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Theoretical simulation of oxygen tension measurement in tissues using a microelectrode: I. The response function of the electrode
Umeå University, Faculty of Medicine, Department of Radiation Sciences.
Umeå University, Faculty of Medicine, Department of Radiation Sciences.
Umeå University, Faculty of Medicine, Department of Radiation Sciences.
Umeå University, Faculty of Medicine, Department of Radiation Sciences.
2001 (English)In: Physiological Measurement, ISSN 0967-3334, E-ISSN 1361-6579, Vol. 22, no 4, 713-725 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2001. Vol. 22, no 4, 713-725 p.
URN: urn:nbn:se:umu:diva-3939DOI: 10.1088/0967-3334/22/4/306PubMedID: 11761078OAI: diva2:142854
Available from: 2004-05-06 Created: 2004-05-06 Last updated: 2010-08-24Bibliographically approved
In thesis
1. Theoretical modelling of tumour oxygenation and influences on treatment outcome
Open this publication in new window or tab >>Theoretical modelling of tumour oxygenation and influences on treatment outcome
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

One of the main problems in curing cancer resides in the different microenvironment existing in tumours compared to the normal tissues. The mechanisms of failure are different for radiotherapy and chemotherapy, but they all relate to the poor blood supply known to exist in tumours. It is therefore very important to know the tumour microenvironmental conditions in order to devise techniques that will overcome the problems and will therefore improve the result of the treatment.

The aims of the thesis were the modelling of tumour oxygenation and the simulation of polarographic oxygen measurements in order to assess and possibly to improve the accuracy of the electrode in measuring tumour oxygenation. It also aimed to evaluate the implications of tumour microenvironment for the radiotherapy outcome.

The project used theoretical modelling as the main tool. The processes of oxygen diffusion and consumption were described mathematically for different conditions, the result being very accurate distributions of oxygen in tissues. A first simple model of tissue oxygenation was based on the oxygen diffusion around a single blood vessel. A more complex model built from the basic physical processes and measurable parameters allowed the simulation of realistical tissues with heterogeneous vasculature. This model also allowed the modelling of the two types of hypoxia known to appear in tumours and their influence on the tumour microenvironment. The computer simulation of tissues was also used for assessing the accuracy of the polarographic technique for measuring tumour oxygenation.

The results of this study have shown that it is possible to model theoretically the tissue oxygenation starting from the basic physical processes. The particular application of our theoretical simulation to the polarographic oxygen electrode has shown that this experimental method does not give the oxygen values in individual cells. Because the electrode measures the average oxygenation in a relatively large tissue volume, the resulting oxygen distributions are different from the real ones and the extreme high and low values are not detected. It has further been found that the polarographic electrode cannot make distinction between various types of hypoxia existing in tumours, the geometrical distribution of the hypoxic cells influencing mostly the accuracy of the measurement.

It was also shown that because of the averaging implied by the measurement process, electrode results should not be used directly to predict the response to radiation. Thus, the differences between the predictions in clinical tumour control obtained from the real or the measured oxygenations are of the order of tens of percents in absolute value. A method to improve the accuracy of the electrode, i.e. to improve the correlation between the results of the measurements and the actual tissue oxygenation, was proposed.

In conclusion, theoretical modelling has been shown to be a very powerful tool for predicting the outcome of radiotherapy and it has the advantage of describing the tumour oxygenation in the least invasive manner. Furthermore it allows the investigation of the invasiveness and the accuracy of various experimental methods.

56 p.
Umeå University medical dissertations, ISSN 0346-6612 ; 897
Radiation sciences, Computer simulation, Electrode, Polarographic measurements, Tumour oxygenation, Hypoxia, Strålningsvetenskap
National Category
Radiology, Nuclear Medicine and Medical Imaging
Research subject
urn:nbn:se:umu:diva-262 (URN)91-7305-667-7 (ISBN)
Public defence
2004-05-28, sal 244, by 7, Norrlands universitetssjukhus, Umeå, 09:00
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved

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