Computer Simulation of the Response of Amperometric Biosensors in Stirred and non Stirred Solution

2003 ◽  
Vol 8 (1) ◽  
pp. 3-18 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Finite Difference ◽  
Mass Transport ◽  
Enzyme Reaction ◽  
Analyte Concentration ◽  
Amperometric Biosensors ◽  
Finite Difference Technique ◽  
Enzyme Layer ◽  
Biosensor Response

A mathematical model of amperometric biosensors has been developed to simulate the biosensor response in stirred as well as non stirred solution. The model involves three regions: the enzyme layer where enzyme reaction as well as mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region, where the analyte concentration is maintained constant. Using computer simulation the influence of the thickness of the enzyme layer as well the diffusion one on the biosensor response was investigated. The computer simulation was carried out using the finite difference technique.

scholarly journals Amperometrinių biojutiklių su sinerginių substratų stiprinimu kompiuterinis modeliavimas

2011 ◽  
Vol 56 ◽  
pp. 174-181
Author(s):  
Dainius Šimelevičius ◽  
Romas Baronas
Keyword(s):  
Mass Transport ◽  
Equation System ◽  
Enzymatic Reactions ◽  
Analyte Concentration ◽  
Dialysis Membrane ◽  
Diffusion Layer Thickness ◽  
Finite Difference Technique ◽  
Substrate Concentrations ◽  
Enzyme Layer ◽  
Biosensor Response

Šiame straipsnyje yra tiriamas amperometrinis biojutiklis, kuriame biojutiklio atsakas yra stiprinamas chemiškai – sinerginiais substratais. Tokiuose biojutikliuose, be substrato, kurio koncentracija matuojama, naudojamas ir pagalbinis substratas, reikalingas substratų sinergetikai. Biojutiklis yra modeliuojamas naudojant nestacionarias netiesines reakcijos-difuzijos lygtis. Modeliuojami keturi biojutiklio sluoksniai: fermento sluoksnis, kuriame vyksta visos biocheminės reakcijos ir difuzija, dializėsmembrana ir difuzijos sluoksnis, kuriuose vyksta tik difuzija ir reakcijos, kuriose nedalyvauja fermentas, o ketvirtasis sluoksnis yra tirpalo dalis, kurioje palaikoma vienoda medžiagų koncentracija. Lygčių sistema sprendžiama skaitiškai, naudojant baigtinių skirtumų metodą. Tiriama biojutiklio atsako bei jautrio priklausomybė nuo substratų koncentracijų ir nuo difuzijos sluoksnio storio.Modelling Amperometric Biosensors with Synergistic Substrate AmplificationDainius Šimelevičius, Romas Baronas SummaryComputational modelling of a biosensor in which chemical amplification by synergistic substrates takes place was investigated in this study. In the biosensors of this type, in addition to the substrate (analyte), another auxiliary substrate is used. It is necessary to achieve the substrates synergy. The operation of the biosensor is modelled using non-stationary reactiondiffusion equations. The model involves four regions: the enzyme layer where the enzymatic reactions as well as the mass transport by diffusion take place, the dialysis membrane and the diffusion limiting region where the mass transport by diffusion and non-enzymatic reactions take place, and the convective region in which the analyte concentration is maintained constant. The equation system is solved numerically using the finite difference technique. The biosensor response dependency on substrate concentrations and the diffusion layer thickness, as well as the biosensor sensitivity dependence on the same parameters have been studied."line-height: 18px;"> 

Computational Modelling of a Sensor Based on an Array of Enzyme Microreactors

2004 ◽  
Vol 9 (3) ◽  
pp. 203-218 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys ◽  
M. Sapagovas
Keyword(s):  
Digital Simulation ◽  
Enzymatic Reaction ◽  
Computational Modelling ◽  
Enzyme Reaction ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Analyte Concentration ◽  
Finite Difference Technique ◽  
Kinetics Of ◽  
Biosensor Response

This paper presents a two-dimensional-in-space mathematical model of a sensor system based an array of enzyme microreactors immobilised on a single electrode. The system acts under amperometric conditions. The model is based on the diffusion equations containing a non-linear term related to the Michaelis-Menten kinetics of the enzymatic reaction. The model involves three regions: an array of enzyme microreactors (cells) where enzyme reaction as well as mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region, where the analyte concentration is maintained constant. Using computer simulation the influence of the geometry of the enzyme cells and the diffusion region on the biosensor response was investigated. The digital simulation was carried out using the finite difference technique.

Computer Simulation of Amperometric Biosensor Response to Mixtures of Compounds

2002 ◽  
Vol 7 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
J. Christensen ◽  
F. Ivanauskas ◽  
J. Kulys
Keyword(s):  
Computer Simulation ◽  
Enzymatic Reaction ◽  
Diffusion Equations ◽  
Response Data ◽  
Finite Difference Technique ◽  
Stationary Diffusion ◽  
Biosensor Array ◽  
Menten Kinetic ◽  
Biosensor Response

A mathematical model of amperometric biosensors has been developed. The model bases on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetic of the enzymatic reaction. The model describes the biosensor response to mixtures of multiple compounds in two regimes of analysis: batch and flow injection. Using computer simulation, large amount of biosensor response data were synthesised for calibration of a biosensor array to be used for characterization of wastewater. The computer simulation was carried out using the finite difference technique.

