Popovtzer R, Neufeld T, Ron EZ et al (2006) Electrochemical detection of biological reactions using a novel nano-bio-chip array. Sensor Actuat B-Chem 119:664
Samarskii AA (2001) The theory of difference schemes. Marcel Dekker, New York-Basel
Schulmeister T (1990) Mathematical modeling of the dynamic behavior of amperometric enzyme electrodes. Selective Electrode Rev 12:203
Schulmeister T, Pfeiffer D (1993) Mathematical modelling of amperometric enzyme electrodes with perforated membranes. Biosens Bioelectron 8:75
Smith JM, Szathmary E (1996) On the likelihood of habitable worlds. Nature 384:107
Suzuki H (2000) Advances in the microfabrication of electrochemical sensors and systems. Electroanal 12:703
Ivanauskas F, Kaunietis I, Laurinavicius V et al (2005) Computer simulation of the steady state currents at enzyme doped carbon paste electrode. J Math Chem 38:355
Briggs GE, Haldane JBS (1925) A note on the kinetics of enzyme action. Biochem J 19:338
Ikeda T (1995) Enzyme-modified electrodes with bioelectrocatalytic function. Bunsuki Kagaku 44:333
Matuszewski W, Trojanowicz M (1988) Graphite paste-based enzymatic glucose electrode for flow-injection analysis. Analyst 113:735
Mulchandani A, Rogers K (eds) (1998) Enzyme & microbial biosensors: techniques and protocols. Methods in biotechnology. Humana Press, Totowa, New Jersey
Wang J, Liu J, Cepra G (1997) Thermal stabilization of enzymes immobilized within carbon paste electrodes. Anal Chem 69:3124
Mello LD, Kubota LT (2002) Review of the use of biosensors as analytical tools in the food and drink industries. Food Chem 77:237
Wanekaya AK, Chen W, Mulchandani A (2008) Recent biosensing developments in environmental security. J Environ Monitor 10:703
Amine A, Kauffmann JM, Guilbault GG (1993) Characterization of mixed enzyme-mediator-carbon paste electrodes. Anal Lett 26:1281
Hale PD, Lan HL, Boguslavsky LI et al (1991) Amperometric glucose sensors based on ferrocene-modified poly(ethylene oxide) and glucose oxidase. Anal Chim Acta 251:121
Kulys J, Hansen HE, Buch-Rasmussen T et al (1994) Glucose biosensor based on the incorporation of Meldola blue and glucose oxidase within carbon paste. Anal Chim Acta 288:193
Kulys J, Hansen HE (1994) Carbon-paste biosensors array for long-term glucose measurement. Biosen Bioelectr 9:491
Kulys J, Hansen HE (1995) Long-term response of an integrated carbon paste based glucose biosensor. Anal Chim Acta 303:285
Lawrence NS, Deo RP, Wang J (2004) Biocatalytic carbon paste sensors based on a mediator pasting liquid. Anal Chem 77:3735
Liang JF, Li YT, Yang VC (2000) Biomedical application of immobilized enzymes. J Pharm Sci 89:979
Miscoria SA, Barrera GD, Rivas GA (2005) Enzymatic biosensor based on carbon paste electrodes modified with gold nanoparticles and polyphenol oxidase. Electroanal 17:1578
Mizutani F, Yabuki S, Okuda A, Katsura T (1991) Glucose-sensing electrode based on carbon paste containing ferrocene and polyethylene glycol-modified enzyme. Bull Chem Soc Jpn 64:2849
Mizutani F (1999) Application of enzyme-modified electrodes to biosensors. Bunseki Kagaku 48:809
Pandey PC, Kayastha AM, Pandey V (1992) Amperometric enzyme sensor for glucose based on graphite paste-modified electrodes. Appl Bioch Biotech 33:139
Sakura S, Buck RP (1992) Amperometric processes with glucose oxidase embedded in the electrode. Bioelect Bioenerg 28:387
Schachl K, Turkušić E, Komersová A et al (2002) Amperometric determination of glucose with a carbon paste biosensor. Collect Czech Chem Commun 67:302
Wang J (2001) Glucose biosensors: 40 years of advances and challenges. Electroanal 13:983
Wu BL, Zhang GM, Zhang Y, Shuang SM, Choi MMF (2005) Measurement of glucose concentrations in human plasma using a glucose biosensor. Anal Biochem 340:181
Suzuki H, Arakawa H, Karube I (2001) Fabrication of a sensing module using micromachined biosensors. Biosens Bioelectron 16:725
Manz A, Graber N, Widmer HM (1990) Miniaturized total chemical analysis systems: a novel concept for chemical sensing. Sensor Actuat B-Chem 1:244
Reyes DR, Iossifidis D, Auroux PA, Manz A (2002) Micro total analysis systems. 1. Introduction, theory, and technology. Anal Chem 74:2623
Urban PL, Goodall DM, Bruce NC (2001) Biosensor microsystems. Sens Update 8:189
Urban PL, Goodall DM, Bruce NC (2006) Enzymatic microreactors in chemical analysis and kinetic studies. Biotechnol Adv 24:42
Vojinovic V, Esteves FMF, Cabral JMS, Fonseca LP (2006) Bienzymatic analytical microreactors for glucose, lactate, ethanol, galactose and l-amino acid monitoring in cell culture media. Anal Chim Acta 565:240
Zhang Q, Xu JJ, Chen HY (2006) Glucose microfluidic biosensors based on immobilizing glucose oxidase in poly(dimethylsiloxane) electrophoretic microchips. J Chromatogr A 1135:122
Whitaker S (1999) The method of volume averaging. Kluwer, Boston
Hobbs DW (1999) Aggregate influence on chloride ion diffusion into concrete. Cem Concr Res 29:1995
