Comparison between model-predicted tumor oxygenation dynamics and vascular-/flow-related Doppler indices

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Abstract

Purpose

Mathematical modeling is a powerful and flexible method to investigate complex phenomena. It discloses the possibility of reproducing expensive as well as invasive experiments in a safe environment with limited costs. This makes it suitable to mimic tumor evolution and response to radiotherapy although the reliability of the results remains an issue. Complexity reduction is therefore a critical aspect in order to be able to compare model outcomes to clinical data. Among the factors affecting treatment efficacy, tumor oxygenation is known to play a key role in radiotherapy response. In this work, we aim at relating the oxygenation dynamics, predicted by a macroscale model trained on tumor volumetric data of uterine cervical cancer patients, to vascularization and blood flux indices assessed on Ultrasound Doppler images.

Methods

We propose a macroscale model of tumor evolution based on three dynamics, namely active portion, necrotic portion, and oxygenation. The model parameters were assessed on the volume size of seven cervical cancer patients administered with 28 fractions of intensity modulated radiation therapy (IMRT) (1.8 Gy/fraction). For each patient, five Doppler ultrasound tests were acquired before, during, and after the treatment. The lesion was manually contoured by an expert physician using 4D View® (General Electric Company - Fairfield, Connecticut, United States), which automatically provided the overall tumor volume size along with three vascularization and/or blood flow indices. Volume data only were fed to the model for training purpose, while the predicted oxygenation was compared a posteriori to the measured Doppler indices.

Results

The model was able to fit the tumor volume evolution within 8% error (range: 3–8%). A strong correlation between the intrapatient longitudinal indices from Doppler measurements and oxygen predicted by the model (about 90% or above) was found in three cases. Two patients showed an average correlation value (50–70%) and the remaining two presented poor correlations. The latter patients were the ones featuring the smallest tumor reduction throughout the treatment, typical of hypoxic conditions. Moreover, the average oxygenation value predicted by the model was close to the average vascularization-flow index (average difference: 7%).

Conclusions

The results suggest that the modeled relation between tumor evolution and oxygen dynamics was reasonable enough to provide realistic oxygenation curves in five cases (correlation greater than 50%) out of seven. In case of nonresponsive tumors, the model failed in predicting the oxygenation trend while succeeded in reproducing the average oxygenation value according to the mean vascularization-flow index. Despite the need for deeper investigations, the outcomes of the present work support the hypothesis that a simple macroscale model of tumor response to radiotherapy is able to predict the tumor oxygenation. The possibility of an objective and quantitative validation on imaging data discloses the possibility to translate them as decision support tools in clinical practice and to move a step forward in the treatment personalization.

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