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Theoretical modelling of tumour oxygenation and influences on treatment outcome
Umeå University, Faculty of Medicine, Radiation Sciences.
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.

Place, publisher, year, edition, pages
2004. , 56 p.
Series
Umeå University medical dissertations, ISSN 0346-6612 ; 897
Keyword [en]
Radiation sciences, Computer simulation, Electrode, Polarographic measurements, Tumour oxygenation, Hypoxia
Keyword [sv]
Strålningsvetenskap
National Category
Radiology, Nuclear Medicine and Medical Imaging
Research subject
radiofysik
Identifiers
URN: urn:nbn:se:umu:diva-262ISBN: 91-7305-667-7 (print)OAI: oai:DiVA.org:umu-262DiVA: diva2:142859
Public defence
2004-05-28, sal 244, by 7, Norrlands universitetssjukhus, Umeå, 09:00
Opponent
Supervisors
Available from: 2004-05-06 Created: 2004-05-06Bibliographically approved
List of papers
1. Theoretical simulation of oxygen tension measurement in tissues using a microelectrode: I. The response function of the electrode
Open this publication in new window or tab >>Theoretical simulation of oxygen tension measurement in tissues using a microelectrode: I. The response function of the electrode
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.

Identifiers
urn:nbn:se:umu:diva-3939 (URN)10.1088/0967-3334/22/4/306 (DOI)11761078 (PubMedID)
Available from: 2004-05-06 Created: 2004-05-06 Last updated: 2017-12-14Bibliographically approved
2. Theoretical simulation of oxygen tension measurement in the tissue using a microelectrode: II. Simulated measurements in tissues
Open this publication in new window or tab >>Theoretical simulation of oxygen tension measurement in the tissue using a microelectrode: II. Simulated measurements in tissues
Show others...
2002 (English)In: Radiotherapy and Oncology, ISSN 0167-8140, E-ISSN 1879-0887, Vol. 64, no 1, 109-118 p.Article in journal (Refereed) Published
Abstract [en]

Background and purpose: The objectives of this study were to make a computer simulation of tissues with different vascular structures and to simulate measurements of oxygen tension using an Eppendorf-like electrode in these tissues and to compare the response to radiation of the tissues with the real oxygen distributions (called input distribution) with the response to radiation of the tissues in which the oxygen distribution is given by the results of the simulated measurements (called output distribution).

Materials and methods: The structure of various tissues and the measurements of oxygen tension using a microelectrode were simulated using a computer program. The mathematical model used combines the description of a gradient of tissue oxygenation and the electrode absorption process.

Results: We have compared the oxygen distributions resulting from diffusion (input) with those obtained from a simulation of measurements (output) for various tissues in the same points. Because the electrode measurement is an averaging process, the calculated oxygen distributions are different from the expected ones and the extreme high and low values are not detected. We have then calculated the survival curves describing the response to radiation if there is a small fraction of truly hypoxic cells (expected values) or a large fraction of cells at intermediate values (observed results) in order to determine the differences between them.

Conclusions: The results of our study show that oxygen electrode measurements do not give the true distribution of pO2 values in the tissue. However, our results do not contradict the numerous empirical correlations between the Eppendorf measurements of tumour oxygenation and the outcome of treatments. Measurement results will be misleading for modelling purposes since they do not reflect the actual distributions of oxygen tensions in the measured tissue. Decisions based on such modelling could be very dangerous, especially with respect to the clinical response of tumours to new treatments.

Keyword
Electrode, Oxygen, Tumour, Hypoxia, Eppendorf, Histogram
Identifiers
urn:nbn:se:umu:diva-3940 (URN)10.1016/S0167-8140(02)00148-2 (DOI)12208581 (PubMedID)
Available from: 2004-05-06 Created: 2004-05-06 Last updated: 2017-12-14Bibliographically approved
3. Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia
Open this publication in new window or tab >>Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia
2003 (English)In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 48, no 17, 2829-2842 p.Article in journal (Refereed) Published
Abstract [en]

The tumour microenvironment is considered to be responsible for the outcome of cancer treatment and therefore it is extremely important to characterize and quantify it. Unfortunately, most of the experimental techniques available now are invasive and generally it is not known how this influences the results. Non-invasive methods on the other hand have a geometrical resolution that is not always suited for the modelling of the tumour response. Theoretical simulation of the microenvironment may be an alternative method that can provide quantitative data for accurately describing tumour tissues.

This paper presents a computerized model that allows the simulation of the tumour oxygenation. The model simulates numerically the fundamental physical processes of oxygen diffusion and consumption in a two-dimensional geometry in order to study the influence of the different parameters describing the tissue geometry. The paper also presents a novel method to simulate the effects of diffusion-limited (chronic) hypoxia and perfusion-limited (acute) hypoxia.

The results show that all the parameters describing tissue vasculature are important for describing tissue oxygenation. Assuming that vascular structure is described by a distribution of inter-vessel distances, both the average and the width of the distribution are needed in order to fully characterize the tissue oxygenation. Incomplete data, such as distributions measured in a non-representative region of the tissue, may not give relevant tissue oxygenation.

