Modeling the Interplay Between Tumor Volume Regression and Oxygenation in Uterine Cervical Cancer During Radiotherapy Treatment

Abstract

This paper describes a patient-specific mathematical model to predict the evolution of uterine cervical tumors at a macroscopic scale, during fractionated external radiotherapy. The model provides estimates of tumor regrowth and dead-cell reabsorption, incorporating the interplay between tumor regression rate and radiosensitivity, as a function of the tumor oxygenation level. Model parameters were estimated by minimizing the difference between predicted and measured tumor volumes, these latter being obtained from a set of 154 serial cone-beam computed tomography scans acquired on 16 patients along the course of the therapy. The model stratified patients according to two different estimated dynamics of dead-cell removal and to the predicted initial value of the tumor oxygenation. The comparison with a simpler model demonstrated an improvement in fitting properties of this approach (fitting error average value <5%, p < 0.01), especially in case of tumor late responses, which can hardly be handled by models entailing a constant radiosensitivity, failing to model changes from initial severe hypoxia to aerobic conditions during the treatment course. The model predictive capabilities suggest the need of clustering patients accounting for cancer cell line, tumor staging, as well as microenvironment conditions (e.g., oxygenation level).

Tumor radio‐sensitivity assessment by means of volume data and magnetic resonance indices measured on prostate tumor bearing rats

“…In contrast to previous work, 26 we did not include an explicit model of tumor reoxygenation along the treatment course or its influence on the radio-sensitivity in the present study.…”

“…22,23 In the past decade, the role of oxygenation in tumor growth and responsiveness has been tackled using mathematical models at both macroscopic and microscopic scales. [24][25][26] In Ref. 26, we proposed a macroscopic model including interdependent dynamics of tumor evolution and oxygenation based on the following assumptions: (1) the larger the tumor volume, the greater the hypoxic fraction; (2) tumor radio-sensitivity is proportional to oxygenation.…”

“…[24][25][26] In Ref. 26, we proposed a macroscopic model including interdependent dynamics of tumor evolution and oxygenation based on the following assumptions: (1) the larger the tumor volume, the greater the hypoxic fraction; (2) tumor radio-sensitivity is proportional to oxygenation. At the time, oxygenation could not be assessed and the model validation was based on volume measurements only.…”

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

“…32,33 First, we proposed a relationship linking the oxygen dynamics to tumor volume, and another to relate the change in oxygenation to a proportional radiosensitivity increase/decrease. 32 Such model overperformed a simplified version featuring a constant radiosensitivity in fitting the volume evolution of cervical cancer patients. However, no oxygenation data were available for validation.…”

“…In conclusion, either the relation between tumor volume and oxygenation was neglected in the modeling 33,34 or there were no data available for its validation. 32 The aim of the present work was to propose an innovative macroscale model combining tumor volume evolution and oxygen variation, which was validated on longitudinal oxygenation data (intra-and interpatients). The model parameters were estimated on the tumor evolution of seven cervical cancer patients (volume data only).…”