A mathematical model of brain tumour response to radiotherapy and chemotherapy considering radiobiological aspects.

Glioblastoma is the most frequent and malignant brain tumour. For many years, the conventional treatment has been maximal surgical resection followed by radiotherapy (RT), with a median survival time of less than 10 months. Previously, the use of adjuvant chemotherapy (given after RT) has failed to demonstrate a statistically significant survival advantage. Recently, a randomized phase III trial has confirmed the benefit of temozolomide (TMZ) and has defined a new standard of care for the treatment of patients with high-grade brain tumours. The results showed an increase of 2.5 months in median survival, and 16.1% in 2 year survival, for patients receiving RT with TMZ compared with RT alone. It is not clear whether the major benefit of TMZ comes from either concomitant administration of TMZ with RT, or from six cycles of adjuvant TMZ, or both. The objectives were to develop our original model, which addressed survival after RT, to construct a new module to assess the potential role of TMZ from clinical data, and to explore its synergistic contribution in addition to radiation. The model has been extended to include radiobiological parameters. The addition of the linear quadratic equation to describe cellular response to treatment has enabled us to quantify the effects of radiation and TMZ in radiobiological terms. The results indicate that the model achieves an excellent fit to the clinical data, with the assumption that TMZ given concomitantly with RT synergistically increases radiosensitivity. The alternative, that the effect of TMZ is due only to direct cell killing, does not fit the clinical data so well. The addition of concomitant TMZ appears to change the radiobiological parameters. This aspect of our results suggests possible treatment developments. Our observations need further evaluations in real clinical trials, may suggest treatment strategies for new trials, and inform their design.