Kalnin JR, Kotomin EA, Maier J (2002) Calculations of the effective diffusion coefficient for inhomogeneous media. J Phys Chem Solids 63:449
Xi Y, Bazant ZP (1999) Modeling chloride penetration in saturated concrete. J Mater Civil Eng 11:58
Baronas V, Ivanauskas F, Kulys J (1999) Modeling a biosensor based on the heterogeneous microreactor. J Math Chem 25:245
Lide DR (ed) (2007-2008) Handbook of chemistry and physics, 88th edn. CRC Press, Boca Raton
Weibel MK, Bright HJ (1971) The glucose oxidase mechanism. J Biol Chem 246:2734
Zhu ZQ, Zhang J, Zhu JZ (2005) An overview of Si-based biosensors. Sensor Lett 3:71
Deslous C, Gabrielli C, Keddam M et al (1997) Impedance techniques at partially blocked electrodes by scale deposition. Electrochim Acta 42:1219
Gueshi T, Tokuda K, Matsuda H (1978) Voltammetry at partially covered electrodes. Part I. Chronopotentiometry and chronoamperometry at model electrodes. J Electroanal Chem 89:247
Wightman RM, Wipf DO (1989) Voltammetry at ultramicroelectrodes. In: Bard AJ (ed) Electroanalytical chemistry, vol 15. Marcel Dekker, New York, pp 267–353
Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, London
Nernst W (1904) Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen. Z Phys Chem 47:52
Wang J (2000) Analytical electrochemistry, 2nd edn. Wiley, New-York
Fraser DM (ed) (1997) Biosensors in the body: continuous in vivo monitoring. Wiley, Chichester
Guilbault GG (1980) Analytical uses of immobilized enzymes. Marcel Dekker, New York
Scheller F, Schubert F (1992) Biosensors. Elsevier, Amsterdam
Ivanauskas F, Baronas R (2008) Numerical simulation of a plate-gap biosensor with an outer porous membrane. Simul Model Pract Th 16:962
Somasundrum M, Aoki K (2002) The steady-state current at microcylinder electrodes modified by enzymes immobilized in conducting or non-conducting material. J Electroanal Chem 530:40
Song M-J, Yun D-H, Jin J-H et al (2006) Steady state kinetics of cyclic conversions of substrate in amperometric bienzyme sensors. Jpn J Appl Phys 45:7197
Laurinavicius V, Razumiene J, Ramanavicius A, Ryabov AD (2004) Wiring of PQQ-dehydrogenases. Biosens Bioelectron 20:1217
Baeumner AJ, Jones C, Wong CY, Price A (2004) A generic sandwich-type biosensor with nanomolar detection limits. Anal Bioanal Chem 378:1587
Bergel A, Comtat M (1984) Theoretical evaluation of transient responses of an amperometric enzyme electrode. Anal Chem 56:2904
Frew JE, Hill HO (1987) Electrochemical biosensors. Anal Chem 59:933A
Pfeiffer D, Scheller FW, Setz K, Schubert F (1993) Amperometric enzyme electrodes for lactate and glucose determinations in highly diluted and undiluted media. Anal Chim Acta 281:489
Scheller FW, Pfeiffer D (1978) Enzyme electrodes. Z Chem 18:50
Arshak K, Jafer E, McDonagh D (2007) Modeling and simulation of a wireless microsensor data acquisition system using PCM techniques. Simul Model Pract Th 15:764
Corcuera JRD, Cavalieri R, Powers J, Tang J (2004) Amperometric enzyme biosensor optimization using mathematical modeling. In: Proceedings of the 2004 ASAE/Csae Annual International Meeting, Paper No. 047030 American Society of Agricultural Engineers, Ottawa
Ferreira LS, Souza MBD, Trierweiler JO et al (2003) Aspects concerning the use of biosensors for process control: experimental and simulation investigations.Comp Chem Eng 27:1165
Stamatin I, Berlic C, Vaseashta A (2006) On the computer-aided modeling of analyte-receptor interactions for an efficient sensor design. Thin Solid Films 495:312
Wu X, Detzel CJ, Van Wie BJ, Haarsma SJ, Kidwel DA (2004) Model-based optimization of a conductive matrix enzyme electrode. Biotechnol Bioeng 88:135
Baronas R, Ivanauskas F, Kulys J (2007) Computational modeling of amperometric enzyme electrodes with selective and perforated membranes. In: Simos TE, Maroulis G (ed) Computation in modern science and engineering: proceedings of the international conference on computational methods in science and engineering 2007 (ICCMSE 2007), vol 2, parts A and B. AIP Press, pp 457–460
Ivanauskas F, Baronas R, Kulys J (2005) Mathematical modeling of biosensors with perforated and selective membranes. Rakenteiden Mekaniikka - J Struct Mech 38:63
Lyons MEG, Murphy J, Rebouillat S (2000) Theoretical analysis of time dependent diffusion, reaction and electromigration in membranes. J Solid State Electrochem 4:458
Turner APF, Karube I, Wilson GS (1987) Biosensors: fundamentals and applications. Oxford University Press, Oxford
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Baronas, R., Ivanauskas, F., Kulys, J. (2010). Modeling Biosensors of Complex Geometry. In: Mathematical Modeling of Biosensors. Springer Series on Chemical Sensors and Biosensors, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3243-0_9
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DOI: https://doi.org/10.1007/978-90-481-3243-0_9
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