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The optimization-based quantitative determination of multianalyte concentrations from biased biosensor responses is investigated under internal and external diffusion-limited conditions. A computational model of a biocatalytic amperometric biosensor utilizing a mono-enzyme-catalyzed (nonspecific) competitive conversion of two substrates was used to generate pseudo-experimental responses to mixtures of compounds. The influence of possible perturbations of the biosensor signal, due to a white noise- and temperature-induced trend, on the precision of the concentration determination has been investigated for different configurations of the biosensor operation. The optimization method was found to be suitable and accurate enough for the quantitative determination of the concentrations of the compounds from a given biosensor transient response. The computational experiments showed a complex dependence of the precision of the concentration estimation on the relative thickness of the outer diffusion layer, as well as on whether the biosensor operates under diffusion- or kinetics-limited conditions. When the biosensor response is affected by the induced exponential trend, the duration of the biosensor action can be optimized for increasing the accuracy of the quantitative analysis.

In this paper, an amperometric glucose biosensor is modeled numerically. The model is based on non-stationary reaction-diffusion type equations. The model consists of four layers. An enzyme layer lies directly on a working electrode surface. The enzyme layer is attached to an electrode by a polyvinyl alcohol (PVA) coated terylene membrane. This membrane is modeled as a PVA layer and a terylene layer, which have different diffusivities. The fourth layer of the model is the diffusion layer, which is modeled using the Nernst approach. The system of partial differential equations is solved numerically using the finite difference technique. The operation of the biosensor was analyzed computationally with special emphasis on the biosensor response sensitivity to oxygen when the experiment was carried out in aerobic conditions. Particularly, numerical experiments show that the overall biosensor response sensitivity to oxygen is insignificant. The simulation results qualitatively explain and confirm the experimentally observed biosensor behavior.

This paper presents a mathematical model of carbon nanotubes-based mediatorless biosensor. The developed model is based on nonlinear non-stationary reaction-diffusion equations. The model involves four layers (compartments): a layer of enzyme solution entrapped on a terylene membrane, a layer of the single walled carbon nanotubes deposited on a perforated membrane, and an outer diffusion layer. The biosensor response and sensitivity are investigated by changing the model parameters with a special emphasis on the mediatorless transfer of the electrons in the layer of the enzyme-loaded carbon nanotubes. The numerical simulation at transient and steady state conditions was carried out using the finite difference technique. The mathematical model and the numerical solution were validated by experimental data. The obtained agreement between the simulation results and the experimental data was admissible at different concentrations of the substrate.

In this paper the operation of an amperometric biosensor producing a chemically amplified signal is modelled numerically. The chemical amplification is achieved by using synergistic substrates. The model is based on non-stationary reaction-diffusion equations. The model involves three layers (compartments): a layer of enzyme solution entrapped on the electrode surface, a dialysis membrane covering the enzyme layer and an outer diffusion layer which is modelled by the Nernst approach. The equation system is solved numerically by using the finite difference technique. The biosensor response and sensitivity are investigated by altering the model parameters influencing the enzyme kinetics as well as the mass transport by diffusion. The biosensor action was analyzed with a special emphasis to the effect of the chemical amplification. The simulation results qualitatively explain and confirm the experimentally observed effect of the synergistic substrates conversion on the biosensor response.

The response of an amperometric biosensor based on a chemically modified electrode was modelled numerically. A mathematical model of the biosensor is based on a system of non-linear reaction-diffusion equations. The modelling biosensor comprises two compartments: an enzyme layer and an outer diffusion layer. In order to define the main governing parameters the corresponding dimensionless mathematical model was derived. The digital simulation was carried out using the finite difference technique. The adequacy of the model was evaluated using analytical solutions known for very specific cases of the model parameters. By changing model parameters the output results were numerically analyzed at transition and steady state conditions. The influence of the substrate and mediator concentrations as well as of the thicknesses of the enzyme and diffusion layers on the biosensor response was investigated. Calculations showed complex kinetics of the biosensor response, especially when the biosensor acts under a mixed limitation of the diffusion and the enzyme interaction with the substrate.

The response of a peroxidase-based optical biosensor was modelled digitally.A mathematical model of the optical biosensor is based on a system of non-linear reaction-diffusion equations. The modelling biosensor comprises two compartments, an enzyme layerand an outer diffusion layer. The digital simulation was carried out using finite differencetechnique. The influence of the substrate concentration as well as of the thickness of both theenzyme and diffusion layers on the biosensor response was investigated. Calculations showedcomplex kinetics of the biosensor response, especially at low concentrations of the peroxidaseand of the hydrogen peroxide.

The response of an amperometric biosensor at mixed enzyme kinetics anddiffusion limitations was modelled digitally in the case of substrate inhibition. Digitalsimulations were carried out using a finite difference technique. Calculations showedcomplex kinetics of biosensor response. At low enzyme activity and substrate concentration(S0), the response of the sensor looks like it is limited by a simple substrate diffusion. Atsubstrate concentration comparable to the Michaelis-Menten constant (KM), the responsechange shows a maximal value. A sharp response change was indicated at high enzymeactivity and high (4.9 > S0/KM > 4.5) substrate concentration. This was explained by multiconcentrationof substrate generation inside the enzyme layer. This conclusion wasconfirmed by the analytical solution of the simplified biosensor model with externaldiffusion limitation at steady-state conditions. The complex kinetics of response changeproduces different calibration graphs for biosensor response at transition and steady state.

A plate−gap model of a porous enzyme doped electrode covered by a porousinert membrane has been proposed and analyzed. The two−dimensional−in−spacemathematical model of the plate−gap biosensors is based on the reaction−diffusionequations containing a nonlinear term related to the Michaelis−Menten kinetics. Usingnumerical simulation of the biosensor action, the influence of the geometry of the outermembrane on the biosensor response was investigated at wide range of analyteconcentrations as well as of the reaction rates. The numerical simulation was carried outusing finite−difference technique. The behavior of the plate−gap biosensors was comparedwith that of a flat electrode deposited with a layer of enzyme and covered with the sameouter membrane.

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

Abstract: A mathematical model of biosensors acting in a trigger mode has been developed. One type of the biosensors utilized a trigger enzymatic reaction followed by the cyclic enzymatic and electrochemical conversion of the product (CCE scheme). Other biosensors used the enzymatic trigger reaction followed by the electrochemical and enzymatic product cyclic conversion (CEC scheme). The models were based on diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. The digital simulation was carried out using the finite difference technique. The influence of the substrate concentration, the maximal enzymatic rate as well as the membrane thickness on the biosensor response was investigated. The numerical experiments demonstrated a significant gain (up to dozens of times) in biosensor sensitivity when the biosensor response was under diffusion control. In the case of significant signal amplification, the response time with triggering was up to several times longer than that of the biosensor without triggering.

A mathematical model of amperometric biosensors has been developed. The model is based on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reaction. Using digital simulation, the influence of the thickness of enzyme membrane on the biosensor response was investigated. The digital simulation of the biosensor operation showed the non-monotonous change of the maximal biosensor current versus the membrane thickness at the various maximal enzymatic rates. Digital simulation was carried out using the finite difference technique. Results of the numerical simulation was compared with known analytical solutions. This paper presents a framework for selection of the membrane thickness, ensuring the sufficiently stable sensitivity of a biosensor in a required range of the maximal enzymatic rate.