Theoretical modelling of tumour oxygenation also allows the separation between acutely and chronically hypoxic cells, a distinction that cannot always be seen with other methods. It was observed that the fraction of acutely hypoxic cells depends not only on the fraction of collapsed blood vessels at any particular moment, but also on the distribution of vessels in space as well.

All these suggest that theoretical modelling of tissue oxygenation starting from the basic principles is a robust method that can be used to quantify the tissue oxygenation and to provide input parameters for other simulations.

National Category
Cancer and Oncology
Identifiers
urn:nbn:se:umu:diva-3941 (URN)10.1088/0031-9155/48/17/307 (DOI)14516104 (PubMedID)
Available from: 2004-05-06 Created: 2004-05-06 Last updated: 2017-12-14Bibliographically approved
4. The relationship between temporal variation of hypoxia, polarographic measurements and predictions of tumour response to radiation
Open this publication in new window or tab >>The relationship between temporal variation of hypoxia, polarographic measurements and predictions of tumour response to radiation
2004 (English)In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 49, no 19, 4463-4475 p.Article in journal (Refereed) Published
Abstract [en]

The polarographic oxygen sensor is one of the most used devices for in vivo measurements of oxygen and many other measurement techniques for measuring tumour hypoxia are correlated with electrode measurements. Little is known however about the relationship between electrode measurements and the real tissue oxygenation. This paper investigates the influence of the temporal change of the hypoxic pattern on the electrode measurements and the tumour response.

Electrode measurements and tumour response were simulated using a computer program that allows both the calculation of the tissue oxygenation with respect to the two types of hypoxia that might arise in tumours and the virtual insertion of the electrode into the tissue. It was therefore possible to control the amount of each type of hypoxia in order to investigate their influence on the measurement results. Tissues with several vascular architectures ranging from well oxygenated to poorly oxygenated were taken into consideration as might be seen in practice. The influence of the electrode measurements on the treatment outcome was estimated by calculating the tumour control probability for the tumours characterized either by the real or by the measured tumour oxygenation.

We have simulated electrode oxygen measurements in different types of tissues, covering a wide range of tumour oxygenations. The results of the simulations showed that the measured distribution depends on the details of the vascular network and not on the type of hypoxia. We have also simulated the effects of the temporal change of the acute hypoxic pattern due to the opening and the closure of different blood vessels during a full fractionated treatment. The results of this simulation suggested that the temporal variation of the hypoxic pattern does not lead to significantly different results for the electrode measurements or the predicted tumour control probabilities.

In conclusion, it was found that the averaging effect of the electrode leads to a systematic deviation between the actual oxygen distribution and the measured distribution. However, as the electrode reflects the general trends of the tissue oxygenation it has the potential of being used for the general characterization of tumour hypoxia even if the actual type of hypoxia measured by the electrode cannot be determined. Indeed, the change in time of the acute hypoxic region does not compensate for the lack of oxygenation at a specific moment and therefore does not influence the polarographic oxygen measurements.

Identifiers
urn:nbn:se:umu:diva-3942 (URN)10.1088/0031-9155/49/19/002 (DOI)15552411 (PubMedID)
Available from: 2004-05-06 Created: 2004-05-06 Last updated: 2017-12-14Bibliographically approved
5. Conversion of polarographic electrode measurements – a computer based approach
Open this publication in new window or tab >>Conversion of polarographic electrode measurements – a computer based approach
2005 (English)In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 50, no 19, 4581-4591 p.Article in journal (Refereed) Published
Abstract [en]

The polarographic measurement of tissue oxygenation is one of the most widely used methods in clinical practice for the quantification of tumour hypoxia. However, due to the particular features of the electrode measuring process, the results of the measurements do not accurately reflect the tumour oxygenation. This study aimed to find a correlation between the electrode measurements and the tumour oxygenation in an attempt to improve the accuracy of the predictions regarding the response to treatment based on electrode measurements. A previously developed computer model that allows the simulation of tumour tissue and electrode measurements was used. The oxygenation of a large number of tumours with biologically relevant distributions of blood vessels was theoretically calculated. Simulations of electrode measurements allowed the comparison between the real tissue oxygenation and the results obtained with the electrode. A semi-empirical relationship between the hypoxic fraction measured by the electrode and the real hypoxic fraction in the tissue has been found. The impact of the correction of the electrode measurements in terms of predictions for tumour control probability was estimated for a few clinical examples. The range of possible true values corresponding to one measurement has also proven useful for explaining the apparently unexpected response to the treatment of some patients. The corrected hypoxic fraction which is believed to be closer to the real value of tissue hypoxia predicts much smaller control probabilities than the raw electrode measurements. This could provide an explanation for the apparently unexpected failure to respond to the treatment of some of the patients with apparently favourable tumour oxygenation. This also means that the electrode measurements cannot be used directly for the quantitative modelling of tumour response to the treatment. The conversion method proposed in this paper might however strengthen the statistical power of the correlations between the electrode measurements and the treatment outcome.

Identifiers
urn:nbn:se:umu:diva-3943 (URN)10.1088/0031-9155/50/19/011 (DOI)16177491 (PubMedID)
Available from: 2004-05-06 Created: 2004-05-06 Last updated: 2017-12-14Bibliographically approved

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