scholarly journals Mathematical modelling of biosensors with substrate and product degeneration

2012 ◽  
Vol 53 ◽  
Author(s):  
Liana Stonkienė ◽  
Feliksas Ivanauskas
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Linear Term ◽  
Diffusion Equations ◽  
Enzymatic Reactions ◽  
Amperometric Biosensors ◽  
One Dimensional ◽  
Non Linear ◽  
Kinetics Of

This paper presents a one-dimensional-in-space mathematical model of the amperometric biosensors with substrate and product degeneration. The model is based on diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. It was analyzed effect of substrate and product degeneration for the biosensors response.

scholarly journals Some Remarks on Modelling and Simulation of Physical Phenomena

1997 ◽  
Vol 28 (3-4) ◽  
pp. 151-165 ◽  
Author(s):  
H. J. Bunge
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Mathematical Modelling ◽  
Modelling And Simulation ◽  
Theoretical Physics ◽  
Texture Formation ◽  
First Case ◽  
Non Linear ◽  
Non Linear Operator ◽  
Physical Phenomena

Mathematical modelling and computer simulation of physical phenomena is a rapidly growing field of work in all areas of pure and applied sciences. In principle, mathematical modelling of physical phenomena has been the field of theoretical physics from the very beginning of physics although the computer has increased the potentials of this method by many orders of magnitude. Modelling and simulation are often used as synonyms. It may, however, be meaningfull to distinguish the development of a mathematical model from its use in computer simulation. Also, a mathematical model in this sense must be distinguished from mathematical expressions interpolating experimental data. In the field of textures, models of texture formation, models of materials properties, as well as the combination of the two are being used. In this connection it is important whether a texture formation model is linear or non-linear. In the first case the texture formation operator can be reduced to the orientation space whereas a non-linear operator operates in the full texture space.

scholarly journals Mathematical modeling of the influence of interfering species on the performance of an amperometric biosensor with porous membrane

2014 ◽  
Vol 55 ◽  
Author(s):  
Liana Stonkienė ◽  
Feliksas Ivanauskas
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Porous Membrane ◽  
Amperometric Biosensor ◽  
Diffusion Equations ◽  
One Dimensional

This paper presents a one-dimensional-in-space mathematical model of the amperometric biosensor with porous membrane influenced by the presence of interfering species. The model is based on diffusion equations. Various effects regarding amperometric bias, caused by the presence of interfering species, have been analyzed.

scholarly journals Mathematical modeling of the influence of interfering species on the performance of an amperometric sensor

2013 ◽  
Vol 54 ◽  
Author(s):  
Liana Stonkienė ◽  
Feliksas Ivanauskas ◽  
Albertas Malinauskas
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Amperometric Sensor ◽  
Diffusion Equations ◽  
Amperometric Sensors ◽  
One Dimensional

This paper presents a one-dimensional-in-space mathematical model of the amperometric sensors influenced by the presence of interfering species. The model is based on diffusion equations. Various effects regarding amperometric bias, caused by the presence of interfering species, have been analyzed.

scholarly journals Mathematical Modelling of Oscillatory Processes in Transmission of Movement of an Electric Drive with Non-Linear Long Elastic Elements

2021 ◽  
Vol 23 (2) ◽  
pp. C54-C64
Author(s):  
Andriy Chaban ◽  
Tomasz Perzyński
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Mathematical Modelling ◽  
Electric Drive ◽  
Linear Relation ◽  
Electric Drive System ◽  
Non Linear ◽  
Strength And Deformation ◽  
Elastic Elements ◽  
Oscillatory Processes

Mathematical model of transmission of movement of an electric drive system that includes long elastic elements, including the non-linear relation between tensors of strength and deformation is presented in this article. Mentioned type of transmission is applied in the tasks related to special-purpose transport. A method that is based on integral modification of variational HamiltonOstrogradsky principle was applied for the presented model. Results of the computer simulation of oscillatory processes in transmission of movement of an electromechanical system are presented in the article.

Modelling of a microreactor on heterogeneous surface and an influence of microreactor geometry

1998 ◽  
Vol 3 ◽  
pp. 19-30 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys
Keyword(s):  
Concentration Gradient ◽  
Enzymatic Reaction ◽  
Heterogeneous Surface ◽  
Linear Term ◽  
Diffusion Equations ◽  
Carbon Paste ◽  
Amperometric Biosensors ◽  
Carbon Paste Electrodes ◽  
Stationary Diffusion ◽  
Geometrical Form

A model of an action of the amperometric biosensors based on carbon paste electrodes encrusted with single microreactor is analyzed. The model is based on non stationary diffusion equations containing non-linear term related to the enzymatic reaction. The biosensors current, which is a function of the concentration gradient of the reaction product on the electrodes, is used for analyzing of dynamics of the reaction. An influence of a size of microreactor, a geometrical form of microreactor and a position of microreactor on the biosensors action is investigated.

scholarly journals Calculation of the apparent Michaelis constant for biosensors using reaction-diffusion equations

2014 ◽  
Vol 55 ◽  
Author(s):  
Pranas Katauskis ◽  
Feliksas Ivanauskas ◽  
Sigitas Laukevičius
Keyword(s):  
Mathematical Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Michaelis Constant ◽  
Amperometric Biosensors ◽  
The Relationship

The relationship between the apparent Michaelis constant and the diffusion module for one and two-layer biosensors is studied using a mathematical model describing action of the amperometric biosensors.

Imprecision of Laboratory Determinations and Diagnostic Accuracy: Theoretical Considerations

1974 ◽  
Vol 13 (03) ◽  
pp. 151-158 ◽  
Author(s):  
D. A. B. Lindbebo ◽  
Fr. R. Watson
Keyword(s):  
Mathematical Model ◽  
Diagnostic Accuracy ◽  
Diagnostic Process ◽  
Clinical Laboratories ◽  
Non Linear ◽  
Theoretical Considerations ◽  
Made In

Recent studies suggest the determinations of clinical laboratories must be made more precise than at present. This paper presents a means of examining benefits of improvement in precision. To do this we use a mathematical model of the effect upon the diagnostic process of imprecision in measurements and the influence upon these two of Importance of Diagnosis and Prevalence of Disease. The interaction of these effects is grossly non-linear. There is therefore no proper intuitive answer to questions involving these matters. The effects can always, however, be calculated.Including a great many assumptions the modeling suggests that improvements in precision of any determination ought probably to be made in hospital rather than screening laboratories, unless Importance of Diagnosis is extremely high.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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.

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