scholarly journals Kompiuterinis optinio biojutiklio savybių tyrimas taikant bedimensį modelį

2009 ◽  
Vol 50 ◽  
pp. 306-310
Author(s):  
Evelina Gaidamauskaitė ◽  
Romas Baronas
Keyword(s):  
Mathematical Model ◽  
Digital Simulation ◽  
Reaction Diffusion ◽  
Optical Biosensor ◽  
Reaction Diffusion Equations ◽  
Computational Investigation ◽  
Linear Reaction ◽  
The Mathematical Model ◽  
Enzyme Layer ◽  
Biosensor Response

Šiame darbe, siekiant nustatyti pagrindinius kinetinius peroksidazinio optinio biojutiklio matematinio modelio parametrus, buvo sudarytas bedimensis modelis. Biojutikliui taikomos reakcijos-difuzijos lygtys su netiesiniu nariu, aprašančiu fermentinę reakciją. Biojutiklio veikimas modeliuojamas fermento ir difuzijos sluoksniuose. Ištirta biojutiklio atsako ir jautrio priklausomybė nuo bedimensio biojutiklio modulio. Suformuluotas uždavinys sprendžiamas baigtinių skirtumų metodu. Gauti rezultatai pagrindžia šio modelio pritaikomumą. Atliekami peroksidazinio optinio biojutiklio eksperimentiniai tyrimai leis nustatyti modelio taikymo ribas.A Computational Investigation of the Optical Biosensor by a Dimensionless ModelEvelina Gaidamauskaitė, Romas Baronas SummaryIn order to determine the main governing parameters, a dimensionless mathematical model of a peroxidase-based optical biosensor is derived. The mathematical model of the biosensor is based on a system of non-linear reaction-diffusion equations. The modelled biosensor comprises two compartments, an enzyme layer and an outer diffusion layer. The influence of the dimensionless diffusion modulus on the biosensor response and the sensitivity is investigated. The digital simulation was carried out using a finite difference method.

A Study of Unsteady Natural Convection in Cryogenic Storage Tanks for Densified Propellants

2003 ◽  
Author(s):  
L. Manalo ◽  
K. M. Akyuzlu
Keyword(s):  
Mathematical Model ◽  
Boundary Condition ◽  
Heat Flux ◽  
Finite Difference ◽  
Transient Temperature ◽  
Variable Boundary ◽  
Flux Boundary Condition ◽  
Cryogenic Storage ◽  
Finite Difference Technique ◽  
Heat Flux Boundary Condition

A two-dimensional, unsteady, two domain (liquid and vapor) mathematical model is adopted to investigate the thermo-hydrodynamic behavior of a propellant in a cryogenic storage tank. The physics based mathematical model consists of conservation of mass, momentum, and energy equations for the liquid subjected to variable boundary conditions at the liquidvapor interface and constant heat flux boundary condition at the walls of the container. The density of the liquid is assumed to be temperature dependent only in the buoyancy term of the momentum equation (Boussinesq approximation). The vapor in the ullage is assumed to be an ideal gas with uniform thermodynamic properties and is modeled by single node conservation equations for mass and energy. The two domains are coupled through a set of interface equations for mass and energy exchange between the liquid and the vapor. The resulting nonlinear governing equations for the liquid domain are solved by an implicit finite difference technique (where the pressure distribution is determined by solving the Poisson’s equation) to predict the transient temperature and velocity fields inside the propellant. The equations for the vapor are solved by a simple explicit finite difference technique. The model is tested for a benchmark case (numerically and experimentally) to verify the accuracy of the numerical scheme. Finally, the model is used to predict the transient circulation patterns and resulting thermal stratification in a densified cryogenic propellant for a constant wall heat flux boundary condition.

Modelling of Moisture Movement in Wood during Outdoor Storage

2001 ◽  
Vol 6 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
I. Juodeikienė ◽  
A. Kajalavičius
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Climatic Conditions ◽  
Two Dimensional ◽  
Moisture Movement ◽  
Finite Difference Technique ◽  
Long Term Storage ◽  
Space Formulation ◽  
Term Storage

A model of moisture movement in wood is presented in this paper in a two-dimensional-in-space formulation. The finite-difference technique has been used in order to obtain the solution of the problem. The model was applied to predict the moisture content in sawn boards from pine during long term storage under outdoor climatic conditions. The satisfactory agreement between the numerical solution and experimental data was obtained.

On the Motion of Granular Materials Due to Shear

2000 ◽  
Author(s):  
Mehrdad Massoudi ◽  
Tran X. Phuoc
Keyword(s):  
Finite Difference ◽  
Granular Materials ◽  
Continuum Model ◽  
Theory Model ◽  
Governing Equations ◽  
Flat Plates ◽  
Material Parameters ◽  
Finite Difference Technique ◽  
Linear Differential ◽  
The Continuum

Abstract In this paper we study the flow of granular materials between two horisontal flat plates where the top plate is moving with a constant speed. The constitutive relation used for the stress is based on the continuum model proposed by Rajagopal and Massoudi (1990), where the material parameters are derived using the kinetic theory model proposed by Boyle and Massoudi (1990). The governing equations are non-dimensionalized and the resulting system of non-linear differential equations is solved numerically using finite difference technique.

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