scholarly journals Computational modelling of the biosensor acting under parallel substrates conversion with dialysis membrane

2012 ◽  
Vol 53 ◽  
Author(s):  
Vytautas Ašeris
Keyword(s):  
Mathematical Model ◽  
Dimensional Space ◽  
Effective Diffusion ◽  
Computational Modelling ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Dialysis Membrane ◽  
Layered Model ◽  
Diffusion Layers ◽  
Model Response

A mathematical model of biosensor acting under parallel substrates conversion is investigated in this paper. Model consists of reaction-diffusion equations with non-linear terms, which in general case are solved numericaly. The mathematical model describes biosensor action in one-dimensional space, which consists of enzymatic, dialysis and diffusion layers. The purpose of this work was to define for which parameter values the layers of diffusion and dialysis membrane can be replaced by one external layer, described by the effective diffusion coefficient. The simulation error of two-layered model response was investigated by comparing it to the values of three-layered model response. 

scholarly journals Computational Modelling of Biosensors with an Outer Perforated Membrane

2009 ◽  
Vol 14 (1) ◽  
pp. 85-102 ◽  
Author(s):  
K. Petrauskas ◽  
R. Baronas
Keyword(s):  
Diffusion Coefficient ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Enzymatic Reaction ◽  
Computational Modelling ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
D Model ◽  
Kinetics Of ◽  
Biosensor Response

This paper presents one-dimensional (1-D) and two-dimensional (2-D) in-space mathematical models for amperometric biosensors with an outer perforated membrane. The biosensor action was modelled by reaction-diffusion equations with a nonlinear term representing the Michaelis-Menten kinetics of an enzymatic reaction. The conditions at which the 1-D model can be applied to simulate the biosensor response accurately were investigated numerically. The accuracy of the biosensor response simulated by using 1-D model was evaluated by the response simulated with the corresponding 2-D model. A procedure for a numerical evaluation of the effective diffusion coefficient to be used in 1-D model was proposed. The numerically calculated effective diffusion coefficient was compared with the corresponding coefficients derived analytically. The numerical 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.

Analytical Studies of Diffusion by the Dissociative Mechanism in the Case of a Foreign Atom Source

2004 ◽  
Vol 233-234 ◽  
pp. 15-28
Author(s):  
A. Benmakhlouf
Keyword(s):  
Mathematical Model ◽  
Perturbation Method ◽  
Numerical Study ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Analytical Treatment ◽  
Dissociative Mechanism ◽  
Foreign Atom ◽  
Atom Diffusion ◽  
Atom Source

The analytical treatment of dissociative diffusion by using the matched perturbation method given in the literature deals with a virtually infinite foreign-atom source producing a constant^concentration at the boundary. In this paper, a new mathematical model is developed for analysing the dissociative diffusion of the solute atoms in the case of finite-source conditions. The mathematical model combines the reaction-diffusion equations which govern solute atom diffusion by the dissociative mechanism and the boundary condition expressing the fact that the rate at which solute leaves the source is always equal to that at which it enters the sheet over the surface x=0. Solutions obtained by applying the matched perturbation method and their comparison with those of the numerical study are also presented in this paper.

scholarly journals A Comparison of Finite Difference Schemes for Computational Modelling of Biosensors

2007 ◽  
Vol 12 (3) ◽  
pp. 359-369 ◽  
Author(s):  
E. Gaidamauskaitė ◽  
R. Baronas
Keyword(s):  
Finite Difference ◽  
Computational Modelling ◽  
Computation Time ◽  
Reaction Diffusion ◽  
Difference Schemes ◽  
Reaction Diffusion Equations ◽  
Finite Difference Schemes ◽  
Enzymatic Reactions ◽  
Calculation Results ◽  
Kinetics Of

This paper presents a one-dimensional-in-space mathematical model of an amperometric biosensor. The model is based on the reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. The stated problem is solved numerically by applying the finite difference method. Several types of finite difference schemes are used. The numerical results for the schemes and couple mathematical software packages are compared and verified against known analytical solutions. Calculation results are compared in terms of the precision and computation time.

