Theoretical simulation of oxygen tension measurement in tissues using a microelectrode: I. The response function of the electrode

Abstract

The aim of this article is to determine the correlation between the actual oxygen distribution in tissues and the distribution of oxygen measured by microelectrodes. This correlation is determined by the response function of the electrode, which depends on the oxygen consumed by the electrode. In tissue it is necessary to consider the gradients resulting from cellular respiration. A computer program has been used to simulate the vascular structure of various tissues and also the measurements of oxygen tension using a polarographic electrode. The electrode absorption process is described using a theoretical model. The gradient of oxygen in tissue is described by a mathematical model that takes into consideration both diffusion and cellular consumption of oxygen. We have compared the results obtained using the response function of the electrode and some simplifications of it. The results of these comparisons show that there are some differences in the ‘observed’ distributions of the oxygen tension in tissues predicted using different formulae for the electrode response function. Also, there are considerable differences between the input oxygen distribution and the measured values in all cases. All the results of the simulations of the oxygen tension ‘observed’ by a 12 μm polarographic electrode, using different response functions of the electrode, show that the electrode averages the values from many cells. Care should be taken in using a simplification for the response function of the electrode, especially if the results are going to be used as input values in modelling the tumour response to new treatments and/or as a basis of selecting patients for treatments. A computer simulation of measurement of oxygen tensions in regions of steep pO2 gradients shows that extremely high and extremely low pO2 values will not be detected.