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IMA Journal of Management Mathematics 1999 10(1):41-53; doi:10.1093/imaman/10.1.41
© 1999 by Institute of Mathematics and its Applications
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A mathematical model of silicon-based thermobiosensors

V. ROSSOKHATY and N. ROSSOKHATAJA

Semiconductor Physics Department, Kiev University Kiev-222, PO Box 493, Ukraine
Department of Cybernetics, Kiev University Kiev-222, P0 Box 493, Ukraine

A mathematical model of a silicon glucose thermobiosensor that detects changes in temperature produced by a biocatalytic reaction is proposed for calculation of transient temperature and reactant concentration profiles, time-dependencies of the output signal, and calibration curves. Mathematically the model is reduced to a one-dimensional linear initial-boundary-value problem of the heat-conduction equation with a thermal source F(x, t). In order to find F(x, t), a system of the second-order nonlinear partial differential equations for glucose and oxygen concentrations, describing a combination of diffusion-membrane theory and Michaelis-Menten enzyme reaction theory, has been solved. The computed dependencies of transient temperature profile and sensor response to various conditions such as oxygen buffer concentration, membrane thickness, enzyme loading, and operation mode are analysed for the optimal design of the tensor.

Keywords: model; biosensor; thermal sensor; enzymatic reaction; initial-boundary-value problem; partial differential equation


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