The Influence of the Diffusion Space Geometry on Behavior of some Processes in Biochemistry and Electrochemistry

2000 ◽  
Vol 5 ◽  
pp. 3-38 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys ◽  
M. Sapagovas ◽  
A. Survila
Keyword(s):  
Mathematical Model ◽  
Reaction Diffusion ◽  
Electrode Reaction ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Carbon Paste ◽  
Diffusion Type ◽  
Function Modelling ◽  
Partially Blocked Electrodes ◽  
The Mathematical Model

The reaction-diffusion and diffusion equations were applied for modelling of some processes in biochemistry and electrochemistry. Modelling of the amperometric biosensors based on carbon paste electrodes encrusted with a single nonhomogeneous microreactor is analyzed. The mathematical model of the biosensor operation is based on nonstationary reaction-diffusion equations containing a non-linear term given by Michaelis-Menten function. Modelling of a simple redox-electrode reaction, involving two soluble species, is also considered. The model of the electrode behavior, taking into account the resist layer of the partially blocked electrodes, was expressed as a system of differential equations of the diffusion type with initial and boundary conditions. The mathematical model generalizing both processes: biochemical and electrochemical is presented in this paper. The generalized problem was solved numerically. The finite-difference technique was used for discretisation of the model. Using the numerical solution of the generalized problem, the influence of the size, shape and position of a microreactor as well as the thickness of the resist layer on the current dynamics was investigated.

The boundary knot method for the solution of two-dimensional advection reaction-diffusion and Brusselator equations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mehdi Dehghan ◽  
Vahid Mohammadi
Keyword(s):  
Mathematical Models ◽  
Dimensional Space ◽  
Reaction Diffusion ◽  
Implicit Scheme ◽  
Coupled Systems ◽  
Reaction Diffusion Equations ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Time Step ◽  
Content Type

Purpose This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a semi-implicit scheme in time for finding a new numerical solution of the advection–reaction–diffusion and reaction–diffusion systems in two-dimensional spaces, which arise in biology. Design/methodology/approach First, the BKM is applied to approximate the spatial variables of the studied mathematical models. Then, this study derives fully discrete scheme of the studied models using a semi-implicit scheme based on Crank–Nicolson idea, which gives a linear system of algebraic equations with a non-square matrix per time step that is solved by the singular value decomposition. The proposed approach approximates the solution of a given partial differential equation using particular and homogeneous solutions and without considering the fundamental solutions of the proposed equations. Findings This study reports some numerical simulations for showing the ability of the presented technique in solving the studied mathematical models arising in biology. The obtained results by the developed numerical scheme are in good agreement with the results reported in the literature. Besides, a simulation of the proposed model is done on buttery shape domain in two-dimensional space. Originality/value This study develops the BKM combined with MAEM for solving the coupled systems of (advection) reaction–diffusion equations in two-dimensional spaces. Besides, it does not need the fundamental solution of the mathematical models studied here, which omits any difficulties.

scholarly journals Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor

Molecules ◽  
2021 ◽  
Vol 26 (23) ◽  
pp. 7310
Author(s):  
Naveed Ahmad Khan ◽  
Fahad Sameer Alshammari ◽  
Carlos Andrés Tavera Romero ◽  
Muhammad Sulaiman ◽  
Ghaylen Laouini
Keyword(s):  
Mathematical Model ◽  
Hydrogen Peroxide ◽  
Complexity Analysis ◽  
Enzymatic Reaction ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Supervised Machine Learning ◽  
Reaction Diffusion Equation ◽  
Data Set ◽  
Dimensionless Concentration

In this study, we have investigated the mathematical model of an immobilized enzyme system that follows the Michaelis–Menten (MM) kinetics for a micro-disk biosensor. The film reaction model under steady state conditions is transformed into a couple differential equations which are based on dimensionless concentration of hydrogen peroxide with enzyme reaction (H) and substrate (S) within the biosensor. The model is based on a reaction–diffusion equation which contains highly non-linear terms related to MM kinetics of the enzymatic reaction. Further, to calculate the effect of variations in parameters on the dimensionless concentration of substrate and hydrogen peroxide, we have strengthened the computational ability of neural network (NN) architecture by using a backpropagated Levenberg–Marquardt training (LMT) algorithm. NNs–LMT algorithm is a supervised machine learning for which the initial data set is generated by using MATLAB built in function known as “pdex4”. Furthermore, the data set is validated by the processing of the NNs–LMT algorithm to find the approximate solutions for different scenarios and cases of mathematical model of micro-disk biosensors. Absolute errors, curve fitting, error histograms, regression and complexity analysis further validate the accuracy and robustness of the technique.

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