Theoretical simulation of tumour oxygenation--practical applications.
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Animals↗
Biomedical subjects
Iuliana Toma-Daşu
Publications and source records attributed to Iuliana Toma-Daşu.
Theoretical simulation of tumour hypoxia measurements.
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Animals↗
Conversion of polarographic electrode measurements--a computer based approach.
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.
Animals↗
The effects of hypoxia on the theoretical modelling of tumour control probability.
Theoretical modelling of tumour response is increasingly used for the prediction of treatment result and has even been proposed as ranking criteria in some algorithms for treatment planning. Tumour response to radiation is greatly influenced by the details of tumour microenvironment, especially hypoxia, that unfortunately are not always taken into consideration for these simulations. This paper intends to investigate the effects of various assumptions regarding hypoxia distribution in tumours on the predictions of treatment outcome. A previously developed model for simulating theoretically the oxygenation in biologically relevant tissues, including results from oxygen diffusion, consumption and perfusion limitations in tumours, was used to investigate the effects of the different aspects of hypoxia on the predictions of treatment outcome. Thus, both the continuous distribution of values and the temporal variation of hypoxia patterns were taken into consideration and were compared with a 'black-and-white' simplification with a fully hypoxic compartment and a fully oxic one. It was found that the full distribution of oxygenation in the tissue is needed for accurate results. The 'black-and-white' simplification, while showing the same general trends for the predictions of radiation response, could lead to serious over-estimations of the tumour control probability. It was also found that the presence of some hypoxia for every treatment fraction leads to a decrease in the predicted local control, regardless of the change of the hypoxic pattern throughout the duration of the whole treatment. The results thus suggest that the assumptions regarding tumour hypoxia influence very much the predictions of treatment outcome and therefore they have to be very carefully incorporated into the theoretical modelling.
Cell Hypoxia↗
Dose-effect models for risk-relationship to cell survival parameters.
There is an increased interest in estimating the induction of cancers following radiotherapy as the patients have nowadays a much longer life expectancy following the treatment. Clinical investigations have shown that the dose response relationship for cancer induction following radiotherapy has either of two main characteristics: an increase of the risk with dose to a maximum effect followed by a decrease or an increase followed by a levelling-off of the risk. While these behaviours have been described qualitatively, there is no mathematical model that can explain both of them on mechanistic terms. This paper investigates the relationship between the shape of the dose-effect curve and the cell survival parameters of a single risk model. Dose response relationships were described with a competition model which takes into account the probability to induce DNA mutations and the probability of cell survival after irradiation. The shape of the curves was analysed in relation to the parameters that have been used to obtain them. It was found that the two main appearances of clinical data for the induction of secondary cancer following radiotherapy could be the manifestations of the particular sets of parameters that describe the induction of mutations and cell kill for fractionated irradiations. Thus, the levelling off appearance of the dose response curve could be either a sign of moderate to high inducible repair effect in cell survival (but weak for DNA mutations) or the effect of heterogeneity, or both. The bell-shaped appearance encompasses all the other cases. The results also stress the importance of taking into account the details of the clinical delivery of dose in radiotherapy, mainly the fractionated character, as the findings of our study did not appear for single dose models. The results thus indicate that the shapes of clinically observed dose response curves for the induction of secondary cancers can be described by using one single competition model. It was also found that data for cancer induction may be linked to in vivo cell survival parameters that may be used for other modelling applications.
Cell Survival↗
The use of risk estimation models for the induction of secondary cancers following radiotherapy.
Theoretical predictions of cancer risk from radiotherapy may be used as a complementary criterion for the selection of successful treatment plans together with the classical approach of estimating the possible deterministic effects. However, any such attempts must take into consideration the specific features of radiation treatment. This paper explores several possible methods for estimating the risk of cancer following radiotherapy in order to investigate the influences of the fractionation and the non-uniformity of the dose to the irradiated organ. The results indicate that dose inhomogeneity plays an important role in predicting the risk for secondary cancer and therefore for predictive purposes it must be taken into account through the use of the dose volume histograms. They also suggest that the competition between cell killing and the induction of carcinogenic mutations has to be taken into consideration for more realistic risk estimations. Furthermore, more realistic parameters could be obtained if this competition is also included in analyses of epidemiological data from radiotherapy applications.
Dose-Response Relationship, Radiation↗
The relationship between temporal variation of hypoxia, polarographic measurements and predictions of tumour response to radiation.
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.
Cell Survival↗
Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia.
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.
Acute Disease↗
Should single or distributed parameters be used to explain the steepness of tumour control probability curves?
Linear quadratic (LQ) modelling allows easy comparison of different fractionation schedules in radiotherapy. However, estimating the radiation effect of a single fractionated treatment introduces many questions with respect to the parameters to be used in the modelling process. Several studies have used tumour control probability (TCP) curves in order to derive the values for the LQ parameters that may be used further for the analysis and ranking of treatment plans. Unfortunately, little attention has been paid to the biological relevance of these derived parameters, either for the initial number of cells or their intrinsic radiosensitivity, or both. This paper investigates the relationship between single values for the TCP parameters and the resulting dose-response curve. The results of this modelling study show how clinical observations for the position and steepness of the TCP curve can be explained only by the choice of extreme values for the parameters, if they are single values. These extreme values are in contradiction with experimental observations. This contradiction suggests that single values for the parameters are not likely to explain reasonably the clinical observations and that some distributions of input parameters should be taken into consideration.
Cell Survival↗
Computer simulation of oxygen microelectrode measurements in tissues.
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Animals↗
Theoretical simulation of oxygen tension measurement in the tissue using a microelectrode: II. Simulated measurements in tissues.
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 pO(2) 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.
Cell Hypoxia↗